Lux presents Hollywood. The Lux Radio Theatre brings you Casanova Brown starring Gary Cooper, Thomas Mitchell and Joan Bennett. Ladies and gentlemen, your producer, Mr. Cecil D. DeMille. Greetings from Hollywood ladies and gentlemen. When you hear the name of Casanova, you probably think of him as a notorious Italian lover of the 18th century, but he was a lot more than that. He was an author and a diplomat and a man of learning and good taste, and while his life was not without its lurid side, he ended as an innocent librarian. In tonight's play, you'll meet his namesake and descendant, Casanova Brown. What Casanova's record is in amorous adventure you are about to learn, but like the earlier Casanova, he too is a man of taste and learning, and most decidedly a family man, which may go somewhat oddly with the Casanova name, and he is Gary Cooper. For Gary plays Casanova Brown in tonight's production of that current international picture. Costard with Gary is Charming Joan Bennett and the versatile Thomas Mitchell. Together they bring us the memoirs of a modern Casanova. I won't tell you more than that except to say that when Gary worked for me making the story of Dr. Wassell, I put him through some very difficult predicaments, but none so odd as in tonight's play where he finds himself taking care of a three weeks old baby. Gary tells me that his fan mail now gives him advice on baby care. I don't know whether those letters mentioned washing baby villains in Lux Flakes, but a 70 year old lady writes me that she has knit over 150 pairs of socks for men in the service. She says I wash them all in Lux Flakes just as soon as I finish each pair so that they'll be pleasant to wear. To that kind lady should go a reward for both our patriotism and our good taste. And now it's curtain time again. And here's act one of Casanova Brown, starring Gary Cooper as Kaz, Thomas Mitchell as J.J., and Joan Bennett as Isabel. Isabel, you've got to listen to me. It was all a terrible action when I know, but it doesn't have to come between it. Look, I'll make up for it somehow, I'll... Oh, Kaz, why did you have to spoil it all? But nothing spoiled really, Isabel. Or is it? Look at me. No, no. All right, Isabel. I'm sorry for everything. I'm sorry we ever met each other. And I'm sorry for what I couldn't help. Goodbye, Isabel. Goodbye, Kaz. Well, he's lost her. Another romance on the rocks. The original Casanova would have kissed away the lady's tears and swept her back into his arms. But our Casanova, Casanova Brown, simply sighed, went to the Grand Central Station and bought a one-way ticket for his hometown. Now, in Rossmore, Illinois, he's getting off the train and running up to meet him is a different young lady. Yes, Kaz, darling. Oh, Maj. Turn over and let me out of your sight again, please. Why, darling, what is it? Is something the matter?  I'm not safe without you, Maj. Oh, well, darling, we'll be together again. And it's true what you said in the telegram. Is what true? That you want us to get married. Right away and settle down and have a happy quiet life together.  You'll get a good night's rest and tomorrow you can talk to Dad. Talk to JJ? Why? Well, isn't the prospective groom supposed to ask permission of the bride's father? But to JJ? I know, but it's merely a formality. Tomorrow, darling, tomorrow. I've just about reached the end of my patience. It's intolerable that I should continually be called out of the chamber. Oh, wait a minute, darling. There's someone in there with Dad. It's an apparently endless series of vulgar accusations. And now I'm afraid I must ask you to leave. But, Grandpa, somebody took my piggy bank. If I hear another word about that blasted piggy bank of yours, I'll flatten your mechanoset. Did you hear that? Oh, Dad's always angry since Mother and I put him on an allowance. Well, don't you think we ought to wait for a more proficient moment if he's already angry? Just blast that gridly bear stuff. He really loves us very much. I do not. I adore you, that's all. Kaz wants to talk to you, Dad. Oh, hello, Kaz. How are you, JJ? Well, Madge, there's no call for you putting your nose into this, is there? None-whatever, Dad. I'll see you downstairs, Kaz. What a revolting female she is. Well, sit down, Kaz. Here, take my chair. Thanks, JJ. Ouch! What's the matter? Something under the cushion. Oh, a piggy bank. Piggy bank? Odd place to put it. Well, Kaz, what can I do for you? Well, you know, I've missed our little talk since you went east, not that I was the sole reason for your frequent visits. Oh, that was... Oh, it's quite all right, Kaz. I've not been blind to this little dead-fall marriage asset for you, my boy. But you're much too intelligent to be taken in by that very female. Well, perhaps I'd better make my position clear, JJ. Well, I mean, Kaz. Well, uh, you've known me. You've known my family for a good many years. Oh, yes. We've never been well-to-do, but we've always maintained a certain respectability. Proud but poor, I suppose you might describe us. Of course. If the poor can get any satisfaction out of being proud, why not? Costs nothing. Uh, my salary as professor of literature isn't unificent, but it's adequate. And as for my character, I believe I behave reasonably. I'm not overly susceptible to girls. So what? The point of this whole thing seems to have eluded me somewhere. Well, I'm simply trying to tell you that I want to marry her. Marry whom? Marry Madge, of course. Madge? You out of your mind? I am not. For whatever on earth for? Well, because I love her, of course. Now, Madge? Ho-ho-ho, cop now, Kaz. That's just downright silly. You must have a better reason than that. What is it, her money? Now, just a minute. Because if it is, you might just as well forget the whole matter. I have precisely the same idea with her mother. I haven't the slightest interest in Madge's money. Oh, they've got it all right. Bucket some of it. By George, I've dreamed about that dough just to get my mitts into that cash box for ten minutes. But no, no, no. Well, they turned me down cold. I'll never forgive them, Kaz. Never. And I think you've got exactly what you deserve for being a shameless, unmitigated scoundrel. I suppose so, but it was a bit of disappointment, just the same. Mrs. Ferris has already given her consent. Then I used to dream about outliving her. Just sit it out, as it were. But along came Madge and her sister and now her odious little boy. No use, Kaz. I tell you, they're eternal. All of them. Listen, JJ, yes or no, just for the record. No. What? You'll probably go right ahead and marry that repulsive female anyway. When is the hanging to take place? In June. Mrs. Ferris wants it to wait. And thanks a lot for giving us your blessing, JJ. All right. Hey, now wait a minute, Kaz. Where did I put that urchin's piggy bank? Oh, hiya, JJ. Time for the rehearsal? Just about. Bogey up the morning mail. Thanks. Look, Kaz, you still got time to crash out of this booby trap. There's a fast train leaving for Chicago. By one o'clock it could be across the border into Canada. No use, JJ.  They cut my allowance again today down to $25 now. Good. The shape of things to come, my boy. Now, where else could you get $25 a week just by sitting around developing stomach ulcers? Look through that mail while I finish up, will you, JJ? Uh-huh. Well, they're just bills, bills and ads. Willow Street Cleaners, New York University. Ellen Harris Maternity Hospital, North Haven Country. Well, I'll be shoving along, Kaz. Anything I can do to ease your misery? No, thank you, JJ. See you in church. Uh-huh.  This is going too far. Huh? Ellen, where is it? This is, uh... See here, Kaz. Are you planning already to have a family? Would you object to minding your own business? This is my business. How many grandchildren he has is every man's business. And if you're negotiating already with a maternity hospital... What? Let me see that letter. Some men say they can't have too many grandchildren, but I'm one that can. Huh. But you don't want to add when you see one? Add? Well, they've got a nerve. Let's see. What excuse they give for soliciting a man's business before he's even married? Sounds unethical to me. Mr. Kazanova Q. Brown. Dear sir. Hmm. Well, this is rather a sinister method of solicitation. Listen to this. A matter of personal importance and one which I would rather not take up in correspondence unless you prefer. You know, Kaz, I was involved in a little blackmail accident at one time. Letter sounded exactly like this. Uh, I suggest that at your earliest convenience you call at the hospital and consult with me. Cordially yours, Martha Zanicki M.D. Let me see that. You know this female or this hospital? Never heard of either. Strange, very strange. Hey, great Scott, the time. We're going to be late for the wedding rehearsal. Holy smoke. Hand me that side, JJ. Well, here's the sucker. John, I do wish you wouldn't have heard of Kaz like that. I said here's the sucker. When do we test the scaffold? We're starting the rehearsal right away. Mr. Ferris, will you take your blade beside Mrs. Ferris? Now, when everybody gets ready, please everybody gets ready. Uh, just a minute, Kaz. If this was a mistake, how will they get your address? Uh, I don't know anything about it. You didn't write to them asking about prices or anything like that. No, of course not. Well, there may be some, Mr. Brown. Mr. Ferris, up beside the bride, please. Kaz? Lovely, lovely. He doesn't care. Uh, Madge, do you know anything about the Ellen Harris Maternity Hospital in Chicago? Well, I've seen a so rough bride. She goes straight up through the stairs. Seems that somebody's counting on you having quite a family. Yeah, but I haven't seen about any, doctor. Splendid, splendid. Now, may we have quiet please? And another thing, Kaz. What about the queue? Well, if there was a mistake, how will they get you middle initial? Father. What? The rehearsal. Is he all right? I heard that. Oh, quiet please, please. Someday somebody's going to say that just once too often. Dad. Suppose somebody asked you if you were out of your mind. How would you feel and how would you prove you weren't? Oh, John, dear. Huh? Kaz, Kaz, what is it? Oh, I'm sorry. I don't feel very well. Well, Kaz, darling. I'm sorry. I'll please excuse me for a few minutes. No. Well, I don't wonder. If I was in his shoes, I'd certainly feel nauseated. Hey, Kaz. Wait for me. Close the door, JJ. Unlock it. Now, look, Kaz. If that letters a mistake, we're in a position to knock off quite a little quick dough.  We'll threaten to sue them, then we'll settle out of court. Why not? Well, because it may not be a mistake. But of course it's a mistake. What'd you say? I said it may not be a mistake. Oh. Oh. What is, Kaz? I don't know. I tried to call her on the phone long distance, but she wasn't there. Called whom? I just don't know what to do. Kaz, if you fail to touch a base somewhere, I'm not without a measure of experience. No, no, no. Nothing like that, JJ. Yes? I'm in a very, a very peculiar situation.  Oh, of course, Kaz. The trouble is, I just can't be sure. I mean, why Chicago? I don't know. Why? If it had been New York, yes. But Chicago?  Look, last year I wrote a book about that scandalous ancestor of mine called Casanova in Florence. Well, now, Kaz, don't you think we can skip the high-minded aspects and get strictly down to the nubbin? Uh, I took the manuscript to New York, and while I was there, I met a girl. Ah, now, you're getting somewhere. Isabelle. Isabelle, eh? What was she like? Well, have you ever seen the sun come up at dawn? Yes, I have. It settled my stomach. Well, I like the way she walked and her eyes, her eyes were like burnt charred embers in a field of snow. Hmm, large face, eh? She was going to college in the city. Well, what was the score at this point? Well, I, I was driving home one night in a car that I had rented. Oh, it's such a lovely night. Oh, nice moon.  Well, why go indoors? It's early yet. How about driving up the river? Oh, I'd love to. Well, that is, if you think it's all right. Why wouldn't it be all right? I mean, you probably got a girl back home. Girl back home? Well, hasn't you? Well, no, that is, well, yes, except. Except what? Well, what she got to do with it. Nothing. We can still be good friends. You know, I feel so comfortable when you're around, Kaz. I feel as if I'd known you all my life. We drove on up the river, J.J. She told me about herself, about her folks. Yes, I was going to ask you about that, Kaz, her parents. Do they have to? Oh, plenty of it. Good, good now. This is getting more instinct. Well, we drove until midnight. And finally, we came to a little town.  Sleepy? Uh-uh. I could drive on like this forever. You don't mind my head on your shoulder. No, I like it there. Where are we? Just outside Mayfield. Mayfield? Yep. You know someone here? Well, Kaz, isn't this the place where they have so many runaway marriages? You know, by justice of the team, people come from New York so they won't have to wait. Yeah, yeah, I guess it is.  No, I, well, I swear I didn't do the bell, but, but it's a bell. Uh, do you believe in predestination? I never thought about it, Kaz. Do you? Well, I never did, but tonight I almost feel like could. Look, Kaz, that sign there, underneath the light. Wilfred Brunkel, justice of the team. Caesar, Kaz. You mean you married her? That's right, JJ. We got married by the justice of the team that night. Good grief. I see. I see what you mean by saying you're in a very peculiar situation. JJ, I've got to get to the bottom of this whole thing. I should think you do, my boy. But how? Where's my bag? I'm going to Chicago. Right now. Now before our stars return with act two of Casanova Brown, I've got a Christmas quiz for Libby. What kind of a quiz, Mr. Kennedy?  What's the first one? Christmas. Tree. Good. Now, uh, mistletoe. Oh, quiz. Oh, just made it. Here's another. Stockings. Locks. But Libby, you were supposed to say presents. You know the presents in the stockings. Not me, Mr. Kennedy. When anyone mentions stockings, I just naturally think of Washington with locked plates. Now, if you said presents, then I would have said stockings. Because stockings are one of the most popular Christmas presents. In spite of no nylons? Oh, my yes. The new rounds are so lovely. Girls really like them now. And there are lots of interesting new cop meshes for country and sportswear. You win. Uh, how do you win? Reap. Chimney. Stockings. Oh, no. I was thinking of Santa Claus. But I see what you mean. The stockings were hung by the chimney with care. Mm-hmm. Although, of course, nobody would ever hang good stockings by a chimney or any other kind of heat. The right care for those Christmas stockings is gentle luck's care. I see.  So I'll just add that strain tests prove stockings washed with gentle luck's flakes last twice as long as those washed with strong soap or rubbed with cake soap. Like this. You get twice the wear from every pair with gentle luck's care. We pause now for station identification. This is CBS, the Columbia Broadcasting System. Act two of Casanova Brown, starring Gary Cooper as Kaz, Joan Bennett as Isabel, and Thomas Mitchell as JJ. Not many men learn on their wedding eve that they may be the father of an unsuspected heir resulting from a previous unadmitted marriage, but true to the best traditions of his name say Casanova. Our Casanova finds himself in this somewhat odd predicament. In his bachelor rooms he tries to explain the situation to his prospective father-in-law who takes it as probably few fathers-in-law would. But why do you want to rush off to Chicago? Because I want to know the truth. I don't want any secrets between me and Madge. Madge?  I'm not married to Isabel. Huh? Her parents had the marriage annulled. Oh, they didn't take kindly to the idea. Well, there were attending circumstances not too helpful. I see. You hadn't been married before that. Had you? No, no, it was this way. A few days after we were married, we went over to meet her parents. Home in the suburbs was like a palace. We knew they were upset so we agreed that I'd wait in the drawing room while Madge went in and calmed them down. I can just imagine what a grilling that poor girl went through. Well, how did you meet him? Who introduced you? We just met at the library, Mother. We asked for the same book at the same time. Uh, what does he do? He's an author, Dad. Oh, like Mr. Louis Brownfield? Not exactly. They didn't accept Kaz's book. Oh, but it's wonderful, Mother, all about his ancestor, Kazanova. Kazanova? You're married in Italian? Oh, Kazanova's a historical character, Edward. Rather sad. Oh. But Mother Kaz is nothing like that, believe me. He's kind and gentle. Just meeting him and talking to him will tell you why I fell in love with him. I'll get him. No, no, not yet, dear. In moments like this, there is one place we can always turn for guidance. To the stars. Mother, you're not going to drag that astrology stuff in, oh, Dad. Oh, no, dear. Mother knows this. And the stars know better still. Now, here's the book I was looking for. Astrology and Marriage. Oh, when was he born, dear? His birthday's April 8th. He's 37. April 8th, 1907. April the 8th. Ah. Oh, dear.  Well, there's nothing to begin by keeping these facts from him. Invite him in, dear. Oh, the poor, poor, sad dear. Are they sore? No, no, but be careful, will you? Oh, you're smoking. Yes, I was a little nervous waiting. Oh, I forgot to tell you. Mother can't stand men who smoke. The butler told me, but I couldn't find an ashtray. Any place to put it. Oh, hurry. Do something with it. A handkerchief. I'll smother it in my handkerchief. Now, be careful, dear. Won't you? You won't do or say anything. I'll do my best, of course. Tell you how depressed I am, Mr. Brown. I want you to understand that there's nothing personal about it. Well, I hope not naturally. Mr. Brown, this whole project is broke with disaster. Thank you, pardon. Do you realize, Mr. Brown, where Sagittarius was on the day of this marriage? No, I'm afraid I don't. On September 3rd, Sagittarius was in the fifth through the House of Neptune. Oh, really? On that same day, listen closely, Capricorn was adverse, Virgo was discordant, and Taurus. Taurus was in textile aspect of Venus. In short, catastrophe. But that's astrology. Of course. Who else would we know how to govern our lives? Do you smoke? No. No, thank you. No, that is... I thought for a moment I detected a slight order of tobacco or something. Well, now, let us turn to your birthday. Excuse me, Mrs. Rury. Yes? Do you mean that you would base your approval or disapproval of your daughter's marriage on that nonsense? Nonsense, Mr. Brown. It wouldn't possibly have picked a worse word. You don't believe in astrology, I take it? No, I don't believe in astrology. I don't believe in crystal gazing and I don't believe in Beersud's reading. And if I did, I wouldn't impose that belief on the lives of two people who love each other. What does that mean? Do you even know their marriage spell calamity? What kind of calamity? There's no chance of any calamity in this marriage. Mr. Brown, are you on fire? What? He seems to be burning something in his pocket. Oh, I'm sorry. I can't understand it. Package it, package it. Caught on fire. Careful, dear. His coat's on fire, too. Well, how do you like that? It must have burned right on through. Yes, I know. It's burning the rug. I sugar it. Oh, look, the chair. Oh, step on it, somebody. The chair's on fire, too. Charles, Charles. Get some water from that bug. This is most embarrassing. Some water, Charles. Now, what are you doing to that chair? It's got down into the stuffing. I have to pour it out. Oh, look out. The curtain catch you. Water, water! What did you have in your pocket, Roman Kendall's? Oh, beat it out. Come help me beat it out. No, no, no. You're just fanning it. Where's Charles with that water? Water won't help now. You need a hose. Call the fire department. Fire department, fire department. No, Edward, no. Telephone! Oh, yes, telephone.   That's what you are, a fiend. Help! Help! Help! Oh, the firemen have gone. The firemen have gone? The house is gone. Mr. Drury, uh, Mr. Drury. Don't you come near me. I find myself in an extremely awkward position. You certainly do if I'm any judge of awkward positions. I know. I know I owe you both a genuine sincere apology. That's good. He burns down a $750,000 house and he apologizes. That's very good indeed. Get away from here. But Mr. Drury. Isabelle.  Isabelle, come away from that infidel. Oh, look, Mrs. Drury. Don't you come near me. I would as soon associate with a time bar. But Mrs. Drury, it's a terrible thing. I know, but don't you understand an accident? Accident? You call it an accident with Sagittarius in the fifth solar house of Neptune? Sagittarius, my eye. That's downright idiotic. Don't care, please. Listen, Mrs. Drury, you may interpret your life through fingernail pairings, but that's got nothing to do with me and Isabelle. You can leave Isabelle out of your calculations, Mr. Brown. I will not see her fly twice in the face of astral warning. Astral warnings? What have I married into? Who do worshipers? Kaz, you can't talk to my mother like that. Then tell her to shut up about those stars. With Sagittarius in the fifth...  I burned that house down. Sagittarius had nothing to do with it. It was me. And now he's boasting about it. Isabelle. Oh, Mother, what shall I do? Isabelle, you've got to listen to me. It is all a terrible accident. I know, but it doesn't have to come between us. Kaz. Look, I'll make up for it somehow. Kaz, why did you have to spoil it? Nothing spoil really, Isabelle. Or... Or is it? Look at me. No. No. All right, Isabelle. I'm sorry for everything. I'm sorry we ever met each other, and I'm sorry for what I couldn't help. Goodbye. Goodbye. Goodbye. And if I can think of any way to train the law on you, I'll do it. And that's all, J.J. That was the end. Yeah, I can see what you mean by circumstances attending the annulment of the marriage. It happened so fast I never had a chance to break the engagement with Madge, and then when it was over, I just wanted to forget to come back here and take up what I'd left off. Well, now your first wife may be about to present you with a child on your wedding eve. What have you got to do about it? Go to Chicago, like I said. I can catch the midnight, find out what happened, and fly back tomorrow afternoon. But this is a chump idea, even if it is a baby. Why do you have to do anything about it? Well, if it's true, I'm going to make a clean burst of the whole thing tonight. Cast. Promise me one thing. Don't go crashing in there yelling, I'm the papa.  Chicago is a big city. A lot of activity, and if there's been a misdeal somewhere, you don't want to be left holding the spare card, do you? No, I understand. From the moment you step into that hospital, walk on eggs. No matter what anybody says, no speaking.  You were attending a bean supper in the YMCA in Cleveland. And good luck, my boy. Ellen Harris Hospital. Good morning, Mr. Ministry. Ellen Harris Hospital. Excuse me. My name is Brown. Katherine Over Brown. Good morning, Mr. Brown. Take writing here, please. We'll call you when we're ready. Well, I'm looking for Dr. Martha Zernickie. I know, I know. We'll call you as soon as you're to go in. But surely you can tell me something. You have nothing to worry about. Mother and child are doing nicely. Oh, then it is a child. Well, what did you think it was going to be? Please wait for an order in the father's room, Mr. Brown. I know just what you're going through, bud. If they had nine watches in this hospital, they wouldn't tell a father what time it was. Is this your first? Yes. How long you been married? Oh, I'm not married. What? Oh. Oh, an onion, hey? Here comes an order, again. Hey, what's new? Mr. Brown, will you please come with me? I wanted to see Dr. Zernickie.  Yes, I understand. Just come with me. Okay.  What are you talking about? And put this gown on. Just a minute now. I came here to see Dr. Zernickie. I know it.  All they want is a physical exam. Physical examination? Me? Well, you're the father, aren't you? It's a matter of routine. Oh, well. Well, it just seemed kind of funny. I've just been over your report, Mr. Brown. It seems you're in excellent physical condition. Well, I'm mighty glad to hear it, Dr. Zernickie. And I want to thank you for coming here. A report like this on file simplifies the case tremendously. We know what possible complications might develop. And in this instance, I would say the baby was very fortunate. By the way, wouldn't you like to see her? Well, uh, is it all right? Of course. Right through this door. She's such a darling. Even the nurses are fallen in love with her. Of course we have to keep them behind this glass partition. But if you look in that third crib, you will see her. The name Drillie. There she is. Well, well, what do you know? Like her? Oh, she's fine. But, uh, how would you say she compares with others of her age, her weight? Oh, perfectly normal. Oh, just normal, huh? Well, perhaps a bit better. And, uh, I know this sounds rather foolish, but has she all of her arms and fingers and toes, I suppose? Nothing missing, I mean. A full set. The customary number and variety. Have you seen her mother? Who? Her mother, Miss Drillie. Oh, was she here, too? By strange coincidence, yes. She's in the solarium. Uh, and, uh, her parents. Only Mr. Drillie, and he's not with her now. Wouldn't you like to see her? Oh, very much, please. It's right down there, into the corridor, then to the right. Uh, it doesn't strike you, and I don't say that just because she's my child either, but it doesn't strike you that her head seems to be just a little better shaped than, uh, uh, usual at such an early age. Oh, there's no question about it. It'll be a very lucky family that gets that child. Oh, thank you. Turn to the right, you said. That's right. Hey! Hey, wait a minute. Yes? What did you mean by the family that gets that child? I mean the family that gets it for adoption. For adoption? What adoption? Well, I thought you understood. Miss Drillie's registered the child for adoption. That's why we needed your medical record. Well, who had that fool idea? Well, I'd hardly describe it as a fool idea.  Miss Drillie's title of the child is clear and legal. Well, what about the father? Well, what's he supposed to do? Just stand around and twiddle his fingers? Really, Mr. Brown, these are matters you must take up with Miss Drillie. If you'll excuse me. Certainly. Thanks. Oh, hello, Karen. Look here, Isabelle. What's this about, uh... Oh, geez. Isabelle, you look good. Thank you, Karen. You're looking quite well yourself. No, uh, complications? No, isn't it wonderful? I was so scared. I suppose everybody is, but everything went right on schedule. Did you see the baby? Did I? Oh. Oh, yes. Say, what's the idea of giving my baby away? Your baby. Isn't it? Technically, yes. All right, then. What's the idea of giving my technical baby away? If you're going to raise your voice, Kaz, I'm afraid I'll have to go back to my room. I'm not raising my voice. I just want to know what's the idea. If you're going to shout. I'm not shouting. I'm... I'm sorry. I'm not excited with that, but... but what is the idea? I'm afraid you forget, Kaz, that I'm under no obligation to account to you. What I choose to do with my baby is my own affair. Well, that's a fine attitude. However, suppose a girl was thinking of getting married again. Suppose this marriage meant the chance of a lifetime for perfect happiness. What are you talking about? Suppose this man idolized you, even as you loved him. Would you take the chance of destroying this whole future by suddenly presenting him with another man's child? Great. Scott, are you planning to get married again? I said, suppose. Well, that's ridiculous. You can't marry anybody. Why can't I?  Well, that's not stopping you. What are you talking about? I'm not a mother. You're a father and you're getting married again. Who told you that? I read it in the paper. What paper? Well, that's what paper. How'd you get ahold of a Rossmore paper? What difference does it make? It's true, isn't it? You're getting married tonight. Well, but that's different. Oh, is it? Then how would you like to go to marriage tonight and say, look, darling, I've got a little surprise for you and then flash a baby? Well, of course. All right. If you don't want your happiness spoiled, neither do I. But you can't do it, that's all. You just can't throw that baby away. And you can't marry that creep you've dug up either. But you'll be happy, Kaz. But happy with other strangers? But everybody's a stranger to a newborn baby. She doesn't know anybody. She knows us all right. Oh, that's absurd. Why didn't you write to me? Why didn't you write to me? You knew I loved you. You knew there was no one else on earth in the world for me, no matter how nutty your mother was. How was I enough? After the way you left? Well, that fire was an accident, darling. Believe me. I waited and waited and nothing. Not a word. I waited until it seemed foolish to wait any longer. As far as I could see, you just forgot. Forgotten? I've never forgotten. Oh, don't, Kaz, please. It's true, darling. I've tried again and again, but I can't forget you. Please, Kaz, you're in love with someone else. Me? Who? You're engaged to be married. That's right. Holy mackerel. Kaz, why did you wait so long? Isabelle, look, I've got to catch the plane home. But before I get out of here, you've got to do something about that baby. It's too late, Kaz, and there's nothing you can do about it. Oh, isn't there, huh? Well, we'll see if there's nothing I can do about it. Hello? Yes? Chicago? Uh, Mr. Ferris? Yes, he's here. Chicago calling you, Dad. Chicago? He'll be calling from there. Hello? Yes, yes, speaking. Oh, Kaz. Kaz and Chicago. Well, how are you, my boy? Uh, JJ, listen. I find myself in an extremely awkward position. What's that blasted noise behind you? It sounds like a baby. It is a baby. I've kidnapped her. You what? Uh, Isabelle had a baby. She was going to let it be adopted. Give it away. I couldn't let that happen, so I took it. I dressed up like a doctor and sneaked it out of the hospital. Well, how do you like that? Uh, where are you now? Uh, in a telephone booth. Well, I can't stay there. Or can you? Listen, what I want you to do is explain as best you can to Madge and Mrs. Ferris, then take the first plane and meet me at the Hotel Windsor. Uh, bring some money. Money? Where do you expect me to get money? You know the tight wad that I live with. Well, uh, do the best you can. Well, of course, my boy. I'll try to handle it with all the tact and delicacy of a crooked diplomat. Goodbye. That was Kaz. What was he? Just telling me that he met an old friend. But in Chicago, the wedding is at 8. Is he on his way back? Uh, no, he asked me to join him there. No time to lose. By the way, I should have said a new friend. Very new. We'll be back with Act 3 of Casanova Brown in just a moment. Listen. Superports, Red Japan. Carrier planes, attack Jap bases. U.S. Task Force thinks Jap ships.  Yes, we've started back. Guam and Leyte are just the beginning on the road that leads to Tokyo. But wait a minute. Before we think the war is won, the Japs still have Burma on the China coast. They hold Java, Malaya, and most of the Philippines. And with them, our sources for a billion pounds of fat a year. No, the war isn't over yet. And it's hard to fight it without that billion pounds of fat the Japs have taken from us. Fat that's needed for the clear plastic windows through which our fliers sight the enemy. For synthetic rubber tires for the planes and life rafts for the Navy. And that's where you come in, Mrs. Housewife. It's up to you to help make up that billion pounds of lost fat by saving every drop left over from your cooking. And keep on saving it. Even when we take those palm and coconut groves again, don't let up. It will take time to restore them. Meanwhile, your government urges you to go right on saving fat.  And this is important. Be sure to strain it. Some of the plants where your waste fat goes for rendering say that almost half of what they get is not suitable because it hasn't been strained. So don't let's lose any precious fat. Always pour your used fat through a strainer into the tin can while it's hot to get out food particles. Or cool and skim off after other liquids settle to the bottom. Save every drop every day. When your salvage can is full, take it to your butcher. He's still giving four cents and two red ration tokens for every pound. Now, Mr. DeMille returns to the microphone. As you know, Gary Cooper is now a producer with international pictures. And after the play as a brother producer, I'll try to pry out of him some of the secrets of his new job and you're invited to pry with me. Now here's Act 3 of Casanova Brown, starring Gary Cooper as Kaz, Thomas Mitchell as JJ, and Joan Bennett as Isabelle. It's Casanova's wedding day in Rossmore, Illinois. But far away in Chicago, the groom is otherwise involved and very much so. An hour ago, he kidnapped his three-week-old daughter from a hospital. And now he's hiding in a hotel room, waiting for JJ to join them. Meanwhile, Isabelle, the baby's mother, has just dropped a bum shell in the lap of Dr. Zinnickie. Let me understand, Mr. Rury. You never had the slightest intention of releasing the child for adoption? Oh, I couldn't, Dr. Zinnickie, my own child. But I had to do something to get Mr. Brown to come to us. I see, but I can hardly pretend to approve, Mr. Rury. The deliberate use of the hospital in a scheme to unveil the father's interests. But I just had to know if he still loves me, don't you see? And Dr. Zinnickie, he still does. He belongs with us. Well, what's done is done. Let's hope for the baby's sake that it hasn't been in vain. I suggest now that you find Mr. Brown, bringing the child and settle on when you want to leave the hospital. But now I don't know where he is. Well, from your description of his attitude, he won't leave this hospital without the child. We'll find him, but first let's get the baby. Can I help you, Doctor? Yes, we've come for the Drury, baby. Oh, so Dr. took her out. Took her out? What doctor? I don't know. I'm new here, but he had on a mask and I just assumed he was Mr. Rury's doctor. You mean he took the baby and left? What did he look like? What you could see? He was tall, with dark brown wavy hair and brown eyes. I think he had on a brown suit underneath his gown. Yes, that's correct. He's kidnapped my baby. Hey, Jay, close the door. I expected you here yesterday. Yeah, I know. I couldn't get reservations on the plan. Who's that? Oh, this is Monica, the chambermaid. She helps me with the baby. How do you do? Good grief. And is that it while all the trouble has been about? Yeah, yeah. Here, Monica, you take her while I fix these scales. She even feels as if she's gained. Did you bring any money, JJ? Money?  Yeah, I was afraid you wouldn't. With a hundred smackers hope? Huh? A hundred dollars? JJ? Where did you get a hundred dollars? Well, I picked it up in a little friendly card game on the plane. JJ, I'm worried. Oh, nothing to worry about. I probably never see the man again. I mean about the baby. She's gained two ounces since I took her from the hospital. Was that bad? Two ounces. That's practically a pound a week. 52 pounds a year. So what? A lot of people like big women. Not that big. Well, at that rate, she'll be about 12 feet high and 4 feet square. At first, I thought it might be glam. Already? But now I'm convinced that it's a formula. We've got to find a formula that will slow her down. Yeah, well, I always thought they threw in a formula, like the next pair of pants. Oh, the formulas at the hospital. Now, we've been following these baby books I bought. Why don't you get the formula from the hospital? Well, how can I? You could telephone. Well, they'd probably recognize my voice and trace the calls. Well, I could telephone. Well, no, no. Now, if anybody calls, it should be Monica. They'd be less apt to suspect a woman. Who should I talk to at the hospital? Dr. Martha Zanicki. State 64567. You'll have to give my name, but that's all. Now, don't tell them anything. Operator, get me state 64567. Uh, Dr. Zanicki, what shall I ask?  And remember, don't ask her any questions. What about the telegram, Dr. Zanicki? Excuse me, please, Mr. Jory. Hello? Dr. Zanicki, what are we going to do? Yes, Dr. Zanicki. Dr. Zanicki, what do you feed us three weeks old baby? Well, I'm sorry, but I couldn't possibly describe a formula for a baby I don't know, especially over the phone. Who is this speaking? Hello? Hello? That's strange. I'm sorry, what were you saying? About the telegram. Oh, yes. Well, Mr. Jory, I must say your husband, Mr. Brown, is the most unusual father. He's already sent us six telegrams on the baby's health. And if they're true, you have no serious concern on that score. I've engaged a detective agency, and I'd like to give them those telegrams. Of course, Mr. Jory. No, Kaz won't let anything happen to her. I know that, but I want my baby. Naturally. And as for Mr. Kazanova Brown, society isn't safe with him around. Burns down homes, marries girls right and left, steals babies. There's only one place he belongs in jail. Has the detective agency made any progress? I don't so far know, but I'm confident at given time they will. I got it. Look, look, the formula. Formula? What formula? One for the hospital. See, I got Frank the bellboy here to get it. That's right, Mr. Brown. No trouble at all. They look here. You didn't tell them anything. No, sir. Don't be silly, Kaz. I told them that absolute secrecy was vital. And they didn't ask you? Sure they asked me. The minute they heard me say Kazanova Brown, that's the first thing they wanted to know. Where was you? Well, they recognized the name. Recognize it? Both for me. What did you do to that hospital, Mr. Brown? You didn't tell them anything. Not even your phone number? Phone number? What would they want with that? I didn't tell a phone. I went right over to them like Mr. Ferris said. You went to the hospital? I was sure. In that uniform? Why not? The hotels don't care. Oh, uniform? Great scout. I never thought of that. Well, what's the matter with my uniform? Look at your cap. You're dummy in your pocket. What does it say? Hotel Windsor. Pride of the look. Gee, Mr. Brown, I... Please. I... Let me think. Do you think they'll come for her? You bet they'll come for her. And why don't you get out of here? Go somewhere else. Sure. And how easy is that going to be? They probably got the techies on our trail right now. They'd trace us easily. What'll they do with the baby? Do with her. We're going to give her away. People are going to drop around and look her over like picking out a second-hand car. If they like her, they take her. Oh, how can they if you're the father? Being a father is not enough. You've got to be a mother, too. Precisely. No man born a woman ever gets away from them. A man's not capable of taking care of a child, not according to the courts. He can build bridges. He can fly around the world. He can be president and run the whole United States. But taking care of a child is too much for him. You've got to be a woman for that, any woman. Don't you worry, honey. We're not licked yet. But if you're, if you're married again, you could keep her, couldn't you? Married? Yes, that's right. Uh, married. A wife. Uh, Monica. Yes, sir? Uh, I find myself in an extremely awkward position. Seems to me I've heard that statement before. The sizzle of the fuse before the bomb burst. Uh, Monica, are you married? Me? Are you engaged? Well, no, not definitely. Uh, what I'm going to say may come to you as somewhat of a surprise. How's that, Mr. Brown? Will you marry me? Do what?  Well, how do you like that? Go on. Go on? Uh-huh. Go on. Oh, well, it must be obvious that I'd never make such a proposal involving my whole life in happiness and the whole life in happiness of my daughter if I hadn't fallen under the spell of your warmth and your attractiveness and beauty. Well, you're cute. I'll say that for you. Will you? What do you think, Mr. Ferris? Young woman, the idea of any cerebral effort being pregnant to this proposal is absurd. Uh-huh. All right, I accept. Okay, get out of that apron. We're off to the city hall. Hey, you're going to leave that female chair with me? No, take her with us. I'll take along a bottle for her feeding. You're going to take the baby with you to get married? Why not? Well, it makes as much sense to the rest of this. J.J. J.J., look, wait right here, will you? We'll be back in half an hour, or I'll call you. I'm sure they said this room. Hey, it's Isabelle, and there's somebody with her. Hey, how can we get out of here? I got a maid's key from the bathroom to the next suite. Come on, man. Quick. There he is. Or, no. Where is he? Sir? Where is Brown? And where's my baby? Baby? What baby? There's no baby here. And what are you doing with those bottles? Uh, just sampling them.  I'll never mind about him, Dad. I want my baby. I don't know what you're talking about. If you mean the infinite belongs to all this apparatus, and it's farther than where they are, out walking in the park. Out walking in the park? Very well. We'll sit and wait. And, Mr. Ferris, when I find you, Mr. Casanova Brown, I intend to demand the fullest penalty that I'll allow. Ah, Tommy Brown. Stop it. Both of you, I just can't stand it. All is waiting. Well, you ought to be back in the city hall by now. City hall? I thought you said he was walking in the park. Well, you have to cross the park to get to the city hall. What on earth are you doing there? Getting married. Again? Yeah, he seems to be in the sort of an up to a rut. No. No, it can't be. He is, though. Who made bingo this time? Oh, by the name of Monarch, I think it was. It was something of a whirlwind courtship. Oh, Cas, no, no. What's the matter with her? Where is she going? Probably out for a little air, maybe something of a shock to her. He's getting married. Hello? Yes? Where are you? I'm in room 347 down the hall. We didn't think it was safe to come into my room. Ah, I'll perfectly right, my boy. I'll call you later. Who is that, Brown? Yes, yes, he's in St. Louis. He went to our business. In St. Louis? I thought you said he'd gone to City Hall. Oh, he's a very peculiar young man. Now while your daughter is wrestling with her emotions in the hallway, what do you say to a little game of gin rummy, huh? All right, all right, now. Daddy's doing the best he can. Now, here's the bottle. Nice and warm. There. See? Here's the belt. What? Is she all right? Of course she's all right. How did you get here? I heard her crying from the hall. I know her voice anywhere. Oh, Kaz. Kaz, how she's grown. I know. It's terrible. Oh, no, no, she's just perfect.  Don't touch her when she's feeding. It makes her nervous. Oh. She's very high strong. Not too high strong, is she? No, no, no, just sensitive.  Well, of course not. She had the best of care. Quite concerned about her now, aren't you? All of a sudden? What do you mean? I hardly notice such solicitude the last time we discussed her. Oh, Kaz. How could I have been such a fool? Please, darling. I mean, here's the belt. Don't, honey. I never meant to give her away, darling. I might just as well give away my heart. I couldn't live without it. Well, why did you say you were going to? Because I wanted you to come running to stop it. I wanted you to see her and warn her and warn me again. That's why I came to Chicago. So it'd be easier for you to get here. Good heavens. That's the truth, Kaz. But one little word. Just one word. I know. I know now. Now that it's too late. Oh, excuse me. The bottle's empty. What do you do now? Well, after feeding your baby at this age, you hold her like this. Supporting the smaller back with a left hand. And then pat her gently. Let me, will you? OK, but hold her carefully. That's right. Your left hand here. Now, pat. But not too hard. Aw. Oh, mama, so sorry. Very gently. That's a ticket. Oh, Kaz. Isn't she just a little green? Well, uh, well, I've gotten quite used to her, of course. But say, look, what did you mean by now that it's too late? That man. Back in your room, he told us. Told you what? What you've done. And I do want you to know, Kaz, I do hope deeply and sincerely that you'll be very happy. Me? Oh, both of you, of course. Both of who? Didn't you, didn't you get married this afternoon? No. You're not married at all to anybody? No. You can't get married like that in Chicago. You have to wait three days. Really? No, I'm not married to anybody. Are you? No. Oh, Kaz, Kaz, come closer. I can't see you. Oh, I'm here all right. Oh, don't stop patting her.  What am I patting her for? Don't you know? Well, after every feeding. What? Now, wait. Wait, I think she's about ready. Listen. Kaz, isn't that wonderful? Right after each feeding, just as regular clockwork. Oh, darling, I have so much to learn. But don't you worry. I'll teach you. Mama. Our stars will be back for their curtain calls in just a moment. Now, Sally has a word game that sounds like fun. You take a word like sweater, for example, and then you spell it out. S-W-E-A-T-E-R. Same for each one of the letters stands for C. I get it. You start. S is for sweaters, so fluffy and bright. W for wool. You should care for it right. E is the E's for which luxe says you're done. A is for always use lukewarm luxe ups. T is for roll and a towel to dry. E is for ease it to shape by and by. R is, um, oh, radiator. Don't drive them there. Sweaters stay lovely with gentle luxe care. That's fun, Sally, and instructive, too. It's an easy way to remember all the important rules for washing woolens. Lukewarm luxe sides, rolling in a towel to remove moisture, easing the shape, and drying away from heat. And that's how to have soft, fluffy sweaters. Luxe is so gentle it keeps precious woolens lovely longer. Here's the way that you had better wash that precious woolen sweater. Lukewarm luxe flakes, nothing stronger. Help keep woolens lovely longer. And now, back to Mr. DeMille and our stars. Our congratulations go to Gary Cooper, Thomas Mitchell, and Joan Bennett for three excellent performances. Very excellent.  How do you like being both a producer and a star, Gary? Well, it's kind of hard to make up your mind which one's a favorite. How do you mean, Gary? Well, when it comes to writing out the checks, do you give yourself a raise or take a loss on the picture or cut your salary and make a profit? Now, what finally decides you? Well, if I'm playing opposite a lovely girl like Joan and I have the chance to, you know... Yeah, yeah, yeah. Well, I can persuade myself to take a lower salary. Gary, somehow I can't imagine you as an executive behind the desk. You mean what does he do with his legs? Oh, you ought to see Gary's office, Joan. It's really quite a sight. Full of lariat shadows and pistols, I imagine. No, no, no. Quite the opposite. White and yellow curtains, bottle-green chairs, bright red sofas, and a desk of... What is a desk made of, Gary? Pickled pine. How's that? Pickled pine. Are the walls plastered too? I suppose the picture you're making is a hundred proofs. What is the picture that you're making, Gary? Well, I guess you'd call it a romantic western melodrama called the Long Cane Joan. Well, we'll hope to have that picture for this theater, Gary, when it's finished. What do you have on deck for next week, Mr. DeMille? For next week, we have a play that was as big a hit on the stage as on the screen. The 20th Century Fox beautiful drama, Barkley Square, and our stars are Ronald Coleman and Marina Sullivan. I think it's no exaggeration to say that this is one of the great plays of our generation. The story of Peter Standish, whose love for the past carries him back into the 18th century, where his love for a girl struggles to overcome the barrier of time that lies between them. You couldn't find a better part for Ronald Coleman, CB. I'll be listening. Good night. Good night. Good night. Good night. You personally did cast an over up down. Our sponsors, the makers of Lux Flakes, join me in inviting you to be with us again next Monday night. When the Lux Radio Theatre presents Ronald Coleman and Marina Sullivan in Barkley Square with the Cecil B. DeMille saying good night to you from Hollywood. This Christmas, while our men are fighting for freedom overseas, it helped join the fight against America's great enemy at home, Tuberculosis. Buy Christmas seals and buy them generously. Use them on every gift or card or letter. With the threat of wartime epidemics, your help is needed more than ever. Buy extra Christmas seals today. Gary Cooper will soon be seen in the international picture along came Jones. Thomas Mitchell, co-author of the book from which Casanova Brown was taken, appeared through the courtesy of 20th Century Fox. He can currently be seen in Dal-Axanic's Technicolor feature, Wilson. Joan Bennett is now appearing in the title role of the international picture, Woman in the Window. Heard in tonight's play were Verna Felton, Anne O'Neill, Leo Cleary, Norman Field, Dorothy Scott, Leon Ledoux, Sarah Selby, Charles Seal, Eddie Emerson, Jacqueline DeWitt, and Sharon Douglas. Our music was directed by Louis Silvers. This program is broadcast to our fighting forces overseas through cooperation with the Armed Forces Radio Service. Our Lux Radio Theatre production of Casanova Brown, starring Gary Cooper, Thomas Mitchell, and Joan Bennett, have come to you with the good wishes of the makers of Lux Flakes, the tissue-thin soap used by smart housewives everywhere. In the Lux Radio Theatre next week, we will have as usual our producer, Cecil B. DeMille. This is your announcer, John M. Kennedy, reminding you to tune in again next Monday night to hear Barkley Square with Ronald Coleman and Moreno Sullivan. The cooking's so delicious. Won't you kindly tell me why? All the secrets very simple. Now I'm cooking with fry. Takes, pies, fried foods. Everything tastes better made with used fry shortening. Yes, them to be a better cook. Yes, I'm cooking with fry. Be sure to listen in next Monday night to the Lux Radio Theatre presentation of Barkley Square with Ronald Coleman and Moreno Sullivan. This is CBS, the Columbia Broadcasting System. Copyright© OSHO International Foundation


Most of this information comes from the form 1040 Instructions Tax Year 2022. You can find on the IRS website, irs.gov, irs.gov. Looking at the income tax formula, we're focused down here on tax before credits and other taxes. Now remember, the first half of the income tax formula is in essence an income statement, although a strange one where we have income minus the adjustments to income, which you can think of as the above the line deductions getting us to the subtotal of adjusted gross income minus the greater of the standard or itemized deductions to get us to the taxable income, which is similar to net income in a normal income statement structure. We're gonna take that net income as you would expect in an income tax system and apply the tax rates to it. However, that's more complicated than you would think at first because it's not a flat tax that we will be using. We have a progressive tax system, which means that we might have multiple taxes, tax rates that are applied to the same income level. So we talked a little bit about a progressive tax system versus a flat tax system and prior presentations, but just note that it can get somewhat complicated to try to figure out what the actual tax is without the use of, you can use tables, for example, to kind of figure out the tax. And of course, we can use software to help us to figure out the tax as well. And also realize that once we figure the tax, we're not done there, that's not it, because we also have the credits that we have to deal with down here, the credits that are going to be the non-refundable credits that we'll deal with. We also have other taxes we might have to deal with, such as the self-employment tax. And then we could have the refundable credits that we have to deal with, as well as the payments that we have already made through withholdings or estimated tax payments to get down to the bottom line. All right, so that said, we're moving on to the tax calculation, line 16. This is the second page of the form 1040. We're focused then on this tax calculation. We often rely heavily on tax software to help us with that tax calculation because we'll be using at minimum that progressive tax structure to do the calculation. Plus, we might have certain items of income that are being taxed in other formats, such as qualified dividends might have a more favorable rate as opposed to ordinary income rates, capital gains, for example, might be taxed at more favorable rates than the ordinary income rates. So the actual tax calculation on the net income that we got to can get quite complicated. All right, line 16, tax. So include in the total on the entry space on line 16 all the following taxes that apply. Tax on your taxable income, figure the tax using one of the methods described later. Tax from form 8814 relating to the election to report child's interest or dividends. Check the appropriate box. Tax from form 4972 relating to lump some distributions. Check the appropriate box. Tax with respect to a section 962 election, made by a domestic shareholder of a controlled foreign corporation to be taxed at corporate rates, reduced by the amount of any foreign tax credits claimed on form 1118, C section 962 for details. Check box three and enter the amount and 962 in the space next to the box. So that's a more unusual situation on that one. So recapture of an election credit. You may owe this tax if you claim an education credit in an earlier year and either tax free educational assistance or a refund of qualified expenses was received in 2022 for the student. So once again, these are somewhat more unusual situations. C form 8863 for more details, obviously of tax software can help us with some of these situations as well. So any tax from form 8621 line 16E relating to a section 1291 fund, check box three and enter the amount of the tax and 1291 tax in the space next to the box. Tax from form 8978 line 14 relating to partners audit liability under section 6226 check box three and enter the amount of the liability and quote form 8978 in the space next to the box. Net tax liability deferred under section 965 I. So if you had a net 965 inclusion and made an election to defer your net 965 tax liability under section 965 I check box three and enter as a margin as a negative number. So triggering event under section 965 I if you had a triggering event under section 965 I during the year and did not enter your transfer agreement, check box three and enter the amount of the triggered deferred net 965 tax liability and enter quote 965 INC end quote on the line next to that box.


Nice hit, you know life is much more interesting when velocity and position can change. I mean think about the simple act of throwing a softball and hitting it. It's much more interesting if I'm able to take the ball from rest and get it moving to some velocity before the batter then has to move a bat from rest to some speed. The two connect and then the velocity of the ball can change. Acceleration makes life much more interesting and in this lecture we're going to explore as many aspects of describing acceleration and looking at some kinds of constant acceleration as we possibly can. Just as we did with velocity we're going to begin this part of the lecture video by learning to describe acceleration in a single dimension that is acceleration along only one coordinate axis. The position of an object is given by defining a coordinate system and then applying a system of units to specify the location in that coordinate system. So for instance in the previous lecture we were thinking about a train moving along a track it could go either forward or backward that is almost a textbook definition of one-dimensional motion as long as we define the dimension as being forward along the track or backward along the track and we can denote that the x-axis of our coordinate system. We can then specify where the train is considered to be at its origin and then all positions ahead of the origin are positive locations along the x-axis and all positions behind the origin are negative locations on the x-axis. We can use units like meters or kilometers which is just a thousand meter units to then specify the location in that coordinate system giving physical meaning to where one is on that coordinate axis. The velocity of an object like the train is merely the change in its position as time changes and then from this we were able to come up with a few ways of mathematically assessing velocity. If we want to characterize the velocity of an object over extended periods of time we can define a quantity that's quite simple mathematically and that is simply the average velocity. We take the change in the position from where the train is considered to have started to the final location where the train arrives after some time t and you take the change in the position, the later position minus the initial position and you divide by the later time minus the initial time and that ratio is the average velocity. That time duration can be long or it can be short but typically when we're talking about average velocities we're not talking about infinitesimal little units of time we're talking about long periods of time, macroscopic periods of time seconds, minutes, hours, etc. Now the instantaneous velocity is a mathematical riff off of the average velocity it's a deeper dive into the mathematics of what you mean when you say velocity. This is the average velocity but in the limit that the time duration that you are considering approached an infinitesimal that is delta t approaches zero in size. Now instantaneous here in a mathematical sense means average but over so short a period of time that you don't really care about the duration the duration size is really meaningless it's as if you specified the velocity at exactly one and only one time because that time duration that you're considering is so short and we saw in the previous example that if one graphs this it is the slope of the line that relates position and time that tells you the velocity, the velocity is just the slope of the line the instantaneous velocity is the slope of just a very narrow piece of the line that line could be very complex, it could be a curve for instance now it's natural at this point to go one step further and define the new concept after all if velocity is the change in spatial position during a change in time we can then ask what is the change in velocity during that same change in time what does that quantity represent? Velocity does not have to remain constant throughout the time period under consideration and we saw that in the previous lecture and the answer is acceleration this is the concept we're going to explore in this lecture and using acceleration we're going to take a slightly deeper dive into the same mathematical concepts that we explored in the lecture on position, time and velocity as you will see its units, the units of acceleration are meters per second squared so they are meters per second per second velocity is meters per second and if velocity changes in time then we must have a change in meters per second per second or meters divided by seconds squared this is the most compact way to represent this unit now as was the case with velocity there is average acceleration which we will denote with a subscript AVG A subscript AVG and that is equal to the change in the velocity divided by the change in time and then just as we did with velocity we can define instantaneous acceleration as the average acceleration but in the limit that that time slice that we're considering delta t is becoming smaller and smaller and smaller and smaller and smaller approaching zero we will put this into practice in this lecture so far we've really played around with the idea of an instantaneous quantity in a fairly abstract way but we're going to give it concrete and definite form in this lecture and you're going to see how to exercise this concept with a real situation let's take a closer look at acceleration now here we're going to riff off the definition of instantaneous acceleration and dig a little bit deeper look a little bit more closely at how to handle that mathematical definition with its funny limit of delta t goes to zero and I promise you that this will be a deep dive but it will be extremely rewarding because when you master the concepts that we will look at in this portion of the lecture you will have taken the first steps into a much larger mathematical world a mathematical world that as we will likely discuss in class not only is important for physics but also for chemistry and biology it's important for engineering and it's important for a very hot topic these days artificial intelligence of which is the mathematics that we are going to learn right now so what do we really want when we want instantaneous quantities like instantaneous acceleration or instantaneous velocity it doesn't matter which one but we'll use acceleration as our example because that's the topic of this lecture what we really want to know is the acceleration at a specific time and let's call that time t it could be 3 seconds, it could be 10 seconds but we'll use a variable t to represent it all we can really do though so far is calculate average acceleration and we saw that that's defined as the ratio of the change in velocity divided by the change in time where for average acceleration the change in time is typically considered to be a macroscopic or large scale time seconds, minutes, hours, days something like that not microseconds or picoseconds or femtoseconds or something like that but when we're doing limits and sending delta t to zero what we are in practice doing is considering smaller and smaller and smaller units of time and looking at the slope of the line that relates velocity and time to one another in those narrower and narrower chunks of time so what we have to calculate is delta v and we want to do this to get an instantaneous quantity for as tiny a step of time as we can imagine so what this means is let's imagine that we can find the velocity using some kind of instrument we can find the velocity at some time t and then using that same instrument we can find the velocity again at a slightly later time t plus delta t where delta t is some add-on to the original time that we were making our first measurement and so we can just go ahead and compute this we can compute the average velocity using the sampling of the velocity at time t and the sampling at the slightly later time t plus a little delta t so let's write that down this is what that average velocity would look like mathematically we have v as a function of time that's what the parentheses represent velocity is a function of time the later time is t plus delta t so v of d plus delta t is really the velocity at that later time and then we have v of t which is the velocity that we measured at the earlier time and we simply take the difference and we divide by the time delta t over which this measurement was made from the initial measurement to the later measurement so this is just average acceleration now what we want to do is to compute that ratio in as short a delta t as possible so we finally arrive at a firmer mathematical definition of the instantaneous acceleration we are now going to take the limit as delta t goes to zero and we're going to define the limit of this ratio as instantaneous acceleration or simply acceleration so whereas before we had the limit of delta t goes to zero of delta v over delta t now we see what the structure of that delta v is that structure has now been revealed to us by making this thought experiment where we think about what it means to measure velocity at a slightly earlier time t and a slightly later time t plus delta t if we know this either we know the form of this function or have the number and we know this for instance again having velocity as a function of time a well defined function of time and if we know delta t or if we can get rid of delta t somehow by expanding out the mathematics of this ratio and cancelling out as many delta t's as we can then we can finally take that limit we can send delta t to zero and we can get acceleration a and in fact that is exactly what we are going to do in this lecture we're going to look at a concrete example of doing exactly this we're going to define the velocity at a later time t plus delta t we're going to define it at an earlier time t we are going to have a functional form for that this will allow us to mathematically get rid of a bunch of delta t's that are left will send to zero and will actually be left with a quantity that isn't zero at the end it's remarkable so let's do that so here is the usefulness of this closer look that we just took why was this so useful because now if we are given firm mathematical statements about how velocity changes with time we can answer questions like the following at time t equals three seconds what is the instantaneous acceleration before we just had an equation with nothing to plug into it we had no way of answering this question but now we can actually take the first steps in addressing this question with a firm answer so for example we could be told that the velocity is a function of time and that the functional form is what is shown here that the velocity is equal to a constant which I'll talk about in a moment times a function of time which in this case I have selected to be t squared now what is B well B is really anything we want it to be and I'll put some concrete number in here in a little bit but I want to walk us through the mathematics of this first B is just a constant and it has units such that when it multiplies t squared you get something with units of velocity what are the units of velocity per second so if we have time squared on the right hand side that means we have seconds squared in the numerator and that means that B must have seconds cubed in the denominator to make those seconds squared cancel out and give us just meters per second at the end of this so check that it's a simple algebraic exercise good practice good exercise at this point in the course to make sure that that makes sense so feel free to pause the video here and verify that whatever B is it must have units of meters divided by seconds cubed now that we have this information we can start using this function in the definition of instantaneous acceleration to find the acceleration at any time t that is valid for this functional relationship here so let's begin doing that in the first step we simply begin by writing down the equation for the instantaneous acceleration A is the limit as delta t goes to zero of V at a time t plus delta t minus V at a time t that whole quantity divided by the delta t well that's all nice but we actually have the function now for V we know that V equals Bt squared so whatever appears inside the parentheses here and here we will substitute into where you see t squared in this equation and we'll replace the V's of t's with an actual function that is Bt squared so let's do that so if I do that going one step into this process I replace the V as a function of t with the actual function B times the time quantity squared well for the left term in the numerator the time quantity is t plus delta t so that whole thing gets squared and then in the second term in the numerator it's just V of t so we have Bt squared so the t remains unchanged in this case we don't have to add anything to it and then square it it's just t now if this step was a little uncomfortable rewind the video listen to the process one more time try it yourself and make sure that this step feels comfortable to you well now that we have done this substitution we see that we have an exercise in sort of high school algebra polynomial expansion where we have a quantity t plus delta t all squared well we can actually write that out we can expand that out so let's do that that's the next step we expand out the square of t plus delta t so that leaves us with a term distributing the B constant through the three terms we'll wind up being in this expansion we have a term that goes as Bt squared we have a term that goes as 2 Bt delta t and that's because we have two terms that are Bt delta t and Bt delta t and you can just add them together and then finally we have a term that's B times the quantity delta t all squared so that's the expansion of the polynomial and then over here on the right we still have that lingering second part of the numerator the minus Bt squared now if you stare at this for a moment you'll begin to realize that we can make one simplifying step forward and that is to observe that we have a term negative Bt squared and we have a term positive Bt squared and they're added together so we can cancel them out and I will highlight them in red and I will explicitly show you that this cancels with this and that leaves us with just delta t plus B delta t squared in the numerator now things get really interesting because when we throw out those terms that cancel out we immediately see that we have one more thing we can cancel out of this ratio and that is delta t delta t appears as a multiplier of 2 Bt and it appears squared next to the second term in the numerator times B and it appears once in the denominator so you can make this step any way you like I have chosen to simply notice that because the numerator contains the delta t here and the delta t squared here I can cancel one delta t in each of these terms with the one delta t in the denominator and I've highlighted those in red so that completely removes this delta t leaving just a number one behind because delta t divided by delta t is just one and over here we can only get rid of one of the delta t's that are squared so the square goes away but we're still left with delta t to the one power which is just delta t and finally this leaves us with a greatly simplified looking thing and this is the thing that we are now going to act taking the limit as delta t goes to zero what do you observe about the argument of the limit function the first term in the argument contains no delta t's nothing will happen to this term when delta t is sent to zero but the second term contains a delta t multiplying the constant b so what will happen when delta t is sent to the value of zero in the limit of delta t goes to zero if you said that the second term in this argument will itself also go to zero you are absolutely correct and that means that the final result after sending delta t to zero is simply that the acceleration goes to two times b times t two times a constant times your time variable this is a concrete result if somebody asked you at a time t equals three seconds what is the instantaneous acceleration you are one constant away from being able to answer that absolutely concretely we just need to know what the value of b is congratulations whether you have realized it or not you have just done calculus first on first semester derivative calculus here is the shortcut that you would learn in a calculus course the activity that you have just completed on the previous slide is known as taking the first derivative of a function of time which we can generically denote f of t the parentheses are translated into English as of the argument so f being a function of t time what was the function of time that we took the first derivative of well f of t was v of t and v of t was bt squared so our function is the velocity and the variable of which it is a function is time so when we took the derivative that is when we took the limit of the average acceleration for the case that delta t goes to zero in the language of calculus we were taking the derivative of the velocity with respect to time that's what this quantity really represents acceleration is the first derivative with respect to time of v and that is denoted by this more compact notation dv dt this thing d over dt is really itself known as an operator in mathematics it is the quantity that acts on a function and returns a function that is for our purposes what an operator is the first derivative is an operator you feed it a function it returns a function that's its duty what is the mathematical form of the first derivative with respect to time it's this thing we've been playing with it's the limit as delta t goes to zero of the change in velocity over the change in time now for our specific function we can simply write out what the first derivative was the acceleration was the first derivative with respect to time d over dt of the function velocity which is itself a function of time plugging in that function that was bt squared and we got the answer we did all this out using all the steps on the previous slide we got the answer 2 bt 2 times b times t you've just taken your first time derivative whether you realized it or not there are many more time derivatives ahead of you so if this was uncomfortable to you go back practice it one more time pick a different function try using a different function try using bt cubed that now it's important to note that if you stare at this page closely you'll see the shortcut there is a nice shortcut that you learn when you do calculus for the first time when you're learning the derivative and you are learning the tricks of calculus to make the derivative go more quickly when you have to do it say on a homework assignment or on an exam or in the real world in a chemical gradient problem something like that there is a shortcut that gets you to the functional answer much faster to take the first derivative of a simple function like this one where we have a constant times time to some power all you have to do is simply multiply the function by the power of t and then reduce the power of t by one unit so take a look at this this function was bt squared and I can tell you that if you use what I just said here a moment ago multiply that function bt squared by the power of t and then reduce the power of t by one unit you will get to the answer that we got to after all those steps on the previous slide this is much faster so here's the shortcut take the power of t two multiply this whole function by two so you would wind up getting two bt squared and reduce the power of t by one unit which then gives us two bt to the one or just two bt and that indeed was the answer that we got so now you see what calculus really is it is considering quantities where we send aspects of that quantity to for instance zero size and evaluate the pieces that are left over may not in fact be zero at the end this is just one example but there are many more that are going to come up in this class so this is definitely a good couple of slides to practice or review many times during the course the power of calculus cannot be understated in fact as a branch of mathematics it was invented in the form we know it today nearly simultaneously by two brilliant individuals who did this development within about 10 years of one another and those two individuals were Sir Isaac Newton who we will learn more about as we go through this course and Gottfried Leibniz using this mathematics we contain as they needed to tame very complex problems and in fact from the perspective of Isaac Newton the reason that he needed to invent calculus in the first place was because it was impossible to describe in a simple way the observations of the natural world that he and his predecessors had made up till that point without this new kind of mathematics that considers quantities in the limit that they go to very small values and then what happens to the functions of those quantities as a result of that Isaac Newton had a wealth of information about planetary motion about the motion of the moon and the sky about objects falling to the ground on earth pulling, sliding down hills, etc but in order to make sense of the natural laws that underlie all of those phenomena he needed a mathematics that would allow him to describe changes as a result of some variable and that is what we now call the calculus or simply calculus and you see how this is extremely powerful given a function that relates velocity and time you are now able to compute the acceleration at any time of motion and so for instance using the previous example where we had velocity as a function of time being given by bt squared we can now define the constant so for instance I am going to define b to be 2 meters per second cubed and given the original question what is the acceleration at t equals 3 seconds we can answer the question we know that acceleration equals 2 times b times t and if we plug in b equals 2 with units of meters per second cubed t equals 3 with units of seconds we can then do the remaining mathematics at this point multiply 2 times 2 times 3 we have 4 times 3 which is 12 and the final answer is 12 meters per second squared so we see checking our answer that we have a number with the correct units for acceleration meters per second squared I mentioned earlier that you would see how the units of acceleration are meters per second squared this problem demonstrates this quite nicely but we could have gotten to this conclusion simply by looking at the definition of average acceleration which is delta v meters per second divided by delta t which is seconds so that must be meters per second per second or meters per second squared and indeed checking our answer here we have a number with units of meters per second squared so we can at least be assured we got the units worked out correctly and that when we did the derivative that is when we took the limit of the average acceleration in the limit that delta t goes to 0 indeed we arrived at a quantity that has the correct units for acceleration now let's consider a special case of acceleration and that is when acceleration is constant in that case it would mean that the ratio of delta v 1 and delta t 1 in one time duration would be identical to the ratio of delta v 2 and delta t 2 in any other time duration okay now I've written this out here in a sort of mathematical way the acceleration at some in some time duration 1 would be given by this ratio delta v 1 over delta t 1 and what we're saying is that under the special case that in any other delta t so for instance some delta t 2 in the motion the delta v divided by delta t in that unit of time gives you the same number then we can say that the acceleration is some constant so all of these are equal to each other under that special case and we can represent this graphically using the same techniques that we did for position versus time now for velocity versus time so over here on the right I have a graph of velocity on the y-axis and time on the x-axis or the vertical axis and the horizontal axis depending on how you want to say it and the arrow, the black arrow represents the relationship between velocity and time and if we slice the velocity at two different time segments so for instance here is delta t 1 the first of the two segments in the wide green rectangle the t 2 the second of the two time segments and the second rectangle we can look at specifically the slope of the line inside of those segments here and here and ask questions like is the slope changing after all you would be getting for instance a different delta v over delta t in those two time slices so what you can see in this graph here however is that the slope of the velocity versus time relationship is the same in both time slices I could imagine taking this little line right here and just transporting it down here and you'd see that it lays right on top of the line inside of this green left green rectangle so it must be the case that the slope is the same and since the slope of this line is the acceleration it must be the case that the acceleration is the same so the acceleration can be said to be constant and in fact this kind of graph that you see here is exactly what happens when acceleration is constant it's worth noting that this same argument can be applied back to constant velocity that is if the slope of the change in position with respect to the change in time is the same in any two durations of time it must be the case that the velocity is constant if the slope is the same just as here because the slope of the velocity versus time is the same in the two units it must be the case that the acceleration is the same now the beneficial thing about considering constant acceleration is that when you have that situation there are some extremely handy equations we call equations of motion and they relate spatial location, time, velocity and acceleration assuming that the acceleration is constant with time if acceleration is not constant with time these equations do not necessarily apply in the form that you will see written here so we're going to look at these equations we're not going to go into any depth about them right now we're going to use class time you should use the reading to expand your depth and understanding of these equations and class time and homework will be your first practice with utilizing them to answer questions about the physical world but here I will merely introduce them and we will also look at some new mathematical terminology that appears in these equations it's fairly straightforward terminology to grasp once you see the pattern so the first equation is simply that the velocity at some time t is equal to the initial velocity plus the acceleration times the time that has passed it's always assumed that the motion began at time zero which is why you don't see a t with a subscript zero appearing in these equations that very well could put that in here this equation is very useful if for instance you know the initial velocity you know the constant acceleration and you want to find the velocity at any other time t after time zero it's also useful if you know the final velocity but don't know the initial velocity but have the acceleration and the time and you can solve for your unknowns if as long as you only have one unknown then one equation will do just fine but if you need more than one unknown you need more than one unique equation in order to solve for the unknowns two unknowns you need two unique equations three unknowns you need three unique equations and so forth this should remind you of high school algebra where you should have learned to solve systems of equations with one or more unknowns that needed to be determined the new terminology introduced in this equation is the v with a subscript zero which merely refers to the object's velocity at time t equals zero and you can see that for instance if we set t explicitly to zero in this equation then v is equal to v with a subscript zero the next equation relates velocity, acceleration and position the first one related velocity, acceleration and time so now we see that we have the final velocity squared is equal to the initial velocity at time t equals zero squared plus a term that is two times the constant acceleration times the displacement in space during that time x minus x naught and x sub zero or x naught is simply the object's position at t equals zero you may hear this kind of mathematical notation stated in various ways so x sub zero or x subscript zero or x naught which is n, a, u, g, h, t for zero x naught is typically how I will refer to this or v naught the next equation we have is the displacement x minus x naught is equal to the initial velocity times time plus a term that is one half the constant acceleration is equal to one half the initial velocity plus the final velocity that whole quantity you're going to divide by two and that is multiplied by a half and that whole thing is multiplied by the time and then finally we have that the displacement is equal to the final velocity at time t multiplied by that time minus one half the acceleration times time squared you'll note that this equation is very similar to the third one but with the key difference we have the initial velocity and so if the acceleration is positive we would expect this to displace the object further forward along the x-axis thus the plus sign but here if we've displaced in the forward direction along the x-axis and we only know the final velocity we need to subtract this term to get back to the initial conditions anyway you'll have lots of opportunities to practice this beginning in class more so on the homework to give you some level of mastery and of course we will use and reuse these equations throughout the entire course to relate space, time, velocity and acceleration assuming that the acceleration is constant with time and that's what I want to emphasize here at the end of this part of the lecture it's important to remember that at all times the acceleration a is constant and the velocity v and the displacement x is measured at time t now let's consider a force that yields a constant acceleration this is a great way to employ these equations of motion to begin tackling problems in the natural world right away and that case is gravity near the earth surface gravity as a force close to the earth surface is an excellent example of a constant accelerating force if you take an object and you drop it in the gravitational field very close to the surface of the earth regardless of the mass of the object what you will find is that the acceleration experienced by those objects is always the same now we're going to study gravity in some detail later in the course and you'll see why it is that at least in this part of the physics curriculum the mass of the object doesn't matter that the acceleration felt by any two objects is the same close to the surface of the earth but for now it's simply sufficient to know that if you take an object you hold it out and you drop it near the surface of the earth it will accelerate toward the center of the earth that is it will head toward the floor or the ground and the acceleration that you are witnessing as it falls is nearly uniform and constant and independent of the mass of the object you drop now the reason I have a star here is I'd like to put a little caveat here of course when you drop an object close to the surface of the earth you are not dropping it in empty space with no other matter in it you are surrounded by the atmosphere by air, nitrogen, oxygen, etc air exerts a little bit of resistance on the motion of a moving object and as we will see later when we explore forces that dragging force that air exerts always opposes the motion of an object if you try to move an object to the left the force of the air resistance will push to the right so it is certainly true that when you drop objects near the surface of the earth the shape of the object combined with its mass may change the amount of air drag that the object experiences as it accelerates toward the ground or the center of the earth but if you can concoct a situation where that drag force is negligible then you can witness the reality that the acceleration due to gravity is independent of the mass so this star here is the caveat that yes there is air resistance but we will try to consider situations where it can be neglected for the time being so that we can make progress in understanding the natural world here once we start thinking about forces now this acceleration this constant acceleration near the surface of the earth is a useful number to memorize it is 9.8 meters per second squared and this number is so useful that it is actually given its own symbol little g and it is referred to as the acceleration due to gravity near the surface of the earth or simply g and g is 9.8 meters per second squared we reveal the character of the constant accelerating force of gravity near the surface of the earth by dropping something like a tennis ball the video physics software allows us to track the motion of the tennis ball as it falls now in the previous video the motion was slowed down artificially using apple ios slow motion video capability but for the video physics software analysis we want to return the video speed to normal and so the analysis that follows in this lecture is done using the video at normal speed the video physics software allows you to track the motion of the tennis ball and what the software does as you can see in this still image is that it places a dot at each location in the video as the video advances where it thinks the tennis ball can be found now i didn't do any precise estimates when i dropped the ball in this video but based on where the ball starts up near my forehead and where it hits on the floor and knowing my height i would estimate that the ball fell a distance of about 1.73 to 1.77 meters or so something in that range using that information and using the graphs that you can obtain from the video physics software it's possible to get an estimate of the acceleration due to gravity that the tennis ball experiences this is one of the graphs that the video physics software can return to you using the data that it obtains from frame by frame analysis of the video tracking an object frame by frame and knowing the time of each frame in the video in the top graph we have a reporting of the why coordinate of the ball as it falls during the time interval of the video the video begins at time zero but the ball is not dropped until about four tenths to five tenths of a second into the video at that point once the ball is released by my hand you'll notice that it's why coordinate changes and it does so more rapidly with each interval of time the slope of the why coordinate graph versus time is not constant it changes in time now using delta y divided by delta t in each time interval the software then converts this distance versus time information into velocity versus time information and so here we can see it was roughly this point at about 0.45 seconds or so into the video it was at this point that the ball was released and began its descent to the floor what we observe is that while the why position the vertical position versus time has a curve that has a changing slope with time the slope of the velocity versus time graph does not change of course until the ball hits the floor and then it bounces and then it changes quite rapidly and we see it rebound as the velocity changes in the graph but let's only focus on this portion of the graph that I'm highlighting here with the arrow from the time when the ball is released from my hand to about the time where it hits the floor it goes slightly off the camera frame when it hits the floor so the most reliable data point for the last part of the motion is probably somewhere back here around 0.93 seconds into the video so our first data point with a velocity of about 0 is at around 0.45 seconds and our last data point that I would consider reliable while the ball is still essentially in view is somewhere around 0.95 seconds and we see that at this point the ball is moving in the negative direction it's moving down toward the ground with a velocity of about negative 5.5 meters per second and if you take delta v and divide by delta t using the numbers I just gave you about that the acceleration due to gravity over this period was on average about negative 10 meters per second squared and given the rough estimate of where the ball's height started from and how far it dropped that's pretty good considering the true answer is around 9.8 I would assume I'm accurate with my height measurement to know more than about 5-10% and we've certainly gotten to within the ballpark 8 meters per second squared for the acceleration due to gravity now is that acceleration constant on the tennis ball well it sure looks like it this graph here while it's not a perfectly straight line and that can be attributed to uncertainty in the measurement from the frame by frame video analysis is pretty close to a straight line on average all the way down until the ball goes out of the frame of the camera that's the floor so we see here on the tennis ball that there definitely is a constant acceleration of 9.8 meters per second squared I promised you that gravity is a force of acceleration near the surface of the earth that is constant and independent of the mass of the object that has dropped let us demonstrate that I have here a hammer that weighs much more than the tennis ball it feels much heavier in the hand than a tennis ball does but if I drop them starting from exactly the same height so that the head of the hammer held upside down is just about the same height as the base of the tennis ball and let them go we can see what happens indeed the head of the hammer and the bottom of the tennis ball strike the floor at just about the same time despite the fact that the hammer is the tennis ball indeed objects near the surface of the earth dropped in the gravitational field of the earth and neglecting air resistance experience exactly the same acceleration a constant acceleration of 9.8 meters per second squared the key ideas we have learned in this section of the course are as follows we have learned to define acceleration we've seen that the average acceleration and the instantaneous acceleration have been defined using identical techniques to those same average and instantaneous concepts in velocity but in this part of the course we've taken a deeper dive into instantaneous quantities and we've used acceleration as our practice, our example and we've seen how what emerges from considering instantaneous acceleration is a glimpse at the power of the calculus or just calculus which is extraordinarily useful in handling complex mathematical situations we have learned how to define the first derivative with respect to time of a function of time, the function of time we have considered is velocity we have learned about constant acceleration and how to relate position, velocity, time and acceleration under that condition, at least we've seen the equations that do it you will get more practice and insight from the reading from class and from homework and we have learned that the earth's gravitational force close to the earth's surface is approximately a situation of constant acceleration it is independent of the mass of the object experiencing the gravitational attraction and this concludes this lecture on acceleration and concepts related to acceleration in motion


So, yeah, my name is Chesco Fowli, I am from Valencia, Spain, but I live in Granada, and I am the QA engineer in the Document Foundation. Well, it was about finding interoperability regressions in LibreOffice. It's based on a tool created by Milo Sareb, something like that, I don't know how to pronounce it. And, well, he gave a talk in LibreOffice conference in Brenno, so I've been working on this tool and, well, my talk in first-time was about this. Basically, what we check with this tool is if we introduce interoperability regressions in the documents, so we compare it with Microsoft Office 2010 and we see if documents are displayed correctly or we have introduced regressions in the display of the document. With this tool we check how the documents are imported into LibreOffice, but we also check how they are exported. So what we do is we open it with LibreOffice, we export it, and then the resulted document we have, we check it and we open it with Microsoft Office and see if everything is correct. It's kind of, let's say it's 80% automated, so all the scripting and import, export and comparing the documents is automated, but in the end we have to check it manually if we have introduced a regression or not. The more documents we test, the better, because we have a better coverage. So right now we are working with a thousand documents, but it has been moved to a virtual machine recently, so the idea is to, let's say, 5,000 documents or even 10,000 documents, so that would be ideal. Yeah, we take them from the backtrackers, from different backtrackers, Baxila, well, from LibreOffice backtrackers, we also take them from Abigual backtrackers, Caddy backtrackers, so from different backtrackers we gather all these documents here. I knew about LibreOffice, the day it was forked, I read it on the internet, so I got curious about the project and I joined the mailing list and so on, and the same year I was able to participate in the Google Summer of Code, so it was in 2011, and yeah, I succeeded in this Google Summer of Code and since then I've been contributing to the project every now and then when I had some spare time. I did some development and I also contributed in QA and then this year I had the opportunity to join the team as QA engineers, so yeah, it's useful to us nowadays to the QA team because we can more or less find how many classes or how many users are affected by that class, so that's kind of important information to us, so we can set the priority based on these numbers. That's one of the priorities we have nowadays and I think it's going well because when I joined the project, well, I didn't say it but I joined the project in September 2016 and at that time the numbers were around 750 and right now are around 500 or even sometimes even 450, which is, well, we got a good gain here, so we reduce it a lot, the numbers. Well, it's important that everything is as much detail as possible, then we appreciate if there are some clear steps to follow in order to reproduce the bug, then it's also important to have a document in order to reproduce the bug and I think it's important that reporters try to find if the same bug was reported before, otherwise we are reporting the same bugs again and again, so then it's more work for us to do in order to find this duplicated bug. So we have different communication channels, we are going to leave them here in this video, in the description and I think that's the direct approach just to go to this communication challenge and contact us directly. Otherwise, well, we have some easy tasks for newcomers and one of them is to try to confirm and confirm bugs and we also have some old bugs that need to be re-tested, so that's another task a newcomer can do, so basically go through the list of bugs and see, okay, I'm interested in this bug, let's see if it's fixed in the latest version or not and there's another interesting task which is when a bug has been fixed just to confirm that the bug is indeed fixed, so just to verify that the bug is fixed, so it's basically you just download the latest version, the latest master version and then you check that the bug is fixed. Then we have all the interesting tasks which need a bit more of knowledge but yeah they're all in the wiki page or they can just ask us in the in the channel and that's all.