Good evening friends This is your host again to welcome you through the creaking door into the inner sanctum Come in Come on in. I want you to meet Ambrose our Man-shy ghost the other night in a graveyard. He bumped into a human and was so frightened. He turned flesh color Yes, poor Ambrose He's got a bad case of ants in his fantasies He's so upset. He's just a ghost of his former ghost Where's the time when we held high hope for Ambrose? Oh, yes at abnormal you he was cited by his crass mates as the Personality most likely to split And now let's visit murder mansion For over a hundred years the old house is stood on the cliff Weathering the relentless ocean winds that have battered at its gray shingles Now in the living room the real estate agent and the new buyer are completing the arrangements of sale Only one thing bothers me mr. Griffin That graveyard just outside the window there Are you sure nothing can be done about it? I'm sorry mr. Burley. You know the condition sat down in the deed The Crandall family burial ground must remain on the property Untampered with hmm those Crandall's must have been a morbid family Having themselves buried right next to the house they lived in yes, they were peculiar. I Guess they figured it was a way of keeping the family together You shouldn't laugh mr. Griffin. What what are you doing here? This is the gentleman who's planning to buy the house mr. Burley's already bought it. Oh I'm sorry. Hey look, what is this Griffin? Who is this woman? I'm Emily Robbins Mr. Burley, please you must sell this house immediately to me sell it.  I just bought it Mr. Griffin never should have allowed you to now see here. Mrs. Robin just a minute Griffin I want to hear what she has to say. Well, all right, but you can see she Isn't exactly accountable You promised to sell the house to me, but you couldn't wait until I had the money, could you I'm in the real estate business Not charity. Mrs. Robbins. I still want to hear why Griffin shouldn't have sold me this house Because mr. Burley a house isn't just a thing made of wood and stone and mortar It's almost a living breathing creature It accepts and rejects people just the way we do. I Was born a Crandall and only a Crandall may live here Anybody but a Crandall would be an enemy within its walls You'd never spend a happy moment here. Oh, you see mr. Burley. I told you she doesn't make sense Please mr. Burley for your own sake sell it. Ah Oh, you can't frighten me into a quick sale. No, I know a buy when I see it My wife and I will be living here within a few days I'm sorry mr. Burley, but I don't think you will I Don't think you will ever live here Helen oh, Helen Yes, Ada, where's Mrs. Burley? I want to tell her I got that house at my price. Oh, sir You'd better go upstairs. The doctor's still there Dr. What's the matter? Oh, mr. Burley. What is it Ada? What is it? Your wife is dead She seems so well after lunch she was upstairs napping and when she didn't come down at a usual time I went up.  He said Oh Hello, well, mr. Burley can't come to the phone right now. It's all right, Ada. I'll take it. Yes Hello Can I bring you something mr. Burley? No Ada. Thank you Sir, I know it's none of my business, but maybe you shouldn't have come to live in this house Maybe you should have sold it to Mrs. Robin. I had to come here. I Have to prove to myself that a house can have no evil influence over life and death, of course it can't and yet according to the doctor My wife passed away almost at the very moment I I Bought this house. I'm so confused.  I'm just trying to find them things out Standing there staring out at that graveyard. I'm all right now. Let me along. Yes, sir. Good night, mr. Burley. Good night That graveyard out there when the lightning flashed just then I saw it so what? There was a new headstone among the old ones a brand-new headstone Mr. Griffin How long ago was the last candle buried in the graveyard out there the last one. Let's see. Oh Yes, it was a Vincent Crandall. He died 20 years ago 20 years Then his headstone would have been a little worn by this time. Well, sure it would but what are you then? What is the meaning of the new headstone? You come to the window. I showed you oh now mr. Burley There's a brand-new headstone out there over a fresh grade. Oh, but that's impossible I saw it first when the lightning flashed.  Burley Maybe you better see a doctor Doctor there. They're all old headstones out there The new one is only in your mind Give me that flashlight Mr. Griffin you've been under terrible strain your wife's sudden death and all I don't know What made me think I saw a new headstone out there? I I want to sell this house right away. Well, you know it takes a little time to arrange a sale Well, what about that robin's woman? She'll buy it. She's been bothering me all along to sell it to a missus Robins can't pay you Decent price. I don't care. I'll take anything she offers. I want you to get in touch with that. All right, mr. Burley I'll call her in the morning. No, no, I Can't wait until then I Want this house sold tonight? Mr. Griffin why mr. Burley had to bring me out here this time of the night and he's made up his mind to sell He wants to close the deal tonight Look, mr. Robins.  Griffin and not in business for love your wife. Where can we go? It was as crazy as you are Doesn't he answer the door what's taking him so long No one's screaming came from Save the garage. There's a light in there. Come on No, it's who find out It's a chance I'm going to have to take Ada But that was you who screamed Yes, why what happened? What is it Ada what about mr. Burley he's dead What he left the house an hour ago. I looked out of the window and noticed that the garage here with lit I came out. I found him clumped over in the car dead Well, this place is filled with carbon monoxide films it wouldn't have happened none of it If he hadn't bought the house now look mrs. Robins. This is no time for that superstitious nonsense She's right, mr. Griffin. He is nonsense. What do you mean Ada? Look on the back seat of the car Good Lord a new headstone Everybody want to buy a house the Crandall place is a real buy all you have to give for it is your life Too bad about our friend mr. Burley, huh? All he was getting a bargain basement, but instead he's ended up in a basement. He didn't bargain for Yes, he should have taken old lady Robins advice, which in a phrase was one man's manage is another man's More Well, now let's get back to our mystical manner a Week has passed since Burley's death and the real estate agent mr. Griffin has found a new buyer Here's your check mr. Griffin. Thank you mr. Wagner.   I guess wouldn't live here if you paid him superstition never bothered me Mr. Griffin, yeah, what are you looking at that way? There's graveyard out there. I I Don't understand Understand What are you trying to say? There were always ten graves out there, I'm sure But now there's a letter I'm sorry, mr. Robins, but nothing you say can persuade me to sell Please mr. Wagner for your own sake. Don't be stubborn. It may cost you your life You know what happened to mr. Burley and his wife. Well, I've always prided myself on being a jink wicker Be sensible that's a very silly reason to to live here. Maybe I have another reason to I mean Charles Burley was a very close friend of mine. Oh, I I didn't know that I told it to mr. Griffin now.  Oh, but he didn't commit suicide You seem to know a lot about it. I do Then maybe you can tell me who killed him. I can This house is the killer now look. Oh, it is mr. Wagner. I know You don't believe me, do you? Of course not soon. You'll find out that I'm telling the truth That sounds like a threat. No, no, mr. Wagner. I'm not threatening you. I'm just trying to help I'm just giving you a chance to live One more chance to Serve me this house at my price And if I refuse If you don't sell it to me now, but then I'll buy it after your death I see Well, mr. Robbins, there's nothing more we can talk about I'm sure you know your way out Good afternoon. Good day, mr. Wagner What are you doing here? Oh, didn't you know I'm mr. Wagner's new maid Hello Yes Who is this yes, but who is this? Hello Hello, hello Operator get me main 6539 and hurry. Yes, it is connected. What well, that's impossible I just spoke to someone at that number try them again. I'm sorry. Mrs. Robbins What are you doing here at the Crandall house? I was waiting for you, mr. Griffin. I don't understand Come in, please I was the one who called you on the phone to come out here I didn't say who I was because I didn't want to mention names But I tried to get the phone here right after you hung up the operator said the line was disconnected it is The wire has been cut. I walked down the road to the mobile gas station to call you to come out here This is Robbins. Just what is this all about anyway? Why are you here and where is Ada and mr. Wagner? Ada's left she's gone away What On the hall table over there a note from Ada to mr. Wagner Explaining why she left and what about mr. Wagner himself? Where is he in the dining room? Wait, wait, please don't go in there yet. He's dead Mr. Wagner dead when I came in he was slumped over the table When you came in, huh? With the way you say that mr.  Wagner Well, what should I think? Oh, I wouldn't do a thing like that And suppose you tell me exactly what you're doing out here tonight. Well, it's like this mr. Griffin I was home in bed, but I couldn't sleep a Strange feeling kept running through me that I should come out here and try to convince mr. Wagner that He should sell the house before another day pass. Oh a feeling you can believe me. Oh, sure When I arrived out here the door was open and Everything is just as you see it. What about the police? I didn't call them. Why not? Because I wanted to speak to you first speak to me with a murdered man in the next room. It wasn't murder It was just the will of this house and I want this house You do anything to get it, wouldn't you? Yes anything Even murder Yes, Mrs. Robbins. I'm driving down the road to make a phone call to the police What are you doing here? I was watching you and Mrs. Robbins through the window mr. Wagner is dead. I know But how could you you left the house this morning? I saw his body slumped over the table You think the same as I do don't you know what do you mean by that? You suspect mrs. Robbins, too in a way But I also suspect you waiter Me but I can't exactly figure out what your game is game I have no game and why did you leave a note saying you were going away? Not note There's no use lying. I saw it myself on the whole table, but you must be mistaken today is my day off I left the house early this morning. I didn't write a note if you are telling the truth. I am I am Then I know who did write that note You wait right here for me. I'll be back in 10 minutes. Keep your eye on the house Where are you going? The phone inside is disconnected. I'm going down the road to call the police. I'll go with you Why I'd rather not stay here alone. Mrs. Robbins doesn't know you're out here. You're safe But just the same I'd feel better if I went with you. I'm not taking you with me You act as if you're afraid of me Maybe I am but why why? Because when mrs. Burley died you were in the house The same with mr. Burley and now mr. Wagner You were there whenever victim died, Ada. I Won't let you in this car with me I You called the police mr. Griffin. Yes, they're on the way out now By the way, what are you doing here in this kitchen? Oh, I was just walking through the rooms Recalling the happy moments. I spent here when when I was young. You sure that's the only reason Oh, yeah Thought maybe Ada had something to do with it Ada You know very well. She's left. You saw her note Ada didn't write that note Well, I talked to her outside this house 15 minutes ago She was to wait out there for me until I got back She wasn't there. What's happened to her? I didn't see a death But wait What is it about five minutes ago? I I thought I heard something move down the cellar The cellar. Yes, but then I I thought it was just my imagination hold on a minute Just now I heard it too Something or someone is down there Come on. We're going down into the cellar to look around Mr. Griffin look look it's it's lit down there in the cellar.  Huh, one of the stone flooring slabs has been removed. There's an old well down there I remember it was sealed up when I was a little girl. Yes And I can see the slab was freshly removed. I Wonder why it's Griffin. What now be behind you in the shadows. Look, there's a woman's body It's Ada Yes, I know Why you say it as if you were sure we would find this way I was sure You see Mrs. Robbins I Killed her. I Didn't have quite enough time to dispose of her body in the old well here I heard you moving about upstairs in the kitchen Because she insisted on living in this house like the others then it wasn't this house It wasn't because they weren't grand of course not but your idiotic Superstition about this place helped my plan Mrs. Burley's sudden peculiar death was a lucky coincidence for me It gave me the idea for the others I Needed a series of deaths to completely destroy the value of this place So no one would ever live in it, but why? On several occasions you mentioned my wife, Mrs. Robbins You see you were wrong about her as everybody else was wrong She didn't run away from me She would have that I killed her and her body is down at the bottom of that well Just as a does will be and just as yours will be But the police are coming Foolish old woman. Do you think I really called them now, Mrs. Robbins?  No my leg. Let me go. Let me go the well As they say all as well that ends in a well Folks what about that griffin character just goes to show how a property agent can sink to such a an Unreal a save Yes, sir. That's what I call tripping over your own plot Now, Mrs. Robbins will never be lonely Now when things get dull she can always step outside the house and dig up for relative or two


During the last lecture, we have been talking about the Poisson's and Laplace's equation, and we also discussed how to obtain capacitances of few geometries starting from Poisson's and Laplace's equation rather than from the intuitive nature of the potential which we had earlier. In this lecture, we will continue with the formal solutions of Laplace's equation which is the equation which is valid in regions where there are no charges. You recall that Poisson's equation which is del square of the potential is equal to the charge density divided by epsilon 0 with a minus sign. That was valid in regions where there are charge sources of charge present, but we will be talking about source free region namely charge density is equal to 0. Therefore, the equation that we are looking for is the Laplace's equation which is del square of phi equal to 0, phi is my notation for the potential. What we will do is to look at formal solutions of these equations in 1, 2 and 3 dimension. So, let us look at first the simplest of the problem. Namely, I look at the problem in one dimension for which this equation is d square phi by dx square is equal to 0, the simplest of the second order equation that you can think of. So, if the second derivative is 0, the first derivative d phi by dx that is equal to a constant. So, let us call it some m and phi itself is one more integration which gives me m x plus a constant equal to c. We all know that y equal to m x plus c is an equation to a straight line. So, as a result the equation that I have, the graph of the potential versus the distance is something like this. So, straight line, so notice one thing the solution of this equation as we will see it is a common feature with Laplace's equation is essentially featureless, the very monotonically increasing function in this case or decreasing function. And important point is that if you are looking at the value of the potential at any point x, since this is a straight line, what you could do is to find out for example, what is the value of the point x. You could find out what is the potential at let us say x plus a and at x minus a and you can easily show that the potential at the point x is the average of the value of the potential at a point x plus a and x minus a, a is absolutely arbitrary. So, of course it is very clear from the nature of the solution that there are no maxima or minima in the solution of this problem. We will see that this averaging is actually a common feature of the solutions. So, since it is an averaging I cannot obviously have the minimum or a maximum because then the value at a midpoint between maximum and medium, minimum cannot be actually an average. So, let us look at what happens in two dimensions. Once again the same statement is true namely the function which are solutions of Laplace's equations, they do not show any features, they do not show any maximum or minimum. Let me illustrate this with a very simple example. Let me look at a form of an equation which satisfies the Poisson's equation. For example, consider a function of x y which is simply a by 4 a is a constant into x square plus y square. Now, let us look at what is del square. Remember we are in two dimension. So, del square implies d square by d x square partial derivatives plus d square by d y square partial derivatives. So, therefore, my del square of phi in two dimension is simply equal to a. You can see it first derivative gives you 2 x a by 4 that is a x by 2. The second derivative will give me another it will reduce the power by 1. So, I will have a by 2 into x just a by 2 I am sorry just a by 2. And similarly, the second derivative of this will be another a by 2 and as a result the total second derivative is equal to a. Now, this is of course, not a Laplace's equation. This looks like a Poisson's equation. Now, this solution if you plot here is a genu plot of the function. You notice this function that it looks like a cup and so there is a minimum at the point x equal to 0, y equal to 0. And that is very obvious, because this is a positive function everywhere. And since the function is positive it is absolute minimum value can be 0. So, once you are at the once you are at the bottom then of course, the value of the function has to rise no matter which direction you go to. So, this is a function with a minimum. Now, consider for example, a slightly different function namely phi of x y the phi of x y is let us say instead of a by 4 x square plus y square I have x square minus y square. Now, you can immediately check that del square of phi works out to be equal to 0 which means this is Laplace's equation. Now, supposing you are to plot this function this is del square phi equal to 0 a by 4 x square minus y square. Now, what happens at the point x equal to 0 y equal to 0 is that a minimum the answer is now. Look at this structure here. Now, the point x equal to 0 y equal to 0 is what is known as a saddle point. You all know what is a saddle. A saddle is a seat on the back of a horse. Now, if you have looked at a saddle you will realize that in one direction the if you go in one direction that is along the back of the horse this function will go down, but on the other hand if you go in the other direction the function will go up. It is a saddle it is not a maximum because there are regions which where the value of the functions is greater than the value at x equal to 0. On the other hand it is not a minimum because there are regions for example, in this part where the value of the function is smaller than its value at x equal to 0 y equal to 0. So, once again that tells me that the Laplace's equation solutions at least from the examples that we have pointed out. They do not show any features it does not have a minimum it does not have a maximum end. So, we have seen that the averaging property works and things like that. A consequence of this type of thing that we are doing is what is known as an Ernst's theorem. Now, Ernst's theorem states that supposing you have a charged particle the theorem states that it is not possible for a charged particle to be an equilibrium static equilibrium only by action of electrostatic forces. There are other ways of keeping it in equilibrium, but if the only force that is there is an electrostatic force you cannot keep the charge in equilibrium. Now, why now look at this I know that if I have a charge q in a potential field v the energy of that will be equal to q times v. Now, if the energy is q times v and the charge is in a region which satisfies Laplace's equation because there are no sources in that region. So, I have del square v equal to 0 which implies that the del square of the energy function which is q times the potential that is also equal to 0. Now, if del square of v equal to 0 or del square of q v I am using the symbol v for both potential and phi also for potential should not cause any confusion at this moment. Now, this solution does not have a minimum at least we have seen just now. Now, if the energy function does not have a minimum then clearly the configuration cannot be stable it cannot be in stable equilibrium. So, this is known as Ernst's theorem follows from the fact there is no minimum in energy which in term follows from the fact that the potential function satisfies the Poisson's equation. Now, we will come back to solutions of Laplace equation in two dimension little while later, but at this moment we will jump to these solutions in three dimension in different types of geometries. The three types of geometry which we are concerned with primarily are the rectangular Cartesian for which the Laplacian equation is simply del square phi by dx square del square phi by dy square and del square phi by dz square this is Cartesian form. These spherical polar form depending upon distance r polar angle theta and azimuth phi is given by this expression here we will be talking later about this equation in detail. In cylindrical rho theta z coordinate as you know that the z coordinate is same as that of the Cartesian. So, therefore, the Cartesian expression remains the same and the other two are basically the polar in the x y plane and that is the way it looks like. So, let us look at the solution of Laplace equation in three dimension first we will take up the rectangular or the Cartesian coordinates and then we will look at the spherical polar. Now, in Cartesian coordinates we have seen that I have got del square phi by dx square plus del square phi by dy square plus del square phi by dz square equal to 0. We know that we would like to solve this problem subject to some boundary conditions. Now, let me let me say I have chosen a region of a rectangular parallel piped whose dimensions are length breadth and height are l 1 along the x direction, l 2 along the y direction and l 3 along the z direction on the six surfaces. I have certain values of the potential specified. So, these are my boundary conditions. Now, what we will do however is use the fact that the solutions obey superposition principle. So, instead of giving all the six conditions I will work out in detail the solution for the problem where on the five sides of the rectangular parallel piped the potential will be taken to be 0 if they are conductors it means they will be grounded and on the sixth side I will say that the potential function is known to be. So, let me state that in this way. So, I have this this is my x y and the z direction coming out of the plane of the picture and on five of these that is when x is equal to 0 and x equal to l 1, y is equal to 0, y is equal to l 2 and z is equal to 0 these five surfaces the potential value is 0. On the sixth surface which is at z is equal to l 3 the potential distribution as a function of x y is known to be. So, that is f x y how does one solve this problem. Now, supposing you have six different boundary conditions I could actually solve these subject to a given boundary condition on each one of them and then sort of make a superposition of these to get a general solution, but at this moment I am looking at a specific problem where on five surfaces the potential value is given to be 0 and on the sixth surface which is at z is equal to l 3 the potential function is known to be some given function f which is of course, a function of x and y because the z is constant there. Now, so let us look at this equation the method that one follows is what is known as separation of variables. The separation of variable works this way that this function phi is taken to be a product of three functions function capital X which depends upon x only function capital Y depends upon y only and function capital Z depends upon z only. Recall at this moment I do not know whether this trick will work or not, but if this trick works then I will fall back on the uniqueness of the solutions and say that look by this trick I have found the solutions and so therefore, that must be the only solution. So, let us look at this. So, you notice this that so the what will happen is look at this term d square phi by d x square. So, since capital Y and capital Z are constant I will get from this term y z times d square capital X by d x square plus here I will get x z d square capital Y by d y square plus x y d square capital Z by d z square that is equal to 0. Let me divide this equation by capital X y z that will give me 1 over capital X d square x by d x square plus 1 over capital Y d square y by d y square plus 1 over capital Z d square z by d z square that is equal to 0. Now, look at this equation in this equation I have got three terms the first term depending on X only, second term depending upon Y only, third term depending upon Z only and there are variations here with respect to X here with respect to Y and here with respect to Z and I am making a big demand that some of these three must be equal to 0. Now, since x y z they vary arbitrarily in this space this is too tall an order and the only way we can do that is that if each one of these terms is a constant subject to the fact that three of those constants coming from three equations become equal to 0. So, this is purely because of the fact that the variation of each is independent. So, what do I get? So, let me write then the first equation will be 1 over x d square x by d x square is a constant. So, let me take this to be equal to some let us take minus k x square times constant this k x square the this x is because I am getting this constant related you know associated with this x. So, this is a constant value let me take d square y over d y square is equal to minus k y square into y, but d square z by d z square then this is a constant then has to be related to these two constant in such a way that the corresponding k z square if I take it.  Now, let us look at what happens to the corresponding boundary conditions. Remember on five of the faces the potentials were 0. So, I can translate that and say that look since x the depends only on x. So, this implies that the capital X function at x equal to 0 must be 0 and it also has to be 0 at the value l 1 the same is true for y, y must be 0 at 0 and at l 2 about z of course, I have a slightly different story because the value of capital Z must be equal to 0 at z is equal to 0, but at z is equal to l 3 it must be equal to constant. The solutions of these equations for example, the first equation which I have taken as d square x by d x square is equal to minus k x square x and also we learn to all of us and the solutions of course, are capital X as a function of x is a sin k x x. What is that I have chosen these two surfaces the at x equal to 0 I have got the value of the capital X equal to 0 it is automatically satisfied because I have taken a sin function, but there is a one more demand we say that x at x equal to l 1 is also equal to 0. This implies that sin of k x l 1 is equal to 0 which immediately tells me that the k x values are equal to must be such that it must be multiple of pi over l 1 where m is an integer m is an integer it is plus or minus 1 plus or minus 2 etcetera. I cannot take m to be equal to 0 because that would mean that the function itself is 0. So, which is of course, not what we are looking for. Now, identical statement is true for the y function. So, y of y is equal to sin k y y the boundary condition at y equal to 0 is automatically satisfied and the boundary condition at l 2 tells me that this should be an integer n divided by l 2. So, what is so good the four on four sides the solutions have been satisfied. Now, once I have taken once I have taken k x square and k y square to be positive or k x square and k y square to be positive the k z square term which is associated with the z equation is a negative that its solution cannot be trigonometric function because that equation now is d square z by d z square is equal to plus k z square z and since this is positive value I know its solution will be exponential with real arguments. However, I also have one more condition to be satisfied and that is the value of capital Z. At z is equal to 0 is also 0. Now, I know they are not trigonometric function they are exponential function and. So, therefore, what I do is to choose this solution to be a hyperbolic sin function. So, we will take capital Z to be given by hyperbolic sin of k z z remember sin hyperbolic of z at z equal to 0 is 0. So, this is this is the solution I take is actually not equal to, but should be constant times that. Now, let us look at the k x k y and k z we have seen that k z square is equal to k x square plus k y square. So, that tells me that this k z is given by square root of k x square plus k y square and since k x is m pi over l 1 square and k y is n pi over l 2 square root. So, this quantity k z can be also written as k m n it tells me that in order to specify k z you need 2 indices m and n. So, therefore, my solution which is phi x y z is now a linear combination linear combination because m and n can vary from 1 to infinity each one of them. Coefficient c m n sin function of m pi over l 1 into x another sin function of n pi over l 2 into y and of course, sin hyperbolic of k m n z. So, this is my solution, but there is still a sixth boundary condition to be satisfied and this sixth boundary condition is that when z is equal to l 3 the value of the potential at every point on that plane that plane you remember z is given, but x and y varies and that is a known function f of x y. So, if you look at this then we get phi of x y and z is equal to l 3. This is simply substituting z is equal to l 3 into this equation, but this value is a function given function of x and y. So, this is equal to just to rewrite m n equal to 1 to infinity c m n sin of m pi over l 1 x sin n pi over l 2.  Now, I can determine this constant c m n by using the properties the orthogonal properties of the integrals. You notice that here I have given you an integral this is d x of sin m pi x over l sin m pi x over l where m prime is another index.  So, that is why it is written as l by 2 times this is called a Kronecker delta m m prime that is equal to 0 if m is not equal to m prime and is equal to 1 if m is equal to m prime. Now, if you recall that integration that you notice that I come to this equation here I integrate I I multiply this both sides by sin m pi x over l 1 and n pi y over l 2 and integrate actually speaking what I do is to multiply with I should have said m prime n prime, but I know that unless m prime equal to m and n prime equal to n these c m n's will go away. So, this is what I get there this is what I get there and so that tells me that if I know the function f x y and I have been given everything else that I require there and in principle if I can do those integrations then in principle c m n these coefficients are known to me. So, let us let us take a very special case if I take a special case where I take this function f x y let us say is constant. Now, if you go back notice this that in c m n I have 2 integrals double integral over x and y, but if this f x y is constant then of course, these integrals become 2 product of 2 different independent integrals and sin integrals are very trivial integrals to be done. So, I use the fact that integral of d x sin m pi x over l is l by m pi cosine m pi x over l and the limits of integrations are from 0 to l 1. So, for d x integration this is l 1 and that is l 1, but this is a generic relation. Now, in the upper limit I have cosine of m pi I know that is nothing but minus 1 to the power m lower limit is of course, 1. So, this integral is l by m pi minus 1 to the power m minus 1. This tells me that this has a value of which is 0 if m is even because then it becomes 1 minus 1. If m is odd I get a minus 2 there because minus 1 to the power odd number is minus 1 and I also have another minus 1 there. So, I get so the result of this equation is it is equal to minus 2 l by m pi if m is odd and is equal to 0 if m is even. So, if you look at this expression for c m n is l by l 1 l 2 etcetera and I have this f x y which is now constant and product of 2 integrations and each one of the integral I know how to do it. So, if you plug it in you find this to be equal to 16 over m n pi square 1 over sin hyperbolic k m and l 3 and this will be non 0 only if only if neither m nor n is even because if any one of them is even because it is being multiplied they into corresponding integral is 0. So, when both m and n are odd c m n is non 0 in this case. So, that essentially completes our solution in the rectangular coordinates and with this we will go over to the solution of Laplace's equation in spherical coordinates. Spherical coordinates Laplace and form is a little complicated, but it turns out that the principle of separation of variable that we talked about still works here though with a slight bit of a modification. So, let us look at what does it get me first my del square of phi here I will be a little careful in writing the potential function phi because the azimuthal angle is also denoted by phi. So, this is given by 1 over r square d by d r of r square d phi by d r is the radial part polar the angle part is r square sin theta d by d theta of sin theta d phi by d theta. And finally, I have got 1 over r square sin square theta d square over d phi square this is my azimuthal angle of phi that is equal to 0. Now, what we will do is we will have the same trick that is look at the possibility of separation of variable in this problem. So, we write capital phi as product of 3 functions capital R which is a function of r capital P which is a function of theta and let us write capital F which is a function of phi. Now, if you plug it in let us see what you get.   Now, we do the same thing again that is divide this equation by r P F and the other thing that you notice is there is a 1 over r square all over and. So, therefore, I can take that r square to the right hand side it becomes 0. So, I am left with the equation which looks like the following.  Now, here the first thing that we need to do is to realize that in this equation in this equation I can take this sin square theta multiply the entire equation by sin square theta and realize them these two equation these two terms the radial term and the polar term they are both theta appears there on the other hand this will give me just 1 over F d square F by d F square. So, let me let me do that.  Now, I give the same argument again the left hand side is a function of r and theta and small r and small theta varies of r. On the left hand side the right hand side however depends only on phi and we are expecting this should be equal to that that is not possible unless each one of these terms happens to be a constant. So, let us let us write that constant to be equal to some quantity like m square. Now, I can I am now in a position to solve what is known as the azimuthal equation. The azimuthal equation then becomes d square F over d phi square is equal to minus m square F. We know that the solution of this equation is e to the power plus or minus i m phi. What is m? The value of m can be fixed by saying that if phi increases by 2 phi then this I am back to the same point if the azimuthal angle changes by an amount 2 phi I am back to the same point. So, my value of F must be cyclic in the sense whatever is the value of F at some value of the azimuthal angle phi that must be having the same value when the azimuth increases by an amount 2 phi which is possible if e to the power plus or minus i m into 2 phi is equal to 1. So, if e to the power i m into 2 phi that is equal to 1 then it is possible which tells me that m is an integer positive or negative integer. So, in this equation my m is an integer that has been worked out. Let us look at the next equation now having done that identified m. So, I will now write the equation in this way remember I had divided by sin square theta, but now I have brought the sin square theta to wherever it is and I have written 1 over r d by d r of r square d r by d r is equal to 2 terms one is this term which was already there and the other one is m square by sin square theta. This has made it possible for me to separate r and theta the polar separation. So, therefore, once again with the type of argument that we have been given each one of these terms must be constant. I do not know what that constant is, but anticipating some result let me put that constant to be equal to l into l plus 1 of course, I have not yet said what is l. So, therefore, I can write my constant anyway I like. So, I have got now 2 equations. So, the main equation is the polar equation is 1 over sin theta d by d theta sin theta d p by d theta plus this l into l plus 1 minus m square by sin square theta into p equal to 0. You can simplify this equation by making a substitution of variable mu is equal to cos theta. If you do that mu is equal to cos theta d mu is equal to minus sin theta d theta. Now, since I know that the polar angle goes from 0 to pi the mu which is taken to be equal to cos theta goes from minus 1 to plus 1. Straight forward to check that this equation can now be written in terms of the new variable mu like this. We will not actually be trying to solve this equation, but it turns out that this equation is well known in the field of differential equation. The field of differential equation and the solutions are known to be associated Legendre polynomials. So, this is an equation whose solutions people know. We will be talking about the nature of solution little later, but let us look at that. So, this is called associated Legendre polynomials. So, my part of the difference of the Laplace's equation now has an e to the power i m phi times the associated Legendre whose which are characterized by l in addition to m. Now, incidentally there are two types of solution there.    Let us take a simple specific case supposing my solutions do not have azimuthal dependence. What it means is my problem does not have a dependence on the azimuthal angle in other words there is azimuthal symmetry in the problem. Now, if there is azimuthal symmetry in the problem the solutions cannot depend on phi and the only way to do it is to take the m to be equal to 0. Now, if you put m to be equal to 0 in the equation of associated Legendre polynomials the equation that I get is d by d mu 1 minus mu square this time I have removed the l m index d p by d mu plus l into l plus 1 into p equal to 0. This is known as the equation for Legendre polynomial the previous one is called associated Legendre polynomial. So, the Legendre polynomials are essentially special cases of associated Legendre polynomial having m is equal to 0. Now, the solutions of these Legendre polynomials are also well known and the you can actually check very easily the solutions. It happens to be a polynomial in mu which is a polynomial in cosine of theta. For instance you will find that the zeroth order polynomial is 1 it is very straight forward to check that if p is equal to 1 the left hand side is identically equal to 0 because d p by d mu. If my if l is equal to 1 l is equal to 0 p 0 cos theta is 1. If l is equal to 1 then of course, this becomes 1 into 1 plus 1 which is 2 and you can check that p 1 of mu is nothing but mu itself you can that is very fairly straight forward because if p is mu d p by d mu is 1 I have got a 1 minus mu square there. So, when you differentiate this with respect to mu I get a minus 2 mu there. So, therefore I get a minus 2 mu there and here I got l is equal to 1. So, it is 1 into 1 plus 1 which is 2 and p is mu. So, therefore this equation is satisfied and likewise you can find that p 2 cos theta is half into 3 cos square theta minus 1. So, this is the spherical polar equation. So, what have we seen? We have seen that when I have azimuthal symmetry my solutions are given by the angular part of the solutions are given by Legendre polynomial. I have not yet touched the radial equation, but in the remaining time let us look at what the radial equation looks like.  So, this is the equation split of this equation you get a equation like this. This is actually a very equation which is very easy to solve you can check if you take capital R to be going as R to the power n then the equation is satisfied and the value that n takes is l or l plus 1.  Next lecture we will look at some applications of this solutions in three dimensions.


hey everybody welcome back to the channel today we're doing a thing where are we we're doing a demolition derby we're trying to kill each other we're going to crash and kill each other we're going to crash and come okay who thinks who thinks we're going to tire who thinks we're going to we're going to actually you might want the gold all right listen so we're here at a demolition derby we're going to run cars around we're going to run them into each other most of this video is going to be my point of view but if you want to go to youtube.com slash off canny you can see the full video with everybody's points of views and all the things and you can hear make say a bunch of stuff in irish do you know how to speak galey uh shayna fina both corners of tattoo dig wet fish a glop fish a glop fish a glop i got curious man am i going to get cancelled because of okay yeah you no i agree with that you think your fans are going to know galey i don't know a couple of uh depending on what was said i don't take any responsibility for that you can't cancel me you can't cancel me okay thanks welcome to the off-candy derby tour of my car before we quick also so sorry about the wind it's very windy uh but here's my car i call her cream it's not gonna be right because now there's a huge


Yn cael plant. Roeddwn ni'n cael ei ffwyllt yn gyd-grwyso fel adventure, bydd y cyfanc, ysgogel fydd yn cael ei bodster yn gyd-grwyso fel y blog. Dyna'r bobl yn gondol ychydig i ddechrau fibre yn gynrych. Roeddwn i'n cael ei ffwyllt yn gynrych. Roeddwn i'n cael ei ffwyllt yn gondol, roeddwn ni'n ceisio ymddangos o gyd-gynall mewn ddechrau fel y gyrfa. On i roedd ychydig i chi fel, yma'n rhaid i yn gyd-grwyso fel cymaint oherwydd hynny, I won't be offended I'm a WordPress consultant I'm a WordPress developer and agent Sienna I'm a WordPress designer I'm a WordPress builder of client websites I'm a WordPress agent Sienna I'm a WordPress designer I am a WordPress business owner We've built companies We've developed technical solutions We started from scratch We've designed to be inclusive We've worked from coffee shops From co-working spaces and offices We've supported clients We are the WordPress community We've hidden our fears We've battled internally We've hurt the ones we love We've put on a mask We've questioned ourselves We've not been open We've struggled No-one ever said it would be this hard We've learned new skills We've developed as individuals We've spoken out We've built relationships We've moved forward We've overcome It's a lie to think you can't achieve this As a member of the WordPress community I'm speaking out Isolation Depression and anxiety Loneliness Fear Our community's mental health needs support Statistically, one in six of us will experience work-related mental health issues Because I'm self-employed Because I'm a freelancer Because I'm a small business owner Because I'm a remote worker Because I'm a solo business owner That statistic increases to one in four of us Help us, hashtag press forward WP and UP are promoting and supporting positive mental health in the WordPress community And now is the time to have an honest conversation about our mental health Join your local WordPress meet-up Attend, volunteer or support WordCamps I'm not alone You're not alone At its core WordPress is the community Nine years ago I started freelancing I discovered WordPress about 10 years ago and wanted to provide services using the software Five years ago I started supporting and organizing the WordPress London Meet-Up It was a great opportunity for me to get involved in the community And contribute back It was my way of giving back to the community Four years ago I supported my first WordCamp If you've not been involved in WordCamps previously Highly recommend getting involved Get on as a volunteer Sign up as an organizer They're an incredible way to Integrate yourself into the community Three years ago I left my job as if Being a freelance owner A small business owner Wasn't running or having a job A proper job One year ago I sold my business I succeeded I'd achieved what I was looking to do To set out to do Nine months ago I started working alone Give you an idea My background is in strategic business management I've been self-employed for 21, 22 years in one form or another I've always worked and built teams to support me Nine months ago I started working alone No one ever said it would be this hard Isolation was a major factor for me Not having other individuals to interact with and engage with on a daily basis If you're a solo business owner, a freelancer, a member of a distributed team You may be able to relate with this issue HTML, CSS, PHP, JavaScript, Photoshop, Illustrator, UX, UI Version control DevOps, Workflows, Continuous Integration These were just some of the things that I needed to have a handle on And some of the things I needed to understand As a small business owner, as an individual running the business So let's throw in corporation tax, VAT, PAYE, National Insurance Some other great stuff, stakeholders expectations, project management The list goes on of the things that I needed to understand And I needed to have some sort of grasp on You individually may also be able to relate with this I think, where do we go? What do we do? How do we manage this? Something had to change I couldn't continue doing this on my own No one said it would be this hard Through the work that I've been doing with the Wepris London Meetup I have a lot of conversations with the community, a lot of discussions with individuals I knew that actually I wasn't the only person Struggling with these issues Please say hello to WPN Up The idea of supporting the community Was not a new concept for me It wasn't something that was just born out of a silly idea It was actually something that was personal If you look back at the WPN Up Twitter You'll find that the first tweets were sent in January 2014 It had been on my heart for a long time It was something that I wanted to bring to the community I wanted to ensure that there was a way for small business owners, freelancers, remote workers To be able to engage and be supported and interact But I kept putting it off, I kept putting it back There was always another reason I'm trying to focus on my business I'm trying to focus on myself Through some of the conversations I had at the back end of last year 2017 This had to happen Together we can press forward We are a community And we're good at being a community But there are times when we are also very, very isolated And we do need support And we need to reach out To promote and support positive mental health within the WordPress community Is WPN Up's mission It's what we're looking to achieve WPN Up is very much a community-driven project Excuse me We're providing support through what we're calling our health hubs We have our code health Our business health Our physical health And our mental health To give you an idea of how this is a community project And how it is evolving very rapidly Code health has actually been switched to skills health Based on conversations that have happened in the UK WP Slack team If you're not part of that WP Slack.uk Head over and get yourself in there As well as conversations that have happened at events Such as this So the code health, now skills health Is focusing on supporting individuals If you are potentially struggling with skills We provide free training and education Business health We have free mentorship programmes We have one-to-one support available For an individual that feels you need support with your business Come and see us Physical health, this is a big one for me I'm not too good at it But physical health is directly related to mental health There is a direct correlation between the two And mental health The overarching focus of WPN Up Again, this one is at the core for me And if you're an individual that feels that potentially You're struggling with the issues related to isolation, depression, anxiety Or any other of the mental health related issues Please do come and have a chat with us I want to say a big, big, big thank you to the volunteers We've now got a team based on conversations from this weekend Of 20 volunteers supporting WPN Up That team consists of event organisers, advisers Specialists within their own individual fields And support So each and every individual And there are several sitting in this room right now I want to say a huge, huge thank you If the things that I've touched on here I've touched you If you feel actually I could potentially do With just having a conversation Please do visit www.wpnup.org Slash www.wcbtn On there you'll find just a tiny little form You can send that in anonymously And we just want to understand If you're interested in the skills health The physical health The business health or the mental health If you're interested in getting more information Drop your details in there completely optional I want to say a big thank you to all of you Thank you for your time for listening to this I appreciate that you have taken the time to come and listen to this subject matter As I say, if anything I've discussed Is an issue with you If you are aware of somebody potentially that is struggling Please do drop me an email Or visit the site We have the ability to contact us anonymously If you need to Thank you all very much Thank you Dan, this is a wonderful initiative I'm going to be filling out that form Do we have any questions in the room? Can we get involved Just by the website? Absolutely If you're interested in supporting www.wpnup Visit the site, drop in your details in our contact form And we will get you We will find ways to To use your skills In the best way possible We're very conscious of individuals time Within www.wpnup It's something that we wanted to ensure There's no point creating a charity That's promoting positive mental health If it's actually putting additional pressure On you as an individual, as an organiser Or as a supporter, a volunteer of it If you're interested in supporting us We'd love to hear from you We're also In the WP UK Slack team It's another route to contact us It's www.wpslack.uk If you want to get an invite in there We'd love to hear from you This is a charity, right? How do we give you our money? Thank you www.wpnup.org We are In the process of creating the registered charity We don't quite have the registered charity number yet But we are Hopefully within days away from that at the moment We are Requiring quite a bit of financial support To bring A quality service to the community We're in discussions with a number of large companies Within the ecosystem already But if you are interested And would like to get your brand In and support www.wpnup Again, we'd love to hear from you We're running events across the UK We have an event every single week Across the UK currently We're also in discussions About launching our first two events overseas So there are lots of opportunities To get coverage I think one last question Hi I'll open And already are you To expand outside of the UK Completely open This is a global issue It's not something that's specific to the UK By any means We are We already have individuals That are overseas That are part of the volunteer team Currently And we are very open And willing to have further discussions With a much wider community outside of the UK To support it And if I wanted to get a mentor Because I've always wanted to have one What do I do? Do I just go on the website And start there? Head to the website So there is no One size fits all solution With WPNR What is the reason for you coming to us?


Hello everybody, HoodedCoverCommander788 here, and we're going to do another vintage vehicle unboxing and assembly. We've done a few of these lately, more than I ever thought I would, but I've just gotten really lucky in the last few months, finding vintage, boxed, and unassembled GI Joe vehicles. So, when I can find these at a good price, I'm going to put these together. I've got my window behind me, it's still daylight out there. It will probably be dark by the time I finish this, so I'm backlit right now, but that will not be the case by the time we finish putting this together. This time we are going to assemble the 1993 Cobra Invader from the Star Brigade subset. Now, I would not do this with a rare vehicle, something from earlier in the line, something that would probably be pretty expensive, but this is pretty common. There's not a great market for these. There are still plenty of them still in the box, so I don't think anything is really lost by taking this out. Plus, I got this at a price that was less than what I would have paid for a loose, complete example. So, I think this is fair to take out and put together. This box is not sealed. It was sealed when I got it, but I opened it up just to look at the contents inside, make sure everything was okay. There was some stuff rattling around in there. Some of the parts have popped off of the plastic tree. That's kind of to be expected with a vehicle this old, especially if it's been moved around and not stored very carefully. So, some of the bits kind of rattle around in there, but everything is there. Some of the parts in here are a bit fragile and it has some gold parts, and those may be susceptible to gold plastic syndrome. This could be the first assembly video where I break apart. I hope not, but if I do, I'll just glue it. I don't care that much. It's the invader. I have the tools that I will need to put it together. I have my clipboard so I can use that to cut things so I don't cut my table. So, let's do it. Let's unbox the invader and put it together. Alright, let's open it up. These 90s vehicles did this thing where they have a tray inside the box, a cardboard tray that has all of the pieces. So, there we go. I've got an instruction sheet, a sticker sheet. We've got a sealed part of canopy, and then we've got, let's see, that's part of the body. There's a gold piece that, honestly, it does feel kind of brittle. Yeah, these pieces, I don't know if they are. I don't know how something feels brittle, but I mean, if you touch these, they kind of do. They feel like they could break pretty easily. So, I'll try to use some caution with those, but they may be hopeless. They may be so brittle that they will snap under any pressure. We'll see. More gold parts, the legs. We've got, it looks like the seat for the cockpit. Missiles, because it does have a spring-loaded missile feature. We've got the spring-firing missile launcher. Some gold parts that are still on the tree. I don't know, it might not be hopeless.  We've got an empty plastic tree that I believe the missiles were attached to, but they've all popped off. And one more with all the wires and hoses and stuff. So, those are the pieces. So, let's look at the instruction sheet and start putting them together. All right, let's look at the instructions. One thing I like about doing these assemblies is being the first person to ever put this toy together. I know that everything's really there. The stickers are all there. No parts have been swapped around. And sometimes when you get vintage toys, you just never know what a previous owner has done to them before you can really look at them and inspect them. So, this at the very least, I know where it's been. I know that everything's there and everything is as it should be. So, let's see. Step one is the cockpit assembly. We've got the hull. We have the pilot seat. And we are supposed to place this in here. Let's see how this goes. Line up front tab on the green cockpit. That's this bit. With arrow inside black hull, then fit side tabs into notches and hull. Okay, there's an arrow on here somewhere. Where is it? There's an arrow. I don't see an arrow. I found it. Sorry, I found it. It's right there. Where was it? Now I've lost it. Where was it? See, I saw the arrow and then I dropped the dang thing and now I can't find it again. Oh, there it is, there it is. Okay, I see it. Okay, so the front goes there in these little tabs. I got it. I got it. Okay, well that's easy enough. That's lined up. Alright, what next? Looks like they want us to assemble the canopy. And the green translucent pieces are in here. So let's open the factory sealed bag and pull these out. Okay. And with canopy locks facing up. Yeah. Fit the posts on the green canopy half onto the rear notches in the bronze colored hull top as shown. Okay, that goes that way. Oh, okay. Alright, I think I get it. So it kind of hooks under like that. Okay. Like so. That's an interesting way to do it. Except you've got to do it right. Put it on the correct side. Oh, yeah. I think this one's going to be easier than that AGP assembly. So that goes like this, I believe. Okay. And let's see. It comes together like so. And locks. Okay. Alright. Make sure the canopy locks line up. The canopy locks appear to line up. Yes, they do. Okay. So, next. Now we have to attempt to put this on. Let's see how does it go. We have some tabs there that that's supposed to line up with. Now this could be the first test of this plastic to see whether or not it's going to go on without snapping. Because I'm going to have to put a little bit of pressure on it. And if it's brittle, it could snap. So let's see. So far so good. Alright. One more tab to fit in. Come on now. It's trying. But it's not quite there. Oh, it's popping out. These canopies get in the way and I don't like them. They don't really even cover the whole top of the vehicle. It's not a very good canopy design if you ask me. And I know you didn't ask me, but I told you anyway.  These parts are all the same as the Pogo just in different colors. But it's done. It's assembled. And the canopy is staying on and it functions as it should. But that was not fun. Alright. What's the next part? Okay. It looks like we are supposed to take this piece and on it place this gun and these nobles. So I got to cut these off. This will be the first parts that I cut off of the plastic tree. Alright. This vehicle is new to me. Of course I was out of GI Joe long before 1993. And I think the Pogo was new to me as an adult collector too. In 87, that was kind of the tail end of my GI Joe collecting. We did still stick around for a little while. But I never got the Pogo. I just thought it was a goofy looking thing. So at that point, I wasn't trying to get everything. I was just getting the stuff that I liked. And I was doing a lot of customization at the time. So if I didn't like a figure or a vehicle, I just skipped it. Before that though, I really was trying to get everything. And I didn't get everything but I got a lot of it. And between me and my brother and our friend Sam, that was a friend of ours in our neighborhood, we had nearly everything from 1982 up to... I think 1986 was the last year we were really trying to collect everything related to GI Joe. We had almost everything except for the mail away stuff. We never got the mail away offers. None of us did. None of the kids in our neighborhood really sent away for the mail away stuff and I'm not really sure why. Maybe we just needed that immediate gratification of getting the toys in the store, I don't know. But at any rate, we did miss out on those. But yeah, we got loads of stuff. Most of the vehicles. Our friend Sam, he had a lot of the really big stuff. He had the USS flag, he had the Terror Drone. My brother and I had a lot of the medium and smaller vehicles and a ton of figures. Alright, that's all together. The gun, the thruster, nozzles, everything assembled there. So now, it looks like we have to snap this onto here. It doesn't say that it goes any particular way. But yeah, we'll just press it on. Yeah, oh, that was easy. Hey, that was easy. Awesome, something was easy. Great. So my brother, Eric, is almost two years younger than me. Not quite, but close. And in our neighborhood, we had a friend named Sam. He was about half a block away down the street. And during the summer times, we were at his house or he was over at our house every day. Let me make sure I do this right.  We would put all of our toys together and just have these huge sprawling battles usually in the backyard, sometimes indoors. Yeah, that worked. Hey, and it didn't... Well, no, I take that back. Didn't work. Let's see, how is this supposed to go? Let's see. Alright, that slide's up there. Alright, now I have had to put the legs on the pogo before and it sucks. It's not a good... It's not well engineered. It just isn't.  And I'm really worried about breaking the tabs on this thing, trying to put this on. There's one. Alright, we got two more to go. So anyway, yeah, we would create these scenarios and play situations that we would put our Joe's in. And they tended to be really big. And once he got the USS flag, most of our missions tended to start out there.  A mission during the summertime was often in the backyard. Sam's backyard since he had the flag. And then we'd send them out and they'd set up a base in some jungle where they were having to either fend off Cobra or invade a Cobra stronghold. Come on. Yeah, almost, I think we almost got it. Close, close, close. And these missions would tend to last usually several days until everything had been blown up or we had accomplished whatever objective we set out to do. Alright, those legs are on, good. And then next day we'd come up with something else. Okay, I've got to take some more parts off of the plastic trees. Let's see what it calls, what does it call for? It calls for, let's see, this big hose and the antenna, which is still on here, let's go ahead and cut that off. And I haven't seen Sam since we moved out of that neighborhood when I was about, I want to say, 14 years old and of course we were all kind of out of GI Joe by then. Although I did continue to read the comic books for a while after I had given up the toys, but ever since we moved I have not seen Sam and I can't seem to find him anywhere on social media. I don't know what happened to the guy. I'd love to catch up with him, see how he's doing. Maybe he would be surprised that I have a GI Joe channel on YouTube. Maybe not. But I think it would be really awesome to catch up with him. So that's one regret I have is not keeping in touch with Sam. Of course at the time in the era before social media, you couldn't just add somebody on Facebook, you could get a phone number but then people move and their phone numbers change. You lose phone numbers. So yeah, that kind of thing happens. All right, now how does this work? This connects to that, I see, I think I see. Okay, this goes here, all right, here and here. One thing that GI Joe vehicles did that I think is remarkable now is give us a lot of colors without paint. They rarely had paint applications on the vehicles. There are a few that they did, and the few that did were pretty cool, but most of them they just used different colored plastic for different parts and just by using different colored plastic they were able to really give us a lot of cool colors. And despite having no paint applications, they tended not to be too monochrome. It says to put the missiles on, so I'm going to go ahead and do that. Even though I think that's really kind of too early in the assembly stage to put the missiles on, it says to do it so I'm following the instructions. Now I've got to put the antenna on too. All right, these missiles work with the spring-loaded missile launcher. Let's see, there's an extra missile and I guess this one goes in the launcher, so we'll put the launcher on in a minute. Now we are supposed to put the antenna on. There's the antenna. And where was the slot for it? I just saw it. Where was it? I was just looking at it. There it is. Slot for the antenna. But yeah, G.I. Joe was a big part of our lives, especially in the summertime when we can get outdoors and we were just outdoors all the time. And our backyards became jungles. They became the whole countries that Cobra would invade. G.I. Joe would have to come to the rescue. And despite doing a lot of different play storylines, there were a few that we really didn't do. I didn't really do much with the spies, like chuckles. Never had a whole lot of use for chuckles. And the medics, like Doc, which I really like Doc now, but at the time just didn't use them. If I could travel back in time, I might suggest to myself some alternatives that might have been fun. But you know one thing that we never did, I don't think we ever did, was recreate scenes from the cartoon or comic book. And we watched the cartoon and we read the comic books, but we didn't see those as something to recreate. We just kind of made our own sort of alternate universe with the things that we wanted to happen and the characters that we cared about. But the comic book especially was a big influence on us because it had that kind of real military feel to it. It used military terminology. And man, we just ate that up. I mean, adding kind of a pseudo-realistic military flavor to our playtime just made it seem more real. And yeah, we loved that a lot. Okay, we've got, let's see. We've got three small ones and of these little green wires and one big one. And I've got to make sure these go in correctly. Insert curved end of small green propulsion tube into a hole on the left side of one landing leg. Bend tube and insert straight in into the hole as shown. Repeat with remaining small green tubes and landing legs. Okay, according to the instruction sheet, these green cords go into the holes and kind of in the knee of the legs. But man, I'll be dinged if they don't want to go. Get in there. I don't want to break the thing, but it's just got to go. It's got to go in. Yeah, I've looked at the instructions multiple times to confirm that this is the way I'm supposed to go and that is the way it's supposed to go. But the holes that they have it, they're showing it being placed in, too small. Okay, I got it in. I got it in. It was not easy. I don't like this. This is more frustrating than the HEP assembly. I don't like this at all. All right. I mean, it instructs you to bend the plastic, which to me doesn't seem like a great plan. I wouldn't like to do this on a new toy, let alone a vintage toy. Okay, that one's in. I'm having to use the needle nose pliers to get these wires in and I know it's not showing up very well on camera. I'm sorry, these wires are tiny. And plus I have to do it facing me. But that's just how it is. Let's see here. How is that? Okay, all right. Don't worry about it. Getting ahead of myself. This one goes in here. It fits easily enough into the hole. There. But getting it into the leg, as the instructions show, it's not easy at all. So it's, come on, come on. That's about done it. But yeah, that's a lot more pressure than I want to put on this toy. I don't like that one bit. Okay, one more. One more. Okay, this one, it just says to put it in the remaining hole, holes on the hole. So that's there. And then it'll have to go all the way around to this side and plug in there. It seems a bit of a stretch. These missiles are in the way. It instructs you to put the missiles on in step five, or at least some of the missiles. And this is too early, because they're in the way. If I can do this. Okay, all right. It's done. Wow. That was a lot more difficult than it needed to be. Now let's put the parts back on that fell off or had to take off. There's the tab for the antenna missiles. Okay, now we have to put the spring-loaded launcher on. Let's see. Fit green missile launcher into landing leg as shown. All the legs are the same. So I guess it doesn't matter which one you put it in. Which one do I want to put it in? Let's see. Let's put it on one. Let's put it on this one here. There. And then there's the missile that goes into it. Let's go ahead and put this in. There. Snaps in. Let's test fire it. There. Ooh, yeah. All right. That worked. Okay, now at last it's time to put the stickers on. I think this assembly is taking longer than the others. It's just not an easy vehicle to put together. And I'm sorry if that's boring for you, but I never know how these things are going to go until I get started. Okay. So there are the stickers. Let's orient this as it's shown. There is a rescue sticker with an arrow that actually goes on the glass canopy. Is that real? Okay, yes, real deal. Okay, let's pull this off. There are two of them. Let's see. But there's a ridge on that canopy, and it seems like a sticker should not go over that ridge. So I'm going to put it like this. It seems the right way to do it. These are paper stickers, not vinyl stickers, not my preference. Let's see. And then where does that go? Okay, we've got multiple of these Cobra Moon Strike stickers. And one of them is supposed to go on the canopy. Oh, no, no, no. It goes on here. Okay, all right. That makes more sense. So let's line it up. I've got to say I don't love it. I'll have plenty of comments about this vehicle when I review it. I don't intend to review it while I'm assembling it. This is supposed to just be an assembly video, but I can't help but notice certain things while I'm putting it together. One thing I have to notice is that this thing takes a lot of effort for quite a silly vehicle. I'll tell you, these paper stickers are not very forgiving if you don't lay them right the first time. Okay, all right. And one of those Cobra Moon Strike. So I guess this is allegedly Cobra's attacking the moon, which is fine, whatever.  Okay, and then that one. Okay, we've got, what is this? It's just some kind of warning sticker that goes somewhere. Goes. Goes like right under. It goes there. These are stickers that are going on a vehicle that was designed for an entirely different set of stickers. So may not necessarily work very well. So, I mean, now you can see, sorry, I know you can't see these as I'm assembling them, so I apologize for that. So I got to say I have not greatly enjoyed this particular assembly. Now, I don't think the fun is totally worn out of them. If I were assembling a better vehicle, I think I would still enjoy it, but it's the Invader. Star Brigade. It's Cobra. It's goofy. It's bizarre. It's a reissue of a vehicle that was already pretty strange the first time around. And they found ways to make it even stranger. All right. Oh, I missed, did I miss something? I think I did. That's okay. Go back to it. Come on. Trying to get these stickers off without scratching the paper since they're not final stickers. It was there. So anyway, I always hoped that someday Sam would see one of these vehicles and recognize me and say hello. It hasn't happened yet, but you know, someday it could happen. By golly, there is one that's supposed to go on the canopy and that just doesn't look right. Okay. All right. One thing at a time. One thing at a time. Let's take off this vectored pod unit sticker. These stickers don't even want to come off the sticker sheet very well. I'm marring the stickers trying to get them off. I don't like that. There's been much about this assembly that I've not enjoyed, so I'm sorry about that. On next. Okay. The other rescue sticker, which looks to me like it should go right there. These rescue arrows are pointed at the connector for the canopy, which kind of makes sense. Okay. And this is going to go like this. Okay. I've got a couple stickers left over and I've got to figure out where they go. And I only see where one of them goes. It's like an extra sticker on here. All right. This one allegedly goes on the canopy. It looks like they want you to put one of these Cobra Moon Strike stickers directly on the clear canopy, but I'm just not going to do that. I don't like the look of that. I ain't going to do it. This one. I'm going to dismiss a lot of the way. It's going to go here. And I don't care if it's right. It looks better. It looks better than the way they're instructing it. So I'm doing it the way I think it should be done. But there's an extra sticker. I swear there's no place to put this. Well, I don't want to leave an extra sticker on the sticker sheet. It's one of these vectored pod unit stickers. And I'm going to put it there. Look. Look. See? Look at this. Look at this. It shows one, two of the vectored pod unit stickers on the instructions. But there are three on the sticker sheet. All right. That's okay. I'm going to just blame 1993. It's 1993's fault. 90's, it's all your fault. I'm putting it here because that seems like where it's supposed to go. All right. There. Now let's put this stuff back on that I had to take off. Put stickers on. And that's it. It's complete, such as it is, the 1993 Cobra Invader. Which is basically just the Pogo in different colors and with a spring loaded missile launcher. Yeah. There it is. That was the assembly of the Star Brigade Invader. See? It's dark out now. So I don't plan to get any more vehicles like this in the near future that I would feel comfortable taking out of the box and assembling. Not something I normally do. I just got kind of lucky the last few months and so we've done a few of these. But I don't know when I will do this again. But if I do it again, I'm trying to find something better than the Invader. But thanks for watching. I hope you enjoyed this unboxing and assembly video more than I did. This one was a lot more headache than a vehicle like this is worth quite frankly. And now I kind of wish I had just bought this thing loose and complete. But at least I do have the benefit of knowing that it's been assembled correctly by me. All the pieces are there, unbroken. The stickers are all applied as they're supposed to. So it's about as mint as you can get for a review of it. I have no plans to review this in the near future. But I will be back soon with more vintage GI Joe toy reviews. I hope to see you then. Thanks for watching and I'll see you next time.


okay guys this is a follow-up video of the question I asked about whether I should kind of restore this old tripod or leave it like it is because it's got character well I forgot to upload this video so it's my fault but it was unanimous everybody felt the same way we should leave it like it is so that's what we're going to do and if there was a tie that's what monkey and I was going to tie break that we was just just gonna leave it like that it just it's scratched up but it's got character you know how many you know cameras has this hope this held how many you know still images or video has this thing you know it just it's awesome but so I wanted to let you guys know how that turned out so yeah we're we just decided we're gonna keep it that way so thanks for watching guys appreciate it hope everyone's week is going well bunch of stuff on my screen so until the next one say bear the myth man legend I'm gone for now guys excuse me and we'll chat soon bye bye and take care