Call the order of the public works meeting for the night for this evening Do a quick roll call? We'll see who we have online here all the person acoly Yeah All the person Phillips all the person Phillips all the persons of Aglio These kids coming on okay all the person so on here here. He's here. Okay all the person Sorenson Here, okay We'll start out with the pledge of allegiance already We'll start out with 2.1 approval of minutes from March or from February 23rd 2021 move to approve minutes of our last meeting second motions been made and seconded Any other discussion on those minutes All those in favor any opposed? Motion carries. All right 3.1 dead, Laurence 39 2021 document 6.2 ordinance amending section 110 210 of the Shueggen municipal code relating to assessments of cost for sidewalks Dr. Miele Thank You mr. Chair This this ordinance that is before you this evening is to change a Current standard that we've had in place. Oh probably for a good 20 years plus And currently what it is there's a city the city pays for 40% Of the sidewalk replacement of the squares adjacent to a city tree and the homeowner is responsible for 60% of the cost This this has been I don't recall even though I've been here a long time And I don't know why it was the 4060 split that was I it's just an odd number and it and it has been very Concerning a contentious for the department and Over the years We really haven't been replacing a lot of trees and With our forestry So what has happened is? Many of these properties that have trees we've cut the roots we replaced the sidewalk But yet the roots grow back and we start seeing some of these panels lift So some of these properties have had this occur multiple times not everyone but quite a few and now with us removing trees and wanting to replant and Start our urban forest in the city We're starting to get tremendous pushback from property or saying no way. I don't want a tree It's going to damage my sidewalk again. You keep charging me to repair the sidewalk It's the city tree so forth and so on so what this ordinance change does is Says the city's going to pick up if the new tree that we plant or the existing tree that you have today If it lifts the sidewalk as part of our sidewalk replacement program the city will pay a hundred percent of those squares immediately adjacent to the tree Up to 75 square feet maximum so it's not like you have a tree and next thing you know You have the whole sidewalk in front of your house. It doesn't work that way It's got to be immediately adjacent and that's about roughly three squares of sidewalk panels to give you a reference So Ultimately what we're since we're we're we're now we've cut down a tremendous amount of ash trees with the emerald ash borer and We're in the replanting stage This will help us Foster that and it will be a good will and good faith effort to the property owner saying we're going to give you a new tree This is part of the urban forestry it's very important for the city to have this urban forest for the numerous benefits and With that the sidewalk that's immediately Jason if in whatever if it would ever happen again We would pick up the the the squares immediately adjacent now In the past what has happened is when we planted trees years and years ago There it was a little indiscriminate I would say that it they in many cases the wrong species of trees was planted in the area that maybe it shouldn't have been With Tim Buller new Forester They've evaluated and picked out the right species of trees for certain terrace areas that should Eliminate quite a bit of this past problem of too large of a tree in too small of an area So It is our recommendation To move this forward that this will roughly we estimated in the past in past years It was roughly between 15 to 20,000 of our program of a hundred thousand dollar program annually Moving forward again, we don't think it will be as high Because the new trees that are being planted are the right species in the right space But nevertheless that it still will be a cost and I would have been sure it would probably be about it's a $10,000 hit to our overall sidewalk program But nevertheless, we're also fostering the getting the trees replaced and we think this is a good balance Cost on one side for the sidewalk versus being able to get more trees planted throughout the city and and reduce that that That burden and fight with the property owners. We want it to be a positive We want to reassure them that Moving forward in the future. This won't be a burden to them or a financial cost as well Thank you. One question. Do you always contact the property owner before you plant a tree on those or do you just Does that normally work we notify him and We say this is part of this urban forestry program. You're scheduled for a tree It's just good. It's it. It's good public policy to at least know most people are receptive they want a tree but they do there are some that are adamant and You know, it's contentious at times and we and it shouldn't be We want this to be a positive and it's a good thing not only for the property owners Well for the community as well. Do I hear any discussion on this at all? Anybody else have any questions? All of them in Decker, I've got a question or several actually you might if I just Dave if you wouldn't mind how big is a cement panel as you called it how many square feet? That's about they're about 25 Square feet. So we would only we would only offer three panels Adjacent to a tree in other words, that's what the 75 square foot. That's that's roughly Gives you a perspective of what we're talking about And this follow up to that is how many trees are on the average person's property lane? Typically one there are a few that there have been more than one But we try when we look at our forestry program. It's usually one tree per pop property Thank you, and how are we handling if somebody has a corner lot with two rows of trees? Is it it does this ordinance address? per side or is it just per parcel it would it would it would occur occur at on each side if necessary again it is our intent that The this this issue shouldn't be much more reduced moving forward as when we're planting the new species of trees They're the right typist tree for the right Area that should be planted where as I mentioned in the past it it has been a little bit more problematic Isn't it possible for me to jump in and just essentially clarify that answer a little bit To go ahead So as as written It's 75 square feet per parcel per year So if you're a corner lot and it's so one parcel it's that 75 square feet But it's per year. So for you to hit that you would have to have both of your trees cause Cause damage to the sidewalk in the same year Thomas I Guess What would be some language that would change that to be per side that would be appropriate in this instance? You could you could say something like up to a maximum of 75 square feet of sidewalk per Side of parcel adjacent to right-of-way for a year. I Would make an amendment to this document to say exactly that. Can I do that right? Can I have a second? Okay Motion has been made to amend it to include the wording as Marcus said it you know, we have the wording right correct and it's been second Okay, we'll amend it to so that it covers both sides of the house on a corner lot Do we anybody any other discussion on this at all? I guess this is Ryan Does that amendment help or make things? I mean is it beneficial? It helps those Clearly on a corner lot it gives them the ability if they had Sidewalk on on both sides of that they would on a corner lot And if they had a tree in the front and on the side and it was lifting the sidewalk clearly this this would help But that type of property owner that has a corner lot it gives them You know a little better benefit versus and quite they have a bigger burden They have more sidewalk obviously to maintain show as well as cost. So I I I this the amendment is would be Good for me is it has my support if that's what you're asking. All right, yep That's yeah answer both my point. So I appreciate that. Thanks David. Okay any other discussion on this All those in favor I Any opposed chair votes aye that passes. Thank you Okay, 3.2 general ordinance 4020 21 Yes, go ahead That was the amendment so now it's been amended now we still need to pass Okay, I'm sorry. I'm sorry. We'll go back to the first thing Do I have a second okay Motion made by Marcus seconded by Rose any other discussion on that all those in favor on the on the original ordinance Any opposed chair votes aye now we're set on that one. Thank you Document 6.3 ordinance placing a stop sign at the southeast corner of north 1st Street and Park Avenue Right. Okay. Yeah, this is an intersection located over by a ballrath park. Okay. It's a T intersection where one of the roads goes East and west the other road this ties into the T intersection Normally with policy we don't put up a stop sign at the T intersection unless we have requests by the neighborhoods because that The the road that ties into the road They have to stop anyways because it is a T intersection, but it's a neighbor's request a stop sign We will put one up on north 1st Street So so it does there is a stop for there for the T Okay, but an arm learned its policy. We don't but it's a request There was a request by several of the neighbors in the neighborhood and it's a busy area lots of pedestrians Obviously with the park and everything so okay make sense make sense Anyone ever so approval? Motion is made by Ryan second by Marcus any other discussion on that. Okay. All those in favor Any opposed? Chair votes aye and that is approved Next meeting date is March 23rd 2021 seeing as we've exhausted the agenda. Is there a motion to adjourn? Move to adjourn Motion made in seconded any other discussion all those in favor Aye Any opposed we are adjourned. Thank you


So you want to make money with SQL programming? You can use the right video. Let me explain. This video was brought to you by DigiLink Academy. You're no more a source to learning programming fast and get to that six-figure freelance salary you desire. Our courses include our SQL project course, our freelance Kickstarter, our Python course, and our interview programming course and much much more. So if you haven't already go ahead and click the link below to get to our free seven-step freelance guide so that we can help take your career to the next level. I'll see you guys in the course. All right guys, let's get into SQL programming and how you can make money and kind of go over the problems you guys are having first with this and I like to cover. I got a couple of points here I wanted to kind of get started with but before I get started give me the reason you guys are struggling trying to make money with SQL programming below in the comment section guys. I want to get your opinion or your perspective or your experience on making money with SQL programming so that we can start dialogue here. And I want to kind of start to help you guys specifically, but what I see from my side I see two main problems guys. One of them is you don't know where to focus your skills at and I see that a lot. A lot of you guys will come in and just try to learn everything. That's the first problem. We want to get you focused specifically on the stuff that makes your money, that what the client need, get you off to the races and other things that we're going to talk about later in this video. Number two, showcasing your value. Just because you have the skills don't mean a client or anybody know that you can help solve a problem. Hence, make money.  And I want to help you guys with that as well. So we're going to cover those two problems in detail. And like I was saying, go ahead and give me your experience below what you're struggling with. Just any details. Just go ahead and kind of tell me your experience and what you're struggling with to make money with SQL programming. So if you guys don't take away anything from this video, what I want you to take, get your little pen and pad, what I want you to take away from this video is focus on the customer pain points when it comes to solving problems. Let's talk specifically about SQL. Customer software pain points. You need to know that from an industry perspective, ideally, but definitely for that particular client you're trying to attract so that they can start giving you money to solve your problem. And I'm going to give you that. And you're going to notice that the examples that I'm going to give you guys, you're going to really dive into that and kind of get you guys started. So let's focus on that specifically. All that being said guys, I want to cover some of the points here, but I can't cover them all. I have links below to my 7 Step Guide. It's going to put you in a position so that you can start making money with SQL programming and put you in a position to win. If you already registered or signed up for my free 7 Step Guide, go ahead and roll in the Academy Guide. Links are below. It's going to help you take your SQL skills to the next level. And it's going to put you in a position to win and then take your career to the next level. So links below for everything below in the description box so that you guys can get started. So one of the things that you can do to actually start making money with SQL programming is reporting and alerting. A lot of you guys may say, right, that's not programming. How can I make money? I want to program. Well, at the end of the day, all you're really doing is creating stored procedures that handing the data over to the reporting app or the alerting app. The same thing you do for an application or current application, the displaying data you're preparing data to provide to that back end process and eventually get to the front end of your application. Same thing with reporting. The only thing you got here, guys, that's going to give you an advantage is you can do it fast and you can actually make money right away doing this. You don't actually have to worry about modifying data, creating tables and all that. You're leveraging existing data that's there. But what you're doing is putting in a reporting form that's going to be a value to them and really help 10X their business and put them in a position to know more about their business and insights. Same on the alerting side, guys. Same concept. The only difference is a report is usually coming in on a timer or something like that. But when you get an alert, it happens at a specific action. Like, just let's just say, hey, driver payroll day or the bank haven't had three deposit in a certain amount of time. I want to be alerted of that. That's the type of value that's going to put you in a position that you can start making money as a SQL developer. As a beginner, guys, this is something you can do with a simple select statement. Select statement, guys. I'm going to really put you in the game and making that money that you need to do. And you don't have to necessarily know everything out at the beginning and be able to. And the best part about this, guys, you can showcase this pretty easily with some of the stuff I tell you. My seven step guide on Odu and presenting Excel spreadsheets. You can do Tableau, you can do Power BI, all those tools. But again, we talk about that in our guide. Number two, performance improvement, guys. That's a good one as well. Database performance improvement, store procedures running slow, slow running applications, things like that. Really good way to make some money doing a lot of SQL programming, guys. Number two, process, or number three, actually, automating processes and procedures. You're going to find that a lot of people are doing just manual data entry, just to move data from one application to another. That's easy pickings for you guys. Good money. And then you can have a return on investment on that on their time.  Your process is consistent. Your process is going to do a day in and day out. Don't complain and everything is going to be as expected. You can you can showcase that and you can actually present that to your customer to make money with that, guys, and all that good stuff as well. Last but not least, guys, and I'm just covering these four. You can do a maintenance plan, a maintenance plan to be a combination of all these three I just listed and much, much more. I can't cover all the ways you can make money with SQL guys. These are some of just very high level ones with the maintenance contract. It can be something as simple as a break fix. Hey, this happened, I'll fix this or you can do monthly to where, hey, I want to keep your database running at a certain level. I want to make sure your tables are cleaned up at a certain level. I want to make sure that if something breaks, you have a number to call and you don't have to worry about that. You just worry about running your business. You don't have to worry about your database performing at the highest level. This is what a monthly contract. You get a couple of these guys. You're going to really build that that income that's coming in every month and then you're going to put yourself in a position to where if you get the same clients and you have a couple of maintenance plans, now you're getting to the money now. Now you're going to have infrastructure set up the database where everything's working. Yeah, you're going to have some problems here and there, but you should be able to predict when the problem going to happen. Acts of when they do that upgrades, acts of when they do major processes throughout the week as far as payroll and all that. You're going to be able to see this through your database, the statistics. But these are some of the things that's going to help you make money. And the guys, these are just a few of many and we can tailor this to your industry, your skill set, what you want to do in your city. But we can't cover them all in this video. That's why I tell you guys to go ahead and check out that seven step guy. And if you already enrolled in the seven step guy, go ahead and roll in the Academy guys links to everything below. So what's the takeaway guys? Focus on the customer pain points, pain points, pain points with reporting, pain points with automation, pain points with just having to deal with stuff that I can't run my business. I don't want to have to worry about my database and doing all this secret programming. That's what you are for. That's where you can make that money, guys. That's where it's going to put you in a position to win. So like subscribe to my like, share and subscribe to my content. You have any questions, comment below, guys, share your experiences. Give me feedback on how you are doing so far on taking your career to the next level. And we're going to help you with that. Like I already said, guys, I put a link to my seven step guy on the screen and I'll see you guys in the next video.


That's it. I have no slides, which I apologize for, and you'll hear me. I work at Google on the global public policy team, and in that role I lead our policy efforts on privacy globally. I'm coming at this from a very different perspective, and I have very little to say that's new, which is going to make it quite different from the previous two talks, but that in itself might be illustrative of the different perspective that a practitioner would bring to this. I got the invitation to participate in this panel, and I looked at the title, and I skipped over the word risks, because I didn't quite read it all carefully, and I saw the beauty of a hyper-public life. Why would anyone invite me to talk about that? Because I can't actually see much beauty in it, because to me the framing a hyper-public life implies a Paris Hilton-like existence. It implies this, you're publishing stuff about yourself constantly, streaming to the world, and making not just your identity, but your behavior and your identifiable behavior available for everyone to watch and see. Then I read the description of the panel, and the description actually implied something quite different. The description implied a data-driven life, and that's much closer to what these guys are talking about, right? I want to make that distinction very explicit, because from the perspective of somebody who's practicing this stuff day-to-day on the actual discussions that are happening today in the policy world, that distinction can be blurry, and it's really important, I think, that we draw the distinction cleanly. There's a tremendous amount of good that can come from data-driven services, and I would say that is the beauty of what we're talking about in this panel, is predictive analytics and what that type of analysis can provide the world. The types of examples that people from Google talk about all the time are things like Google Flu Trends. Does everyone in the room know what that is? I won't go into explanation if you all do. Looks like yes. Other examples of that, right? We continue to build those types of tools out, dengue trends. We've recently made that data, the underlying data set that we use to build those tools, basically accessible via an API, so very much in line with some of the things that Adam was saying. There's a tremendous amount of public good there that we can get at with big data analysis. There's also some just baseline economic good, so a study out of Europe last September found 100 billion euros of consumer surplus from advertising. So I think in the privacy community we like to sort of demonize advertising. That's a tremendous amount of value that's created for consumers above and beyond anything that anybody is paying or generating in revenue. There's a lot of good that can come from this type of predictive analytics. I typically think about those predictive tools in two ways, and there's just one design question in here for the room. The first way to think about it is predictive analytics for you based on your own behavior, so Amazon, Netflix, recommendation engines. Very clear in those systems they've designed it in really clearly to say this is the data that we are using to give you a prediction about what you might like. It's very clear to the end user what's going on and the privacy concerns are a lot more minimal. The second type is a prediction for you based on primarily other people's behavior.  And we can talk about the benefits of each of those types of predictive models and we could talk about how we should or shouldn't be using them. I think it's fair to say that both create a tremendous amount of value. And so then you ask what's the risk because we're talking about the beauty and risks of a data-driven life, I can just sort of rephrase it. I actually think the risk is a hyper-public life, right? So the risk of all of this data-driven living is that at some point all of that data gets attached to us in a way that it can be positioned on itself in one context. So all of the context of your life collapse on each other, the data is re-identified and attached to your identity. And this is the underlying fear that a lot of people who are concerned about privacy are advocating on the basis of. I think there's a piece of that that is missing, that simplifies the statement just a little bit and I'm going to posit a potential solution which is similar to what folks have talked about here. I got on the plane to get out here Wednesday night and I, just a small digression, I was an SFO, they have free Wi-Fi, I turned on my Kindle, I tried to download a book that I had purchased the night before. An SFO Wi-Fi let me down, I couldn't get the book before I got on the plane, so I stuck with my existing library. And I stumbled on a collection of Jonathan Franzen essays. And now I'm just curious how late I was to the game. Do people in the room know the Jonathan Franzen essay, The Imperial Bedroom? Okay, so I wasn't that late to the game. This is a great essay from 1998 about privacy, following the Lewinsky scandal. And it was a really interesting commentary on privacy. I would encourage you guys to go read it. It was quite counterintuitive for me. Someone who at the time that it was written just was, you know, totally unaware of these issues. He said something really interesting in this essay. He said, without shame, there can be no distinction between public and private. The reason I found that interesting is because if you think about shame and what actually sort of causes somebody to feel shame, I don't think it's absolutely true that without identity you can't feel shame. I think you could feel shame even if your behavior was anonymous. But for the most part, the more identifiable you are in doing some sort of behavior that is, quote, unquote, shameful, the more likely you are to feel that shame because you're going to feel the perceptions of all the people around you who know what you've done. And so that brings me to this posited solution, right? Which is that the design problem that we have ahead of us is how to construct multiple identities and manage multiple identities and how to preserve some degree of anonymity and manage that degree of anonymity. And I know a lot of people in the room, we've already heard it today, that anonymity is effectively dead. It will become trivial to re-identify you, Alessandro's work on face recognition and social security numbers. And there's definitely a degree of truth in that. I don't know that we've explored all the policy options available to us in that space. So if you have otherwise anonymous data, are there policy requirements that we could put on the data controller so that there was a punishment for re-identifying users of that data set? This is the sort of thing that Jane Yakowitz at Brooklyn Law School is proposing and it's an interesting idea. So I think we could be exploring some policy options there. And I think on the design side, there's a lot we can do to think about managing multiple identities online in different online spaces that would augment some of the work that folks have talked about today around designing spaces to enable users to express different sites of themselves. Let me ask one question then I'll come out and play. I used to say I'd play Oprah now, I guess I'll say I'll play Katie. Not a big pop culture group. And for those of my age with my hair color, Phil. This question, what we heard before mentions of multiple publics, right, that rather than the notion of having one public sphere, in fact, we have this opportunity to create many, many publics and to join those publics, create and join those publics, act with those publics. That's an important. It's related and unrelated to the idea of multiple identities, right? And Mark Zuckerberg has said, and I tend to agree with him on this, that we have one identity and in our efforts to keep separate identities when those come into conflict, so when we have a problem, I think the real identities we're trying to keep out of conflict are our internal selves, our real selves and our show selves. When those come into conflict we've got problems, but we'll put that aside for a second. In the EU there's talk of trying to bring in a right to be forgotten. Well, that brings out a whole nother tension because if I'm the one remembering you and I'm now ordered to forget you, then my free speech is impinged upon. So I'm trying to understand here, you're surprising me here in your kind of fear of the collection of data and its association with a person. In a minute I'm going to get to its association with a thing, but we'll get there in a place. But going for a little bit more on that, that you're fearing that we're all turned into Paris Hilton, that we're all made more public, is that what I'm hearing you say? And okay, if that's the case, stipulated your honor, but what is it you want to do about that? So I think I'm suggesting that the hyper-public identity is constructed from the collapse of contexts beyond the expectation of the individual who's using whatever technology it is. And this is why you continue to see so many privacy concerns come up because people just aren't aware of the variety of different contexts that are collapsing on their mobile phone, for example. You're moving from place to place and all of those contexts and the people in them are becoming one. And I don't think that many people actually want that. I think they want a separation of the data that's used to personalize an advertisement for them from the data that they are sharing with their friends. I think that people want some separation of that and they want the ability to maintain and control that separation. I think it's quite different from the right to be forgotten, what I'm suggesting. I'm suggesting the ability to understand and maintain those different sort of silos of data about you and your behavior. That's the break wall of the discussion, it's worrying in a sense, isn't it? The data is there, if Dana were here, I would call on her now. And she helped me immensely in my research for my book in separating gathering versus use of data. That if you try to restrict the gathering of data, you're telling people they cannot hear something, they heard, they cannot learn something, they've learned, they can't know something, they know. It becomes absurd after a while. But if you say you can't use this data in a way, then that's a different issue. Right. I'm not sure where you come across on that because in a sense you're saying you want to be able to silo the data and so I... Effectively restrict the use, right? So if you have otherwise anonymous data and you say this data could be used for research purposes or for product development purposes but the second you go and re-identify it, you have somehow violated a law or some other sort of policy solution you could put in place that limits the use of that otherwise anonymous data so that the risks of re-identification and the risks of context collapse are minimized. Okay, I've got to tie this back to Google, of course, because I would think that as a matter of principle, Google would want as few restrictions that are hard to interpret and hard to know on data as possible. That context is very difficult. That that means you've got to have... If it's not collected, if it's not obvious what the context is when the data is collected to have to go then back and find out the context or intuit the context or you should have known the context creates a liability for the likes of Google, doesn't it? That's the design challenge, right? Is helping users understand that and maintain the identities. And so that's where when I talk about the two forms of predictive analytics and where Amazon and Netflix and recommendation engines have done something really good in helping users understand that data, I don't think, for example, search engines or the soda machine have really gotten it quite right yet.


Welcome to Caltrans LSIT LS exam preparation course. One aid in your preparation for California licensure examinations. A word of caution. Don't use this course as your only preparation. Devise and follow a regular schedule of study which begins months before the test. Work many problems in each area, not just those in this course's workbook, but problems from other sources as well. This course is funded by Caltrans, but you and I owe a profound thanks to others, the courses instructors, from the academic community, the private sector, other public agencies, and from Caltrans as well. We wish you well in your study toward becoming a member of California's professional land surveying community. Welcome to today's discussion of the state playing coordinate system. A 1986 change to the public resources code of the state of California created the California coordinate system of 1983, noted as CCS83. The implementation of the system is to be phased in by January 1, 1995, when state playing work must refer to it in most cases. It replaces the previous system of 1927. The old North American datum of 1927, developed by the US Coast and Geodetic Survey, was the basis for CCS27. It used an approximation of the Earth's surface in North America named Clark's spheroid of 1866 as its geodetic reference surface. The North American datum of 1983, that's NAD83, developed by the National Geodetic Survey, underlies CCS83. A new ellipsoid, the geodetic reference system of 1980, also called GRS80, is the basis of the new system. This ellipsoid is geocentric and approximates the surface of the entire Earth, not just North America. Because the geodetic reference surfaces are different, the NAD27 latitude and longitude of a station differ from the NAD83 values for the same station. Overlying those differences are the factors that the adjustment incorporated new observations. The adjustment used was a least squares, simultaneous adjustment of the entire system, and that blunders could be isolated and culled. In fact, the variation between the two coordinate systems vary inconsistently, making only approximate transforms possible. At present, rigorous computation of coordinates is only possible by returning to the original field observations, readjusting and recomputing positions from them. The designers of the coordinate system limited the north-south extent of each Lambert grid to meet certain predetermined criteria. Therefore, six zones comprise CCS83. Zone one is at the north end of the state. The zone numbers increased southerly until zone six extends to the Mexican border. Each zone is based upon a cone whose axis is coincident with the GRS80 spheroid axis of rotation. The cone is a secant cone because it intersects the surface of the ellipsoid at two standard parallels rather than simply resting on it. This minimizes distortion while projecting data from the ellipsoid onto the cone. As enacted by the state legislature, the new coordinate systems linear units can either be meters or US survey feet. To date, NGS has implemented NAD83 as a metric system. It has published all CCS83 station data in meters. State plane coordinates expressed in one unit can be converted to the other unit simply by multiplying the north end and east end by the foot meter equivalency. This will be described later in this presentation. One may work the California coordinate system in either feet or in meters, but one must be consistent. Not only must all distances be uniformly in feet or in meters, but tabled constants must also correspond consistently with the linear unit used. This discussion is presented in terms of meters, but the accompanying written material is presented both in feet and in meters. The NGS recommends using polynomial coefficients and algebraic equations to simplify calculations for state plane coordinates. Polynomial coefficients are easy to use. Therefore, they are appropriate for both manual and programmed calculation applications. Through their use, projection tables become unnecessary. They can produce millimeter accuracy using hand-held calculators carrying only 10 significant digits. The NGS developed the coefficients by polynomial curve fitting of an array of data points for each zone. For those wishing to use projection tables, the California Land Surveyors Association has published a book of projection tables as special publication number 55 slash 88. NGS is now publishing a similar table. Please be aware, if you are preparing for the Land Surveyors examination, the new coordinate system will be phased in through the beginning of 1995. However, nothing prevents the state board from asking questions about the older system on future examinations. You need to prepare for both. While this presentation concentrates on the California coordinate system of 1983, it is broadly applicable to the system of 1927. Calculations for the older system are not as sophisticated as those used now. Therefore, if you understand the system of 1983, it is much easier to master the older system. State plane coordinate systems are intended to permit the calculation of positions on a grid using measurements made on the curving surface of the earth and at different elevations. If those measurements are accurately made and extended over a long distance, plane geometry calculations will yield inconsistent values for the position of the stations. The state plane coordinate systems were devised to provide a calculation technique that produces coordinate values that correctly relate to each other even over long distances and compare favorably with those calculated by geometric means. First, we will look at a series of pictures to help us visualize the coordinate system. The first set of illustrations is intended to acquaint us with the relationship between the ellipsoid and the cone that is the basis of the system. We now see depicted the geodetic reference system of 1980, also referred to as the GRS-80 system ellipsoid. It approximates the shape of the planet earth. Like the earth, it is slightly flattened. The polar radius is about 13 miles less than the equatorial radius. The GRS-80 ellipsoid underlies the California coordinate system of 1983 or CCS-83. The National Geodetic Survey developed the recently revised coordinate system. The system uses information from the North American datum of 1983, NAD-83, adjusted during the period 1975 through 1986. We also see depicted the axis of rotation of the ellipsoid that is the same as our planet earth's axis. We now see the addition of the equator. The equator is formed by the intersection of the surface of the ellipsoid with a plane that is at right angle to the axis of rotation and located midway between the poles of the ellipsoid. Next, two latitudes are presented north of the equator. These two latitudes are defining elements for each portion of the California coordinate system. Each selected latitude is called an exact scale or standard parallel. Latitude is measured by the angle formed at the intersection of the equatorial plane with a line normal to the surface of the ellipsoid. The two latitudes are called the north and south exact parallels. And note it as B sub n and B sub s. Now we see a cone generated through the two exact scale parallels. This means that it is a secant cone. In other words, the surface of the cone is within the surface of the ellipsoid between the standard parallels and outside it towards its apex and towards its skirt. The axis of the cone is coincident with the axis of rotation of the ellipsoid. For each unique pair of standard parallels, a unique cone will be created. Another parallel of latitude occurs between the two standard parallels where the separation between the ellipsoid surface and the cone is greatest. This latitude is nearly midway between the standard parallels, and therefore its name is the central parallel. Its notation is B sub o representing the latitude of the origin of the projection. Each zone has its own central parallel, a tabled constant for that zone. For each zone, the geometry of the cone fixes the distance from the apex to the central parallel. The notation for that distance is r sub o standing for the mapping radius of the projection origin. The angle between the axis of the cone and its surface will have a value that is equal to the latitude of the projection origin. Next, we see a geodetic meridian of longitude projected onto the cone. That is a true north-south line. The designer of the zone has selected a particular meridian to fulfill best the needs of those who will use the zone. It will form the center of the east-west extent of the zone. Therefore, it is called the central meridian and is a tabled constant. At the intersection of the central meridian with the central parallel is the projection origin. Now we see the addition of another parallel of latitude. It is the north geodetic latitude of the grid origin. At its intersection with the central meridian is the origin of the grid. In every zone, that point is assigned a northern value of 500,000 meters and an easting value of 2 million meters. The notation for the latitude of the grid origin is b sub b because through it will pass the baseline of the grid. Associated with grid latitude of the grid origin is a particular distance from the apex of the cone. This distance is known as the mapping radius through the grid origin, noted as r sub b. It is a tabled constant for each zone. Next, we see the customary north-south limits of the grid and the customary east-west limits of the grid illustrated. These limits are customary only when there is a good reason for doing so, the grid may be expanded beyond them. Before we continue to our next graphic, let's look at a simple model with a paper cone representing the large cone with its apex way above the north pole of the ellipsoid. On this cone, we can see that the geodetic meridians have been projected through and they form now north-south geodetic lines. You'll also see that the latitude line has been projected through so that they form what appear to be parallels on the cone's surface. Now, the interesting thing that this cone is to illustrate is that when we develop this cone, that is when we flatten it out, which we'll do right now, those lines that appear to be parallel become large semi-circles here. And the lines that used to be running to the apex of the zone now converge at a point so the geodetic meridians converge while the parallels of latitude become large arcs of circles. We will now see a series of pictures portraying the developed cone, that is the cone once it has opened up and flattened into a plane. On that developed cone, we will see the various lines that relate it and the grid that creates a state-plane coordinate system. This picture shows the cone for a zone developed that has opened up and flattened. The cone entirely encircled the ellipsoid. In other words, it represents a full 360 degrees of longitude, but now that it has been developed, the central angle at the apex of the cone is considerably less than 360 degrees. The central angle at the apex of the developed cone equals 360 degrees times sine B sub o. This gives us the ratio that we can use to proportion differences in longitude when calculating the corresponding central angle on the developed cone. Sine B sub o is the sine of the latitude of the projection origin, a tabled constant. The latitudinal line illustrated for our developed cone is B sub o through the projection origin. We see that the mapping radius of B sub o has been labeled as R sub o. It is the distance from the line of latitude B sub o to the apex of the cone, a tabled constant. Now added is the northern axis. The northern axis coincides with the central meridian. Therefore, its longitude is the same as that of the central meridian passing through the projection and grid origins. Next we see the addition of another latitude in the line and its mapping radius. The latitude is that of the parallel passing through the grid origin. Its latitude is noted as B sub B. It is a tabled constant for each zone. The mapping radius is labeled as R sub B. It is the mapping radius through the grid origin and is a tabled constant. Next we see the addition of the easting axis. It passes through the grid origin and is at a right angle to the central meridian. Next can be seen lines of longitude, approximately delineating the customary east-west limits of the zone. Also added is a segment of the latitude, approximately delineating the customary northerly limit of the zone. The customary southerly limit is the easting axis. Next, a meridian of longitude extends from the apex of the cone to a station, which coincidentally is on the central parallel. A longitude is a true north-south geodetic line, a geodetic meridian. The notation for the west geodetic longitude of a station is capital L. If we create a grid north line through the station, it will be parallel with the northern axis. The plane convergence angle is the angle formed on the developed cone between the central meridian and the line of longitude through the station. Lowercase gamma symbolizes the plane convergence angle. It can be seen on the screen that the difference between grid north and geodetic north at the station equals the plane convergence angle at the apex of the developed cone. The plane convergence angle is equal to the difference between the longitude of the central meridian and the longitude through the station multiplied times sine B sub o. Both the longitude of the central meridian L sub o and sine of B sub o are tabled constants for each zone. This principle imposes the same proportioning previously imposed upon the central angle for the entire cone. Let's now look at another set of illustrations dealing with the grid. It will make clear the grid's construction and its relationship to certain elements of the cone and the lipsoid. On the screen, we see the two standard parallels of geodetic latitude. Each California coordinate system zone has two of these lines of exact scale where the cone intersects the surface of the GRS-80 ellipsoid. The northern one is noted as B sub n and the southerly as B sub s. Now we see the circular arc of the central parallel added to the illustration. Noted as B sub o is a parallel of latitude that is approximately midway between the standard parallels. Along this line occurs the minimum scale within the zone. Associated with the central parallel is its mapping radius, the distance from the apex of the cone to the central parallel, a distance noted as R sub o. Both the latitude of the central parallel and its mapping radius are tabled constants. Next, we see the addition of the central meridian. It is the projection of a true north-south geodetic line noted as L sub o. The central meridian also is the northern axis of the grid. It passes through both the projection origin and the grid origin. As such, its notation is also E sub o. By definition, the central meridian has an easking value of 2 million meters in all zones. At the intersection of the central parallel and the central meridian is the origin of the projection. This location has geodetic coordinates that is latitude and longitude of B sub o by L sub o. We now see another parallel of latitude has been added. Noted as B sub b, it is the projection of the geodetic latitude passing through the grid origin and is a tabled constant. It also has a particular mapping radius associated with it, a tabled constant noted as R sub b. At the intersection of the central meridian with B sub b is the origin of the grid. Consequently, its geodetic coordinates are B sub b by L sub o. Through the grid origin, and at a right angle to the central meridian, runs the easting axis of the grid. It is the baseline of the grid noted as N sub b. A northern value of 500,000 meters is associated with the easting axis. Therefore, the origin of the grid has plane coordinates of 500,000 meters in northern by 2 million meters east. This is true for all zones by definition. Parallel with the baseline of the grid and passing through the projection origin is an east-west grid line. Its northern value is noted as N sub o, a tabled constant. Therefore, the grid coordinates of the projection origin are N sub o by E sub o. On the screen, we see the approximate customary east-west extent of the zone depicted. These limits are customary only, but it is usually not necessary to extend the coordinate zones too far into the Pacific Ocean or into adjacent states easterly of us. Next on the screen, we see the approximate north-south customary limits of the grid. The customary southerly limit is the baseline of the grid. More grid lines are added parallel with the northern axis. Each line runs grid north. Remember that geodetic meridians converge toward the apex of the cone, while grid meridians are not parallel, are all parallel. Therefore, the difference between geodetic north and grid north at any particular point on the grid depends upon the position of the point. Now grid lines paralleling the east-ing axes have been added to the display. They all run grid east and at a right angle to the north-south grid lines. Now that we understand the basic geometry of the ellipsoid cone and grid, we will view a series of pictures illustrating the geometry that allows us to convert geodetic coordinates, in other words latitude and longitude, to state plane coordinates are familiar northings and eastings. We now see on the screen a single line of latitude projected onto the developed cone surface. This line of latitude is the central parallel of the zone noted as B sub O. The central parallel is a tabled constant for each zone. We now see the central meridian, a geodetic north line added to the picture on the screen. This line is also the northern axis of the grid. All other grid north lines will be parallel with it. Its east-ing value is 2 million meters by definition. That value is noted as E sub O and is a tabled constant. The intersection of the central meridian with the central parallel is the projection origin. Now we add the east-ing axis or baseline of the grid noted as N sub B. This line runs at a right angle to the northern axis. Its northern value is a tabled constant and is 500,000 meters by definition. This northern value sometimes is called its false northern. The intersection of the northern axis with the east-ing axis is the origin of the grid. The screen now shows a dimension line extending from the apex of the cone to the grid origin. This distance is the mapping radius through the grid origin noted as R sub B. It is a tabled constant. By inspection, we can see that by adding together N sub B and R sub B, we can calculate the northern of the apex. Now added to the display is a station at which the geodetic coordinates and the grid coordinates are to be equated. We see a parallel of latitude added through the station. Its latitude is noted as capital B. Next added is a geodetic meridian of longitude extending from the apex of the cone to the station. The notation for its longitude is capital L. Now another line has been added. It is a line through the station extended at a right angle from the northern axis. The latitude through the station has a particular mapping radius associated with it. Labeled as capital R, the length of the mapping radius through the station can be measured along the meridian from the apex to the station. As shown on the screen now, the central parallel has its own particular mapping radius noted as R sub O. It is a tabled constant. The value of the mapping radius R through our station will be needed for converting geodetic coordinates to state plane coordinates and vice versa. So that we can do this, NGS devised a method to calculate the radial distance between the parallel of latitude through our station and the central parallel. It involves the use of equations employing tabled coefficients and the difference in latitude between the origin of the projection and the station. The distance obtained by this method is labeled small u on the screen. When a station is north of the central parallel, u is negative. When the station is south, it is positive. By inspection, it is apparent that the mapping radius of our station R equals the sum of the mapping radius through the central parallel, R sub O, and the radial difference, u. Remember that we previously discussed that the central angle of the developed cone could be found by multiplying 360 degrees of longitude by sine b sub O. Similarly, an angle on the grid between the central meridian and any other geodetic meridian can be found by multiplying their difference of longitude by sine b sub O. This angle is the plane convergence angle located at the apex of the cone. The plane convergence angle sometimes is called the mapping angle. Its symbol is the lowercase Greek letter gamma. We now can see that we have developed a giant right triangle, the conversion triangle. One leg of it is the mapping radius through the station. One angle of the triangle is the plane convergence through the station. Using classical Euclidean trigonometry, we can calculate the other two legs of the giant triangle. As noted on the screen, the leg along the northern axis of the grid can be found by multiplying the mapping radius through the station R by the cosine of the plane convergence angle. This yields the difference in northings between the apex of the cone and our station. Remember that we previously determined that adding n sub b with r sub b yielded the northing of the apex. Therefore, subtracting the value r cosine gamma yields the northing of the station. The northing is noted by small letter n. Next we see that the remaining leg of the giant conversion triangle, labeled r sine gamma, is shown the value found by solving this trigonometric equation is positive if the station is east of the northern axis and negative if west. We can calculate the easting of our station noted as small e by adding the result to e sub o. Thus, we have a method to convert our station's geodetic coordinates, b and l, to its equivalent grid coordinates, small n and small e. Reversing the procedure provides for the inverse computation, starting with plane coordinates and going to geodetic coordinates. We will cover three broad classes of calculations for state plane coordinate systems in this presentation. They are first, conversions of coordinates between ellipsoid and grid. Second, manipulation of observations. These are adjustments applied to lengths and asmas when converting field measurements to grid values and vice versa. Third, transformations from zone to zone. We first will consider forward or direct computation, which is the conversion from geodetic coordinates to plane coordinates. In other words, we will change latitude and longitude of a station into the corresponding northean and easting. Direct or forward mapping equations are used to compute state plane coordinates from geodetic coordinates. In the forward computation, we must find the mapping radius through the station. This may be done in two ways. The first is by using tabled polynomial coefficients, the method preferred by NGS. The coefficients are used in algebraic equations to provide the missing link in calculating the mapping radius through the station. This missing link is the radial distance, noted as small u, previously illustrated. The polynomial equations are straightforward although the numbers are long. But let us not forget that the machine does the hard work. All that we must do is press the buttons accurately. Another method for determining the mapping radius is to interpolate it from projection tables. This will be discussed in its proper place during our discussion of forward computation. We begin by calculating the difference of latitude between the station to be converted and that of the central parallel. This equation takes the north latitude of the station, noted as b, and subtracts the latitude of the projection origin on the central parallel, a tabled constant noted as b sub o. It yields the difference in latitude between them. If working on a calculator computing only 10 significant digits, such as the HP 41, it is necessary when subtracting latitudes to truncate tens of degrees. That is, if the latitude is 33 degrees, truncate it to three degrees. We can now use the difference in latitude just calculated to compute the value of u. Remember that we previously saw that u is the radial distance from the station to the central parallel. We will use L polynomial coefficients for this calculation. These coefficients can be found listed at the end of the California Coordinate System written material. Each zone has its own set. They also differ for feet or for meters. Using the latitude difference just obtained, we enter it into an either equation now displayed on the screen to calculate the value of u. Some persons feel that the second equation is easier for handheld solution because it has a nested form. Each equation takes the difference in latitude or the difference raised to a power and multiplies at times a polynomial coefficient that is tabled with the zone constants. Each coefficient used in these equations is noted with the capital L. Each has a subscripted number to indicate its proper position within the equation. Be careful to keep track of arithmetic signs. The radial difference, u, has a positive value if the station lies northerly of the central parallel and a negative value if it lies southerly. After we have calculated u, the radial distance from the station to the central parallel, we can calculate the mapping radius for our station. The equation now displays shows that by taking the length of the mapping radius of the central parallel, r sub o, and subtracting the radial distance measured from the station to the central parallel, u, we calculate the mapping radius through the station. Be careful with arithmetic signs. An alternative to using polynomial coefficients is obtaining the mapping radius from projection tables if they are available. The projection tables are entered with the latitude of the station and the mapping radius can be read in an adjacent column. Usually projection tables list latitude in whole minutes. Therefore, values of the mapping radius for a latitude line between whole minutes must be interpolated. Remember from our previous discussion that during a forward conversion, we are solving a giant right triangle. Whether obtained using polynomial coefficients or from projection tables, we now know the mapping radius of our station. In other words, we now know the length of the hypotenuse of our giant right triangle, the conversion triangle. Next, we must find the value of the angle of our conversion triangle located at the apex of the cone. As we learned earlier, this angle is the plane convergence angle. To determine the plane convergence angle, symbolized by lowercase gamma, we use the equation displayed on the screen. It determines the difference between the longitude of the central meridian, a tabled constant noted as l sub o, and the west longitude through the station, noted as l. It then proportions that difference by sine b sub o, a tabled constant. This is the same relationship that the central angle of the developed cone has to 360 degrees of longitude as previously discussed. If working on a calculator, computing only 10 significant digits, such as the HP 41, it is necessary when subtracting longitudes in this equation to truncate tens and hundreds of degrees. That is, if the longitude is 117 degrees, truncate it to seven degrees. Furthermore, it is necessary to carry all significant digits for this calculation. Therefore, it is suggested that you use register or stack arithmetic. Now that we know both the length of the hypotenuse and the angle at the apex of the cone, we may use them to solve our conversion triangle. Its solution provides the remaining elements needed to calculate the northern and east end of our station. First, we calculate the northern of our station using the equation displayed on the screen. It adds the mapping radius of the grid origin, r sub b, to the northern of the grid origin, n sub b. This gives us the northern of the apex of the cone. We then solve r cosine gamma, which is the difference in northings between the apex and the station. This is then subtracted from the northern of the apex, leaving only the northern of the station noted as small n. Finally, we calculate the east end of the station. By solving r sine gamma, we find the east end difference between the central meridian and the station. The value will be positive if the station is east of the central meridian, negative if it is west. Add the value to e sub o, the east end of the central meridian to obtain the east end of the station noted as small e. We now have finished the process known as direct or forward computation. We begin with the latitude and longitude of a station, its geodetic coordinates, and we converted them to their equivalent northern and east end, its plane coordinates. Next, we will study inverse mapping equations, which are to convert plane coordinates to geodetic latitude and longitude. The geodetic coordinates are measured on the ellipsoid of reference as latitude and longitude while the northern and east end is on the grid. Either polynomial coefficients or projection tables may be used in the process. First, we must solve for the plane convergence angle. This equation subtracts e sub o, the east end of the grid origin, from the east end of the station noted as small e. This yields the difference in east ends from the northern axis to the station. It then divides that difference by the sum of r sub b, the mapping radius of the grid base, which is a constant, and n sub b, the northern of the grid base, less the northern of the station, small n. This quantity is the difference in north ends from the apex of the cone to the station. These two quantities are the opposite and adjacent legs of the large conversion triangle. It is necessary to carry all significant digits of the plane convergence angle resulting from this calculation. Therefore, you should use register or stack arithmetic. Next, we proportion the plane convergence angle by dividing by sine b sub o. This is the reverse of the procedure that we saw earlier when learning forward computation. This equation is used to calculate the longitude through the station. Remember in our previous discussion, we found that we can proportion or scale the difference in longitudes between the central meridian and a station by the tabled constant sine b sub o when calculating the plane convergence angle. This equation takes the plane convergence angle symbolized by lowercase gamma, divides it by sine b sub o, thereby calculating the difference in longitudes. We then subtract that difference from the longitude of the central meridian, l sub o, to calculate the longitude through our station, noted as l. If working on a calculator computing only 10 significant digits, such as the HP 41, it is necessary when subtracting longitudes in this equation to truncate tens and hundreds of degrees. Furthermore, it is necessary to carry all significant digits in this calculation. Therefore, you should use register or stack arithmetic. Now that we have the longitude of our station, we are left with the problem of figuring its latitude. Similar to the direct conversion, we need to use the mapping radius through our station while calculating the latitude. This necessitates our use of the radial difference, noted as u, unless projection tables are available. We will proceed for now as if no projection tables are available. First, we will calculate the radial difference, u. In this equation, we seek the value of the radial difference between the mapping radius of the central parallel and the mapping radius through the station in question. First, the difference in estines between the station and the northern axis, e sub o, is multiplied by the tangent of half the station's plane convergence angle. We then subtract the result from the difference between the northern of the station, noted small n, and the northern of the projection origin, a tabled constant noted as n sub o, giving us u. Next, we must use the radial difference to compute the latitude of the station. G polynomial coefficients are used for inverse computation. After the radial distance has been calculated, G polynomial coefficients are used in algebraic equations to calculate the difference between the latitude of the station and that of the projection origin. The equation then adds the length to the latitude of the projection origin, and thereby we receive the latitude of the station. Either one of these equations may be used to calculate the latitude of the station using the previously calculated value for u and multiplying it by the G polynomial coefficients tabled constants for each zone. The various portions of the solution must be carefully solved and then combined, taking care with arithmetic signs and obtaining the latitude of the station. If working on the calculator, computing only 10 significant digits, such as the HP 41, it is necessary when adding latitudes to truncate tens of degrees. If projection tables are used, the latitude must be obtained by interpolation. The interpolation argues mapping radius against latitude. The mapping radius may be calculated from the following equation. You may recognize the Pythagorean theorem in this equation. This equation takes the square of the leg of the conversion triangle comprised of the difference of eastings, adds to it the square of the leg of the conversion triangle comprised of the difference of northings, and then takes its square root, yielding the hypotenuse of the giant triangle, which is the mapping radius through the station. All terms on the right side of the equation are tabled zone constants, except the northing and the easting of the station. When using projection tables, the mapping radius just calculated is used as an argument against latitude. The mapping radius is interpolated to refine the latitude of the station. We've been at this for quite a while now, and we have finished our discussion of inverse computation, so let's take a short break. Welcome back to our discussion of state plane coordinates. We will begin with adjustments to observations. First, we will deal with azimuths. On the screen, we see the central meridian or northing axis running north-south. It is labeled E sub o, the notation for its easting, which is a constant for each zone. We also see the easting axis labeled N sub b, which is the notation of its northing, also a constant. On the screen now, a station has been added. Now a geodetic meridian, that is, a geodetic north line is drawn between the station and the apex of the cone. This meridian is the line of geodetic longitude through the station. We now see a line running from our station toward another station. It is easterly of us in this case. The grid azimuth of the line to the station is desired. Now shown as an angle labeled alpha. This angle identifies the geodetic azimuth. The geodetic azimuth of the line toward the second station is the clockwise angle from the geodetic meridian around to the line to the second station. For the California Coordinate System of 1983, geodetic azimuth is reckoned from north, not south as previously done. On the screen now, a grid north line through the station has been added. Because it is grid north, it is parallel with the northern axis of the grid. Now we see the plane convergence angle labeled gamma at our station between geodetic north and grid north. In this case, convergence is negative because the station is west of the central meridian. If it had been east of the central meridian, it would have had a positive value. Be careful with arithmetic signs. Plane convergence angle is sometimes called the mapping angle. We now see the addition of an angular dimension, small t. This quantity is the grid azimuth of the line between our station and the one easterly of it. Grid azimuth is the clockwise angle at a station between the grid meridian, that is grid north, and the grid line to the other station. Next we see the equation t equals alpha minus gamma plus delta. Bearing in mind that the plane convergence angle in our drawing has a negative value, inspection of the drawing demonstrates that t is equal to geodetic azimuth minus plane convergence. The other term in the general formula is neglected here. It is variously named often arctochord correction or second term correction. It is usually minute, but may need to be considered for high quality work over long lines. This presentation neglects it. For CCS 83, both geodetic and grid azimuth are reckoned from north. Inverses between stations having state plane coordinates give grid azimuth and may be used directly for calculations on the grid. Plane convergence angles vary with longitude. Therefore, we must specify the station where the convergence was determined when quoting it on a map. Plane convergence may be determined in two ways. Where the longitude is not known without calculation, plane convergence can be calculated using the tabled constants of the zone and the plane coordinates. This is the same equation that we saw earlier in the inverse computation. E sub o, the easting of the grid origin, is subtracted from the easting of the station, small e. This yields the difference in eastings, then dividing the eastings difference by the sum of r sub b, the mapping radius of the grid base, and n sub b, the northing of the grid base, less the northing of the station. This is the other leg of the triangle. These two quantities are the opposite and adjacent legs of the large conversion triangle. Their arc tangent yields the plane convergence angle. If plane coordinates are not known, but the longitude of the station is known, the plane convergence may be calculated using the difference in longitude between the central meridian and the station, which is a constant. B sub o, to calculate the plane convergence angle, we use the equation displayed on the screen. It determines the difference between the longitude of the central meridian, a tabled constant, and the west longitude through the station. It then proportions that difference using sine b sub o, a tabled constant. This is the same relationship that the central angle of the developed cone has to 360 degrees of longitude, as mentioned previously. If using a calculator having only 10 significant digits, such as the HP 41, it is necessary when subtracting longitudes in this equation to truncate tens and hundreds of degrees. Furthermore, it is necessary to carry all significant digits for this calculation. Therefore, use register or stack arithmetic. The last element of grid azimuth is the second term or arc-decored correction. The Lambert system is called conformal because it is intended that field angles and grid angles should be identical. They nearly are. The second term correction is usually minute and could be neglected for most courses under five miles long. It is the difference between the grid azimuth and the projected geodetic azimuth. It increases directly with the change of eastings of a line and with the distance of the occupied station from the central parallel. Figuring it is neglected in this presentation. This is the equation previously seen at the end of the graphics presentation of azimuth. It states the basic relationship that grid azimuth at small t equals the geodetic azimuth alpha minus the plane convergence angle gamma plus the second term correction delta. We have now finished our treatment of azimuths. We will next consider the treatment of distances converting them from the ground surface where they were measured to their ultimate destination, the plane surface of the grid. This product takes the, this process takes the distance over several surfaces that originates at the ground surface. The process then takes it through the surface of what is called the geoid. The geoid is a gravity surface that has an equal potential. This surface is analogous to the idea of mean sea level. However, unlike the common notion of mean sea level as a uniform surface, smoothly curving like an ellipsoid, the geoid curves up and down or undulates. These changes usually occur gradually, but nonetheless are significant over long distances. The next surface involved in our process is the geodetic or ellipsoidal surface of the GRS-80 ellipsoid. The separation between the ellipsoid and the geoid is considered for the California Coordinate System of 1983. This is a new process. The older state plane coordinate system did not consider this separation because for the most part, it could not be readily quantified. The final surface that we go to is the surface of the cone, which is in fact the plane surface of the grid. On the screen, a ground surface is shown. For our present purposes, it has an elevation significantly above sea level. Now another surface is added. It is the surface of the geoid. Practically speaking, this is the surface that serves as the datum for elevations. In other words, mean sea level. The dimension between the geoid surface and our ground surface is labeled H. We commonly know this distance is elevation. Next, we see the addition of a third surface, the surface of the GRS-80 ellipsoid. In this illustration, it lies above the geoid or sea level surface. This is the case for all 48 contiguous states. The distance at a station from the geoid to the ellipsoid is called geoid separation or geoid height, and noted by capital N. For the contiguous 48 states, geoid separation has a negative value because the geoid is below the ellipsoid. Now on the screen, we see another dimension has been added. This is ellipsoidal or geodetic height, noted as small h. It is elevation using the ellipsoid for its datum.  This relationship is now shown on the screen. Now a horizontal measured distance at ground level is added. This distance is a chord and is noted as capital D. Lines are extended normal to the surface of the ellipsoid. They converge towards the center of the ellipsoid. Now on the screen, we see that when a ground surface chord distance is reduced to a chord distance on the ellipsoid surface, the ellipsoidal chord length differs from the chord distance at ground level. The notation L sub C indicates ellipsoidal chord length. If ground length is above the ellipsoid surface, as in this case, the ellipsoidal chord length is shorter. If ground surface is below the ellipsoid, like along the Pacific shore, Death Valley and Imperial Valley, the ellipsoidal chord length is longer than the ground length. The movement of the length through the geoid is embedded in the equations used in this example and is not a separate procedure. Next, we see the addition of the geodetic surface noted S. The geodetic distance occurs on the geodetic surface, that is, the surface of the ellipsoid. It is an arc rather than a chord. It is the geodetic length that is projected onto the cone. The cone's surface is not shown in our illustration but may be located either above or below the ellipsoidal surface. This depends on whether the line is between the exact scale parallels or outside them. It also could cross one or both of them. The line is projected onto the cone's surface by lines normal to the ellipsoid. Geodetic lines between the exact scale parallels shrink when projected onto the cone while lines outside the exact scale parallels get longer. After the line has been projected onto the cone, its length is a grid length, that is, is the distance between points on the grid. We begin our conversion of measured distance to grid distance by calculating the radius of curvature of the ellipsoid. Because the ellipsoid is flattened at its poles, the radius of curvature is uniform only along the equator. Except along the equator, the radius of curvature will vary as the azimuth of the line varies and also as one travels along the line. Because it varies with azimuth, the full name is radius of curvature in the azimuth. There are complex equations for calculating precise values for this radius. An approximate radius for each zone is the geometric mean radius of curvature at the projection origin. It is close enough for all but the most precise work. It can be obtained by the following equation. This equation states that an approximate radius of curvature in the azimuth, noted as r sub alpha plus or minus, may be calculated by dividing the geometric mean radius of the ellipsoid at the projection origin scaled to the grid, a tabled constant noted small r sub o by the grid scale factor of the central parallel which is small k sub o. This calculation yields the geometric mean radius of curvature of the ellipsoid at the projection origin. Using this approximate radius of curvature of the ellipsoid, we'll next calculate the ellipsoidal reduction factor also known as the elevation factor. The value just obtained for the approximate radius of curvature is now used in the upper equation on the screen to figure an ellipsoidal reduction factor noted as r sub e. Calculate the reduction factor by dividing the approximate radius of curvature by the sum of the approximate radius, the geodetic separation noted as capital N, and the elevation to which the measured line was reduced noted by capital H. This equation in effect develops proportion between two radii. The first is the radius of the ellipsoid at the station. The other is the radius at the ground elevation of the station. This is similar to route surveys where the centerline chord lengths of a curve may be scaled to an offset by using the ratio of the centerline radius and the offset radius. The ellipsoidal chord length noted l sub c can be calculated by multiplying the ellipsoidal reduction factor times the ground level horizontal measured distance noted capital D. This is shown in the lower equation on the screen. This ellipsoidal chord length is a straight line distance between two points on the surface of the ellipsoid. It is not a distance measured on the surface of the ellipsoid which would be an arc length called a geodetic length. The elevation used for the measured line is usually one of the following. For triangulation, it is the average elevation of the baseline. For electronic distance measuring devices, it is the elevation to which the slope length was reduced. This is usually the elevation of the instrument or the elevation of the station mark. For tape lines, it is usually the average elevation of the line. Each one meter air in the geoid separation or elevation contributes 0.16 parts per million of air to the distance. Often, geoid separation can be estimated for stations in the general area based upon published values for nearby stations. The value of capital N usually does not vary greatly in a given area. Examining the variations in the proximity of your work can aid in determining if anomalies exist in the area. If precise geodetic lengths are desired, a correction from ellipsoidal chord length to geodetic length on the ellipsoid surface may be applied to lines generally greater than five miles long. Shorter lines and lines measured in segments are essentially arcs and need not be corrected. The ellipsoidal chord length must be nearly nine miles before the correction equals one one hundredth of a foot at over 19 miles before it equals one tenth of a foot. The upper equation on the screen is for calculating the chord correction for lengthening the ellipsoidal chord length to the geodetic length. Remember that arcs are always longer than their chords. You may recognize this equation from route surveying. The equation calculates the chord correction by cubing the ellipsoidal chord length and then dividing it by twenty-four times the square of the radius of curvature in the azimuth. As shown by the lower equation, after determining the chord correction, the correction is added to the ellipsoidal chord length yielding the geodetic length noted as s. Once we have calculated the geodetic length of the line, it must be projected onto the cone. Grid length is calculated by multiplying the geodetic length by a grid scale factor. Grid scale factor is an expression of the amount of distortion imposed on the length of a line from the ellipsoid as it is projected onto the grid cone. It is represented by the small letter k. Scale factor is the ratio of the length of the grid on the grid to the length on the ellipsoid. Scale factor is dependent upon latitude. It is less than unity between the standard parallels and greater than unity outside them. Scale factors can be calculated for points or four lines. For this presentation, point scale factors are used exclusively. If greater accuracy is needed for a long line, the point scale factor for the midpoint may be used. Approximate point scale factors may be interpolated from projection tables. A method precise enough for any plain coordinate work uses polynomial coefficients. We must first find the value of the radial distance discussed previously and noted as small u. If plain coordinates are known, this equation can be used to find the radial difference. This is similar to another equation we saw earlier. You may recognize the Pythagorean theorem in this equation. This equation takes the square of the leg of the conversion triangle comprised of the difference in eastings from the central meridian to the station, adds it to the square of the leg of the giant triangle comprised of difference of northings, then takes the square root of their sum yielding the hypotenuse of the conversion triangle, which is the mapping radius through the station. That mapping radius through the station is then subtracted from the mapping radius of the projection origin to obtain the radial difference. If geodetic latitude for the line is known, the following equations can be used to calculate the radial difference. We have seen them before during our discussion on forward computation. This equation takes the north latitude of the station noted as b and subtracts the latitude of the projection origin, the central parallel. A tabled constant noted as b sub o, it yields the difference in latitude. If working on a calculator computing only 10 significant digits, such as the HP 41, it is necessary when subtracting latitudes to truncate tens of degrees. Using the latitude difference just obtained, we enter it into either equation now displayed to calculate the value of u using polynomial coefficients. Some persons feel that the second equation is easier for handheld solution because it has a nested form. Be careful to keep track of arithmetic signs. The radial difference u has a positive value if the station lies northerly of the central parallel and negative value if it lies southerly. Once we have calculated the radial difference by one of the equations we have just seen, we can use it to calculate the point scale factor using polynomial coefficients. The value calculated above for the radial distance u and the tabled f polynomial coefficients can be used in the equation shown on the monitor to calculate a point scale factor noted as small k. Approximate scale factors for points may also be found in projection tables. The latitude or mapping radius through the station is argued against scale factor. Intermediate values are interpolated. Next we use the point scale factor just found to project our geodetic length onto the grid. This will give us its grid length. The grid length, l sub grid, is calculated by multiplying the point scale factor k together with the geodetic length of the line small s. If no correction from ellipsoidal chord length to geodetic length is warranted and the latitude and elevation differences are not great, measured lengths may be multiplied by a combined factor to calculate grid lengths using a value for average elevation and average latitude. The upper equation states that we can calculate a combined factor noted cf by multiplying an average ellipsoidal reduction factor r sub e by a point scale factor calculated for the mid-latitude of the survey noted small k. The lower equation shows that once we have determined a combined factor, we can multiply each ground level horizontal measured length noted capital D by it to calculate each course's grid length. Grid length may be converted to ground length by reversing the above procedures. For measurements of similar elevation, latitude and short length, ground length may be calculated by dividing a combined factor into the grid length. In dealing with areas calculated on a grid, the areas derived from state plane coordinates must be corrected if ground level areas are desired. The equation shown on the screen may be used to correct grid area to ground area. It shows that the ground level area of the land may be computed by dividing the grid area of the figure by the square of the combined scale factor. In effect, this applies the combined factor to both the length and the width of the figure. A problem arises in converting coordinates from one zone to another. To convert plane coordinates and the overlap of zones from one zone to another, convert the plane coordinates from the original zone using the constants for that zone to geodetic latitude and longitude. Then, using the coordinates for the new zone, convert the geodetic latitude and longitude to the plane coordinates in the new zone. As enacted by the California legislature, linear units may be expressed either in meters or in your US survey feet. Plane coordinates or distances expressed in meters or feet can be converted to the other unit simply by multiplying the north end and east end or the measurement by the US survey foot to international meter equivalency. Shown on the screen, the US survey foot, the linear unit of the California coordinate system, is defined as one US survey foot equals 1,200 divided by 3,937 international meters. It is the specialized foot that is used in surveying. When first using functions in a calculator or computer to convert between feet and meters, you should test to ensure that the correct conversion factor is employed. You should test it by using the machine's functions to convert exactly 3,937 feet to meters. The result should be exactly 1,200 meters. The reverse must also be true. Comparing the result while displaying the maximum decimal places should tell you whether the conversion you are using is for US survey foot. One may work the California coordinate system in either feet or in meters. However, one must be consistent. Not only must all distances and coordinates be uniformly in feet or in meters, but tabled constants must also correspond with the linear units chosen. I hope that this presentation will help you in your understanding of the state plane coordinate system. I also encourage you to study hard and prepare well for your land surveying examination. I wish you the best of luck and success. Thank you.