Descartes (crater)

Transcription

it the then well are not making any money at it well you can use this opportunity to advertise Its called maps and math one it well thanks can you hear me okay I don't mean I've got a mic here but I'm told it doesn't actually communicate with the room so okay so we're going to talk this is my title slide we're going to talk about this guy Leonard Euler and what he had to do with the figure of the Earth Okay so this is basically my outline there's a lot and lots and lots of people connected with this story But the two big names that I want to spend most time on are Isaac Newton and then leonard Euler say it let's go back to ancient Greece real briefly uh... Aristotle wrote a book called De Caelo 'On the Heavens' a lot of his work seem to be copied or borrowed from Annex Agoura but I'm not sure about the story on that but i'm he gave he believed that the earth was um... spherical or round in shape um... there are three basic arguments he gave for that one of them was that uh... well the sphere is the most perfect of all bodies so of course the Earth is spherical the other one was something we'd recognize today which is you see different stars at different latitudes and then the third one which I thought was the most interesting is that if you look at it an eclipse of the moon and you look at the shadow on the body of the moon you see that that shadows actually has a cruved shape to it so that that was kind of interesting i'm not sure how how many whether it was a common belief among all of Greeks to believe that the earth is sphereical but certainly you know Aristotle writing is showed that there was some segemnt that did believe that i have heard i read it someplace in the last few months that the Chinese, this idea never occurred to the Chinese until the uh... until the coming of Marco Polo and in the late middle ages the Chinese always just assume the Earth was flat i don't know any more about that if any, if you have you any more details on that please let me please come and talk to me afterwards anyway let's go back now let's go forward to sixteen fifty or the middle of the seventeenth century pretty much every body by then believed that the earth was in fact round there have been several voyages that'd circumnavigate the earth than it was hard to dispute this anymore but beginning in the late sixteen hundreds there started to be some doubt up until sixteen fifty certainly everybody believed the earth was a sphere as aristotle did then they started be some funny things, some funny piece of evidence started to creep in this first guys named Giovanni Cassini you might recognize his name they named, NASA names a lot of spacecrafts after him now uh... he was probably the leading astronomer of his day he was you know he starting out in Italy and then later became director of the Panzano observatory one of things he did, he did a lot of studies of Jupiter one of the things he did was have one of his telescopes fitted with a set of fine hairs is so he could very exactly measure the degrees of things and discovered much to his and everybody else is surprised that Jupiter was not a perfectly round shape that it was flattened the polls in fact flattened quite a bit more than, much more than the earth it's about ratio one fifteen uh... the polar axis about one fifteen shorter than the equatorial axis of something like that the next piece of evidence k does not come from this guy uh... does not cover Jean-Luc Picard but it comes to his remote ancestor who was named John Felix Picard who, um was well he was an Abbot but he also uh... was one of the first people to do something like our modern what modern surveyors doing the measure um... lengths of distance on the land he in fact one of his projects was to measured the length of degrees of latitude and the route that he chose was from someplace a little bit um... east of Paris up north to Amiens a distance of the just under two degrees latitude I believe you can see in this picture here that you can kind of get an idea of the kind of instruments they're using this picture appears to be taken at night and it looks to me like what they're doing is citing the angle between this distant place and this distant place here's another picture which is even cruder but important thing is if you're measuring latitudes you not only have to measure distances on the ground but you also have to know what latitude your at and in order to do that you have to look at the stars uh... and the uh... what you do is you pick a certain fixed whose motions are known and you wait until it's culminated until it's, till it's on the north-south meridian and then you measure its altitude and these measurements have to be fairly fairly precisely in order to do you any good they have to be well certainly way less than a degree and i believe actually probably less than a minute of a degree and you can see that you these guys are laying on the ground with a ten-foot wooden device and citing through it and you can see how a bunch of errors could creepy in and this in fact was a big source of controversy in early early eighteenth century like uh... how exactly precise were the measurements that people were taking and uh... we'll get to that later in the story too the next uh... little funny piece of evidence came from this newfangled invention called the uh... pendulum clock there's a the this is again John Felix Picard uh... this kind of a side comment from his uh... from is paper but he was talking about uh... let's see if we can find a universal standard of length because right now people in England use one thing people in Germany something else people in France you something else maybe we could use the length of a pendulum cord that makes it tick exactly once per second maybe that would be a good universal standard of length but then he mentions well you know they're starting to be some evidence coming in i dont know how many of you can actually read the French but what he's saying here is that uh... there's some evidence that uh... you know it's it's different that you have to use a different length the pendulum in London in in Italy and in fact there is recently a paper presented to the national assembly showing that uh... or suspect speculating that as you go towards the equator you need to shorten your pendulum in order for it because the force of gravity is less down at the equator let's go back here, I thought I had a picture of Huygens in here well okay what happened was a few years later uh... there is an astronomical expedition that was sent to the island of Cayenne which is still a french possession it's down here very close to your quieter you might also know what as better noise as the kind of the uh... center which uh... supply data infamous prison colony known as devil's island the purpose of our story it's like within five degrees at the equator there is an astronomical expedition was sent there most of their observations had to do with the stars but one of things that kind of included is a footnote is can you measure nixon measurements about the length of a pendulum lay down there and it turned out that yes there is a difference that a pendulum on that scallop replace we calibrated that pair in the long latitude of paris is going to lose ida lee two minutes and fifty seconds every twenty four hours if you said at least if you call it here okay christian likens the inventor the pendulum clocks make clear that well i mean okay certainly things have a little bit less weight equator why is that christian items as well the earth is rotating maybe the singer fickle force of account for it this brings us to isaac newton uh... before we talk in little more detail but needs work alum who want to review with you some of the uh... some of the language having you do with it the lips of the new excitons well first of all we're doing that's we're going to be doing christy right here right itis learn this recently but the difference who's furor dan and heal it saw ideas that is spiro id you can take it you can format babe rotating and he leads it's got to pay taxes that are equal to each other so so for example in this picture well well most recent better pictures later okay we know that okay we know what the major and minor axes of an ellipsoid are and again v_s_ the spiro agnew would have to acces the greek with each other you can't see the third one commit sticking out of there one of the common measures of the shape of the ellipsoid is the ratio of the difference between a major minor axes uh... as a proportion of major axis and this is in fact what newt in use that's because the flattening ratio is often very small it's often more can we need to talk about the inverse of flattening ratio eccentricities used a lot two dimensional geometry it's got to wonderful geometric properties and you're talking about two-dimensional ellipses on the doesn't seem to be news very much in the literature forearm when talking about three-dimensional ellipsoids oiler in his work is dispersed similar constant which is unit gives you the same information it gives you the information about the shape of the left side without specifying the actual size uh... two words that we need to know um... have to use the shape of the earth one is probly which means the it's flattened at the polls and the other as pro-life which means its length of the calls trying to figure out there the organs in his words are low obscura believed that the uh... troll eight was the original word because inl i dont any of you exits that lapd uh... walk to assist the path if you know the word two carriers would bring fear of territory they locked us is the past participle that and trophy areas actually of urban latvians to lengthen so people talk about the pro-labor to be linked to the polls and our boy love them prefix ob means a lot of things but it can mean as an object iraqi skate admit to being being sardine contrary and so you know the people it said it's not pro-life would say it was probably saw anyway obligor slot at the polls relates kind exp so it's pretty newton now um... this is a book three at the print give pia uh... missus proposition eighteen which basically says that if if the waters uh... if the earth discovered i mean the if than birth was not obligated or a newton came out in favor of an object c right said if it did i would not the case then all the waters of the earth week kohl s of the equator lay everything they are under water this not obvious from this this sick argument here but um... there's a theological element here too because a lot of newton's earlier correspondence had to do with what happened all those waters after the flood of noah in fact one of this correspondence a guy named thomas thomas burnett wrote right after the print if you wrote off came out rural long treated saying that newton can't possibly be right now quoted a whole lot and want to quit agency uh... genesis and their so it's gone to so newton says okay the earth is now believes the right now let's calculate the flattening ratio okay so he starts out with me and starts out with some data about you know his rough estimate of the size of the earth and it would know how fast the earth rotates and so basically what he comes up with is at the equator approximate figure for the ratio of the centrifugal force to the force of gravity is about one to two hundred eighty nine okay and then we get to his famous little to canals diagram they've gotten a copy of it here i tried to respected newton's original diagrammed here he's that he's got the uh... polar axis going uh... horizontally and the uh... and the equator going vertically by the way i don't know haha reviewed actually the lifted have treasury different kitty about its what can i say it's not exactly written in the standard format that you use in a modern physics and math book uh... i mean why he's using geometric arguments it makes you know in the sense ally euclid which makes sense but he's also not music easton steve's words a lot more worried we'd use symbols so it's sometimes it's uh... it's kind of a take some getting used to and waiting to be needed to do you do you still in the next few slides here is a government of course from here uh... him okay so okay so we've we've got tom he had this figure represented jpv earth admit and we'd built one canal in from the equator and one canal um... in from the pole and imagine and filled with water well of course they're going to be an equilibrium i mean you know this is you know that there's a little bit hazing is in the last argument in some good things in it were not actually cleared up until the seventeen forties by let's let let's assume that it that always on the right track here i mean sorry newton you can okay so we've already established that the the ratio centrifugal force at the equator judy need-based to the force of gravity of edit for pointed beak waiters wanted to reunite we're going to assume that ratio did vichu canals the length is is uh... one hundred and one on the equator to one hundred and the poll gave this is something else that you have to get used to newt he's actually looks like he's assuming the conclusion is trying to prove but this is not really the case where he's going to do is take this assumption about the racial being one hundred two hundred one and show derived from this you know what what the constant siege something related to constant centrifugal force and you know and it applauded equations later so we've got that so uh... we're looking at in point q and we want to measure the relative okay we know what the force of gravity would be at the if if you're interested or call with this with this radius because that's what the whole first because i think if you have about was how to measure the net force of gravity and the spirit of body we also need no do that to do this the first need net force of gravity of any let's say when you're at the poll new reason for that is because if you take a and look at a point on the poll answer cutting little slices off but although slices their spherical and one of the one of the uh... lam is that noon prudent forgive people one that leads up to his he conclusion about spherical bodies is that if you have a thin little circular slice of matter and you're looking straight at it let's looking straight at its center then the com you can the net force of gravity from that the middle circular slice is the same as if all the forces that surplus lester concentrated at the center kansans were working with spherical slices here army circular slides here we can certainly do that so uh... i have not actually done the computation but what he's doing in his is taking all those little spherical slices and uh... unethically ears and just you nigger essentially integrating over the uh... over the uh... body of the this the right amway comes up with his own approximation approximate ratio of one twenty six two one twenty five that's the racial of the actual force of gravity it to you to do ratio ave to the gravity of would-be theory spirits radius each year he can't really do the same thing when you work with the poll because if you take a point at the on the equator so if you can do the same thing at the crater because if you take a point at the equator the sphere and circling cutting up little slices you get little ellipses and with there's no convenient no fear and controls you know hot what the net force of gravity from as little ellipticals lifestyles uh... so what he does is budgets things a bit piece as well you know if we sit on that that uh... it was a com was actually uh... on the equator of this bigger steer them to get out and we could compute uh... that ratio but since we're actually not talking about uh... at this he uh... steroid whose polls that day it's going to carry the f_ lee in between yet so he gets that the ratio of above the force of gravity that that would be exerted by a uh... sphere with radius a seed is to be actual force of gravity ebt point a as about one twenty six two one twenty five now it puts all these together and get something kundu saw on the one slide but when he gets is the ratio of gravity at who appointed poll to a point at the equator is about five hundred to five hundred and one but the winds today the tooth uh... to canales who met at worst they were said to be with and the ratio of one hundred one to one hundred okay so there's four parts of that length better taken off by centrifugal force with what is really getting at here it is that let's see so what is really getting at here is that that if you just as omg if you assume that the flattening ratio is one out one part one hundred one then the uh... divert the uh... proportionate that has to be shortened from the canal has to be four parts and five oh five and therefore the proportion of the set the the radiation reduces centrifugal force to gravity um... compared to be flattening ratio of the earth is four parts and five we and we already know what that centrifugal ratio is in just a little written and you can you get that the flattening ratio of the differences in upgrades period that the uh... with a flattening ratio of about one part two and thirty i said mention here that britain if it turns out well uh... we know now that you please actually wrong yes that uh... it's your there's no place for your right bar last night itself fucking ratio is actually something like more like one in part two ninety eight nine believe the reason that or knew it was wrong innocent he may be explicit assumption that the earth was uniformly dense throughout it and it certainly has definitely not the case that's what something like five times as dance of course it is surface uh... newton did come out in favor of the knob late sphereit when the printer keepers came out on that received i get so caught a mixed reception um... unit english kite critics are very kind to it but uh... folks a special and the continent work a little bit skeptical meaning did a great job of if u if you assume that the force of gravity is axa corning toot toot to an inverse square law the nest does a great job of explaining not a perfect job but does a great job of explaining the normal uh... motions of the planet as were recorded in late seventeenth century on the trouble is that he doesn't know never does really explain why version the force of gravity should behave according to inverse square law so there are a lot of comments that came out about your in sustainable colt this is kinda like uh... pending on the or calls and how do we know that there's going to be this mysterious force and where is it come from stuff like that recruitment no i don't know me if i don't know what that message said that with the the people that bob um... came out against newton specifically against newton shape of the earth now we think that your there's a prolific steroid and they and many of them relied on at the alternative theory of above of matter which is comin at the time which is which is due to rene descartes now i'm not an expert on rene descartes soft theory of matter on that seems to have something to do with bob there is no matter does not feel the entire universe in the spaces in between matter filled with these vortices turnaround that's what accounts for the motion planets uh... i don't believe that his d carts theory a specific enough to give it a specific mathematical formulations such as inverse square laws and in fact there are a lot of hard part asians are critical items as one who even though they believed dick arts philosophy nevertheless agreed with newton of the earth is in fact flattened the polls there were some interesting papers that came out though on the earth especially in the french academy near the uh... obscenity eerily eighteenth-century that said like if you assume something other than an inverse square law on there were some weird ones like that uit you know your traction and be constant throughout the shape of your throughout the earth and it would be and the direction be towards the uc towards the polar axis you know weird things like this but if you have a sufficiently weird law of attraction you can actually prove the puritans pro-life sphereit uh... a lot of the early papers had to do with going out in getting some evidence there are a lot of people that started collecting millions of pandya lumps in their people that who think that solar schools completed let's see their people it beats clicked engineer people in measured times there were people lots of people that went out and tried to measure the length of ladder of degree of latitude on the ground and in fact are not good little movie here simply complying something about that okay this is going to meet picture of the radius of courage here about the lips at various points on it if it works he had a real so amin when women it's you know and near the um... mccarty near the minor axis it's it can't be repeated tends to be flattering there for the release of curvatures longer where it's at that made points on the major axis the release of courage you get shorter okay that's about all i need to show that would that you get to see that you guys got to see the world premiere that okay anyway so the deal is that then the uh... tourist curvatures relatively long here so as compared to empty qua here amount of of the distance on the ground of one degree of latitude is going to be longer at the poll and his near the equator and if it's a pro it's very graphically reverse is true so in theory all you need to do is make you go away far north and measured agreed latitude in galway part kal close to the equator measured degree of latitude c which is longer as a matter of fact that's the benchley after twenty years of argument that's at the french academy undecided do an eight obtain well funding the two people died in france the days when cedras postage stamp are credited with um... actually doing the measurements there is one expedition to a set north to lapland uh... lose between president boris pizza lead in finland there's another exhibition of a set to bob what was then spanish peru it's now ecuador in these they measured from tito which is almost exactly on the equator measured about half a degree cell anyway that that this is not really fair of the people that french give credit to do today are more bricks we and lock on benin amo perch we had with him are claire always certain italian mathematician and also the the uh... sweetie shot a physicist celsius who knew probably occurred have uh... him uh... walk-on damien well that expedition to ecuador is a cuban crazier on that what going to mean was not even the was not even the leader of the expedition uh... university he became i think he got the credit because when he came back he has spent he spent three years ago went to recent like eight years in ecuador we find it came back he descended to the amazon basin and traveled overland out an applicant came yet incoherent uh... any room for every best-selling book best-selling caddy eighteen th-century on this and so you've got ronald there is actually one members expedition that uh... stating that stayed in ecuador thirty years dollar got married raised a family and there's the jury agreed a very skilled people that tom uh... descent firm from an expedition uh... news of the two people that got credit for that what that what they did was send what you have the one expedition to the north and yet it in the south and so let's backtrack a little bit won the reason for the confusion in the shop cassini who had a big name because he was the son of giovanni cassini uh... went to the south of france and measured degree of latitude and found that it would be reported that it's actually larger than it is in the north and therefore the earth is a pro-life sphereit uh... mirrors still a lot of controversy about how accurate all these measurements were mo perch we returned in seventeen thirty six from god's expedition latham and he said noble at two degrees of attribute latitude is much larger in job in north india side in paris it took a long walk it took a long time for the expedition for from to peru to get home but but they uh... back finally in the seventeen forty save reported back to it in two independent measurements in fact that your yes a degree uh... at the equipped waiter is relatively short compared to a degree in the north i think the clincher though really what kind of the clincher was that terry cassini who was the grandson of giovanni cassini put in this very quick uh... kind of parenthetical note to the french academy in seventeen forty-one saying well gee you know i'm looking at this meeting my father's mirza ms uh... measurements were a little off again there's a famous quote uh... i don't know if you know that voltaire and uh... imo perch we at a famous argument in late in the seventeen fifties and i think both of them irene voltaire had to leave had to leave russia animal print we lost his positions they had a very many kennedy in the seventeen forty zero still friends and voltaire word right two px timo perch reinstate my dear flatten their the globe and that he would add some after that they were terry could seek a ninety six my dear flatten your of the globe and of the cassini's with it lohana this brings us to all either okay so this is the end bitterly seventeen fifteen span in fact well out there's some evidence echo i'll give you the evidence that it's just on that it was head of the written after seventeen fifty three anyway he worries of paper argue what the paper was really about was bomb like spherical trigonometry is a big part of mathematics at this time because the and this is not navigators used so they can get lost in the ocean and it's also what astronomers had used for centuries a uh... we don't stitches in that we don't teach in their curtailing more but it is kind of cool stuff that really x janet and i actually went to a short course in uh... that that math meetings in san diego word this guy's trying to revive the state's trickle strong first-year coach ergonomic tree what out later did in this paper was he said we've got all these great formulas that we get from on the surface of the sphere commits them to the surface of an atmosphere right and so that's what that's really the state this doc the answer is kind uh... but the formulas get real grungy when u and move this surface of the sphereit anyway hit before you that that's the main part of the people were just gunna talk about the first five or six pages of his paper we just before he gets into the the theories he says well what we need to get some have some examples in front of us 'cause what it really had mines measure things on the surface your so the first thing he gives does is look at some of the geometry of the sphereit he's going to give a formula for the uh... radius of curvature two point on the uh... spiroedu uh... i'm not going to go into details here because this priest pretty routine calculus tough interesting thing to note though is that on he's using it as a function of this angle disappear in the stores that surface of the earth how do you know your lab what is the latitude well there's a bunch of different ways to define it one way is to on measure the angle between dizziness straight-up points in the high point on that on the celestial equator and that's different vandy and so that's and so what's and that's exactly what we have here we have busy youth line and we have the equator and that's you note that in general this is different than the line that connects the point on the surface with the center site but anyway ways to do is give a formula for the radius occur richer in terms of this uh... anecdotes latitude and golfie and i'll just put it up there for you it's it's in most calculus tax you could work out and do this if you have a small incorrect to the uh... anglesey or small change in either direction and you measure that distance in radians if you measure that angle your distance in radians then the distance on the ground is just the like that uh... of the uh... radius times that uh... small bit small incriminating for small changing it didn't matter to me more weather does business to do it suggests an algebra ii what do you guys here is that constant delta doctors talked about before which job measures basic account all the information about the shape of the looks like this in this concept delta okay the rest of this is just like how big a major how big the lips and basically so the up asides concept shape constant okay now working with native three has powers not very convenient better weather notes that uh... well you know delta is really a very small number um... so what system needs like everything after that after this first power or what does this way ridiculed and so forth expands into power series groups in his approximates that with this formula here which then me size parameter is called a andy and this is the form of that involves delta we've got some measurements here okay this is the expedition the lock onto mean expedition to peru uh... this uh... this is the expedition to them over tree expedition the lapland this is the measurement that to reconstruct believe this is a measurement victory cassini presented buchanan seventeen forty-one that's it corrected version of his father's estimate and then there's an estimate that uh... the uh... sprint just ran a very delicate ided in seventeen fifty three and that's what we know the paper has to be in after sputnik means after seventeen fifty three and actually believe it was actually presented in berlin in seventeen fifty-four uh... by the way uh... we've got this funny little on where he rocked wise withdrew the standard of length at the time may know you guys are really curious to know exactly how big it wisest and you're lucky as we know exactly i think it was it's that's cool that let's go forward to seventeen ninety five your three different republic very famous law establishes a new set of weights and measures for france uh... defines the meter to be one ten million the distance between the equator in the north pole and wanted to give parents that's great but how big is that dissidents uh... isn't team of astronomers out to figure that distance out the storm is reported back several years later guess what units they use to report the results there you go quickly so we know that uh... so we know that it was a little bit little bit less than two meters headed by legislative fiat i thought that was a cute little sidenote okay so he so we have our own we have these data that we know the latitudes and we have a bit and we have and measured like that about one degree latitude these various places living in do with this this is this is kind of the way always set things up ok well bo put up with in our little formula regis calculated using that uh... size printer and shape parameter and we can solve difficult signs so therefore equations like this we have four equations now and six i know then l required us a little bit of algebra you know he dosent subtracting dividing and comes up with the relationship between pay linear relationship between three vietnam's so far so good unni you know this is before modern statistical theory you know we would have otherwise impressions dating now that okay so we can funny thing is though now he says well you know we can assume all these errors are you call just received like that but they can't be doubted that their that considerable areas of slipped into the measurements of the degree of latitude in france the uh... carolyn easement i mean it's true that the besides that you had mentioned there are lots and lots of people going out measuring in latitudes and frances is easy to get to quit and uh... so it seems to have gotten a bad reputation by this point uh... anne you know he basically juggles if he figures around and says well we think that um... and see why that the ones that the love got a great year we said that you know the friend the friendship errors are very large and weakens and looked to me like that here is that the cape and the reason lapland you're more or less the same and then self south american air uh... is whatever's left over bosnia once we know three-tiered bikinis eligible by the fourth one two questions appeared to me at this point uh... one is how does this at how did the police figures correspond with our modern our knowledge about the shape of the year let's look at that first uh... all by the way weathered then goes undetected the major minor axes of thing spear light and finds that it's almost exactly the figure that newton cable break you almost get the impression g_g_ jugglers figures in just the right way to do this anyway um... modern theory with booking so actually we've got like millions of satellite observations now they so we have a pretty big sacked idea the change shape of the earth wenjie oddest issues is something called the delay which is you take the average sea level of every place on the earth that's the shape they were going to look at okay and uh... and this is and can actually atmosphere right nw genesis caught in the loop side even though it really is a sphereit wanted spirited analytically that's actually very close approximation shape of the earth on the biggest errors on this line this chart are about one hundred meters on there's a the big flats fought off uh... surface of uh... off the coast of india and there's some high points around u dat and but also in the north atlantic there's also it looks like the flattening is little bit bigger at the south pole man at the north pole this is actually something it whether speculated on or how do we know that the flat is the same both polls but really i mean the the scale here i don't know if you can read the scale here but you know we're talking about very small amount compared to the actual sides of the earth anyway the currently accepted dot standard international standard for them for the sphereit uh... called mpg s eighty four there is some politics involved as different countries hectic corny ternational maps and stuff like that and so that's why we started in eighty four standard i hear that by twenty twenty one one one w g f says that the here's here is the actual flattening as we know what today and shape of the earth wasn't what's even more interesting though is to carry the actual errors uh... various data that top or there had to work with turns out that i'm far from being the worst air of measurement egypt from france is actually was the best error what really is screwing things up was that what the more perch we expedition give a grossly exaggerated figure for the um... like the vet albania degree of latitude lapland there's another chart business line here is the true did length of a degree latitude and you know there's some measurements of the press corinne transmit mo perch we wasn't you want to go there yet was more per tree whereas um... way off this was not actually discover into the twentieth century ahmed up until this time you know he was giving there is seem to be seemed to be a lot more evidence than they really was worth it for you know rakesh okay so the everything we can do is take a look at or there is a data and it's not really fair to you to critique or then based on data that you may have available to him but we could take a look at uh... you know how haha lord his idea at the same saturday would be handled modern statistics so we just do a standard straightforwardly squares analysis where these very independent variables and easier unknown errors nusier errr on dependent variables if we just need to to scrape your rep regular routinely squares analysis we find that seems like a living at a pretty good feel for what they did it was really like on you know and the it turns out to be subtly square based on the data that or their had available that france and the largest error and the measurements of cape of good open it lapland were actually roughly equivalent and that's that's what you would get and that actually based on the day to the head or they had available again bed that newman's figure of one party thirty for a flattening ratio is actually pretty close to write on the tsi and i think that's about all i could have won if you want to know how to say thank you and korean so looks like we have time for some questions do there breyer perfect ridiculed show here group who'd be polluters you know something further worked hard to plan uh... interesting allowed breyer sorry and so they would be actually from that they assumed they could actually tell for part for the earth and what they know this is actually because uh... use that v this massage by living at the moon okay so that one has to be annoying reintegrate will this distance and therefore distance themselves uh... they're all walk-a-thon uh... that's it's a instruments that's impressive you know micah yeah i know a lot of the early papers that talk about the three of latitude iraq's according era toss that he's the guy that measure though dejected compare parikh it to the distance it alexandria mineral water problems there are cassidy's measurement but you we compare to do it what was available in the eighteen th that it wasn't that bad agrees white dress undergrads leaders between the north pole noted that the records with interesting predecessors there is a nice and my parts of your honor's based on the mechanical matsuo christy yesterday aunt year let's see on menus something that was kind of like a trainee admitted measure larry was a trying every measure but what you do issued you dot uh... he'd find a high point over here are like a church spire something on the top of the hill over here okay those were the first thing you had to do is they have a baseline and they did all fail kinds of crazy stuff to do that they would take it eight stick that was five it was a small inflated and and it's really got you know something like a distance of what i call on their something like that um... there's obviously some air problems there but then what they would do is from that they would they would take citing his long neck and end of the punitive the two bus stations they measured and and do a very precise correctly creation the angle you can use laws signs to calculate with it you know you know the angle you cancel our scientific that was the actual distances then so you have a whole networker these because you know if you're going one hundred co honors you not to be able to see from one end of the attic together route so they would have been tour way stations and so they do is is boost i reject the i had a picture of the stem from his original bookish about that one but now you get this whole network of bob triangles and then then he would do some he would use to duplicate triangles to make sure that he wasn't too far off in his calculations and then then there is no problem out measuring latitude so uh... lets see well i do but i did at that diagram back here let's see uh... mature progress scale it well you can you can see that ah... okay so the skill does not go down to zero seven get misled by that but you can see that ah... you know out of about a hundred thousand uh... ego okay well at barrio yeah okay so you can see out of bob what is this may be his that okay it looks to me like about a five percent a year or something like that that they would prefer the really bad cases a one perk one or two percent which is supposedly good for the equipment that they had stupid well he admitted it but i don't think that they did at this point i mean you know and being a degree ads one minute of the victory is a very small and often the man harnett howard becker with would be of heavy wooden instruments that you had to carry around and set up which set up for you and make sure you looking at it exactly right how it it will get i'm impressed that they were able to get as good of a worthless things uh... it's about one part into ninety eight uh... lissy i think i actually have been right now well portuguese earned twice that right want wise is about one point nine years one point nine four they look the same on the map will only beutler undergrads airline things well what we could play out to that plagued tightly but measurements with me for serving the american west to lay out the state lines that those surveyors are kind of uh... not blue most accurately road either there's places of the colorado war wyoming wonder looks like that yes when your stats because they're using ab there it there's a difference there is a in nineteen twenties the bad you bring a white man nineteen twenty seven eighty three they might have been using a different day didn't standard at work translating primaries trickery uh... or recited use across the street you research for tori they were all rolled yet to hear okay well thanks for all thinking overall coming