578 



NATURE 



{Sept. 26, 1878 



the length to be 57037 toises ; and if this measurement was not 

 carried out with the greatest care, since Lacaille could only 

 devote two months to it, yet it was so far of no small import- 

 ance, that it was the first which had been effected in the 

 southern hemisphere. In the years 1751-53, Boscovich and Le 

 Maire carried out a triangulation in the States of the Church, 

 in 40° N. lat., and found the length of the degree to be 

 56973 toises. A degree-measurement made in the plains of 

 Turin in 1768, between Andrate and Mondovi, gave for 44° 44', 

 N. lat, a degree length of 57024 toises. Mention should be 

 made also of a series of extended measurements in Austria ; 

 and we may remark that most of the operations above re- 

 ferred to, as well as some of the following, were undertaken at 

 Boscovich's instigation, while the Austrian operations were 

 initiated and carried out by the Jesuit Liesganig. He found the 

 length of a degree for N. lat. 48° 43' to be 57086 toises, and 

 for 45° 57', 56881 toises. It may be seen from a comparison of 

 these two values that, notwithstanding the small difference of 

 latitude, they indicate a flattening at the poles, and if the calcula- 

 tion based upon these values alone give an anomalous result, it 

 must be ascribed to the much too small difference of latitude. 

 Indeed, errors of measurement were subsequently found in them. 

 Finally we have to mention as belonging to this period the 

 measurements after the old method which were carried out by 

 direct measurement of a long meridian distance by means of a 

 surveyor's chain. The one was in America, on the plains of 

 Pennsylvania, by Mason and Dixon 1 over a distance of i| degree, 

 and it gave, in N. lat 39° il' 56", 56888 toises for the degree- 

 length. The second measurement 'of this kind was in Beng^ in 

 1790, by Burrow and Dalby, and it resulted in giving 56725 

 toises as the length of degree in N. lat. 23° 18'. 



During the first forty years of the latter half of the eighteenth 

 century a great number of geodetic operations were undertaken 

 in various parts of the earth, and it was sought by various com- 

 binations of these measurements to ascertain the amount of polar 

 flattening ; but it was soon found that, with the exception of the 

 Peruvian vmdertaking, they were too full of errors to yield a 

 satisfactory result. The scientific men of that time soon became 

 convinced of this drawback, and efforts were made by various 

 academies not only to discover improved methods of measure- 

 ment, but also by offering prizes to induce mechanics to perfect 

 instruments, more especially the chronometer, so indispensable to 

 astronomical observations. Both courses were followed with good 

 results, and by English mechanics especially astronomical and 

 geodetic instruments of measvirement were brought to a high degree 

 of perfection. 



Strange though it may seem, France, with her revolutionary 

 troubles coming fast upon her, was the first to commence the 

 subsequent highly accurate geodetic operations. The multi- 

 plicity of units of measure had at this time reached its ne plus 

 ultra. Not only each little territory, each separate province, 

 but often each town had its own peculiar measure of length ; 

 and the case was nearly as bad with regard to weight, endless 

 difficulties and disputes being the result. It was first resolved 

 in 1790, in the French National Assembly, to come to an under- 

 standing with England on the length of the seconds pendulum, 

 but after a year the French savants declared that, seeing that the 

 seconds pendulum would be of different lengths at different parts 

 of the earth, it would be more advantageous to adopt a given 

 measure of the earth itself as unity, and that as such the ten- 

 millionth part of the earth's quadrant should be taken. But, to 

 settle this point definitely, it was necessary to measure a long arc 

 of meridian with the greatest possible accuracy, and accordingly, 

 March 30, 1791, it was decided to measure the meridian arc 

 between Dunkirk and Barcelona, from which the length of the 

 quadrant and its ten- millionth part, the metre, could be inferred. 

 After the length of the seconds pendulum in France had been 

 accurately observed, measuring operations were at once com- 

 menced, and thus began the great geodetic operation in France, 

 afterwards carried on to the Balearic Isles, and in our own time 

 but little surpassed. Notwithstanding revolutionary storms the 

 operations were carried on and with unvarying accuracy. This 

 measurement, effected by the method of triangulation, consisted 

 of 1 20 triangles, connecting the two points Dunkirk and Montjouy, 

 near Barcelona. The length of the arc between the two points 

 was found to be 551584 toises. 



There were also three intermediate points determined astro- 

 nomically, and in order that the amount of the earth's oblateness 

 might be inferred from this measurement alone, on Mechain's 



The measurement by Mason and Dixon was made with deal rods. 



representation it was carried to the Balearic Isles, and thus the 

 middle point of the measured arc coincided approximately with 

 the middle point of the earth's quadrant. This extension was 

 carried out in the years i8o6-8 by Biot and Arago. The 

 entire measured arc had now an amplitude of 12° 22' 13 '44", 

 the length being 705, 188 "8 toises, and the final result for the 

 length of a meridian degree at 45° N. lat. was 57047 toises. 

 It is characteristic of that time that in order to obtain the 

 length of the metre, the conclusion of this measurement, which 

 was undertaken for this purpose, was not waited for; but a 

 preliminary metre measure was obtained from the results of 

 the Peruvian, the Lapland, and the old French measurements, 

 equal to 443 '443 lines of the toise of Peru. As the results 

 of the first-measured distance, Dunkirk to Barcelona, were 

 known in 1797, the length was changed to 443*296 lines, and 

 two platinum rods of that length (at a temperature of 0° C. ) 

 were prepared as standard measure, one of which was deposited 

 in the Archives of the Republic, and the other in the Paris 

 Observatory ; two copies of these in steel served as the normal 

 measure. On December 10, 1799, the Metre was instated as 

 the legal measure in France, while in England the length of the 

 seconds pendulum in the latitude of London remained as the 

 unit of measure.^ But the original object of the great French 

 degree measurement, to obtain a natural measure of length, was 

 not attained, and It Is erroneous to Imagine that the metre is in 

 reality exactly the ten-millionth part of the earth's quadrant ; for 

 the length of the metre was. In subsequent degree measurements, 

 ascertained more accurately and differently. But what was then 

 attained was more accurate information as to the extent of the 

 earth's oblateness. 



Simultaneously with these French operations was the measure- 

 ment of a degree In England, which was carried out with extreme 

 accuracy In the year 1 784, with the view of a general triangula- 

 tion of the country ; the measurements were made by Gen. Roy, 

 with an accuracy not previously attained. While the angles were 

 observed with theodolites constructed with the greatest accuracy, 

 Roy effected the measurement of a base line with long glass tubes. 

 Again, in the years 1800-2, was a similar geodetic operation 

 undertaken, for the purpose of measuring a degree ; the result 

 was that for latitude 51° 20' 54" the length of the degree was 

 found to be 57180 toises, and for 52° 50' 29"-8, 57017 toises 

 The great elliptlclty of the earth resulting from these numbers 

 gave rise to the Idea that the measurements were Inaccurate ; 

 but It was considered later on that mountain-masses must have 

 exercised a disturbing influence on the plummet, and that the 

 error must be due to this cause. In the years 1801-3 a new 

 degree measurement under the polar circle was carried out by 

 Svanberg and Ofverbom, the results of which, determined with 

 great care, proved the inaccuracy of the earlier Lapland measure- 

 ments by Maupertuis. For lat. 66° 20' 12" the length of the 

 degree was found to be 57209 toises. The operations of Major 

 Lambton In the East Indies, not hitherto surpassed In extent, 

 were begun In 1802, and, as the final result, the length of the 

 degree was found in four different places between 8° and 18° 

 N. lat. 



After so great a series of degree measurements obtained at so 

 many different parts of the earth, it was now endeavoured, 

 on the strictest mathematical principles, to submit thetn all to 

 calculation and test their accuracy. The result was that the 

 great French, the second north polar measurement, and the last 

 measurement carried out in England, were shown to be of such a 

 degree of accuracy as was needed to permit of a certain deter- 

 mination of the figure of the earth. All other measurements had 

 to be cast aside as Inadequate ; In most of them the sources of 

 error were pointed out, and the degree of accuracy noted, but as 

 factors in the working-out of the final results, they could not 

 stand. In the majority of the measurements of the latter kind 

 the sources of error belonged mainly to two classes. The one 

 was the rude, unsatisfactory construction of the geodetic instru- 

 ments ; the other concerned the astronomical part of the opera- 

 tion, and consisted not only In the want of accuracy in the 

 instruments, but chiefly — and this reproach touched the greater 

 part of the savants concerned — in the ignorance of the use of 

 astronomical instruments, for of the majority It Is certain that 

 before they began their geodetic measurements, they never had 

 an astronomical Instrument In their hands. 



I The seconds pendulum never was ttie unit of length in England. But! 

 in the Act of 1824 legalising the " standard yard," reference is made to the! 

 seconds pendulum, and the length of the latter (vibrating in London) is gsvev" 

 in inches of the standard yard, with the intention that should the standard 

 yard be destroyed, it might through the seconds pendulum be restored. 



