Jt. S. Woodward -Mathematical Theories of the Earth. 339 



the point was definitely settled by Maupertuis' measurement of 

 the Lapland arc. For this achievement his name has become 

 famous in literature as well as in science, for his friend Vol- 

 taire congratulated him on having " flattened the poles and the 

 Cassinis" and Carlyle has honored him with the title of 

 "Earth-flattener."* 



Since the settlement of the question of the form, progress to- 

 ward a knowledge of the size of the earth has been consistent 

 and steady, until now it may be said that there are few objects 

 with which we have to deal whose dimensions are so well 

 known as the dimensions of the earth. But this is a popular 

 statement, and like most such, needs to be explained in order 

 not to be misunderstood. Both the size and shape of the earth 

 are defined by the lengths of its equatorial and polar axes ; and, 

 knowing the fact of the oblate spheroidal form, the lengths of 

 the axes may be found within narrow limits from simple 

 measurements conducted on the surface, quite independently 

 of any knowledge of the interior constitution of the earth. It 

 is evident in fact, without recourse to mathematical details, 

 that the length of any arc, as a degree of latitude or longitude, 

 on the earth's surface, must depend on the lengths of those 

 axes. Conversely, it is plain that the measurement of such an 

 arc on the surface and the determination of its geographical 

 position constitute an indirect measurement of the axes Hence 

 it has happened that scientific as distinguished from practical 

 geodesy has been concerned chiefly with such linear and astro- 

 nomical measurements, and the zeal with which this work has 

 been pursued is attested by triangulations on every continent. 

 Passing over the earlier determinations as of historical interest 

 only, all of the really trustworthy approximations to the lengths 

 of the axes have been made within the half century just passed. 

 The first to appear of these approximations were the well 

 founded values of Airy, published in 1830. f These, however, 

 were almost wholly overshadowed and supplanted eleven years 

 later by the values of Bessell \ whose spheroid came to occupy 

 a most conspicuous place in geodesy for more than a quarter 

 of a century. Knowing as we now do that Bessel's values 

 were considerably in error, it seems not a little remarkable that 

 they should have been so long accepted without serious ques- 

 tion. One obvious reason-is found in the fact that a considera- 

 ble lapse of time was essential for the accumulation of new 

 data, but two other possible reasons of a different character 

 are worthy of notice because they are interesting and instruc- 



* Todhunter, History of the Theories of Attraction and the Figure of the Earth, 

 London), 1873, Vol. 1, Art. 195. 

 f Kncyclopedia Metropolitana. 

 % Astronomische Nachrichten, No. 438, 1841. 



