936 SCIENTIFIC NEWSL. 



of the earth were considered as very in\jiiite portions of 

 a spliere, which, in all the extent of each triangle wa« 

 confounded with the spheroid. 



Does this supposition, though less inaccurate than the 

 preceding, promise all the precision which it seems fair to- 

 expect from it ? and since it is a spheroid which is to be 

 measured, why not calculate the triangles as spheroidal ? 

 This question is so obvious that it must at once have 

 offered itself to the astronomers charged with the opera- 

 tion, and to each of the learned men, united from the 

 different parts of Europe, to examine and form a judge- 

 ment of the work which had been executed. In one of the 

 first meetings of the commission, a learned foreigner, M. 

 Tralles, remarked that the bases of Melun and Perpignan 

 could not be simply considered as arcs which should be 

 throughout in the same place, but as curves of double 

 curvature. This remark m as made by Clairaut above 

 fifty years before ; but it was always thought that tho 

 effect of the double curvature could not become even a 

 little perceptible, unless upon intervals much greater than 

 we can directly measure ; and it was concluded that con- 

 siderations of the spheroid would only add an useless de-, 

 gree of complication to calculations already too complex. 

 In fact, the spheroid differs from the sphere much less than 

 the sphere itself does from a plane. Now the sphericity 

 of the triangles does not introduce any terms into the calr 

 jpulations but those of the second order for the angles, 

 and of the third for the sides. It was therefore natural 

 to think that the terms dependant on the spheroid would- 

 be of an order more elevated, and still less sensible on ac- 

 count of their extreme minuteness. But no one yet had 

 written on the subject ; it was not to be supposed that 

 the astronomers would rest contented with vague consi- 

 derations and a simple probability. This point, they 

 inform us will be found discussed in the article *' Calcula- 

 tion of the Triangles/' in the second volume of the Meri- 

 dian, at present in the press ; in which it will be demon- 

 strated, from considerations of great simplicity and 

 elementary throughout, that the difference between the 

 (jpherjcal and spheroidal angles of the greatest of their 

 triangles, is not one sixtieth of a second, and that th^ 



doubly 



