190 CELESTIAL MEASURINGS AND WEIGHINGS. 



calculation of the sides of the triangles, considered as lying 

 not on a plane, but on a spherical surface, and ultimately 

 (as we shall see) on a spheroidal one. It is not our 

 object to dwell on these details, or to describe more 

 minutely any one of the many operations of the kind 

 which have been carried out or are still in progress in 

 France, England, America, Prussia, Austria, Italy (but 

 more especially and on the vastest scale in the Russian 

 and in our own Indian Empire), and in the southern 

 hemisphere at the Cape of Good Hope. We are only 

 concerned here with the final conclusions arrived at, and 

 with the reasons on which they rest, and these are : 



i st. The length of a degree of the meridian, in what- 

 ever region of the earth it is measured, is very nearly the 

 same, nowhere varying from a general average by more 

 than about one 2ooth part of its amount. And from 

 this it follows that the figure of the earth approaches 

 exceedingly near to that of an exact sphere. For the 

 length of such a degree is a measure of the curvature of 

 the surface, it being evident that were any one to travel 

 southward till the meridian altitude of a star was 

 increased by one degree, he must have arrived at a 

 place where the surface on which he stands is just 

 one degree inclined to that at his starting point : so that 

 in walking on he is at that moment pursuing a course 

 deviating by one degree from the direction of his outset. 

 Now this deviation from a straight course is our idea of 

 curvature. The curvature of each geographical meridian 

 then is very nearly the same everywhere. In other 

 words, the earth is very nearly a sphere. The average 



