246 HISTORY OF SCIENCE. 



of the base which he has employed to measure the heavens shows him 

 his own greatness. Let us carefully preserve, and let us increase the 

 treasures of this lofty knowledge, the delight of thinking beings. It 

 has rendered important service to navigation and geography ; but its 

 greatest service consists in having dissipated the fears produced by 

 celestial phenomena, and in having destroyed the errors arising from 

 ignorance of our true relation to nature fears and errors which would 

 soon repeople the gloom were the torch of science extinguished. 



In some such words as the foregoing does one of the greatest astro- 

 nomers of the eighteenth century vindicate the position of his science ; 

 and his expressions are fully justified by the grandeur of the results 

 attained by astronomical science in the peiiod upon which we are now 

 to enter. Of all the sciences, astronomy is that which always has soonest 

 and most deeply influenced man's conception of the universe and of his 

 relation to it, and there is, therefore, a certain fitness in giving it the 

 precedence. Its progress, however, has not been and can never be 

 independent of other branches of knowledge. Two causes of the ra- 

 pidity of this progress in the eighteenth century are obvious in first, 

 the great increase of the powers of mathematical analysis ; and, second, 

 the marked improvement in instruments of observation and measure- 

 ment. Some of these improvements will be mentioned here as we 

 proceed, and some discoveries which bear upon the construction of 

 astronomical instruments will be named afterwards in connection with 

 general physics. 



The first datum for all astronomical calculation is a correct determi- 

 nation of the figure of the earth. We have already seen (p. 197) how 

 Newton's grand idea of gravitation had to wait for its verification and 

 development for a more correct estimate of the earth's magnitude, and 

 had this not been forthcoming, he would probably have laid aside his 

 speculation for ever. No sooner had Picard completed his measure- 

 ment of a degree than the French Academy of Sciences resolved on ex- 

 tending the operation by measuring a prolongation of the arc in both 

 directions. The measurements were commenced in the latter part of 

 the seventeenth century, but it was not until 1718 that the operations 

 were completed, after Picard, La Hire, Dominic and Jacques Cassini 

 had taken part in them. The results indicated that a degree measures 

 on the earth's surface a shorter distance as it is nearer the pole, and 

 at first Cassini supposed that this was consistent with the assumed 

 flattening of the earth at the poles. It was soon pointed out, however, 

 that if these measures were correct, the earth must be elongated at the 

 poles, contrary to the theory of gravitation. That the flattening of the 

 earth's poles would cause the degrees to be longer towards the poles 

 may be understood by referring to Fig. 119, where b a D A B represents 

 a section of the earth though its axis (with the amount of the ellipticity 

 much exaggerated). The part about the pole A B coincides in curva- 

 ture with the circle E A B F, which has its centre at c. Similarly the 



