406 HISTORY OF PHYSICAL ASTRONOMY. 



fleeted from a rectilinear motion, and retained in her orbit." The 

 proof consists in the numerical calculation, of which he only gives the 

 elements, and points out the method ; but we may observe, that no 

 small degree of knowledge of the way in which astronomers had ob- 

 tained these elements, and judgment in selecting among them, were 

 necessarv : thus, the mean distance of the moon had been made as lit- 

 tie as fifty-six and a half semidiameters of the earth by Tycho, and as 

 much as sixty-two and a half by Kircher : Newton gives good reasons 

 for adopting sixty-one. 



The term " gravity," and the expression " to gravitate," which, as 

 we have just seen, Newton uses of the moon, were to receive a still 

 wider application in consequence of his discoveries ; but in order to 

 make this extension clearer, we consider it as a separate step. 



4. Mutual Attraction of all the Celestial Bodies. — If the preceding 

 parts of the discovery of gravitation were comparatively easy to con- 

 jecture, and difficult to prove, this was much more the case with the 

 part of which we have now to speak, the attraction of other bodies, 

 besides the central ones, upon the planets and satellites. If the math- 

 ematical calculation of the unmixed effect of a central force required 

 transcendent talents, how much must the difficulty be increased, when 

 other influences prevented those first results from being accurately ver- 

 ified, while the deviations from accuracy were far more complex than 

 the original action ! If it had not been that these deviations, though 

 surprisingly numerous and complicated in their nature, were vary 

 small in their quantity, it would have been impossible for the intellect 

 of man to deal with the subject ; as it was, the struggle with its diffi- 

 culties is even now a matter of wonder. 



The conjecture that there is some mutual action of the planets, had 

 been put forth by Hooke in his Attempt to prove the Motion of the 

 Earth (16 74). It followed, he said, from his doctrine, that not only 

 the sun and moon act upon the course and motion of the earth, 

 but that Mercury, Venus, Mars, Jupiter, and Saturn, have also, by their 

 attractive power, a considerable influence upon the motion of the earth, 

 and the earth in like manner powerfully affects the motions of those 

 bodies. And Borelli, in attempting to form " theories" of the satellites 

 of Jupiter, had seen, though dimly and confusedly, the probability that 

 the sun would disturb the motions of these bodies. Thus he says 

 (cap. 14), "How can we believe that the Medicean globes are not, 

 like other planets, impelled with a greater velocity when they approach 

 the sun : and thus they are acted upon by two moving forces, one of 



