87 



former, and the gra?ity of one planer t is quadruple 

 to that of any other, which is at double the distance. 

 In general to bring a musical string into unison with 

 one of the same kind, shorter thao itself, its tension 

 ought to be increased in proportion as the square 

 of its length exceeds that of the other, and that the 

 gravity of any planet may become equal to that of 

 any other nearer the sun, it ought to be increased 

 in proportion as the square of Us distance exceeds 

 that of the other. If, therefore, we should suppose 

 musical strings stretched from the sun to each of the 

 planets, it \tould be necessary, in order to bring them 

 all to unison, to augment or diminish their tensions, 

 in the very same proportion as would be requisite t& 

 render the planets themselves equal in gravity. And 

 this, in all likelihood, gave foundation for the reports, 

 that Pythagoras drew his doctrine of harmony from 

 the spheres." 



12. Before I finish this chapter, I must not ne- 

 glect to insert a passage of Galileo's, wherein he ac- 

 knowledges, that he owes to Plato his first idea of 

 the method of determining, how the different degrees 

 of velocity ought to produce that uniformity of 

 motion discernible in the revolutions of the heavenly 

 bodies. His account is, u Plato being of opinion, 

 that no nioveable thing could pass from a state of 

 rest, to any determinate degree of velocity, so as 

 perpetually and equally to remain in it, without first 

 passing through all the inferior degrees of celerity 

 or retardation, concludes, thence^ that Goii, after 

 having created the celestial bodies, determining to 

 assign to tacha particular degree of celerity in which 

 they should always move, impressed upon them, when 

 he drew them from a state of rest, such a force as 

 made them run through their assigned spaces, in that 

 natural and direct way wherein we see the bodies 

 around us pass from rest into motion, by a continual 

 and successive acceleration. And 'he adds, that hav- 

 iug brought them to that degree of motion, wherein 



