ikct.iv.] DISSERTATION SKCOND. 03 



resume the subject of the moon's motion; and the mea- 

 sure of a degree by Norwood having now furnished more 

 exact data, he found that his calculation gave the pre- 

 cise quantity for the moon's momentary deflection from 

 the tangent of her orbit, which was deduced from astro- 

 nomical observation. The moon, therefore, has a ten- 

 dency to descend toward the earth from the same cause 

 that a stone at its surface has ; and if the descent of the 

 stone in a second be diminished in the ratio of 1 to 

 3600, it will give the quantity by which the moon de- 

 scends in a second, below the tangent to her orbit, and 

 thus is obtained an experimental proof of the fact, that 

 gravity decreases as the square of the distance increa- 

 ses, lie had already found that the times of the plane- 

 tary revolutions, supposing their orbits to be circular, 

 led to the same conclusion ; and he now proceeded, 

 with a view to the solution of Hooke's problem, to in- 

 quire what their orbits must be, supposing the centripetal 

 force to be inversely as the square of the distance, and 

 the initial or projectile force to be any whatsoever. On 

 this subject Pemberton says, he composed (as he calls it) 

 a dozen propositions, which probably were the same with 

 those in the beginning of the Principia, — such as the de- 

 scription of equal areas in equal times, about the centre 

 of force, and the elipticity of the orbits described under 

 the influence of a centripetal force that varied invers 

 as the square of the distances. 



What seems very difiicult to be explained is, that, 

 after having made trial of his strength, and of the power 

 of the instruments of investigation which he was now in 

 possession of, and had entered by means of them on the 

 noblest and most magnificent field of investigation that 

 was ever yet opened to any of the human race, he again 

 desisted from the pursuit, so that it was not till srv 



