338 Mr. J. J. Waterston on the Integral of Gravitation, 



§11. 



The condition of a system having both a rotatory and rectilinael 

 motion demonstrates the absurdity of assuming the motion of 

 a body to be proportional to its velocity. 



In the 31st Query of Newton's 'Optics' (vol. iv. p. 258, 

 Horsley's edition), the following occurs : — " From the various 

 composition of two motions, it is very certain that there is not 

 always the same quantity of motion in the world. For if two 

 globes joined by a slender rod revolve about their common centre 

 of gravity with a uniform motion, while that centre moves on 

 uniformly in a right line drawn in the plane of their circular 

 motion, the sum of the motions of the two globes, as often as 

 the globes are in the right line described by their common centre 

 of gravity, will be bigger than the sum of their motions when 

 they are in a line pei'pendicular to that line. By this instance, 

 it appears that motion may be got or lost. But by reason of 

 the tenacity of fluids and attrition of their parts, and the weak- 

 ness of elasticity in solids, motion is much more apt to be lost 

 than got, and is always upon the decay." 



This extract is remarkable as showing the obstinate influence 

 of a preconceived notion upon a powerful intellect. The alter- 

 nate appearance and disappearance of motion in connected globes 

 did not seem to Newton inconsistent with any of the laws of 

 motion previously laid down in his 'Principia.' Let us view a 

 numerical example. The globes suppose to be equal and to move 

 with a circular velocity of 3, and the common centre of gravity 

 with a rectilineal velocity of 4. As often as the globes are in a 

 line perpendicular to the line described by the centre of gravity, 

 the absolute velocity of one is 7, and of the other ], making 

 the sum of their motions 8. As often as the globes are in 

 the i-ight line described by the common centre of gravity, the 

 absolute velocity of each is 5, making the sum of their motions 

 10. From the first to the second position, the motion in one has 

 diminished from 7 to 5, losing 3, and the motion of the other 

 has increased from 1 to 5, gaining 4. Hence not only has the 

 2 been transferred from the one globe to the other, but another 2 

 has been supplied. There is an intermittent augmentation and 

 diminution of motion ; and as by the second law of motion 

 ''the alteration of motion is ever proportional to the motive 

 force impressed, and is made in the dii-ection of the right line in 

 which that force is impressed," it comes to pass, that, by giving 

 motion to the centre of gravity of two revolving balls in the 

 plane of revolution, we introduce the action of a tangential force; 

 but if the same rootioa is given ia a direction perpendicular to 



