100 



cube of the radius. That is, in a sphere of two feet radius, 

 there could exist only twice as many layers, not eight times 

 as many, as in a sphere of one foot radius. So. the author's 

 necessary law of repulsion should be propounded thus — 

 directly as the quantity of matter and inversely as the dis- 

 tance. 



Again on p. 153, he endeavors to deduce the law of the 

 attraction of matter, which is commonly known as the law 

 of gravitation. According to his very peculiar reasoning, 

 this attraction is directly as the area of a section of the 

 sphere or the square of the radius. But such a result is 

 entirely at variance with the induction of Newton, and if 

 true would prove fatal to the stability of the solar system. 

 From numberless computations and deductions it has been 

 proved, that a spherical body attracts not as the square of 

 its radius, but as its mass, which in homogeneous bodies 

 varies as the cube of the radius. His estimate of the rate 

 of decrease of this force is equally unfortunate. He says, 

 speaking of a section of the sphere ; u Any concentric cir- 

 cle in this area is diminished in attraction in proportion to 

 the number of concentric circles that may be made between 

 it and the centre, that is in proportion to the square of the 

 radius of itself." But it is plain that the number of con- 

 centric circles between any circle and the centre must in- 

 crease as the radius and not as its square. 



But admit that the author has proved what he enunciates, 

 namely, that the attraction upon any particle must vary di- 

 rectly as the mass and inversely as the square of the dis- 

 tance ; and that the repulsion must vary directly as the mass 

 and inversely as the cube of the distance. Suppose a sphere 



whose centre is C and its mass M; and let 

 ' P denote a molecule of matter at a distance 

 D from the centre. Denote the attraction 

 of the sphere upon this molecule by A, and 

 the repulsion by R. Then, according to 



