On Cohesion. 85 



the operation mav be carried on ad hifinilnm till the ultimate 

 particles of each are placed together. 



Let it be granted : 

 1st. That orravity and cohesion are effects of the same power fol- 

 lowing the same law ; i. e. diminishing as the square of the 

 distance increases. 

 2d. That the particles of bodies are of different densities and 



magnitudes, and consequently of different gravities. 

 3d. That if two primary particles of matter, the attraction at the 

 surface of one of which is greater than the attraction at the 

 surface of the other, be brought within the sphere of the 

 attraction of each other's particles, the two particles will 

 combine and form one compound spherical particle. 

 4th. That the gravity of the wliole is equal to the sum of the 

 gravities of its component particles. 

 Let a : ^ as the gravities of two equal masses A and B. 

 c : (i as the cohesion of A : cohesion ot B. Then 

 Proklem \. — The magnitudes of the particles of A are to 

 those of D as (/r c^) to (a^ d^). 



Let X : y as magnitudes of particles. 



Then — : — : : the numbers of particles, the masses A and B 



X y 



being equal a-. -.1-. : : ax -.h y : : The gravities of the 



particles (Ax. 4th.); that is, as the quantities of matter they con- 

 tain. V ^ '-y/y '• '• diameter of x : diam. y : '• — r • ~T • * "^uares 

 of diameters inversely .'. -^ : -^ : : a iyf x : h .'^ y : : the at- 



traction at the surface of x : tlie attraction at the surface of y 

 and the number of particles exerting this attraction on any one 

 particle being under all circumstances the same; viz. 9 : : c : d 



.'. ^x : ^y : : be -.ad, and as x : y : : ^' c' : a' dK Q. fi. l>. 



Corollary 1st. — The numbers of |)articles contained A and B 



I I 

 are as •— - : — . 



Corollary 2d. — The gravities of the particles of equal masses, 

 or the gravities of wholes containing equal tmmbcrs of particles, 



are as a-^—— : b~- — - : : cH' : d^ a'. 



Corollary .'Jd. — The diameters of particles as he : ad. 



Corollary 4th. — The cohesions are as the specific gravities of 

 wholes inullij)lied into the diameters of the ])articles. 



Puonf.KM II. — If any number of particles of the mass A be 



presented to an ecpial mmibcr of particles of the mass B, so that 



the particles of A and B may attract one another, and form other 



' F ',i compound 



