On Cohesion. 87 



Then Corollary 2d, c' b^ : d^ a'^ : : gravities of masses contain- 

 ing equal numbers of particles or gravities of [jarticles contained 

 .'.gc^ h'' : as sum of the gravities of the particles of A added 

 to every particle of B to form the compound particles of A + B 

 .'. g C' b'^-\-d^ o^ : d' a- : : gravities of ])artic!es of A + B : grav. 

 of particles of B; and (Prob. 2d), as b' c^ + d' a^ : d^ a' : : mag. 

 of the particles .'. g b^ c^ -\- d^ a^ : d^ a' : : mag. part. A + B : 



mag.part.B .-. (Prop. 3d), — — . — — -: - :: ,,■ ^. . : 1 : : 



Problem V. — The conditions being the same as in the last 

 problem, the cohesion of A + B will be to B as 



Q. E. D. 





1 + 



For Corollary 4th V g Iv c' + aUi'^ x '-'— -.da 



1. Q. E. D. 



hesions : : '+ ^ l + (gxf|' xD') 



"Examples. — Let it be retiuired to find the ratios of the mag- 

 nitudes and gravities of the conijjonent particles of lead and tin, 

 and the weights of masses containing ecjual numbers of particles. 

 The specific gravity of lead being 1 l-y.V2.'), its cohesion 29-25, 

 and the spec, gravity of tin 7"29H, its cohesion 49*25. 



Here a :/-:: 11-.3523 : 7-2914. Log. 2925 =l-46(;i3 



c :f/: : 29-25 : 49-25. Log. 7-2914 = 0-86279 



Log. cb =2-32892 



Log. 11-3523=1-05500 _3 



Log. 49-25 =1-692 14 Log. c' ^-' = 6 98676 



Log. ad =2-74714 



3 



Log. a' b^ =8-24142 



As Log. c5 b^ : Log. a' d' : : G-9^676 : S-24142 : : Log. I : 

 Log. 17.97 .-. c' Zi' : a' J' : : 1 : 17-97 : : magnitude particles of 

 lead to magnitude particles of tin. (Prop. 1st.) 



F4 3x 



