MISCELLANEOUS EX 



\\'hercforc t: lion 



?-*>.- A' 5/A -f ...... =0 



will n.'t involve/^, the molecular aeti<>n between tli 



se co-ordinates arc ,, y,, z, and a? t , y f , e t respectively. 



vs readily from what we. have shewn, tl 

 all tl, -us similar to (4) and (5), and add them to 



we shall have a final equation 



independent of the molecular forces. 

 In like manner we should obtain 



Moreover we can shew that these six equations are the only 

 equations free from the molecular forces, supposing the 

 to be rigid, and consequently the molecules to retain their 

 mutual distances invariable. For if a body consist of : 

 molecules, there must evidently be three independent i 

 cular forces to keep them invariable; if to thes mole- 



cules a fourth be added, we must introduce three new forces 

 to hold it to the others; if we add a fifth molecule we must 

 introduce three forces to hold this invariably to any three of 

 those which are already rigidly connected; and so on; from 

 which we sec that there must be at least 3 -f 3 (n 3) or '.'>. 

 forces. Hence the 3n equations resembling (1), (2), and 

 contain at least 3n 6 independent quant it is to heclimii'. 

 and therefore there cannot be more than six equations of 

 dition connecting the external forces and the co-ordinates of 

 their points of application. 



MISCELLANEOUS KX AMPI 



1. Determine the central axis when tip -iv arc two f 



I Q whose lines of action are defined by z = c, y = x tan , 

 and z = c,y = x tan a respectively. 



