THE SMITHSONIAN INSTITUTION. 



361 



5tli combination is 0.6G6 



fith do 0.375 



Tth do 0.166 



8th do 0.046 



If the resistance of the given circuit is less than 0.1 of the resistance 

 of an element, the least combination must be selected ; but if greater 

 than that of 15 elements, the first must be chosen. If the resistance 

 to be overcome lies between 15 and 4.3, between 4.3 and 2, between 2 

 and 1.08, &c., the selection must fall upon the 2d, 3d, 4th, &c., com- 

 binations respectively. 



We have yet to prove the foregoing proposition. 

 Considering the dilTerent combinations of 24 elements, as repre- 

 sented in Fig. 14, it is easily seen that if the pile be shortened, it 



rig. 15. 



m. 





^imiiEQTs 



TTTTT 



becomes broad in the same proportion ; that is, if fewer elements be 

 placed one after the other, we can, by using the same number of de- 

 ments, place more of them beside each other, in the same proportion. 

 . Commencing with the second combination, we have here 12 double 

 elements. If we reduce the length of the pile by one-half, or to 6., 



