THE SMITHSONIAN INSTITUTION. 367 



Tims the resistance of the wire of the multiplier is less tlkan one- 

 tenth that of the pile. 



Denoting the electro-motive force of the thermo-pile by E, the 

 strength of tlie current is 



S =: E _ E^ . 



18.34 -f 1.75 20' 



this is conveyed around the needle in n coils; hence the magnetic 

 effect is 



20 

 If the same mass had been drawn out into three times the length, 

 its resistance would have been 9 times as great, or 9 X 1.T5 = 15.75, 

 thus nearly equal to that of the thermo-pile. The strength of the 

 current now would be 



o/ E E . 



~ 18.8 H- 17.75 ~ 36 ' 

 and the magnetic effect 



M' = 3 71 1 = w ^ : 

 36 12 



because the current is now conveyed in 3 n coils around the needle. 

 The value M' is thus nearly double that of M. 



With the same quantity of copper wire, the multiplier for the said 

 thermo-pile could have been made twice as sensitive by drawing the 

 wire to thrice the length, so as to give it three times as many coils 

 with a section of only one-third. 



Hence there is no doubt that the reason for making the wire of this 

 multiplier too short and too thick, arose from the assumption that the 

 resistance of the thermo-pile composed of a number of metals could 

 not be great, and thus only a wire tolerably thick and not too long 

 should be selected. It is thus shown that mere conjecture will not 

 suffice in such matters. 



§ 25. Comparison of the effects of different hattcries in given cases. — 

 The strength of the current for any given case can be computed from 

 the constants of different batteries. If the resistance of the closing arc 

 is I, for a zinc and carbon battery with a mean surface of one square 

 decimetre, and using Stohrer cells with dilute sulphuric acid, the 

 strength of current is 



12 -f I 



For a Daniells element, of the same size, with sulphuric acid of the 

 same degree of dilution, the force of the current would be 



470 _ 470 



12 X 1.8 + ^ 21.6 + 1 ' 

 If Z is very small compared with the resistance of the elements, the 



strength of their currents will be to each other as -^^ to -- — , or 



12 21. t) 



as 68.6 to 21.8 ; hence the current of the zinc and carbon battery is 



