36 G TENTH ANNUAL REPORT OF 



Hence, witli a massj? times as great, the wire mu3t have a length 

 yj f times as great, and a diameter ^ y/ p times; the resistance re- 

 maining invariable. 



The mass of copper to he disposed of is 51.7 times as great as that 

 of a normal wire which oifers the same resistance as the elements ; 

 hence, we mnst make of this mass, a wire which is -/Sl.T^T.lS 



times as long, and * V 51.7 = 2.68 times as thick as the normal wire, 

 11.1 metres long. Thus, if the eight pounds of copper wire is to op- 

 pose the same resistance as the Daniell's element, it must he 2.68 milli- 

 metres thick, thus requiring a length of 7.18 X 11.1 = 79.7 metres. 



If the electro-magnet is to he arranged for a Stohrer's element, 

 whose essential resistance is equal to that of 6. 2 metres of the normal 

 Avire, for the same reason, the eight pounds of copper must he a wire 

 3.1 millimetres thick ; which requires a length of 60 metres. 



Using the electro-magnet constructed for Daniell's battery, with 

 this battery, the strength of the current is 



E E 



or 



11.1 -I- 11.1 22.2. 



The wire being placed in n coils about the iron, the magnetic effect 

 may be denoted by 



22.2. 

 Had the wire been twice as long, and consequently one-half in sec- 

 tion, its resistance would have been four times as great, or 44.4, and 

 the strength of the current 



E E 



or 



11.1 + 44.4 55.5; 



but this is passed around the iron in 2 n coils, and the magnetic effect 

 is now 



27.7 



If a wire half as long but double in section had been used, the mag- 

 netic effect would have been 



13.9 27.8 



Thus it is seen that the values of M' and M" are less than that of M. 



According to these principles, we can also determine how, with a given 

 thermo-electric battery, a multiplier of the greatest possible sensibility 

 may be constructed — a question which was solved theoretically long 

 since, but until now the solution has not had a form susceptible of 

 practical application. On this account we shall give this subject some 

 further consideration. 



For instance, our physical cabinet possesses a tJiermo- electric pile 

 with the galvanometer belonging to it. I found the 



Resistance of the thermo-pile =18.34 met. of normal wire. 



" " wire of multiplier = 1.75 '' ^' 



