Contributions to Dynamometry. 353 



Then 



_ dS x dN 2 dN 3 n 



' n dt 



'" 2 dt 





= cir ± ; 



dN 2 



2 dt 



= c 2 r 2 ; 





= c s r 3 ; 



&c. &c. 

 ... E = CR+ ^ Vl + ^c 2 r 2 + -Vs + Ac. 



W! « 2 ^3 



The square of this will be quadratic in c, and the terms will 

 indicate the proper places for dynamometers. The total 

 power is 



EC = C 2 R + r 1 - l Cc 1 + /- 2 ^C C2 + &c. 

 wj, n 2 



The first term heats the primary, and each succeeding term 

 indicates the power employed in heating a secondary and a 

 core corresponding with it. Both in this case and in the case 

 of parallel transformers it appears that the power heating the 

 core and its secondary is indicated by one dynamometer-reading 

 alone, one coil being in the primary and the other in the 

 secondary; the reading requiring multiplication by the ratio 

 of the coil-turns in the primary to those in the secondary, and 

 by the secondary resistance ; i. e. this power 



m _ 

 = r 2 .- jDa. 

 n 



Does not this indicate the direction which efforts should take 

 to effect a really fair mode of measuring Electrical Energy 

 supplied ? 



In some cases a single instrument might be used, even if the 

 formula indicated two terms, to obtain the required measure- 

 ment. Suppose, for instance, that the formula had two terms 

 (ci— CiC 2 ). This may be written Ci{c x — c 2 ); and it is clear 

 that if we had two fixed similar coils both in one plane, and 

 made to carry Ci and c 2 reversed, respectively, and if the movable 

 coil were made to carry c l7 then the indications of the instru- 

 ment would give the required measurement. It might be 

 possible to multiply such coils, and vary their turns and posi- 

 tion so as to meet any case, if desirable. The method is 

 merely indicated here. 



