Contributions to Dynamometry. 319 



given above has changed sign, and is of greater numerical 

 value than the first term, which is necessarily positive. 



The expressions for determining the mean E.M.F. of the 

 machines are: — 



(mean e 2 ) = r 2 l D ] + r 2 3 D 3 + 2r 1 ? , 3 iD 3 ,l taking five dynamo- 

 (mean e 2 ) = r 2 2 D 2 + r 3 2 3 D 3 + 2r 2 r 3 2 D 3 , J meter-readings. 



But this can he simplified, as in the formulas for the powers, 

 thus : — 



^i=nci-f^s = n + ^i+?V2, 



e 2 = r 2 c 2 + r 3 c 3 = r 2 + r 3 c 2 +r 3 c 2 ; 

 ei 2 = n + Tz 2 ^ + r 3 2 2 D 2 + 2 . r x + r 3 . r 3 J)^ 



2 — 



= r 2 + r 3 2 D 2 + r 3 2 ^ + 2 . r 2 + r 3 . r 3 J) 2 ; 



in which expressions there are only three dynamometer- 

 readings, and these the same three as for giving the two 

 powers. 



It is clear that — r 3 c 3 c 2 is the power doing work upon the 

 second circuit ; for it is equal to —fc 2 at any moment ; 

 .'. — r 32 D 3 is the mean power expended in the second circuit. 



This is quite independent of the nature of the apparatus 

 in the second circuit, which may contain any or all of the 

 following : — 



A perfect or absorbent condenser, 



An electromagnet, 



A decomposing-cell, 



A vacuum-tube, 



A motor-circuit, 



A transformer-circuit, 



A generating- circuit, 



A welding-machine, 



A tuning-fork, or other make and break. 



Should the apparatus render it undesirable to have the 

 current c 2 passed through the dynamometer, we may write 



— *W 2 = — r 3 c 3 (c 3 — c : ) = r 3 c y c 3 —r 3 c 3 2 , 

 or Mean Power =r 3 { l D 3 — 3 D 3 }. 



It was by this means that I suggested to Mr. Swinburne he 

 might measure the dielectric hysteresis of his condensers. It 

 would only take two dynamometers, as is seen. 



