Contributions to Dynamometry . 347 



nature of the physical quantity indicated by the reading of a 

 dynamometer, or the angle through which the torsion-head is 

 turned to bring the coils into a standard relative position, 

 which is usually, but not necessarily, one in which the coils 

 are at right angles one to the other. That position has the 

 advantage of introducing no mutual induction in the instru- 

 ment itself. 

 Expressed mathematically, the reading measures the quantity 



T 



if 



C&dt; 



where C 1 and C 2 are the currents at a moment through the 

 two coils, those currents being periodic or constant (one may 

 be constant, the other periodic), and T being an interval of 

 time at least equal to the least common measure of the periods, 

 and so small that the index is not able to move appreciably 

 in the interval T. The larger the moment of inertia of the 

 moving coil, the greater the limit which may be allowed to T. 



In the year 1&85, when I first suggested sending different 

 currents through the two coils of such an instrument, I called 

 a reading taken under such circumstances the " force-reading," 

 to distinguish it from an ordinary dynamometer-reading in 

 the usual case of the currents being identical in the two coils. 

 That name was suggested by the fact that (current) 2 has for 

 its structural formula in the electromagnetic system the same 

 dimensions as force, omitting the dimension of permeability. 

 This fact is shown in Sir W. Thomsons so-called current- 

 balances, where (current) 2 is made to produce equilibrium 

 with a force. 



But (current) 2 has another more important meaning. When 

 multiplied by resistance, it means power, and therefore by 

 itself it means power per unit of resistance ; and this is its 

 true meaning independently of permeability. The dynamo- 

 meter-reading is the mean poicer per unit of resistance. 



If, therefore, we know the proper resistance to multiply 

 the dynamometer-reading by, we shall be in possession of the 

 value of the power ; and it follows that appropriate dynamo- 

 meter-readings must be of extreme value in measuring power. 



It will thus be seen that if the physical quantity Z can be 

 expressed for its momentary value in terms quadratic in the 

 instantaneous currents, these terms will point out to us the 

 appropriate places for dynamometers whose readings, being 

 filled in in the places of those quadratic expressions, will give 

 us the mean value of (Z) . To make this perfectly clear : — 



