524 Prof. R. Clausius on the Transmission of 



If we divide the two equations into one another, we get in the 

 first place 



%_v^ 7 R + 3 



and if in this we develop the fraction containing the magni- 

 tude 7, in powers of 7, disregarding members of higher degree 

 than the first, because y contains the factors a and X, of which 

 the higher powers have already been disregarded in previous 

 calculations, we arrive at 



HC-^f) • • • • • w 



These equations show in a comprehensive manner how the 

 magnitudes T x and T 2 depend on the velocities of rotation, 

 and on the current-strength also affected by these velocities, 

 and in what relations they stand to each other. The equations 

 can therefore be used to draw conclusions how the working of 

 the machine is to be arranged, so as to obtain the most favour- 

 able action under given conditions. 



In this latter respect a conclusion is sometimes adduced, 

 which in the year 1840 M. H. Jacobi drew as to the action 

 of an older form of electromagnetic machine worked by a vol- 

 taic current, and which he thus formulated*: — " The consump- 

 tion of zinc which takes place when the machine is at rest and 

 does no work is double that which takes place when it does 

 the maximum work. " This conclusion has been applied in 

 a modified form to the transmission of power by dynamo 

 machines, in which the velocities of rotation of the two 

 machines could be used as the variables for determining the 

 current-strength and the work, and from which the principle 

 has been deduced that the greatest useful effect is obtained 

 when the ratio of the two velocities is as 2 : 1. 



It must be observed in this connexion that Jacobi drew his 

 conclusion from somewhat inaccurate assumptions, the first 

 of which is — " The strength of the magnetism excited in soft 

 iron by voltaic currents is proportional to the strength of 

 these currents;" and that therefore no great accuracy can be 

 assigned to his conclusions. It must, on the other hand, be 

 observed that this conclusion refers to a strictly defined 

 process, where a voltaic battery, the work of which is governed 

 by fixed laws, served as the source of power ; while, in 

 the transmission of power, other sources may be used the 



* Jacobi, Report of the British Association, 1840, and Pogg. Ann. 

 vol. li. p. 358, 1810. 



