Electromagnetic Action of Dielectric Polarization. 385 
Hence the total cost of working is a minimum when the cost 
1-8 
of power A! Pre is to the lampage B’pv 8 "as . ie 
to unity. 
Now the above investigations show that for Edison lamps 
ais a quantity in the neighbourhood of 63, and 8 near 44; 
hence hee B 19 
and hence ratio of lampage to total cost is ts =17°4 per cent- 
Hence we arrive at this curious result, that independently 
of the cost of the lamp, or electrical energy, we must run at 
such a pressure that lampage is about 18 per cent. of the 
total cost. Now, if instead of employing these approximate 
exponential expressions for the values of /, c, and & in terms 
of the electromotive force, we had introduced the more accu- 
rate forms of equation indicated above, we should have had an 
equation in terms of v to solve as the result of equating the 
differential to zero, which would, by the introduction of the 
proper constants, give the value of electromotive force at which 
the total cost becomesa minimum. In their paper, Professors 
Ayrton and Perry have calculated to a fraction of a volt what 
this economical potential is. As, however, the characteristic 
equations are only approximate, it seems hardly necessary to 
do more than obtain a similar approximate expression for the 
economical working. 
At the Edison lamp-factory in America calculations were 
made, on the assumption of a particular type of lamp and 
length of life and cost of power, to ascertain the ratio of lampage 
to total cost, which made the total cost a minimum, and the 
result appeared to be to fix it at about 16 per cent. These 
calculations are therefore in singular accord with the deduc- 
tion of theory based on determination of the constants of the 
characteristic curves, arrived at both by graphic and analytical 
methods. 
XLI. Experiments on the Electromagnetic Action of Dielectric 
Polarization. By Prof. W. C. R6nTGEN*. 
si Paes theory of electrical and magnetic phenomena proposed 
by Faraday and elaborated by Clerk-Maxwell, is based 
upon the assumption that in insulators bounded by electrified 
conductors there exists a dielectric polarization or displace- 
ment—a change which, in whatever way produced, exerts 
electrodynamic effects exactly like an electric current flowing 
in a conductor. 
* Translated from the Sitzwngsberichte der Berliner Akad. der Wissen- 
schaften for February 26, 1885. 
