1889. ] Temperature on the Klectric Strength of Gases. 329 
Hydrogen at constant density. 
Temp. Air space. 
13 1125) 
30 15 
50 29 
70 2 
100 2°8 
120 me 
140 2 
160 2 
180 2 
200 2 
(3) On the application of Lagrange’s equations to certain physical 
problems. By 8S. H. Bursury, M.A., St John’s College. 
In his Theory of Electricity and Magnetism, Vol. 1. chap. 7, 
Maxwell assumes the energy of a system of two closed currents 
to be of the form 
ae bas +5 
T=hLi?+ Mi,+4 Lay, 
where L,, WV, and L, are functions of the form and relative position 
of the circuits; and by the application of Lagrange’s equations 
to this expression he deduces the known electromotive and electro- 
magnetic forces. 
As a logical process this reasoning is prima facie open to 
objection thus: If the reasoning be sound, it ought (it may be 
said) to be equally applicable to the case of a closed current and 
a magnetic shell. We ought to be able to express the energy of 
the system of circuit and shell, and to deduce the electromagnetic 
forces and electromotive force in the circuit by applying Lagrange’s 
equations to that expression for the energy. 
This however we cannot do. For (see Sir W. Thomson’s 
Papers on Electricity and Magnetism, p. 441, note) if a closed 
electric current be moved in any way in the field of an invariable 
magnet, and the current be maintained constant, the whole energy 
spent, namely, the chemical energy spent in the battery, plus the 
mechanical work required to overcome the forces of the system, is 
exactly represented by an equivalent of heat generated. Therefore 
no change can take place in the intrinsic energy of the system, 
and it can have no other form than 
ie eae 
where 4/n’ is the energy of the closed current 7 in its own field, 
and 4 K¢@’ is the energy of the shell in its own field. 
