242 The Mathematical Electricians of the 



energy is a universal principle of nature : that the kinetic and 

 potential energy of dynamical systems may be converted into 

 heat according to definite quantitative laws, as taught by 

 Kumford, Joule, and Eobert Mayer* ; and that any of these 

 forms of energy may be converted into the chemical, electro- 

 static, voltaic, and magnetic forms. The latter Helmholtz 

 examined systematically. 



Consider first the energy of an electrostatic field. It will 

 be convenient to suppose that the system has been formed by 

 continually bringing from a very great distance infinitesimal 

 quantities of electricity, proportional to the quantities already 

 present at the various points of the system ; so that the charge 

 is always distributed proportionally to the final distribution. 

 Let e typify the final charge at any point of space, and V the 

 final potential at this point. Then at any stage of the process 

 the charge and potential at this point will have the values \e 

 and A F, where A denotes a proper fraction. At this stage let 

 charges ed\ be brought from a great distance and added to the 

 charges \e. The work required for this is 



so the total work required in order to bring the system from 

 infinite dispersion to its final state is 



fi 



or 



By reasoning similar to that used in the case of electrostatic 

 distributions, it may be shown that the energy of a magnetic 

 field, which is due to permanent magnets and which also 

 contains bodies susceptible to magnetic induction, is 



\ 

 where p denotes the density of Poisson's equivalent magnetiza- 



* Julius Robert Mayer (b. 1814, d. 1878), who was a medical man in Heilbronn, 

 asserted the equivalence of heat and work in 1842, Annal. d. Chemie, xlii, p. 233 ; 

 his memoir, like that of Helmholtz, was first declined by the editors of the 

 Annalen der Physik. An English translation of one of Mayer's memoirs was 

 printed in Phil. Mag. xxv (1863), p. 493. 



