GUSTAV ROBERT KIRCHHOFF. 371 



from Ohm's familiar law, he derived two results long recognized in 

 electrical science as Kirchhoff's laws. Between the years 1845 and 

 1852, thirteen other papers appeared, discussing mathematically the 

 most difficult problems in electricity, magnetism, light, heat, sound, and 

 elasticity in general. In 1882, when the number of his separate pub- 

 lications had grown to thirty-eight, Kirchhoff gathered them together, 

 from the various periodicals in which they originally appeared, into a 

 volume of six hundred and forty-one pages, classifying them according 

 to subjects, and chronologically in reference to each subject. The title 

 of this volume is Gesammelte Abhandlungen, Leipzig, 1882. Out of 

 a wide range of physical problems, all of which are treated with great 

 mathematical skill, only a few salient points can be indicated in this 

 notice. 



Ohm deduced his laws for electrical currents from assumptions which 

 are not in agreement with those required by the facts of statical elec- 

 tricity. Kirchhoff proves that Ohm's laws can be derived from the 

 electrostatic repulsion of electricity by bringing to his aid certain as- 

 sumptions in reference to the question which in the electrostatic theory 

 remain open. Neumann and Weber trusted to experiment for the 

 value of the constant on which the intensity of induced currents de- 

 pends. In 1849 Kirchhoff obtained this constant by a purely analytical 

 treatment of the subject, and thereby made the measurements of elec- 

 trical resistance absolute. 



In 1877 Kirchhoff published his theory of the motion of electricity 

 in subterrene and submarine telegraph wires. He begins with the 

 statement that Sir William Thomson had already, in 1855, starting 

 from the hypothesis that the influence of induction, consequent on 

 changes in the intensity of the current, could be neglected in compari- 

 son with the influence of the changes, reached the position that the 

 electricity in such wires was propagated according to the same laws as 

 conducted heat. He says: "I allow myself to lay before the [Berlin] 

 Academy a derivation of this law, which rests upon the same hypothe- 

 sis, but comes out from more general principles than those given by 

 Thomson, and to annex some formulas which, so far as I know, have 

 not yet been published." 



In 1859 Kirchhoff began his work in optics by measuring the angle 

 between the axes of aragonite for rays corresponding to the different 

 Frauenhofer lines. Then, with Bunsen, he studied the spectra of col- 

 ored flames, and recorded the rays, present or absent. Facts then 

 appeared, he says, which gave an unexpected solution to the origin of 

 the Frauenhofer lines, and justified inferences as to the material quality 



