SKETCH OF GU ST AV ROBERT EIRCHHOFF. 123 



tific pursuits may well be doubted. The teacher, it is true, gains 

 a wider, richer field of activity, but the investigator is robbed of 

 a larger part of his time. Kirchhoff was, however, protected by 

 his physical disability against most of the drive of the capital, 

 and was able to labor as he had usually done. . . . His favorite 

 work, and the one having the most enduring results, was his 

 lectures on mathematical physics. His address was impressive 

 by reason of the elegance and precision of his statement. Not a 

 word was wanting, not a word was in excess ; never an error, an 

 obscurity, or an ambiguity. Remarkable also was the exactness 

 of his calculations — a matter of extreme difliculty to laymen. 

 The whole material arranged itself before the eyes of the class in 

 the form of a nicely adjusted master-work of scientific art, so 

 that every part exerted its full efi'ect on the others, and to wit- 

 ness one of his deductions was a real aesthetic enjoyment. The 

 complete understanding of his reasoning on these most diflficult 

 subjects implied, of course, some knowledge of the mathematical 

 language which was his vehicle of thought ; and it might hap- 

 pen, and did in fact sometimes happen, that a hearer could not 

 comprehend why Kirchhoff made this particular deduction and 

 not some other ; but every one was able to follow his course of 

 thought, consider it, and render it correctly. So that, paradoxical 

 as it may appear, it was not impossible, without having really 

 understood Kirchhoff, to reproduce his lectures from the notes 

 into a respectable book. Kirchhoff was able to give his lectures 

 uninterruptedly in Berlin for nine years. But we who heard 

 him could remark the effort they caused him, and how he had 

 to husband his strength. Yet he was always punctual, and the 

 quality of his teachings was never depreciated. Finally, in 1884, 

 the doctors forbade him to read ; and although he was enabled 

 to resume this his favorite occupation for a time, it was evident 

 that his nervous system was shattered." 



Besides the subjects we have already mentioned, Kirchhoff 

 conducted a series of valuable investigations in the equilibrium 

 and motion of elastic solids, especially in the form of plates and 

 rods. His publications were not voluminous. His contributions 

 to the Berlin Academy of Sciences are spoken of as having been 

 about one a year. His collected papers (Gesammelte Ahliand- 

 lungen), about fifty in number, were published in Leipsic in 

 1882, in a single volume. His lectures on dynamics ( Vorlesun- 

 gen uber matliematisclie Physik), first published in 1876, have 

 reached a third edition, at least. They are styled by Prof. Tait 

 somewhat tough reading, but certainly recompensing the labor 

 of following them. They form rather a collection of short trea- 

 tises on special branches of the subject, than a systematic digest 

 of it. His greatest work, " The Researches on the Solar Spec- 



