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 difficulty 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 effect on the others, and to witness one of his deductions was a real aesthetic enjoyment. The complete understanding of his reasoning on these most difficult subjects implied, of course, some knowledge of the mathematical language which was his vehicle of thought; and it might happen, 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 Abhandlungen), about fifty in number, were published in Leipsic in 1882, in a single volume. His lectures on dynamics (Vorlesungen über mathematische 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 treatises on special branches of the subject, than a systematic digest of it. His greatest work, "The Researches on the Solar Spec-
