INTRODUCTION xi avoided. And so I ask you, dear father, for your decision rather than for your advice; for it isn't advice that I need, and there is scarcely time for it now. If you will allow me to study natural science I shall take it as a great kindness on your part, and what- ever diligence and love can do in the matter that they shall do. I believe this will be your decision, for you have never put a stone in my path, and I think you have often looked with pleasure on my scientific studies. But if you consider it best for me to con- tinue in the path on which I have started (which I now doubt), I will carry out your wish, and do so fully and freely; for by this time I am sick of doubt and delay, and if I remain in the state I have been in lately I shall never make a start. . . . So I hope to have an early answer, and until it comes I shall continue to think the matter over. Meanwhile I send my love to you' all, and re- main your affectionate son, HEINRICH. Matters were decided as he had hoped, and, full of joy at being able to carry out his wishes, Hertz now proceeded to arrange his plan of studies. He remained altogether a year at Munich. He devoted the winter-semester of 1877-78 in all seclusion to the study of mathematics and mechanics, using for the most part original treatises such as those of Laplace and Lagrange. Most of the following summer-semester he spent at practical work in the physical laboratory. By attending the elementary courses in practical physics at the University (under v. Jolly) and at the same time in the Technical Institute (under v. Bezold), he was able to supple- ment what he had already learned by means of his own home-made apparatus. Thus prepared he proceeded in October 1878 to Berlin, eager to become a pupil of v. Helmholtz and Kirchhoff. When he had arrived there, in looking at the notices on the black notice-board of the University his eye fell on an intimation of a prize offered by the Philosophical Faculty for the solution of a problem in physics. It referred to the question of electric inertia. To him it did not seem so hopelessly difficult as it might have appeared to many of his contemporaries, and he decided to have a try at it. This brings us to the beginning of his first independent research (the first paper in the present volume). We cannot read without astonishment the letters in which this student of twenty-one reports to his parents the starting of an in-