xiv INTRODUCTION whereas only about half a year ago I scarcely knew any more about it than what still remained in my memory since the time when I was with Dr. Lange. I hope my work won't suffer from this. At present it looks promising. I have already surmounted the difficulties which Helmholtz pointed out to me at the start as being the principal ones; and in a fortnight, if all goes well, I shall be ready with a scanty kind of solution, and shall still have time left to work it up properly. He asks his parents to send on a tangent galvanometer which he had made during the last holidays at home, without having any suspicion that it would so soon be used in this way.2 A week later, in writing to report progress, he is not so cheerful. "When one difficulty is overcome, a bigger one turns up in its place." These were the difficulties mentioned in pp. 5-6. The Christmas holidays were now at hand, and while at home in Hamburg he made the commutator shown on Fig. 1, p. 13, respecting which he later on reports. 12th January 1879. The apparatus which I made works very well, even better than I had expected; so that within the last three days I have been able to make all my measurements over again, and more accurately than before. Within three months after he had first turned his atten- tion to this investigation he is able to report the conclusion of the first part of it. 21st January 1879. Then It has delighted me greatly to find that my observations are in accordance with the theory, and all the more because the agree- ment is better than I had expected. At first my calculations gave a value which was much greater than the observed value. I happened to notice that it was just twice as great. After a long search amongst the calculations I came upon a 2 which had been forgotten, and then both agreed better than I could have expected. I have now set about making more accurate observa- 1 The Head-Master of the Bürgerschule, which he attended up to his six- teenth year. 2 This is the galvanometer referred to on p. 12 (3)—a simple wooden disc turned upon the lathe and wound with copper wire, with a hole in the centre for the magnet. It is still in good order. 1