338 XXII HERMANN VON HELMHOLTZ known to us as the Principle of the Conservation of Energy. It had long before been suspected that in the unending succession of phenomena there was something else besides matter which persisted, which could neither be created nor destroyed, something immaterial and scarcely tangible. At one time it seemed to be quantity of motion measured in this way or that, at another time force, or again an expression compounded of both. In place of these obscure guesses Helmholtz brought forward distinct ideas and fixed relations which led immedi- ately to a wealth of general and special connections. Magni- ficent were the views which the principle opened up into the past and future of our planetary system; in every separate investigation, even the most restricted, its applications were innumerable. For forty years it has been so much expounded and extolled that no man of culture can be quite ignorant of it. It is noteworthy that about this time other heads began to think more clearly of these things; and it came about that as far as the phenomena of heat were concerned other men had anticipated Helmholtz by a few years without his know- ing it. It would be far from his wish to detract from the fame of these men; but it should not be forgotten that their researches were almost entirely restricted to the nature of heat, whereas the significance and value of the principle lie precisely in the fact that it is not limited to this or that natural force, but that it embraces all of them and can even serve as our pole-star amongst unknown forces. It is not generally known that in his mature years Helm- holtz has returned to the work of his youth and has still further developed it. The law of the conservation of energy, general though it is, nevertheless appears to be only one half of a still more comprehensive law. A stone projected into empty space would persist in a state of uniform motion, and thus its energy would remain constant: to this corresponds the con- servation of energy in any system, however complicated that system may be. But the stone would also tend to retain its direction and to travel in a straight line: to this behaviour there is a corresponding general behaviour on the part of every moving system. In the case of purely mechanical systems it has long been known that every system, according