Any theory which is brought forward to explain a phenomenon, or any process which is proposed to effect any operation, must in the first instance submit to the test of the application of these two principles of conservation and dissipation of energy; and any proposal which fails to bear these tests may be at once rejected. The essential feature of the science of to-day is its quantitative character. We must, for instance, not only know that radiant energy comes to us from the sun, but we must learn how much energy is annually received by the earth in this way; and, in the next place, how much energy is radiated by the sun in all directions in the same time. When we have learned this, we want to know what is the source of this energy; and no theory of the sun which does not enable us to explain how this constant expenditure of energy is maintained can be accepted. Last century it was possible to believe, with Sir William Herschel, that the greater part of the sun's mass is comparatively cool, and that it is surrounded by only a thin sheet of flame. To-day such a theory would be rejected at once, simply because the thin shell of flame could not provide energy for the solar radiation for any considerable time. The contact theory of the galvanic cell, as originally enunciated, fell to the ground for a similar reason. The simple contact of dissimilar metals could afford no continuous supply of energy to sustain the current. Applied to the steam-engine, the doctrine of energy teaches us, not only that, corresponding to the combustion of a pound of coal, there is a definite quantity of work which is the mechanical equivalent of the heat generated, and is such that no engine of which we can conceive is capable of deriving from the combustion of the pound of coal a greater amount of work, but it teaches us that there is a further limitation fixed to the amount of work obtainable. This limitation depends upon the range of temperature at our command; and, when the range is known, we can express the amount of energy realizable by a perfect engine working through that range as a definite fraction of the whole energy corresponding to the heat of combustion of the fuel. Thus, if we find that a particular engine realizes only 15 per cent. of the energy of its fuel in work done, we must not suppose that mechanical improvements in the engine would enable us to realize any considerable portion of the other 85 per cent.; for it may be that a theoretically perfect engine, working with its boiler and condenser at the same temperatures as those of the engine considered, could only realize 25 per cent. of the energy of the fuel, reducing the margin for improvement from 85 to 10 per cent., as long as the range of temperature is unaltered. To improve the efficiency beyond this limit, the range of temperature must be increased, that is, generally, hotter steam must be used.