August 28, 1884] 



NA TURE 



413 



application ofithe great laws of thermo-dynamics, or, as it is 

 often called, the mechanical theory of heat. The first law, which 

 asserts that heat and mechanical work can be transformed one 

 into the other at a certain fixed rate, is now well understood by 

 every student of physics, and the number expressing the me- 

 chanical equivalent of heat resulting from the experiments of 

 Joule has been confirmed by the researches of others, and espe- 

 cially of Rowland. But the second law, which practically is 

 even more important than the first, is only now beginning to 

 receive the full appreciation due to it. One reason of this may 

 be found in a not unnatural confusion of ideas. Words do not 

 always lend themselves readily to the demands that are made 

 upon them by a growing science, and I think that the almost 

 unavoidable use of the word equivalent in the statement of the 

 first law is partly responsible for the little attention that is given 

 to the second. For the second law so far contradicts the usual 

 statement of the first, as to assert that equivalents of heat and 

 work are not of equal value. While work can always be con- 

 verted into heat, heat can only be converted into work under 

 certain limitations. For every practical purpose the work is 

 worth the most, and when we speak of equivalents, we use the 

 word in the same sort of special sense as that in which chemists 

 speak of equivalents of gold and iron. The second law teaches us 

 that the real value of heat, as a source of mechanical power, de- 

 pends upon the temperature of the body in which it resides ; the 

 hotter the body in relation to its surroundings, the more available 

 the heat. 



In order to see the relations which obtain between the first 

 and the second law of thermo-dynamics, it is only necessary 

 for us to glance at the theory of the steam-engine. Not many 

 years ago calculations were plentiful demonstrating the in- 

 efficiency of the steam-engine on the basis of a comparison of 

 the work actually got out of the engine with the mechanical 

 equivalent of the heat supplied to the boiler. Such calculations 

 1 'ok into account only the first law of thermo-dynamics, which 

 deals with the equivalents of heat and work, and have very little 

 bearing upon the practical question of efficiency, which requires 

 us to have regard also to the second law. According to that 

 law the fraction of the total energy which can be converted into 

 work depends upon the relative temperatures of the boiler and 

 condenser ; and it is therefore, manifest that, as the tempera- 

 ture of the boiler cannot be raised indefinitely, it is impossible to 

 utilise all the energy which, according to the first law of thermo- 

 dynamics, is resident in the coal. 



On a sounder view of the matter, the efficiency of the steam- 

 engine is found to be so high that there is no great margin 

 remaining for improvement. The higher initial temperature 

 possible in the gas-engine opens out much wider possibilities, 

 and many good judges look forward to a time when the steam- 

 engine will have to give way to its younger rival. 



To return to the theoretical question, we may say with Sir W. 

 Thomson that, though energy cannot be destroyed, it ever tends 

 to be dissipated, or to pa?s from more available to less available 

 forms. No one who has grasped this principle can fail to 

 recognise its immense importance in the system of the universe. 

 Every change, chemical, thermal, or mechanical — which takes 

 place, or can take place, in Nature, does so, at the cost of a 

 certain amount of available energy. If, therefore, we wish to 

 inquire whether or not a proposed transformation can take place, 

 the question to be considered is whether its occurrence would 

 involve dissipation of energy. If not, the transformation is 

 (under the circumstances of the case) absolutely excluded. Some 

 years ago, in a lecture at the Royal Institution, I endeavoured to 

 draw the attention of chemists to the importance of the principle 

 of dissipation in relation to their science, pointing out the error 

 of the usual assumption that a general criterion is to be found in 

 respect of the development of heat. For example, the solution 

 of a salt in water is, if I may be allowed the phrase, a downhill 

 transformation. It involves dissipation of energy, and can there- 

 fore go forward ; but in many cases it is associated with the 

 absorption rather than with the development of heat. I am 

 glad to take advantage of the present opportunity in order to 

 repeat my recommendation, with an emphasis justified by actual 

 achievement. The foundations laid by Thomson now bear an 

 edifice of no mean proportions, thanks to the labours of several 

 physicists, among whom must be especially mentioned Willar'd, 

 Gibbs, and Helmholtz. The former has elaborated a theory of 

 the equilibrium of heterogeneous substances, wide in its prin- 

 ciples, and we cannot doubt far-reaching in its consequences. In 

 a series of masterly papers Helmholtz has developed the concep- 



tion ({free energy with very important applications to the theory 

 of the galvanic cell. He points out that the mere tendency to 

 solution bears in some cases no small proportion to the affinities 

 more usually reckoned chemical, and contributes largely to the 

 total electromotive force. Also in our own country Dr. Alder 

 Wright has published some valuable experiments relating to the 

 subject. 



From the further study of electrolysis we may expect to gain 

 improved views as to the nature of the chemical reactions, and of 

 the forces concerned in bringing them about. I am not quali- 

 fied — I wish I were — to speak to you on recent progress in 

 general chemistry. Perhaps my feelings towards a first love 

 may blind me, but I cannot help thinking that the next great 

 advance, of which we have already some foreshadowing, will 

 come on this side. And if I might without presumption venture 

 a word of recommendation, it would be in favour of a more 

 minute study of the simpler chemical phenomena. 



Under the head of scientific mechanics it is principally in 

 relation to fluid motion that advances may be looked for. In 

 speaking upon this subject I must limit myself almost entirely to 

 experimental work. Theoretical hydrodynamics, however im- 

 portant and interesting to the mathematician, are eminently 

 unsuited to oral exposition. All I can do to attenuate an in- 

 justice, to which theorists are pretty well accustomed, is to refer 

 you to the admirable reports of Mr. Hicks, published under the 

 auspices of this Association. 



The important and highly practical work of the late Mr. 

 Froude in relation to the propulsion of ships is doubtless known 

 to most of you. Recognising the fallacy of views then widely 

 held as to the nature of the resistance to be overcome, he showed 

 to demonstration that, in the case of fair-shaped bodies, we have 

 to deal almost entirely with resistance dependent upon skin 

 friction, and at high speeds upon the generation of surface-waves 

 by which energy is carried off. At speeds which are moderate 

 in relation to the size of the ship, the resistance is practically 

 dependent upon skin friction only. Although Prof. Stokes and 

 other mathematicians had previously published calculations 

 pointing to the same conclusion, there can be no doubt that the 

 view generally entertained was very different. At the first 

 meeting of the Association which I ever attended, as an intelli- 

 gent listener, at Bath in 1864, I well remember the surprise 

 which greeted a statement by Rankine that he regarded skin 

 friction as the only legitimate resistance to the progress of a 

 well-designed ship. Mr. Froude's experiments have set the 

 question at rest in a manner satisfactory to those who had little 

 confidence in theoretical prevision. 



In speaking of an explanation as satisfactory in which skin 

 friction is accepted as the cause of resistance, I must guard 

 myself against being supposed to mean that the nature of skin 

 friction is itself well understood. Although its magnitude varies 

 with the smoothness of the surface, we have no reason to think 

 that it would disappear at any degree of smoothness consistent 

 with an ultimate molecular structure. That it is connected with 

 fluid viscosity is evident enough, but the mcdus operandi is still 

 obscure. 



Some important work bearing upon the subject has recently 

 been published by Prof. O. Reynolds, who has investigated the 

 flow of water in tubes as dependent upon the velocity of motion 

 and upon the size of the bore. The laws of motion in capillary 

 tubes, discovered experimentally by Poiseuille, are in complete 

 harmony with theory. The resistance varies as the velocity, and 

 depends in a direct manner upon the constant of viscosity. But 

 when we come to the larger pipes and higher velocities with which 

 engineers usually have to deal, the theory which presupposes a 

 regularly stratified motion evidently ceases to be applicable, and 

 the problem becomes essentially identical with that of skin fric- 

 tion in relation to ship propulsion. Prof. Reynolds has traced 

 with much success the passage from the one state of things to 

 the other, and has proved the applicability under these compli- 

 cated conditions of the general laws of dynamical similarity 

 as adapted to viscous fluids by Prof. Stokes. In spite of the 

 difficulties which beset both the theoretical and experimental 

 treatment, we may hope to attain before long to a better 

 understanding of a subject which is certainly second to none in 

 scientific as well as practical interest. 



As also closely connected with the mechanics of viscous fluids, 

 I must not forget to mention an important series cf experiments 

 upon the friction of oiled surfaces, recently executed by Mr. 

 Tower for the Institution of Mechanical Engineers. The results 



