478 



NA TURE 



{March 24, 1881 



a whole crew of Maxwell's demons on each atom would 



be required to warp and moor for every movement that 

 mio-ht occur. But so true was Rankine's knowledge of 

 mechanics that all this elaborate refinement did not 

 prevent his hypothesis leading him to correct results. 



This refined organisation, however, which renders his 

 hypothesis in the highest degree improbable, suggests a 

 most important consideration. For the almost infinite 

 complexity of his particular arrangement indicates almost 

 to the extent of a proof that the results he obtained must 

 depend upon circumstances so general as to be indepen- 

 dent of any particular hypothesis, so long as it is in con- 

 formity with the laws of motion, and hence the trail of 

 these general circumstances is crossed. 



In Rankine's hypothesis the temperature comes out 

 as a direct m.easure in any particular substance of the 

 kinetic or actual energy of the molecular motion. 

 This conclusion, to which he adhered in the final 

 foundation of his theory, is general, but it does not appear 

 to be the most general conclusion of which our present 

 e.xperiments admit. It led Rankine to give a definite fonn 

 as well as name to his thermodynamicfunction, which forms 

 the fundamental equation of all the mathematical work. But 

 it was subsequently shown that the differential equation to 

 the same lines could be obtained without the assumption 

 with regard to temperature, and then it did not appear 

 that there was sufficient experimental data for the com- 

 plete determination of the constants which enter into the 

 integral. This is owing to the hitherto impossibility of 

 determining the exact form of the adiabatic curve for 

 solids and liquids. With gases it is different, and with these 

 Rankine's law is found to fit, but so might a law framed 

 on the supposition that in other cases the kinetic energy 

 was some other function of the temperature. What is 

 proved therefore is not that the temperature is a direct 

 measure of the kinetic energy, but that this is some 

 function of the temperature. This is apparently all that 

 has yet been accomplished, so that Rankine's definite 

 conclusion must be looked upon as suggested rather than 

 proved by experiment. There can be no doubt however 

 that this definiteness led to a vast development of the 

 subject, and hence it was no mere fancy or partiality for 

 his own view which led him to adhere to that form of 

 second law which included his earlier view. Nor will the 

 study of Rankine's earlier papers be time wasted on the 

 part of those who seek to understand this extremely 

 difficult subject. They will there find a model of the 

 machinery by which the general result might be obtained^ 

 and if, as is the case with most new inventions, the 

 machinery is unnecessarily complex, it is still the only 

 machine which has accomplished the results. 



They will also find, what must for ever add an interest 

 to these papers, the first use of the terms thermodynamic 

 function, adiabatic curve, potential energy, and others 

 now in general use ; for Rankine's nomenclature, to a great 

 extent his notation, and entirely his graphic method, have 

 been universally adopted. 



Rankine's methods have been called "uncouth," 

 "diffuse and obscure," and without doubt they must 

 seem all this to those who come to the subject with all 

 the latest inventions in the form of mathematical machine 

 tools in perfect working order, — ^just as the axe or adze 

 must seem barbarous when there is a planing machine at 



hand to do the work, and the material has been prepared 

 for it. But let the shape required be of a novel kind, or 

 let the material be in the rough, and then how does it 

 fare with the planing machine ? 



Like that of Green, the whole career of Rankine is one 

 rebuke to those who would exhaust the finest material on 

 this earth — the best brain of our youth — converting it 

 into elaborate mechanism only adapted to reduce, in 

 however elegant a manner, already prepared billets to 

 elegant and improved copies of masterpieces which, 

 having once been shaped, although roughly with primitive 

 tools, can never have to be shaped again. The material 

 at last existed for a great mathematical edifice, of which 

 the want had long been felt, and our great mathematical 

 workshop was crowded with the most refined mechanism 

 rusting for want of material to work upon. But this 

 material was in the rough, and while waiting for some 

 one to strip off the bark the chance was lost, for the 

 obscure, self-taught mechanic who set to work with axe 

 and adze did not stop at the bark, but with rapid and well- 

 directed strokes brought out the form divine. However 

 uncouth Rankine's methods may be, they have the great 

 merit that they require nothing but a bold front — the 

 result being obtained without adventitious aid. They 

 are inscrutable to those who, having learnt the relations 

 between quantities as expressed by symbols, have for- 

 gotten if they ever knew the purpose of their formulse- 

 But to the reader who thinks Rankine's methods are a 

 statement of his thoughts, and though often a rough 

 task, any one who succeeds in understanding Rankine 

 finds to his satisfaction that he has done more than this, 

 that he understands what Rankine understood. 



Nor is this true only of his great work. What seems 

 to us his most useful work is that of showing how 

 the elementary mathematical methods were sufficiently 

 adaptable to be applied to almost all cases of practical 

 mechanics. The results are only approximate ; but where 

 neither the data nor the desired result can be exactly 

 measured, this is all that could be obtained, were the 

 methods never so exact. One might as well set bricks 

 by Sir Joseph Whitworth's millionth-of-an-inch machine 

 as use the exact equation of thermodynamics to deter- 

 mine the probable work to be obtained from a steam- 

 engine. 



The graphic method was Rankine's great weapon. 

 This, which is probably as old as any mathematical 

 method, had been long neglected, except that it was 

 sometimes used for engineering purposes. Rankine early 

 perceived its applicability to the subjects he had to teach, 

 and in his treatises on Apphed Mechanics, Shipbuilding, 

 and the Steam-Engine there are many instances of its 

 novel and useful application which have been copied far 

 and wide, while his graphic treatment of the subject of 

 theiTTiodynamics has been universally adopted. But the 

 height of his achievement in the application and develop- 

 ment of the graphic method is only reached in his papers 

 on the motion of fluids. 



These papers, with the omission already noticed, are 

 collected at the end of the volume, and they constitute by 

 no means its least valuable part. They are comparatively 

 his later work. The first, " On the E.xact Form of Waves 

 at the Surface of Deep Water," was published in 1862, 

 after his thermodynamical work was essentially complete. 



