266 



NATURE 



[July 22, 1897 



physics it is desirable to carry in the memory for instant 

 use. It would be more portable if made explicitly 

 kinematical by being reduced to the form 



acceleration _ ^ifl 

 displacement T* 



where, on the left, numerical values without regard to 

 sign are understood. The introduction of the mass m of 

 the vibrating particle, together with a quantity a, which 

 is the product of m by the positive numerical value of 

 the acceleration, seems an unnecessary complication. 



The authors give in Chapter vi. an excellent elementary 

 account of stress and strain. Everything is clearly and 

 concisely stated, and a student seeking an accurate 

 quantitative outline of the subject as a starting-point for 

 a more complete study of experimental elasticity could 

 hardly find anything more satisfactory. 



We note in this chapter the use of the form " elotropy " 

 for "eolotropy" (or, better, " asolotropy ") to denote 

 difference of elastic quality in different directions in a 

 body. It seems hardly allowable to adopt this spelling 

 in view of the derivation of the first part of the word from 

 aidXoj, meaning quick-moving^ changeful^ variegated. 



It is of considerable experimental importance to point 

 out that what the authors call the constant of torsion of a 

 wire (that is, the torsional rigidity) is calculated on the 

 assumption of perfect circularity of cross-section, and 

 further involves the fourth power of the radius of the 

 wire ; so that it is hardly possible to draw from oscillation 

 experiments exact conclusions as to the value of the 

 rigidity-modulus of the material. 



The definition of perfection of elasticity, on p. 102, 

 seems hardly guarded enough. A body may, after the 

 removal of stress, return to precisely its former configura- 

 tion, so far as that can be tested at least, and yei be sub- 

 ject to imperfections of elasticity. Let the body be 

 subjected to increasing stress, and let the successive 

 configurations be noted ; then let the stress be gradually 

 altered back again to the former value, and the configura- 

 tions in returning be again noted. If the configuration 

 corresponding to a given value of the stress be the same 

 during the removal of the stress as dunng its imposition, 

 the body is perfectly elastic, but not otherwise. If the 

 configurations and stresses be represented graphically, 

 the curves for the transition from initial to final stress 

 may not coincide with that for return from final to initial 

 stress, and energy will be dissipated (in consequence of 

 imperfection of elasticity), the amount of which can be 

 estimated from the area enclosed between the two curves. 



The next chapter (vii.) deals with Hydro-Mechanics, 

 a subject the extent of which must have been very em- 

 barrassing to the authors, considering their plan, and the 

 amount of space at their disposal. On the whole, they 

 have given a fair account of leading principles, and 

 especially of those of capillarity and viscosity ; and we 

 have in these all the merits of treatment that mark the 

 rest of the work. 



In the remarks in this chapter on the experimental 

 verification of Boyle's law (Mariotte's or Boyle's law the 

 authors call it !), there is no reference to what constitutes 

 the real divergence of gases, such as nitrogen, oxygen 

 and hydrogen, from fulfilment of this law. In fact, it is 

 NO. 1447, VOL. 56] 



stated that for a gas the " loss of volume is greater than 

 would be expected from Mariotte's law, the divergence 

 from inverse proportionality increasing as we near the 

 point of condensation." But, as no doubt the authors 

 are fully aware, deviations from fulfilment of Boyle's law 

 are not confined to gases which are in " an intermediate 

 condition preparatory to liquefaction," but are found 

 also in true gases — gases, that is to say, which are far 

 above their critical temperatures. The researches of 

 Regnault, and the later and much more extended investi- 

 gations of Amagat, which have given us most complete 

 and interesting information as to how far " true gases "' 

 conform to Boyle's law, are of great importance from the 

 point of view of kinetic theory, and should surely have 

 been noticed here. 



The account given in Art. 192, p. 136, of efflux of liquid 

 from an orifice in a vessel, seems to require amendment, 

 which should also be extended to Art. 193. As a matter 

 of fact, the pressures at the outside of the jet and at the 

 free surface are practically the same, so that />-A» instead 

 of being equal to xdg, is really zero. Also, though this 

 is a small matter, it would seem better to use p than d 

 to denote density ; as expressions like dv'*'^ dg, are in- 

 stinctively associated with other meanings than those 

 intended. 



Passing now to the part of the book which treats of 

 Heat, we are glad to see so excellent an account of the 

 subject of temperature. It is short, and seems to be 

 correct ; which is more than can be said of nine out of ten 

 of the discussions in text-books on this very important 

 subject. Of the fact that thermometers made with 

 different kinds of glass, and graduated with absolute 

 accuracy, will agree at the temperatures of reference, 0° C. 

 and 100^ C, and will agree nowhere else, the majority of 

 text-book writers seem to be in blissful ignorance. 

 Nothing is more confusing than the customary proceed- 

 ing (much followed by a certain class of writers on 

 thermodynamics !) of defining temperature on a mercury- 

 in-glass thermometer, sometimes with ignoration of the 

 expansion of the vessel, sometimes not ; but always with 

 the further erroneous statement that the increase of 

 pressure of a gas kept at constant volume is the same for 

 each degree of rise of temperature on this scale, a 

 "fact" which is supposed to express the law of Gay- 

 Lussac. It does not occur to such writers that, if Gay- 

 Lussac's law were to thus hold for one thermometer, it 

 could not hold for other thermometers made with different 

 kinds of glass, and therefore having different scales. 

 And, unhappily for those who define their scale of tem- 

 perature with regard to the absolute expansion of 

 mercury, with or without nonsense about mercury being 

 "chosen on account of its uniform expansion," the 

 divergence of the air-thermometer from such a standard 

 is much greater than from a thermometer constructed 

 with ordinary glass. 



The vicious circle thus introduced into the definition of 

 the standard scale of temperature, and the failure to 

 regard the air-thermometer scale and the absolute thermo- 

 dynamic scale of temperature as each derived from its 

 own independent definition, is responsible for much of 

 the prevalent haziness in the application of the funda- 

 mental principles of heat and thermodynamics. 



