AND THE EQUILIBRIUM AND MOTION OF ELASTIC SOLIDS. 317 



when in equilibrium ; for we have evidently no right to assume, either that no such pressure 



exists, or, supposing it to exist, that the medium would expand itself but very slightly if it 



were removed. It will now no longer be allowable to confound the pressure referred to a unit 



of surface as it was, in the position of equilibrium of the medium, with the pressure referred to a 



unit of surface as it actually is. The latter mode of referring the pressure is more natural, and 



will be more convenient. Let the pressure, referred to a unit of surface as it is, be resolved 



into a normal pressure II + p, and a tangential pressure <,. All the reasoning of Sect. iii. 



will apply to the small forces p, and <, ; only it must be remembered that in estimating the 



whole oblique pressure a normal pressure II must be compounded with the pressures given by 



equations (3l). In forming the equations of motion, the pressure FI will not appear, because 



the resultant force due to it acting on the element of the medium which is considered is zero. 



The equations (.<i2) will therefore be the equations of motion required. 



If we had chosen to refer the pressure to a unit of surface in the original state of the 



surface, and had resolved the whole pressure into a pressure H. + P\ normal to the original 



position of the surface, and a pressure /, tangential to that position, the reasoning of Sect. iii. 



would still have applied, and we should have obtained the same expressions as in (."I) for the 



pressures P,, 7*), &c , but the numerical value of A would have been different. According to 



this method, the pressure O would have appeared in the equations of motion. It is when the 



pressures arc measured according to the method which I have adopted that it is true that 



the equilibrium of the medium would be unstable if either A or B were negative. I must 



here mention that from some oversight the right-hand sides of Poisson's equations, at page 68 



of the niL-moir to which I have referred, are wrong. The first of these equations ought to 



. n id'u d'u d'u\ . U d'u , • •, , , . ■ i 



contain — ( ; + -^^ + , instead or — , and similar changes must he made in the 



p ' d dj' dy- dz' I f) di- 



other two equations. 



It is sometimes brought as an objection to the equations of motion of the luminiferous 

 ether, that they are the same as those employed for the motion of solid bodies, and that it 

 seems unnatural to employ the same equations for substances which must be so differently 

 constituted. It was, perhaps, in consequence of this objection that Poisson proposes, at 

 page 147 of the memoir which I have cited, to apply to the calculation of the motion of the 

 luminiferous ether the same principles, with a certain modification, as those which he employed 

 in arriving at his equations (9) page 152, i. e. the equations (12) of this paper. That modi- 

 fication consists in supposing that a certain function of the time <p(t) does, not vary very 

 rapidly compared with the variation of the pressure. Now the law of the transmission of a 

 motion transversal to the direction of propagation depending on equations (12) of this paper 

 is expressed, in the simplest case, by the equation (24) ; and we see that this law is the 

 same as that of the transmis.-.ioii of heat, a law extremely different from that of the trans- 

 mission of vibratory motions. It seems therefore unlikely that these principles are applicable 

 to the calculation of the motion of light, unless the modification which I have mentioned be 

 so great as wholly to alter the character of the motion, that is, unless we supposi' the pns.'ure 

 to vary extremely fast compared with the function (b(t), whereas in ordinary cases of the 

 motion of fluids the function (p(t) is supposed to vary extremely fast compared with the pressure. 



Another view of the subject may be taken which I think deserves notice. IJefore explaining 

 tills view however it will be necessary to define what I mean in this paragraph by the word 

 el'iKlirili/. There are two distinct kinds of elasticity ; one, that by which a body which is 

 uniformly compressed tends to regain its original volume, the other, that by which a body which is 

 constrained in a manner independent of compression tends 10 assume its original form. 'I'he 

 conHtants y/. and B of Sect. III. may be taken as measures of these two kinds of elasticity. In 

 the present par.igniph, the word will be nsc<l to denote the second kind. Now many highly 



