542 Br. C* Chree: Applications of 



suspended with its axis vertical in a homogeneous liquid of 

 density p'. In this species of material the general formula 

 for the elastic change of volume is in place of (2) * 



& =jin (l-'hs-'hsKStf/Ei) + (l-%!-% 3 )(Yy/E 2 ) 

 + (1— Vn— %s)(Z*/E 8 ) \dx dydz 



+ §{ (l-*.-*i)(ItyBi)+ (l-*i-*0(Gjr/BW 



+ (l-%i-% 2 )(H^/E 3 )}^S (22) 



Noticing that the modulus k of resistance to compression 

 under uniform surface-pressure is given by 



i^ = (i_ 7?i2 - 9?i:3 )E 1 - 1 + (i-^-^je; 1 f (i-v 31 -v 82 )^\ 



we find without much difficulty 



Bvlv=g(p-p>)(l- V31 - Vs2 )^jE,)-plk, . (23) 



where f is the depth of the C.G. of the solid below the point 

 of suspension, and p the pressure at this depth in the liquid. 

 If the cylinder were supported on its base we should get in 

 place of (23) 



Sv/v=-ff(p-p r )(l- Va - Vn )^m 3 )-p/h . . (24) 



where f ' is the height of the C.G. above the support, p having 

 the same signification as in (23). 



The last terms in (23) and (24) are the same as if the 

 solid were subjected to a uniform pressure p ; they are inde- 

 pendent of the orientation of the axes of elasticity. The first 

 terms, however, representing the influence of the apparent 

 weight, depend on which of the three principal axes of elas- 

 ticity is vertical. 



It the body were a cube of side 2a, supported in turns with 

 the three principal axes vertical, the corresponding changes 

 Bv u Bv 2 , bv- 6 in the volume are connected by the elegant 

 relation 



8» 1 + 8t), + ^=-)(W-W / )o + 3j?ii}/i, . . (25) 



where W is the weight of the cube, "W the weight of the 

 liquid displaced. 



The formulae (23), (24), (25) apply equally whether the 

 surrounding medium be a liquid or a gas, but in the latter 

 case p'/p, or W/W, would usually be negligible. Supposing, 

 for instance, a cylinder to be suspended first in air then in a 

 liquid of density p\ the barometer remaining steady, the 



* Camb. Trans. /. c. 



