Mr. J. Joly on a Hydrostatic Balance. 271 



material having a high coefficient of expansion, as zinc, such 

 dimensions may be given to the apparatus that the water 

 space will, with change of temperature, increase at the rate of 

 expansion of water. In other words, there would be no 

 expulsion of water or entry of air with atmospheric variations 

 of temperature. Thus for a spherical float in a spherical 

 chamber, and assuming any desirable radius, r, for the float, 

 let x be required radius of outer vessel ; also let g, z, iv, be 

 the coefficients of cubical expansion of glass, zinc, and water ; 

 equating the increments of volume for a rise of one degree. 



x z z = r d g + (a? — ? >3 ) w ; 



,/ = 0'000025; r = 0'000082; ^ = 000015; ^ 3 = l'838r 3 . 



Take now the case of r=3 centims. (a displacement of 113 

 cubic centims.), then £=3*67 centims., which is sufficiently 

 large, and would permit of a vertical travel of one centimetre. 

 Such a little balance would weigh to 100 grammes and the 

 external diameter of the outer case need not exceed 7 # 5 

 centims. 



Again, the expansibilities of iron and zinc would be found 

 suitable. AVith these materials the form of fig. 1 might 

 conveniently be conferred on the balance, and large apparatus 

 constructed, capable of carrying four or five kilogrammes, 

 and indicating, probably, a very small fraction of the load. 



The use of mercury in place of water suggests itself as a 

 means of conferring a greater degree of compactness. In 

 this case iron or wood might be used in their construction. 



For the purpose of determining the specific gravities of 

 solids, I use a little claw for supporting the substance under 

 water, which can be suspended by a fine wire from a hook 

 beneath the pan. The substance is first weighed in the pan, 

 the claw being attached and immersed in a vessel of water 

 placed beneath. On transferring the substance to the claw 

 an increased weight will be required for equilibrium ; the 

 increase is obviously the weight of displaced water. 



It is observable in the hydrostatic balance that, wdien the 

 float is about to descend, the system is one of unstable 

 equilibrium. The descent of the float is accompanied, in fact, 

 by decreased displacement in the liquid due to the emergence 

 of the wire, the effect being similar to that of an ever-increas- 

 ing dow nward pull upon the float : once started, it tends to 

 descend to its lowest point. If we provide a second wire, 

 similar to the emerging wire, extending downwards, and 

 dipping into a vessel of water, as occurs in the operation of 

 determining specific gravity, the effect is in all cases obviously 

 annulled. The correction is, however, with wire of the 



