Mr. Joly on a Hydrostatic Balance. 267 



determination of a?. Or, what is the same, we proceed by 

 simply removing x when equilibrium has been obtained with 

 x+Wj and substituting a weight w u so that equilibrium is 

 again obtained, when w x is the required value of x. It is 

 easy to guard against change of temperature in the brief 

 interval necessary to effect the successive equilibrations. The 

 process of weighing is, in short, the well-known one of sub- 

 stitution, and with the usual correction for unequal air 

 displacements of the weights and the substance is accurate 

 to a degree depending on the sensibility of the float to 

 indicate a small change of load, w T hen the downward acting 

 forces are very nearly in equilibrium with the upward acting 

 forces. This consideration, i. e. the degree of sensitiveness 

 possessed by the arrangement, next claims attention. 



The system as described is, in principle, identical with the 

 Nicholson hydrometer, used as a weighing machine, the latter 

 arrangement being supposed inverted while still retaining the 

 liquid. But the inversion of the hydrometer introduces this 

 important difference, that the stem supporting the pan of the 

 hydrometer, a compression member, becomes in the hydro- 

 static balance a tension member, and hence, stiffness being 

 no longer a requisite, may be made of extreme fineness, and 

 the retarding effect of the adhesion of the liquid on the wire 

 at its circle of emergence much reduced. 



If, indeed, we assume the effect of this adhesion of the 

 surface-film to increase in direct proportion to the radius 

 of the circle of emergence, it would appear — observing that 

 the tensional strength of the wire increases proportionally to 

 the square of its radius — that the sensibility to a small 

 fraction of the entire load falls off only as the square of the 

 carrying capacity or load which the balance will bear. There 

 is, in short, reason to expect that, as we increase the size and 

 carrying capacity of this kind of balance, no diminution of the 

 fractional sensibility occurs, but rather an increase ; the 

 sensibility increasing approximately as the square root of the 

 power of the balance. Thus, if we double the diameter of 

 the wire, the balance will now indeed indicate nothing smaller 

 than double the least weight formerly causing displacement ; 

 but, on the other hand, we may assume a quadrupled carrying 

 capacity. This leaves out of consideration the effect of vis- 

 cosity of the liquid. 



The effect of viscosity will hardly be to reduce the sensi- 

 bility, but rather to render more tedious the use of floats 

 having large displacements. As, however, the tangential 

 resistance to the motion of a solid surface, in the act of com- 

 municating a shearing strain to a liquid, is proportional to 



