•348 Scientific Proceedings, Royal Dublin Society. 



At tills point we know that a total weight W is in the pan. 

 If the added weights amount to iv, suppose, then x = W - w. 

 Practically, however, W is a quantity variable with the tem- 

 perature of the float and of the water, their densities altering to 

 different extents. When, therefore, accurate results are required, 

 we cannot assume any constant for the balance, but must determine 

 afresh the force W with each determination of w. Or, what is 

 the same, we proceed by simply removing x when equilibrium has 

 been obtained with x + w, and substituting a weight w Y , so that 

 equilibrium is again obtained, when w Y 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 substitu- 

 tion, 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, 

 when 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 atten- 

 tion. 



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 hydrostatic 

 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 is much reduced. 



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

 film to increase in direct proportion with the radius of the circle of 

 emergence, it would appear — observing that the tensional strength 

 of the wire increases proportionally to the square of this 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 



