**Zl**, z2,...zn) yl, y2,.

Yl, y 2,...yn) (**zl**, z2,...zn z1, z 2, ï¿½ï¿½ï¿½zn xi, 'X' 2,...

If the steam at A were dry and saturated, we should have, assuming Regnault's formula (to), H A -H D = 305 (0'-O), whence, if S = .475, we have **zL** = .3 0 5 (0 '- 0)-.

By 7 (5); hence, if ~, u, v be now used to denote the component angular momenta about the co-ordinate axes, we have X=~tm(pyqx)ym(rxpz)**zl**, with two similar formulae, or x= ApHqGr=~, 1

If the length of the arms AC =BC =/,CD =a,SD=s, the angle of deviation of ° Z the balance from the horizontal =4), the weight of the beam alone G, the weight on one side = P, that on the other = P +Z, and lastly the weight of each scale with its appurtenances = Q then **Zl** tan:473 - 12 (P+Q)+Z la+G sj From this it is inferred that the deviation, and therefore the sensitive - ness, of the balance increases with the length of the beam, and de - creases as the distances, a and s, increase; also, that a heavy balance is, ceteris paribus, less sensitive than a light one, and that the sensitive - ness decreases continually the greater the weight put upon the scales.

Finally, if a is made extremely small, so that practically tan (A = **Zl**/Gs, the sensitiveness is independent of the amount weighed by the balance.