Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(**Vd-nIA**), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.

The greatest density of the liquid for which the instrument described above can be employed is W/V, while the least density is W/(**Vd-nlA**), or W/(V-Fv), where v represents the volume of the stem between the extreme divisions of the scale.

According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and **vd-dv** is proportional to e-1 3v2 dv, where (3 is equal to 312u 2; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e-0/1 2 =-- e-z = 22.

V'dP' = and (P **VdP** = C Po **vdp**, whence J f P' V'dP' - (P **Vd** .1 P = (P v?dp, I?'