BETWEEN 75 AND 150 MILLIMETRES OF MERCURY, 
421 
When the second manometer is brought into use, the volume must be halved, for 
which purpose the mercury is raised through the bulb until it stands somewhere in 
the upper tube. The whole volume is now Vg + And since 
Vg + V, = 2 (Vg + V,), 
we see that 
Vg ^ V, - 2V„ 
which may be regarded as determining Vg, V^. and Vg being known. A somewhat 
close accommodation is required between Vg, about 19 cub. centims. in my apparatus, 
and the whole contents of the side-tube. 
General Sketch ofTheorii. 
As the complete calculation is rather complicated on account of the numerous 
temperature corrections, it may be convenient to give a sketch of the theory upon 
the assumption that the temperature is constant, not only throughout the whole 
apparatus at one time, but also at the four different times concerned. We shall see 
that it is not necessary to assume Boyle’s law, even for the subsidiary operations in 
the side-tube. 
Vj = volume of two large bulbs together between I and G (about 258 cub. 
centims.), 
Vo = volume of upjDer bulb between G and H, 
Vg = volume between C, G and highest mark J on side-tube, 
V^ = measured volume on upper part of J from highest mark downwards, 
Vg = measured volume, including bulb, of side apparatus from highest mark down¬ 
wards. 
Pi = small pressure (height of mercury in right-hand manometer), 
Pg = large pressure (sum of heights of mercury in two manometers). 
In the first pair of operations when the large bulbs are in use, the pressure Pi 
corresponds to the volume (V, + Vg Vg), and the pressure P 3 corresponds to 
(Vg -p Vg -p V^), the quantity of gas being the same. Hence the equation 
Pl(Vi + Vg-l-Vg) = BPg(Vg-pVg-f V,). '. ( 1 ), 
B being a numerical quantity which would l)e unity according to Boyle’s law. In 
the second pair of operations with a different quantity of gas but with the same 
'pressures, the mercury stands at G throughout, and we have 
Pl(V 3 + Vg') = BPg(V 3 -PV;).( 2 ); 
whence by subtraction 
Pi (Vl + Vg - Vg') = B Pg (Vg .p V, - V/) . 
(3) 
