BETWEEN 75 AND 150 MILLIMETEES OF MEBCUin', 
427 
( 5 ), the actual heights of the mercury (at the same temperature) he Hj, Ho, we have 
for the corresponding H/(l + mr), where m = ‘00017. Thus in the notation 
already employed 
and 
Pi 
Ho 
1 + ’ 
or 
Ho 
1 + niT^ ’ 
H, + Ho Hi + Ho 
— - -^ or — - -^. 
1 + ’ 1 + vn^ 
The quantity of gas at a given pressure occu] 3 }ung a known volume is to be found 
by dividing the volume by the absolute temperature. Hence each volume is to be 
divided by 1 + (iO, 1 + /dr, 1 + ydh as the case may be, where yd is the reciprocal of 
the absolute temperature taken as a standard. Thus in the above example for air 
(p. 426), yd = ^ — 9 ^- equations, expressing that the quantities of gas 
are the same at the single and at the double pressure, accordingly take the form 
Ho 
+ 
Ho, 
^3 
Y 5 
1 + /3ti ' 
1 + j3i 
1 + ^Tg ^ 
\ ’ 
' 5 
1 + /3t 
B(Hi + H, ) r V, Vs + VH 
1 + VlT^ [I + /3^3 I + /d'r 2 j ’ 
B(Hi+H,) Vg-t Vf 
1 + 1 + 
where B is the numerical quantity to be determined—according to Boyle’s law 
identical with unity. 
By subtraction we deduce 
1 BV,(Hi + H,) 
(1 + 7)iT]) (1 + ^0^) ViHjfl + mr^il + ^^ 2 ) 
^V3[ B(Hi + H 2 ) _ B(Hi + Ho) 
LBo( 1 + 4- /drg) Ho(l + (1 + 
_^^_ 
(1 + mTi)(l + ydTi) ‘ (1 + 4- jBr^) 
+ 
B(H, + Ho)Vi 
H,Vi 
V. 
(1 + mT3)(l + /dxg) (1 + mT^ (1 + /3T4) 
1 1 
+ 
Vi 1_(1 + mri) (1 + /3q) (1 + OTTg)!! + /^h)] 
B(Hi + H,)(Ah-V;) 1 
- V, 
HgVi (1 + mr^) (1 + 
1 
Vi (1 + mr^) (1 + /S^g) 
( 6 ). 
The first three terms on the right, viz., those in Vg, V 4 , Yg, vanish if Tj = t . 
3 I 2 
3> 
