ME, W. CEOOKES ON THE ATOMIC WEIGHT OE THALLIUM. 
293 
Subtracting u from t, 
(*2)=2(*01)— 0*00531. 
Then (< 2 +?') + 2s+3(£— u) gives 
(*1)=10(*01)— 0*04286, 
.*. 0*09810997 =10(*01) — 0*04286, 
.*. 0*009810997 =(*01)— 0*004286, 
.*. (*01)=0*014096997 . U. 
From u we get 
0*014096997=(*01r")+0*00413, 
.*. (*01F / ) =0*009966997. ...... V. 
From t we get 
(*02) =0*014096997+ 0*009966997 — 0*00118, 
.*. (*02) = 0*022883994. ....... W. 
From s we get 
(*03)=0*022883994 + 0*014096997 — 0*00642, 
.*. (*03) = 0*030560991 X. 
From v we get 
(•06)=0*030560991 + 0*22883994 + 0*014096997 — 0*00607, 
.*. (-06) = 0*061471982. ....... Y. 
From v we get 
0*014096997 = (*01F) + 0*00410, 
.*. (*01F)= 0*009998997 Z. 
The value of the weights thus given was, however, their weight in air of the ordinary 
pressure; it became therefore necessary to ascertain their value in a vacuum. All 
bodies displace a bulk of air equal to their own volume, and the weight of this air is of 
course greater as their specific gravity diminishes. In delicate investigations this loss 
of weight is important. The reduction of the platinum weights to their true value in 
vacuo I calculated by the following formula : — • 
Let W = weight in air, 
w = „ „ water, 
a = specific gravity of air as compared with water ; 
then 
. . . W —aw 
x, or weight in vacuo , = > 
where 
«=0*001225, and 
1— «=z0*998775. 
The following Table shows the final results of these adjustments: — 
mdccclxxiii. 2 R 
