4 Mr. T. Tate on the Construction of 
in its indications as an ordinary barometer costing about thirty 
shillings, and certainly much more sensitive. 
Let p = the pressure of the atmosphere when the gradations 
for temperature are made; 4 =the height of the column of 
liquid in the tube above the level of liquid in the flask, cor- 
responding to ¢ temperature, V volume and P pressure of the 
gas in the flask, p being constant ; g,= the change of the height 
of the column at ¢, temperature, V, volume and P, pressure, 
p being constant; g, = the change of the height of the column 
(estimated from the last) at ¢; temperature, V, volume and P, 
pressure, and p, atmospheric pressure; @ = the section of the 
tube; b = the section of the liquid in the flask ; s = the specific 
gravity of mercury, that of the liquid being unity ;—then as- 
suming the section of the tube to be uniform, we find 
PoVo=P,V; 
but h 
" Vy=V+aq3 Ve=V+a(+42)3 P=p+ 5; 
1 b—a 1 b—a\ ,1 b-a 
P, =p+=(i+a-5"); and P=p.t+(h+a-5") Tied 3 
hence we get 
b—a 
1 sprh+n—— b 
a — 
Be Paley Say. Stereo i) Oe (1) 
Pam bag e 
When 3 is very large as compared with a, we may take = il, 
and then 1 +h+ 
P-Pe=%0X5) eo tif, ~ + + « (2) 
Pa ae 
where the signs of g, and g, are + when measured upwards, 
and — when measured downwards. 
This formula expresses the change of atmospheric pressure in 
terms of the variables g, and gy. It is obvious that p—pz, is not 
exactly in the ratio of go, although it is so very nearly; for the 
value of the quantity within the brackets is but slightly affected 
Ey any possible values which may be given to the variables q, 
and qo. 
Neglecting g, and g, within the brackets, we obtain the ap- 
proximate formula 
Vv 
s(p—Po) 
Gy es 
