On the Temperature Correction of Siphon Barometers. 207 
horizontal plane below the instrument, and / the barometric 
pressure, all at a temperature of ¢ degrees Centigrade. When 
the temperature rises to ¢+ A¢ degrees, let the above quantities 
become 
h,+Ah,, hotAh,, h+Ah; 
then, if m=cubic expansion of mercury for one degree Centigrade, 
Ah=mhAt. 
And since 
h=h,—h, 
and 
h+ Miz (fy + Ady) — (hp + Als), 
we have 
Ah, —Ah,=Ah=mhAt. 
Now if 
e = volume of mercury in the barometer; 
a = area of the bore of the tube at upper surface of mercury; 
6 = area of the bore of the tube at lower surface; all at ¢ 
degrees ; 
9,= the superficial, and g, = the cubic dilatation of glass ; 
it will be easily seen that, at the temperature ¢+ A? degrees, the 
capacity of that part of the tube which was occupied by the 
mercury at ¢ degrees will become c(1-+9,At); while the capacities 
*of the portions of the tube at the ends of the former mercurial 
column, which are now filled by the expanded mercury, and 
whose lengths are Ah,, Ah,, will be 
a(l+g,Az)Ah,, 65(1+9,Az)Ah,. 
The whole volume of the mercury will therefore be 
(aAh, + bAA,)(1+9, At) +¢e(1+9,Az). 
But the volume of the expanded mercury must also be 
e(1+mAz) ;sx 
whence 
(aAh, + bAA,) (1 +9,At) =c(m—g_) At. 
This equation, along with 
Ah, —Ah,=mhAt, 
Ane 4e(m—go) +bmh(1 +9,Az)t = 
(a+ 6)(1 + 9,42) 
Difige {e(m—g.) —amh(1 +9,A?) pAt 
(a+6)(1-+ 9,42) 
gives 
