Self Registering Barometer. 479 
also 
4 : _ § diminution of buoyant force caused by the increased volume of the mercury 
c” (om — 8) dt. w= se the hydrometer. 
hence by subtraction we deduce 
s¥ 8!" dh+(cl" s!"—c'v") (8m—8) dt 
—— ,W= 4 total increase of the buoyant force of the hydrometer. 
sv—g!!’ 
hence by equating the total gain of weight of the cistern to the total gain of buoyant 
force of the hydrometer, and dividing both sides by w, we deduce the equation 
(cs e's’) (8m—di) dt+c's' (6m+8t) dt—c's” dm dt—s's" dh i 
Ee 
ss" dh+(e"s'" —c's") (8m~—8i) dt 
a ee eee 
vs” 
from whence by the ordinary processes of concinnation we deduce 
Sah 
{es +e"s!) (g's!) — (6's! — c's") (s"' ~81)] (Sm—8i)+e's! (sv 8") (8m+4 61) —C's" (8*— 81) dm 
Vall 
Sra (siRHs))i--sist (v6) 
x dt 
(K) 
being the value, for the entire effect of change of temperature equal to the number of 
degrees of Fahrenheit, df. upon the indication of the instrument. 
From equation (4), when the dimensions of the several parts of a barometer on 
this principle are known, we might, were it desirable, calculate the rising or falling of 
the instrument, consequent upon a change of temperature, for we know from 
the mean of very accurate observations by several eminent philosophers, that 
8m = .0183345 gp, and that 6 =.003367. gp. But any dependance upon such a cal- 
culation would in practice be by no means desirable, as the sources of error would be 
too many to admit of much confidence in the result. The better practical method, 
however, is readily deduced from a careful consideration of the foregoing equation, as 
follows. 
In equation (KX) it is obvious that s, s', s,s’, s’ dm, and 8 are all independant of the 
amount of atmospheric pressure, but that ¢, c’, c’,c” and c’ are all dependant upon that 
pressure, and are each functions of 8h” of the form y+ +‘ dh” ; y and y being certain 
constant quantities. The entire equation () therefore, if such values were substi- 
tuted for each of these equations, would assume the form 
dh=(0 +1" 8h") dt (L) 
In which T and I’ are constants, the values of which are very easily discoverable by 
two simple experiments, in which the effects of two known changes of temperature 
upon a given instrument, while the pressure remained unvaried, should be accurately 
noted, or more correctly should be deduced from means of many pairs of observations, 
VOL. XVII. 4a 
