208 Prof. Swan on the Temperature Correction 
Now since m is greater than g,, the coefficient of c in the above 
values of Ah,, Ah, is positive; and the coefficient of h is also 
positive for all possible values of At—g, being a very small quan- 
tity. It is therefore obvious that Af, can never vanish, but 
that Ah, may be positive, negative, or zero, according to the 
values which may be assigned to a, c,andh. The depression, 
by heat, of the mercury in the open leg of the siphon, or in 
other words, the negative value of AA,, observed by Mr. Negretti, 
and the value zero of the same quantity, observed by Mr. Alex- 
ander Bryson, are therefore both perfectly accounted for. 
It also appears, and this seems to be of practical importance, 
that we can altogether get rid of the temperature correction for 
the lower surface of the mercury, for any one given atmospheric 
pressure, by properly adjusting the value of c, and that thus we 
shall be able to make the temperature corrections for all other 
pressures exceedingly small. 
For this purpose it will be convenient to simplify the expres- 
sions for Ah,, Ah, by rejecting small terms. We then obtain 
c(m—go) +bmh 
Ah,= oat 
At, 
Ai nga) One od 5 
and Ah, will yanish when 
__ amh 
Jo 
A particular case will best illustrate this. Suppose that the 
siphon consists of two tubes of a uniform bore a, connected at 
the bottom by a narrow channel whose capacity may be neglected. 
We have then 
e=a(h+2l) ; 
Ah, = }(m—go)l + (m— 59o)h} At; 
Ahy= }(m—go)l—FGqh} At ; 
and when Ah,=0, 
[ifs Sens 
2(m—Jo) 
We must now select some particular value of h for which the 
temperature correction is to vanish; and we shall have, upon the 
whole, the smallest temperature corrections for extreme values of 
h if we make the temperature correction disappear for its mean 
value. Assuming then A=29°5 inches as sufliciently near the 
