é Temperature of Mercury in a Siphon Barometer. 255 : : 
than 0.00002, «/(¢/—t) (a’—b/+2/) can rarely differ from a con- 
stant mean so much as 0.0009. Wherefore, putting iis 
é = —/+2/)=A’, a constant, (5) 
culation (3) becomes a’ — b! — (a —b)=(A—A’) (t! —t,) (6.) 
This equation is of the a form as (3,) differing from it only 
in the value of the co-efficient of (¢ —t,) and expresses the rela- 
tion between the elements of any two sets of observations, em- 
bracing the corrections for the expansions of the mercury, scale, 
and glass tube. 
Ifthe volume of mercury (p+p’,) with which the barometer is 
charged, were known, as may have been determined with ex- 
actness by weighing the instrument before and after filling ; and 
also the point at which the tube and mounting are united, which 
nakes known the value of (f,) then would A and A’ be known; 
and a would give us | 
vst se A ne Af } (7) 
which shews the mean temperature of the whole column in terms 
of the constants A, A’, (a,) (b,) (¢.) 
But if A and A’ are not known with great exactness ; if we 
compare the elements (2”) (b’) (¢”’ Js of any other oheaerabinaa’ with 
(a,) (,) (t,) ae hays | in dks man 
aat= o) = (A 4’) (v4 (8) 
Eliminating ea 74) between (6) and (8,) there results 
a’- 0 —(a—b).. —t- 
| =e ava ©) 
which expresses ie relation between the elements of any three 
sets of observations, Solving (9) for (¢’) we have 
t’ —t 
’st+ PEED) [a’—b/—(a—b.) | (10.) 
Wherefore, knowing the elements of any two observations (a,) 
(8,) (2) and (a’’,)(b’,)(t’”,) we have the temperature (¢’) in terms. 
of its corresponding readings (a’,) (b/.) 
{t is evident that the observations (a,) (b,) (¢) and (a”,) (b”,) 
(t’,) should be made with great care, in places subject for the time 
to but slight variations of temperature, so that the thermometer 
Which is used, either attached or detached, may be depended 
Upon as indicating truly the temperature of the mercury. It is 
evident also, that accuracy would be materially promoted by us- 
ing the means of a number of successive observations rather than 
individual ones; and also by choosing such temperatures that 
("= 2) may be as large as circumstances will permit. 
a 
