Tempei^ature of Meixury in a Siphon Barometer. 255 



than 0.00002, 8'{t'—t) {a'~b'+2f) can rarely differ from a con- 

 stant mean so much as 0.0009. Wherefore, putting 



s'{a'-b'-\-2f)=A', a constant, (5) 

 equation (3) becomes a' — 6'- (a -6) = (A — A") {f-t.) (6.) 



This equation is of the same form as (3,) differing from it only 

 in the value of the co-efficient of (f — tj) 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. 



If the 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 

 makes known the value of (/,) then would A and A'' be known ; 

 and (6) would give us 



which shews the mean temperature of the whole column in terms 

 of the constants A, A', {a,) (b,) {t.) 



But if A and A' are not known with great exactness ; if we 

 compare the elements {a") [b") [t") of any other observation, with 

 (a,) (6,) {t,) we have in like manner 



a" - h"— (a - 6) = (A - A') {f - 1) (8) 

 Eliminating (A — A^) between (6) and (8,) there results 

 a'-b'- {a-b) t'-t 

 a" - b"'^ {a - b)~F^t ' ^^^ 

 which expresses the relation between the elements of any three 

 sets of observations. Solving (9) for (f ) we have 



Wherefore, knowing the elements of any two observations (a,) 

 (6,) {t) and {a" ,){b" ^){t" ^) we have the temperature {t') in terms 

 of its corresponding readings [a',) {b'.) 



It is evident that the observations (a,) (6,) {t) 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 

 {i'' - 1) may be as large as circumstances will permit. 



