262 Temperature of Mercury in a Siphon Barometer. 



In like manner, if we compare the elements {a„, b,„ t,„) 

 {a„„ b„„ t„„) with (a, 6, t,) successively, we shall have 



R2 



R2 



— (ct,/,-a)-(6,, 

 R= 



&)=4^V+y) r-0(28) 



r 

 R2 



6)=n,— i'+p' (^"'-0(29) 



Eliminating e\-Yp-{-p') from the last three equations, we shall 



have 



R2 



R2 



[a,-a)-{b,-h) 



{a, 



:^{a„-a)-{b 



a)-{b,-b) 



t'-t 

 ''t"-t 



(30.) 



t"-t 



R^ ~t"'—t 



-r{a,„-a)-{b,^,-b) 



(31.) 



Solving (31) for 



R3 



we have 



Ra (^'//-f)(6,-6)-(r-0 6,,-^) 

 ;^2 -(^///_^)«^^_a)_(i//_;() (a,^,_a) ^'^'^•>' 

 The readings in (30) and (32) are those of the supposed inex- 

 pansible scale. To change these equations into terms of the 

 readings taken from the brass scale, after being corrected for the 

 height of the meniscuses, we have 

 from (30 a, =a' -{-e\t' -t){a' +f)'^ 



a,,=a" +B'{t" -t){a" +f) 

 a,„=a"'^B'{t"'-t){a"'-\-f) 

 and from (3'0 b, =b' +^'{1' -t){b' -/) 



b,==b"+e'{t" -t){b" -f) 

 b^,^^b"' + £'{t'"-t) {b"'-f) 

 Substituting in (32,) and reducing, we have 



b"-b + B'{t"-t) {b"-b"')--^{b'" - b) 



(34) 



^' a"-a+e'[t" -t){c 



W33) 



R2 







t"~t 



t"'—t 



{a'" -a) 



Neglecting the third terms in the numerator and denominator, 

 as they are nearly equal and very small, we have 



