254 Temperature of Mercury in a Siphon Barometer, 



J)B' = e{t'-t)p 

 dd' = s{t'-t)p', 



and therefore \m'-^dd'=e{t' -t) {p^-f). 

 We derive from the figure D'D'^ = OD" - OD -DD' 



d'd"=^0d"-0d^dd'. 

 Equating the second members of these last equations, according 

 to (1), and denoting the upper reading OD'' by {a,\ and the low- 

 er reading Od" by (6,), and substituting for \yD'-{-dd' its value 

 expressed above ; we hdive a,-h, — {a — b)=B[t'—t){p-\-p'\ (2) 

 which is of the form a/ — h, — {a — h)=k{t' — t), (3) where A is a 

 constant co-efficient, since (e) is constant, and [p-\-'p') is constant 

 for the same barometer. This equation exhibits the relation be- 

 tween the elements of any two sets of observations, on the sup- 

 position that the scale is not affected by a change of temperature. 

 To correct this for the expansion of the scale, let D^'EFP re- 

 present the brass mounting which bears the scale D'^O' 0"¥ ; 

 and suppose the imaginary zero point O to have been assumed in 

 the same horizontal line with the zero point O' or O" of the brass 

 scale at the temperature {t). Since the expansion of brass is 

 more than twice that of glass, there can be but one point in the 

 graduated line, at which the glass tube and mounting are invari- 

 ably united. Let this point be Y ; and put 0Y=/ Let T>"', d'" 

 be those points in the brass scale, which are conveyed to D"^ d" 

 respectively by the augmentation [f — t) of temperature. Deno- 

 ting by {b') the ratio of expansion of brass in length due to one 

 centigrade degree, and by (a'), {b') the distances O'D''', 0"d"' 

 respectively, which are the actual readings at the temperature (f ) ; 

 we have \y"Vi"'=B'{t' -t){^a' ■\-f) 



d"d"'=8\t'-t){h'-f,) 

 and therefore D'^D'^' - d"d"'=^8\t' -t) (a' -b'+2f.) 

 We have from the figure 0'D''=0'D^"+D"D''^ (3') 



0''d"==0"d'''-{-d"d/'' (3''.) 

 Subtracting the latter of these last two equations from the for- 

 mer, and employing the notation and the above value of D'^D'^^— 

 d"d"", we have a,-b,=a'-b' + E\t' -t) {a' -b'-{-2f.) 

 Eliminating {a, — b,) between this equation and (2) there results 



a'-b'~{a-b)=£[t' -t){p+p')-e'[t'-t){a'-b'-\-%f,) (4). 

 Since the quantity {a' — b') in cylindrical siphon barometers dif- 

 fers from a constant by only about 4 millimetres for a change of 30 

 centigrade degrees in the value of (t' — t',) and since (e') is less 



