268 Mr. T. Tate on a new Self-registering Mercury Barometer. 



"Rise of atmospheric column due to change of density of the 



mercury = P-. 



Vol. mercury in the tubes taking the expansion of glass and 

 mercury into account 



= c -( 1 + J> +i ( 1+ |)(" 1+p D 



Increase of vol. of the mercury in the cup due to the elonga- 

 tion of the tube DK=(c-c 1 )|-. . . (i/"). 



P 



Now assuming that b is large as compared with k, and there- 

 fore that the level of mercury in the cup is not affected by the 

 expansion of the mercury which is in it, we have 



Vol. mercury taken from the cup ==t/' — t/ — 1/ /; 



= {(P-m)A-c,A} \ + {2(c,4 + Am)-(c-c,)A'} ^. 



Neglecting (c— c^h' as being small compared with 2{c l h-\-km), 

 and taking , ■ ■ = 1, which it is in all cases very nearly, we get 



o ~— c 



Weight lost by the mercury in the cup, 



g 

 But Sj = z, h— m' + ro=P; 



a 

 .\ Y—m=h—m', and m=P + m' — h; 



••• * - tt .{<*-«>> ( 1 -|>+( p +'»')*|H*}- (7) 



Again, to find the changes produced by the expansion of the 

 liquid, &c, let z be put for the increment of height of the liquid 

 due to the change of temperature ; then we get 



Vol. liquid before expansion = AH— v, 

 .-. Vol. liquid after expansion = (AH— v) (l+ 3). 

 But taking the expansion of the glass into account, we have also 

 Vol. liquid after expansion =Afl + 5-j(H-f-z)— v ( 1 + - ) 



-(>*& 



