Mr. T. Tate on a new Self-registering Mercury Barometer. 269 



By equating these two expressions, we get 



1 . 1 tTT ^ 

 Zp 



(AH-^+v-i-AI 



(A-*)(l + !) 

 Buoyancy float after expansion = sA 1 +-)+s l a( 1 -f — h; 

 .'. loss of buoyancy of float, w'—sv— tMl-J — J—Sjflf 1 +a-)z* 



m 



Substituting the value of z 9 and observing that s x = ~, 



1+ -0 



we get 



^.•ra«'-?)-M'- 2 4)}- • * 



Now in order that the float may remain stationary under 

 this change of temperature, w' must be equal to w" ; hence we 

 find by equating, 



if I • 1 rH(-K)--("!f)} f W+">|}' 



<MH£) 



which gives the length of the small tube DK, so as to render 

 the instrument self-corrective at mean atmospheric pressure, as 

 regards the disturbances arising from change of temperature. 



Now the relative values of a and v may be determined so as 

 to render this principle of compensation applicable to all other 

 atmospheric pressures. 



Let the pressure of the atmosphere become Pj, and let the rise 

 of the float under this change of pressure be e } ; moreover, let 

 v x = the volume of liquid displaced by the float, Hj = the 

 column of liquid in the jar, m\ — the length of immersion of the 

 tube DK in the mercury; then 



£= 





P 1 = P+£l. jjL m ^M.^iuj H lS =H-/SL; 

 1 f A— a ] A— «' 



and when b = a> 



Substituting these values in equations (7) and (8), we get 



