Mr. T. Tate on a new Self-registering Mercury Barometer. 265 



It must be observed that this increase of range is effected by 

 the action of two independent forces, viz. the force of floatation 

 of the cup, and the gravity of the mercury in the tube ; whereas 

 in the common wheel barometer, the change of barometric column 

 is simply multiplied by mechanical transmission. 



Let P = the height of the mercury column I C measuring the 



atmospheric pressure. 

 v = the corresponding volume of the liquid displaced by 



the float, v 1 being put for the volume corresponding 



to p pressure. 

 M = the corresponding volume occupied by the mercury 



in the float. 

 A = the internal section of the jar H N. 

 a = the external section of the tube E M. 

 D « the diameter of the globe G. 

 b = the internal section of the wide portion of the tube I. 

 c = the external section of the tube D K. 

 k = the internal section of the tube K L. 

 e = the descent of the float corresponding to p pressure 



of the atmosphere. 

 x = the corresponding rise of the mercury in the cup I. 

 E = the corresponding fall of the mercury in the tube KL. 

 S = the specific gravity of the mercury, s being that of 



the liquid. 



Then, when the float descends e inches, we find — 



Increase of volume of liquid displaced, v'—v=ea. ■ . __ - ; 

 Incr. vol. mercury occupied by the mercury in the cup = bx ; 



A 



.\ Sbx—sea 



' A-a' 



ea A, 



Xi 



S b A-a 

 Vol. mercury added to the cup = ec+(b-~ c)x; 

 Vol. mercury displaced from the tube KL=E£; 

 .\ ~Ek=ec + (b— c)x; 



■r. e f sa A ., V T 



But P—j» = E — e + x; 



. _i_ = rs= * (1) 



Phil. Mag. S. 4. Vol. 20. No. 133. Oct. 1860. T 



