Mr. T. Tate on a new Self-registering Mercury Barometer. 267 



M = l*57, then D=3'4 nearly, and vol. globe =21 cubic inches. 

 Assuming a=l, MH = 3, vol. tube IF=1, then 



i>= 21 + 3x1 + 1 = 25 cubic inches. 



As regards the disturbances arising from change of tempera- 

 ture, it is to be observed that the instrument, under all eligible 

 forms of construction, is to a great extent self-corrective as 

 regards the scale d ov c; for whilst the gravity of the float, by 

 an augmentation of heat, is increased by the expansion of the 

 liquid, at the same time this gravity is decreased by the expan- 

 sion of the mercury which causes a portion of it to pass from 

 the cup into the tube, it being borne in mind that the tube is 

 wider at KL than it is at KD. But a certain value may be 

 assigned to a and D K which shall render this correction strictly 

 true for mean atmospheric pressure, and approximately true for 

 all other pressures. 



In order that the float may remain stationary under a change 

 of temperature, the increment or decrement, as the case may be, 

 of the force of floatation must be equal to the increment or de- 

 crement of the weight of mercury in the cup. Keeping this 

 condition in view, let 



Sj, s l = the weight of a cubic inch of mercury and liquid re- 

 spectively at t l temperature, S and s being their 

 respective values at t temperature. 

 v = the volume of displaced liquid at mean temperature t, 



and mean atmospheric pressure P. 

 <?! =a internal section of the small tube DK. 



-, 3, - = the expansion per unit of volume for mercury, water, 



and glass respectively, corresponding to * x — t degrees 



of temperature. 

 m = KC, the column of mercury in the wide portion of 



the tube. 

 m' = ID, the length of immersion of the tube in the mercury. 

 h = DK, the column in the small portion of the tube. 

 h!= the length of the tube DK, measured from its fixed 



point of attachment K to the frame. 

 H as the height of the liquid in the glass jar. 



Then we find— 



Vol. mercury in the tubes DK and KC before expansion 



—c-Ji + km. 

 Vol. of this mercury after its expansion 



= (c 1 h + km)(l+^\....{v'). 



T2 



