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

 and 



If 6= a, then equation (1) becomes 



r= 7~4 - < 3 ) 



Now as e, in equations (1) and (3), is proportional to P— p, it 

 follows, the tubes being uniform in section, that the graduation 

 of the scale d or c must be uniform ; and equation (2) shows 

 that the same observation applies to the scale C. Equations 

 (1) and (3) express the range r of the instrument, estimated on 

 the scale d or c, compared with that of the ordinary barometer ; 

 and similarly, equation (2) expresses the ratio of the range esti- 

 mated on the scale C. 



If k = c, that is, if the tube DG is selected so that it shall 

 exactly pass within the tube KL, then equation (1) becomes 



r= r— (4) 



sa A 



Assuming b to be large as compared with k, then we get ap- 

 proximately, 



E=6?+P-^, and.*. R=r + 1; ... (5) 



that is to say, the ratio of range of the scale C exceeds that of 



the scale d or c by unity 



In the instrument which I have constructed, £='08, c=*04, 



s 1 

 a = l, k = tz~e> A = 16; then from equation (3) we get 



r= j jg = 2 nearly. 



- 04+ i^ x r5( 1+ ' 04 ) 



In this case the range is double that of the ordinary barometer. 



And from equation (2) we get 11 = 2*9, or 3 nearly. In this 

 case the range is three times that of the ordinary barometer. 



Neglecting the weight of the float and the force of floatation 

 due to the displacement of the tubular portions of the float, we 

 find 



*-vf3& ••■•■• n 



This value of D is sufficiently exact for construction, inasmuch 

 as a little more or less mercury in the tube I F would correct 

 any slight error arising from the elements neglected. Thus if 



