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



■*-'-iM(«-*)(-i-£K-i-}*<»> 



*-r £-. ■ rh- i{$0 -a-^('-|)}«- m 



Now in order that the float may remain stationary under 



this change of temperature, we must have «■/' = w x ' ; but vf^u/; 



hence we obtain by equating (10) and (11), and putting 



Aw. 



-j = r, or A=n«, 



A—a Ti—1 



Eliminating r by means of equation (3), observing that 



1 -J- Ot OL 



T-~Ta ~ ~o ver y nearly, and solving the resulting equality for the 

 value of a, we get 



«-")C-^-f-)<-i & 



a= ; , . (12) 



3(»-Dg-» 



which gives the value of a in terms of k, c, n, &c., in order to 

 render the instrument self- corrective for changes of temperature 

 under all atmospheric pressures. No correction, therefore, being 

 required for the indications of the scale d or c, that of C will 

 require the same correction as in the ordinary barometer. 



The rates of expansion of the substances being uniform, this 

 expression is independent of t x —■ t, that is, it holds true for all 

 temperatures. The same observation applies to equation (9). 



Taking t l —t = 18°, then - = p^, - = . , fi „ ; and calculating 



the mean rate of the expansion of water from the experi- 

 ments of Hallstrom between the temperatures of 46° and 86°, we 



find i = ^ = - nearly. Also let *='08, c=-04, - = 13*5. 



p ooU a * s * 



w=16. 



Then from equation (12) we find a = '94. 



From equation (9), taking c, = «026, H = 17, P=29'5,m'=4, 

 and v = 25, we find h = 10*96, or 11 inches nearly. 



The values of a and h here found, form the conditions of com- 

 pensation for the disturbances arising from change of tempe- 

 rature. 



