where 



and 



For the first bulb, 



For the second bulb, 



OF ARTS AND SCIENCES. 



y = a — b = .00364. 

 £ = .0057. 



99 



p = .0058. 



To discuss the error of T due to errors in the constants, we must 

 replace a by its experimental value, seeing that it was determined 

 with the same apparatus .as that by which T was found. As it does 

 not change very much, we may write approximately 



From this formula we can obtain by differentiation the error in 

 each of the quantities, which would make an error of one tenth of 

 one per cent in T. The values are for T '=. 40° nearly; t = 20°; 



H,„ 



h = 270 rara ; and h = 750" 



If x is the variable, 

 T ,,. d. 



Ax ~ dT A T — d T 1000 — ,04 c 



TABLE VII. — Errors producing an Error in T of 1 in 1000 at 40° C. 



From this table it would seem that there should be no difficulty in 

 determining the 40° point on the air thermometer to at least 1 in 2000; 

 and experience has justified this result. The principal difficulty is in 

 the determination of II, seeing that this includes errors in reading the 

 barometer as well as the cathetometer. For this reason, as men- 

 tioned before, I have designed another instrument for future use, in 

 which the barometer is nearly dispensed with by use of an artificial 

 atmosphere of constant pressure. 



The value of -p does not seem to affect the result to any great 

 extent; and if it was omitted altogether, the error would be only 



