ON THE MECHANICAL EQUIVALENT OF HEAT 



367 



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

 replace 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 



^=100 



H h 





I /H loo H\_b m H lw -bH\ 



~m- r t\ 



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; = 20; 

 H wo h = 270 mm. ; and h = 750 mm. If x is the variable, 



, dx *rp dx T _ 04 dx 



~~dT ~oTT 1000 ~ ~dT ' 



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 H, seeing that this includes errors in reading the 

 barometer as well as the cathetometer. For this reason, as mentioned 

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

 the barometer is nearly dispensed with by use of an artificial atmos- 

 phere of constant pressure. 



The value of -^.does not seem to affect the result to any great extent; 



and if it was omitted altogether, the error would be only about 1 in 

 1000, assuming that the temperature t was the same at the determina- 

 tion of the zero point, the 40 point, and the 100 point. It seldom 

 varied much. 



The coefficient of expansion of the glass influences the result very 

 slightly, especially if we know the difference of the mean coefficients 



