a new Air -thermometer. 303 



When t 2 is less than t l — t i the value of x 1 is positive; in this 

 case, therefore, the value of od must be added to the temperature 

 indicated by the scale. 



When t 2 is minus, or when t% is greater than t x — t, then in 

 both cases the value of x' is negative ; in these cases, therefore, 

 the value of x' must be subtracted from the temperature indi- 

 cated by the scale. In both these cases the value of x' increases 

 with / 2 . 



If t and t x be taken as the extreme temperatures of the instru- 

 ment, then we have as the condition of maximum error, 



whence we find 



Max. value of a; '=(^) 2 |(I-3 3 p ,). . (8) 



T i. f QOO ± OfiO P_ £ *_ ■*- * f 



Leu-o^^-oo, p _ 6 , a ,- 18x550 > ^-18x4160' 



then we find max. value of x =*01; that is, in this case the 

 maximum error would be the hundredth part of a degree. 



But as it would be more convenient for construction to take / 

 and t x at certain mean limits, thus, let 3(^ — t) be the extreme 

 range of temperature, that is, t x — t degrees above t v and t x — t 

 degrees below t ; then we find, by substituting -f 2{t x — t) or 

 — (t l — t) for t 2 in equation (7), 



Max. value of x' = -2(-,-0 2 f (j- 3-,)- • (9) 



Let £=50°, ^ = 68°, giving an extreme range of temperature 

 between 32° and 86° ; then taking the values of the other quan- 

 tities the same as before, we find the 



Max. value of x 1 — -0096 ; 



that is, in this case the maximum error would be less than the 

 hundredth part of a degree, — an almost inappreciable quantity. 

 Within this range of temperature, therefore, the indications 

 of the instrument may be taken as perfectly true. 



Hastings, September 14, 1860. 



