Thermometers with Spherical and Cylindrical Bulbs. 141 

 From this last formula, putting t = 0, we find 



£« 8 - 2 = l/4. 



3. Numerical Conclusions for Mercury and Alcohol. 



For Mercury a 2 = -0437 c.g.s. units. 



For Alcohol (C 2 H 5 OH 100 %) . . a 2 = -0009026 „ „ 



Taking the same expansion (same thermometric scale) in 

 each example, and reckoning the coefficient of expansion 

 of alcohol as six times that of mercury, Ave have for the 

 dimensions of equivalent bulbs : 



Mercury Sphere , c= 1 cm. 



Alcohol Sphere c= *550 cm. 



Mercury Cylinder, 10 cm. long . . c= -36 cm. 



Alcohol Cylinder, ]0 cm. long . . c— -145 cm. 



Taking G = "032° O. per second, which corresponds to a 

 gradient of 1°"9 0. per thousand feet of height in the air, 

 and a rate of descent of one thousand feet per minute, 

 we have, taking the first exponential terms onlv, the 

 following lags for the above bulbs : — 



Lag of Mercury Sphere --049*=*045 e~' 4m . 



Lag of Alcohol Sphere .... = '713- -65" £T' 0285 ' 



Lag of Mercury Cylinder . . =-012— -012 e' 1 '^. 



Lag of Alcohol Cylinder . . = -095 - -089 e - ' 248 '- 



Here t is the time in seconds. These lags are not all 

 zero when t — 0, because first exponential terms alone 

 have been taken. The other exponential terms, however, 

 become very rapidly less and less in portant as t becomes 

 appreciable. The above lags reach 95 per cent, of their 

 steady values in the following times : — 



Mercury Sphere 7 seconds. 



Alcohol Sphere 103 „ 



Mercury Cylinder 1*5 ,, 



Alcohol Cylinder 12 



