Lags of Thermometers. 63 



tube for a mercury thermometer, and *203 sq. mm. (diameter 

 = *50 mm.) as the smallest section for an alcohol thermo- 

 meter, we find the value //,= 1/100. While if the smallest 

 urea for the alcohol thermometer is '0506 sq. mm. (diameter 

 = •25 mm.) we find yu,= l/25. The corresponding values o£ 

 /us are 1/4*6 and 1/2*9. Hence, by taking the smallest 

 possible bores for the capillary tubes in the thermometer 

 stems, the accuracy of reading remaining the same for all 

 thermometers throughout, it is possible to reduce the lags 

 for a mercury sphere by a factor whose value is of the order 

 1/5 to 1/3, when the lag for the alcohol sphere has reached 

 its lowest possible value, consistent with the particular 

 accuracy of reading, i. e. linear scale, required. 



Accordingly, if we are seeking to determine the thermo- 

 meter with the least possible lag consistent with the accuracy 

 obtainable with an alcohol sphere of radius *550 cm. and a 

 capillary tube of bore "50 mm. diameter, the lags obtained 

 with mercury in para. 4 must be multiplied by a factor '2 in 

 the case of the sphere, and "1 in the case of the cylinder. 

 The mercury cylinder would thus be the best possible with a 

 lag of '07 for Gr = "028° C./sec. The mercury sphere would 

 have a least possible lag of '24° C, which is less than 

 the least possible lag for the alcohol cylinder of *36° C. 

 Of course these very fine capillary tubes may be very 

 objectionable for various purposes, owing to difficulty in 

 reading readily, or for some other reason. The point which 

 is here emphasized, however, is that the possibility exists of 

 making mercury thermometers with much less lag than 

 alcohol thermometers which have the same linear scale. 

 If the same capillary tube is used with equivalent bulbs, 

 the conclusions of para. 4 stand, and the alcohol cylinder 

 has the least lag. A further variation may occur when the 

 accuracy of reading (linear scale) is changed. This has not 

 been considered. 



6. Bimetallic Thermometers. 



As an example of the application of formulae (2) and (3), 

 the case of a bimetallic recording thermometer by Pastorelli 

 & Rapkin may be considered. In this instrument the pen 

 is moved across a rotating cylinder by the relative thermal 

 expansion of two strips of aluminium and brass, secured face 

 to face. Each strip was 29 cm. long, 1*15 cm. wide, and 

 •09 cm. thick. Hence for each strip, 



XT 1-15 x -09 nr70 , 

 JN= l-^5 + '18 = ( a PP rox 0- 



