50 Mr. A. R. McLeod on the 



lag than alcohol thermometers which have the same accuracy 

 of reading. 



A general expression is given for the steady lag of a bi- 

 metallic thermometer, used in air. The lags of some 

 bimetallic recording thermometers considered are of the 

 same order as those of the cylinders considered, but the com- 

 parison is not based on an equality of temperature scale. 

 The lag of the Dines "ballon sonde" thermometer is very 

 small. 



Experiment shows that the mean surface conductivity for 

 a bimetallic thermometer in the form of a flat spiral which 

 is wound in a cylindrical tube, may be increased 34 per cent, 

 by turning the thermometer from the " end on " position to 

 the " broadside on " position in a wind of 5-10 m.p.h. 



Radiation, convection, and the effects of the glass wall, in 

 the case of liquid-in-glass thermometers, are not considered. 



1. Steady Mean Lag of a Metallic Thermometer. 



The steady lag in the mean temperature of a thermometer 

 may be written in the form 



M* + .?) (1) 



where G is the constant temperature-time gradient in the 

 medium, p is the density, o» the specific heat, K the thermal 

 conductivity, and h the surface conductivity of the thermo- 

 metric substance, and M and N are constants whose values 

 depend upon the shape and dimensions of the bulb. 



Under certain circumstances the internal lag, which is 

 represented by the first term in (1)_, may be neglected 

 leaving only the surface lag, represented by the second 

 term and due to the passage of heat across the surface, to 

 be considered. This may be done if K is large compared 

 with h, which is the case for most metals used in air or some 

 other medium in which the value of h is not too great. It 

 may also be done if one of the dimensions of the thermo- 

 meters is very small, since M depends upon the square of 

 the linear dimensions while N depends only upon the first 

 power. In such cases the steady lag may be written in 

 the form 



XGpo-jh (2) 



and the value of N is given by the ratio 



^j. _ volume of thermometer .„. 



area of exposed surface ' 



