as <!'-fermined Five Platinum Resistance Thermometers. 221 



The harmonic expression to represent the temperature for any ther- 

 mometer will l)e 



= a + tti cos Xt + a-2 cos 2Xt + &c. 



+ b\ sin Xt + b-2 sin 2\t + &c ................ (c), 



or 



where t denotes the time represented as the fraction of the year, and 

 X is equal to 2?r. From the monthly means given above we deduce 

 the following : 



Values of the Coefficients. 



From each wave as observed at any pair of thermometers we obtain 

 two determinations of the diffusivity (&) of the gravel, one from the 

 diminution of amplitude and the other from the retardation of phase. 



In computing the value of the expression ^/(ir/k), the Paris foot and 

 the Fahrenheit degree have been used. 



I have omitted the results for the thermometer No. 1 (6 inches), 

 which are too much affected by the diurnal changes and other causes. 

 From six comparisons of the amplitude and retardation of the annual 

 wave at the remaining four thermometers we obtain twelve determina- 

 tions of the value of v/(;r/&), the mean of which is O'l 189. For the 

 half-yearly wave the mean value obtained in a similar way is O'l 187. 

 This close agreement of the mean values of x /( 7r A") derived from the 

 annual and half-yearly waves is very remarkable, and seems to indicate 

 a high degree of precision in the results. 



The paper deals with the observations of a single year, and the 

 results accordingly exhibit some discrepancies between theory and 

 observations which, although they are less than might have been 

 expected, are greater than one would like to see. These discrepancies 

 are due partly to the fact that the temperature variations are not 

 strictly of a periodic character, as the theory supposes, and as such 

 they might be expected to be diminished in the mean of a number 



