32 



Prof. W. Thomson on the Reduction of 



Twenty-four Feet below Surface. 



Observatory . . . 4G-87 + 0-655cos2tt(£- 1-013) 

 Experimental Gardens 47'09+0-920cos27r(f- -986) 

 Craigleith .... 46-07+ l'940cos27r(*- '849) 



The semi-annual terms in these equations present so great 

 irregularities (those for the Calton Hill station, for instance, 

 showing a greater amplitude at 6 feet depth than at 3 feet), that 

 no satisfactory result can be obtained by including them in the 

 theoretical discussion on which we are now about to enter. We 

 shall see later, however, that when an average for the whole period 

 of eighteen years for the Calton Hill station is taken, the semi- 

 annual terms are, for the 3 feet and 6 feet depths, in fair agree- 

 ment with theory ; and for the two greater depths are as small as 

 is necessary for the verification of the theory, and so small as not 

 to be much influenced by errors of observation and of reduction, 

 or of " corrections " for temperature of the thermometer tubes. 

 For the present, we attend exclusively to the annual terms. The 

 amplitudes and epochs of these terms, extracted from the pre- 

 ceding equations, are shown in the following Table : — 



Table I. Annual Harmonic Variations of Temperature. 



Depths 

 below 

 surface 



in 

 French 

 feet. 



Feet. 

 3 



Ampli- 

 tudes in 

 degrees 

 Fahr. 



7-386 

 5 063 

 2-455 

 0-655 



Epochs of maxi- 

 mum. 



In 



degrees 



In 



months 

 and days. 



Experimental Garden. 



Ampli- 

 tudes ir 

 degrees 

 Fabr. 



226 52 Aug. 19 9 063 



247 5 Sept. 8 6-661 



287 30Oct. 19 3-408 



365 6 Jan. 6 0-920 



Epochs of maxi- 

 mum. 



In 



degree 

 and 



In 

 months 

 and days. 



221 40 Aug. 13 

 239 20! 31 

 281 270ct. 13 

 355 O.Dec. 27 



Craigleith Quarry. 



Ampli- 

 tudes in 

 degrees 

 Fahr. 



8069 

 6148 

 4-216 



Epochs of maxi- 

 mum. 



In In 



degrees months 



and J and 



minutes, days. 



220 OAug. 14 

 233 43 26 



256 42 Sept. 17 

 1-836 |305 46 Nov. 7 



By taking the differences of the Napierian logarithms of the 

 amplitudes, and the differences of epochs reduced to circular 

 measure (arc divided by radius), thus shown for the different 

 depths, and dividing each by the corresponding difference of 

 depths, we find the following numbers : — 



