126 



Prof. W. Thomson on the Reduction of 



rates of variation of logarithmic amplitude and of epoch at each 

 depth, and alter the scale of longitudinal reckoning downwards, 

 so as to reduce the numerical measures of these rates to equality. 

 This, however, we shall not do in either the five years' or the 

 thirteen years' term, which we have hitherto considered sepa- 

 rately, but for a harmonic annual variation representing the 

 average of the whole eighteen years 1837 to 1854. 



26. By taking for each depth the coefficients Aj, B t (not ex- 

 plicitly shown above), derived from the first five years' average, 

 and multiplying by 5 ; taking similarly the coefficients A,, B, 

 for the succeeding thirteen years' average, and multiplying by 

 13; adding each of the former products to the corresponding 

 one of the latter, and dividing by 18; we obtain, as the proper 

 average for the whole eighteen years, the values shown in the 

 following Table, in the columns headed A„ B,. The amplitudes 

 and epochs shown in the next columns are deduced from these 



by the formulas ^(A^ + Bj 9 ) and tan" 



A, 



■espectively : 



Table V. — Annual Harmonic Variation of Temperature in 

 Calton Hill, from 1837 to 1841 inclusive. 



Depths. 



A, 



in degrees Fahr. 



Bi 



in degrees Fahr. 



Amplitudes 

 in degrees Fahr. 



Epochs in 



degrees and 



minutes. 



3 feet 



6 „ 



12 „ 



24 „ 



-5-184 

 -2-080 

 + -5961 

 + -G311 



-4-989 

 -4-416 

 -2-3345 

 + 0306 



7-1949 



4-8812 



2-4094 



•6319 



223 54 

 244 47 

 284 19 

 362 47 



From these, as before, for ten terms of five years and of thir- 

 teen years separately, we deduce the following : — 



Table VI. — Average of Eighteen Years, 1837 to 1844; Trap 

 B-ock of Calton Hill. 



Depths below surface 

 in French feet. 



Diminution of loga- 

 rithmic amplitude, 

 per French foot of 



descent. 



Retardation of epoch 



in circular measure, 



per French foot of 



descent. 



3 to 6 feet 

 6 to 12 „ 

 12 to 24 „ 



•1286 

 •1177 

 •1115 



•1215 

 •1150 

 •1141 



3 to 24 „ 



•1157 -1154 



27. Hence we have as final means, of effects on logarithmic 

 amplitudes and on epochs, for the average annual variation on 

 the whole period of eighteen years, — 



