124 



Prof. W. Thomson on the Reduction of 



Table IV.— Average of Thirteen Years, 1842 to 1854; Trap 

 Rock of Calton Hill. 



Depths below surface, 

 in French feet. 



Diminution of Napiciian 

 logarithm of amplitude, 

 per French foot of de- 

 scent. 



Retardation of epoch in 

 circular measure, per 

 French foot of descent. 



3 to 6 feet 

 6 to 12 „ 

 12 to 24 „ 



•1310 

 •1163 

 •1121 



•1233 

 •1140 

 •1145 



3 to 24 „ 



•1160 



•1156 



22. The numbers here shown would all be the same if the 

 conditions of uniformity supposed in the theoretical solution 

 were fulfilled. Although, as in the previous comparisons, the 

 agreement is on the whole better than might have been expected, 

 there are certainly greater differences than can be attributed to 

 errors of observation. Thus the means of the numbers in the two 

 columns are for the three different intervals of depth in order as 

 follows : — 



Mean deductions from 

 amplitude and epoch. 



3 to 6 feet -127 



6 to 12 „ -115 



12 to 24 „ -113 



numbers which seem to indicate an essential tendency to dimi- 

 nish at the greater depths. This tendency is shown very deci- 

 dedly in each column separately ; and it is also shown in each of 

 the corresponding columns, in tables given above, of results de- 

 rived from Professor Forbes' s own series of a period of five years. 



23. There can be no doubt that this discrepance is not attri- 

 butable to errors of observation, and it must therefore be owing 

 to deviation in the natural circumstances from those assumed for 

 the foundation of the mathematical formula. In reality, none 

 of the conditions assumed in Fourier's solution is rigorously ful- 

 filled in the natural problem ; and it becomes a most interesting 

 subject for investigation to discover to what particular violation 

 or violations of these conditions the remarkable and systematic 

 difference discovered between the deductions from the formula 

 and the results of observation is due. In the first place, the 

 formula is strictly applicable only to periodic variations, and the 

 natural variations of temperature are very far from being pre- 

 cisely periodic; but if we take the average annual variation 

 through a sufficiently great number of years, it may be fairly 

 presumed that irregularities from year to year will be eliminated : 

 and that the discrepance we have now to explain does not de- 



