130 



Prof. YV\ Thomson on the Reduction of 



These reductions I only make for the three-feet deep 



32. Calculating as above (§ 26), for the coefficients A v B v 

 the average values of A 2 and B 2 , from Professor Forbes' s results 

 for his first five years' term, and from the averages for the next 

 thirteen years shown in Table III. above, we find the values of A 2 

 and B 2 shown in the following Table. The amplitudes and 

 epochs are deduced as usual by the formulas -v/(A 2 2 + B 2 2 ) an< i 



tan-? 2 , 



A 2 



and the six-feet deep thermometers, since, for the two others, as 

 may be judged by looking at the thirteen years' average shown 

 in the former Table, the amounts of the semiannual variation 

 do not exceed the probable errors in the data of observation suffi- 

 ciently to allow us to draw any reliable conclusions from their 

 apparent values. 



Table IX. — Average Semiannual Harmonic Term, from 

 Eighteen Years' Observations at Calton Hill. 



Depths below 



surface, in French 



feet. 



A 2 [ B 2 

 in degrees Fahr. in degrees Fahr. 



Amplitudes 

 in degrees Fahr. 



Epochs in 

 degrees and 

 minutes. 



3 feet. 

 6 feet. 



"•1518 



•0461 



°-5842 

 •3911 



°-604 



•394 



75 26 

 96 43 



•604 

 The ratio of diminution of the amplitude here is TqqTjOr 1*53, 



of which the Napierian logarithm is '426. Dividing this by 3, 

 we find 



•142 



as the rate of diminution of the logarithmic amplitude per French 

 foot of descent. 



The retardation of epoch shown is 21° 17' ; and therefore the 

 retardation per French foot of descent is 7° 6', or, in circular 

 measure, 



•1239. 



If the data were perfect for a periodical variation, and the condi- 

 tions of uniformity supposed in Fourier's solution were fulfilled, 

 these two numbers would agree, and each would be equal to 



k/ . Hence, dividing them each by V% we find 



Apparent values of \/—. . 



•100 (by amplitudes). 

 •0877 (by epochs). 



