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XVIII. On the Reduction of Observations of Underground Tem- 

 perature; with Application to Professor Forbes's Edinburgh 

 Observations, and the continued Calton Hill Series. By Pro- 

 fessor William Thomson, F.R.S. 



[Concluded from p. 34.] 



17. APPLICATION to Thirteen Years' Observations (1842-54) 

 at the Thermometric Station, Calton mil.— The observa- 

 tions on thermometers fixed by Professor Forbes at the different 

 depths in the rock of Calton Hill, have been regularly continued 

 weekly till the present time by the staff of the Royal Edinburgh 

 Observatory, and regularly corrected to reduce to true tempera- 

 tures of the bulbs, on the same system as before. Tables of these 

 corrected observations, for the twelve years 1842 to 1854 inclu- 

 sive, having been supplied to me through the kindness of Professor 

 Piazzi Smyth, I have had the first five terms of the harmonic 

 expression for each year determined in the following manner* : — 

 In the first place, the observations were laid down graphically, 

 and an interpolating curve drawn through the points, according to 

 the method of Professor Forbes. The four curves thus obtained 

 represent the history of the varying temperature, at the four dif- 

 ferent depths respectively, as completely and accurately as it can 

 be inferred from the weekly observations. The space correspond- 

 ing to each year was then divided into thirty-two equal parts 

 (the first point of division being taken at the begining of the 

 year), and the corresponding temperatures were taken from the 

 curve. The coefficients of the double harmonic series (cosines 

 and sines) for each year were calculated from these data, with 

 the aid of the forms given by Mr. Archibald Smith, and pub- 

 lished by the Board of Admiralty, for deducing the harmonic 

 expression of the error of a ship's compass from observations on 

 the thirty-two points. The general form of the harmonic expres- 

 sion being written thus — 



V = A + A! cos 2^ + Bj sin 27r^ + A 2 cos 47r^ + B 2 sin47r/ + &c, 



where V denotes the varying temperature to be expressed, and t 

 the time, in terms of a year as unit. The following Table shows 

 the results which were obtained, with the exception of the values 

 of A :— 



* The operations here described, involving, as may be conceived, no 

 small amount of labour, were performed by Mr. D. MTarlane, my labora- 

 tory assistant, and Mr. J. D. Everett, now Professor of Mathematics and 

 Natural Philosophy in King's College, Windsor, N.^. 



