414 . PROFESSOR W. THOMSON ON THE REDUCTION OF 
Calton Hill Trap Rock. |Experimental Garden Sand. |Craigleith Quarry Sandstone. 


re 
ae 1154 

A continuation of the observations at Calton Hill not only leads, as we shall 
see, to almost identical results, both by diminution of amplitude and by retarda- 
tion, on the whole 21 feet, but also reproduces some of the features of discrepance 
presented by the progress of the variation through the intermediate depths; and 
therefore confirms the general accuracy of the preceding results, for all the 
stations, so far as it might be questioned because of only five years’ observations 
having been available. Further consideration of these results, and deduction of 
the conductivities of the different portions of the earth’s crust involved, is deferred 
until after we have taken into account the farther data for Calton Hill, to the 
reduction of which we now proceed. 
17. Application to Thirteen Years’ Observations (1842-1854) at the Thermo- 
metric Station, Calton Hill—The observations 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 temperatures of the bulbs, 
on the same system as before. Tables of these corrected observations, for the 
twelve years 1842 to 1854 inclusive, having been supplied to me through the 
kindness of Professor Piazzi Smyth, I have had the first five terms of the har- 
monic 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 different depths respectively, as completely and accurately as it can be 
inferred from the weekly observations. The space corresponding to each year — 
was then divided into 32 equal parts (the first point of division being taken at 
the beginning of the year), and the corresponding temperatures were taken from 
the curve. The co-efficients 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 published by the Board of Admiralty, for deducing the 
harmonic expression of the error of a ship’s compass from observations on the 
32 points. The general form of the harmonic expression being written thus— 
V=A,+A, cos 2at+B, sin 2xt+ A, cos 4a¢+B, sin 4at+ &e., 
where V denotes the varying temperature to be expressed, and ¢ 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. M‘Farlane, my laboratory assistant, and Mr J. D. Everett, now Professor 
of Mathematics and Natural Philosophy in King’s College, Windsor, N.S. 

