54 



REPORT — 1859. 



Table No. 5. — Showing the Excess or Defect of Rain between those periods when 

 the Moon's motion in Declination is changing, and when it is greatest, or when 

 the Moon is in greatest Declination and crossing the Equator. 



On Thunder-storms. By G. J. Symons. 



On the Reduction of Periodical Variations of Underground Temperature, 

 with applications to the Edinburgh Observations. By Prof. W. Thomson, 

 LL.D., F.R.S. 



The principle followed in the reductions which form the subject of this commu- 

 nication may be briefly stated thus : — 



The varying temperature during a year, shown by any one of the underground 

 thermometers on an average for a series of years, is expressed by the ordinary method 

 in a trigonometrical series of terms representing simple harmonic variations*, — the 

 first having a year for its period, the second a half-year, the third a third part of a 

 year, and so on. The yearly term of the series is dealt with separately for the ther- 

 mometers at the different depths, the half-yearly term also separately, and so on, 

 each term being treated as if the simple periodic variation which it represents were 

 the sole variation experienced. The elements into which the whole variation is thus 

 analysed are examined so as to test their agreement with the elementary formula; by 

 which Fourier expressed the periodic variations of temperature in a bar protected 

 from lateral conduction, and experiencing a simple harmonic variation of temperature 

 at one end, or in an infinite solid experiencing at every point of an infinite plane 

 through it a variation of temperature according to the same elementary law. In 

 any locality in which the surface of the earth is sensibly plane and uniform all round 

 to distances amounting at least to considerable multiples of the depth of the lowest 

 thermometer, and in which the conducting power of the soil or rock below the sur- 

 face is perfectly uniform to like distances round and below the thermometers, this 

 theory must necessarily be found in excessively close agreement with the observed 

 results. The comparison which is made in the investigations now brought forward 

 must be regarded, therefore, not as a test of the correctness of a theory which has 

 mathematical certainty, but as a means of finding how much the law of propagation 

 of heat into the soil is affected by the very notable deviations from the assumed con- 



* By a simple harmonic variation is meant a variation in proportion to the height of a 

 point which moves uniformly in a vertical circle. 



