16 



The sixth section gives the computation of the logarithm of the 

 rate of the lower detached pendulum upon the upper detached pen- 

 dulum (for which the preceding sections have furnished the ele- 

 ments). Then is given in detail the investigation, by the Theory of 

 Probabilities, of the formula for the best combination of the results 

 of the different swings. The advantage of the method of incessant 

 observations with numerous comparisons of the clocks is pointed out. 

 The formula is applied to the four series of observations ; and the 

 results of the first and third series agree very closely, and those of 

 the second and fourth series agree very closely, showing that the 

 pendulums had undergone no sensible change. By comparing the 

 mean of the first and third series with the mean of the second and 

 fourth, the proportion of pendulum rates at the upper and lower 

 stations is obtained independently of the pendulums employed. 

 The conclusion is that gravity below is greater than gravity above 

 by 19 2 88 th part, with an uncertainty of -jyo-th P ar ^ of the excess ; 

 or that the acceleration of a seconds' pendulum below is 2 8 '24 per 

 day, with an uncertainty of less than 8< 01. Reasons however are 

 given for believing that the uncertainty is greater than this quan- 

 tity. 



The seventh section contains a description of the operation for 

 measuring the depth of the mine. It then treats of the process to 

 be employed for computing the proportion of gravity at the upper 

 and lower stations (without reference to the experiments), on an 

 assumed proportion of the density of the mine-rocks to the earth's 

 mean density. It is shown that, supposing the upper surface of the 

 ground about Harton to have the true spheroidal form, it is unne- 

 cessary to give any attention to the irregularities of the surface on 

 distant parts of the earth. It is also shown that there is no reason 

 to doubt the correctness of the law of decrease of the attraction of 

 the earth's nucleus as depending on the elevation of the station, un- 

 less there be some serious irregularity in the arrangement or density 

 of the matter immediately below Harton. Assuming this to be in- 

 sensible, the theory of correction for the inequalities of ground in 

 the neighbourhood of Harton is then considered. The elevation of 

 the upper station is about 74 feet above high water ; and as it ap- 

 pears from this that the depth of inequality can in no case amount 

 to one-tenth of the depth of the lower station, it is easily found that 



