230 Royal Society :— 



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 tftififl th part, with an uncertainty of -jyTfth part of the excess ; 

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

 day, with an uncertainty of less than O^'Ol. 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 dependin^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 

 the excess or defect of attraction will bo computed with sufficient 

 accuracy by supposing the excess or defect of matter to exist abso- 

 lutely at the surface ; in which case the effect on the upper station 

 is nothing, and that on the lower station is easily computed. For 

 depressions like that of the sea bounded (at least for the purposes of 

 computation) by a straight Une near the mine, but unlimited in the 

 other direction, a simple formula is found. 



For the apphcation of these theorems it was necessary to have 

 a map giving the elevations of the ground at various points. By 

 instruction of the Mayor and Corporation of South Shields, the 

 Corporation Surveyor, Christopher Thompson, Esq., prepared such 

 a map. In the use of it, it was found convenient to adopt as unit 

 of linear measure the depth of the mine. A hne at the distance of 

 •ten depths very nearly touches the cliffs of Tynemouth, of French- 

 man's Point, and of some points further to the south-east. The 

 land generally is divided into squares whose sides are one depth each, 

 and these are grouped as appears convenient for representing ap- 

 proximately the form of the ground by compartments each of a uni- 



