17 



the excess or defect of attraction will be 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 line near the mine, but unlimited in the 

 other direction, a simple formula is found. 



For the application 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 line 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- 

 form elevation through its extent. The principal requirements are, 

 besides taking account of the depression of the sea beyond the ten- 

 depth line, to estimate the effect of the curvature of the coast to- 

 wards the mouth of the Wear, to compute the effect of the hollow 

 of Jarrow Slake, and generally to make proper allowance for the 

 absence of matter in the valley of the Tyne. There are also some 

 small elevations to be considered. The general result is, that the 

 attraction of the regular shell of matter is to be diminished by about 

 T foth part. 



Putting D for the mean density of the earth, d for that of the 



shell, the fraction g r{mt 7 b ^ low i s computed to be 1-00012032 

 bravity above 



-0-00017984 x ^. The pendulum experiments give 1-00005185. 

 The comparison of these gives 5=2-6266. 



The eighth section contains a detailed account of the strata passed 

 through in sinking the Harton shaft, and the specific gravities of 

 many of the beds as determined by Professor W. H. Miller. The 

 result for the mean specific gravity is 2'50. Substituting this in the 



VOL. VIII. C 



