6 INVESTIGATION of certain THEOREMS 



this caufe of error is formidable, not only becaufe it may go 

 to a great extent, but becaufe there is not any vifible mark by 

 which its exiftence can always be diftinguilhed. The difference 

 between the primary and fecondary ftrata is probably one of 

 the chief circumftances on which this inequality depends. The 

 primary ftrata, efpecially if we include among them the granite, 

 may often have three times the fpecific gravity of water, whereas 

 the fecondary, fuch as the marly and argillaceous, frequently 

 have not more than twice the fpecific gravity of that fluid. Sup- 

 pofe, then, that a degree is meafured in a country where the 

 ftrata are all fecondary, and happens to terminate near the 

 jun<5lion of thefe with the primitive or denfer ftrata, the line 

 of which jundion we fhall alfo fuppofe to lie nearly eaft and 

 weft; the fuperior attraction of the denfer ftrata muft draw 

 the plummet toward them, and make the zenith retire in the 

 oppofite direction ; thus diminlfhing the amplitvide of the celef- 

 tial arch, and incrcafing, of confequence, the geodetical meafure 

 afligned to a degree. From fuppofitions, no way improbable, 

 concerning the denfity and extent of fuch mafles of ftrata, I 

 have found, that the errors, thus produced, may eafily amount 

 to ten or twelve feconds. 



3. While we continue to draw our conclufions, about the fi- 

 gure of the earth, from the meafurement of fingle degrees, there 

 appears to be no way of avoiding, or even of diminiihing, the 

 efFedls of thefe errors. But if the arches meafured arc large, 

 and confift each of feveral degrees, though there fliould be the 

 fame error in determining their celeftial amplitudes, the efFeA 

 of that error, with refped to the magnitude and figure of the 

 earth, will become inconfiderable, being fpread out over a great- 

 er interval ; and it is, therefore, by the comparifon of two fuch 

 arches that the moft accurate refult is likely to be obtained. 

 But, in purfulng this method, fince the arches meafured cannot 



be 



