495 



below, which it is impossible to discover, and therefore to estimate. 

 The possibility, and even not small probability of such existing 

 without our being able to detect and estimate them, throws an air of 

 doubt and uncertainty over all geodetic operations, whenever it is 

 necessary to know with precision the position of the vertical, freed 

 from the influence of local disturbing causes. This is necessary for 

 determining the curvature of the arc, that it may be used in both 

 the problems of mapping the country with extreme accuracy, and of 

 ascertaining the form of this part of the earth. A note is appended, 

 illustrating the degree of influence which errors in the verticals and 

 the ellipticities may have on the mapping. 



6. The author next applies the results of his paper to ascertain 

 the effect upon the plumb-line of an excess or defect of density, of 

 only 1-1 00th part above or below the density required by the fluid- 

 theory of equilibrium, and prevailing over wide-spread spaces in the 

 interior of the earth. From the fact that specimens of rocks, even 

 of the same description, found at the surface of the earth, vary con- 

 siderably in density, he infers that it is not improbable that there 

 may be as wide variations of density among the masses below, in 

 addition to the variations arising from difference of distance from the 

 centre of the earth and required by the fluid-theory of equilibrium. 

 If this be the case, his calculation shows that his fears expressed in 

 the last paragraph are not unfounded. The result of this part of 

 the calculation is expressed in the following Table : 



TABLE OF DEFLECTIONS caused by a defect or excess of matter 

 throughout a semicubic space of four millions of miles [i. e. 200 

 each way parallel to the surface, and 100 miles in the vertical], the 

 mean density of the excess or defect being 1-1 00th part of the den- 

 sity of the earth at the depth of the centre of the cubic space. 





2 L 2 



