THE NATURE AND INTERPRETATION OF GEODETIC EVIDENCE. 11 



the dimensions of the earth ; but the principal problem of geodesy 

 is the determination of these dimensions, on which depend the 

 calculations by which the observations with the theodolite are con- 

 verted into measures of distance and direction, and into differences 

 of latitude and longitude. 



Were the earth a perfectly regular spheroid, and of uniform 

 constitution throughout, the problem would be a simple one, and 

 a few comparisons, of measured distances with observed differences 

 of latitude, would suffice to determine the form and size of the 

 spheroid. But these conditions are far from being met with in 

 practice. The difference in the astronomical position of two stations 

 is determined by observations of the sun and stars, and a measure- 

 ment of their angular distance from the vertical, as shown by the 

 plumb-line, or from the horizontal, as shown by a fluid surface ; 

 the latter is that actually used, but the two are identical in result 

 for the apparent horizontal plane and the apparent vertical line 

 are always, and necessarily, at right angles to each other. Now 

 the exact direction of the plumb-line, at any point, is determined 

 not only by the attraction of the earth as a whole but by the attrac- 

 tion of local masses, and may be affected either by variations 

 in the density of the rocks at, or below, the surface, or by irre- 

 gularities in the form of the surface near the station. A mountain 

 range, or a mass of rock of greater than average density, to the 

 northwards of a station would attract the plumb-bob and cause the 

 liquid surface to be tilted in such a manner that the latitude, as 

 determined by astronomical observation, would appear to be less 

 than the true latitude of a station situated in the northern hemi- 

 sphere, and a similar excess of attraction to the south would make 

 the apparent latitude greater than the true. Differences in the 

 density of unseen portions of the earth can, obviously, not be 

 allowed for ; they must be searched for and detected by the dis- 

 crepancies between astronomical and geodetic measurements ; but 

 it might be thought easy to calculate, and allow for, the effect 

 of the visible masses of mountain ranges and the visible hollows 

 of the ocean basins, and so it would be were mountains mere ex- 

 crescences formed of material added on to the surface of the spheroid, 

 or the oceans merely hollows carved out of its surface. Such, 

 it has been found, is not the case ; mountain ranges do not attract 

 the plummet to anything like the extent they should do, nor do 

 ocean basins cause it to be attracted away from them, and the 



[ 150 ] 



