dr. Gregory's strictures on don Rodriguez. £5.5 



directed their attention to this subject. There are, obviously, Three causes 

 three causes which may jointly or separately occasion a deflec- ftheplumb- 

 tion of the plumb-line from the true perpendicular to the line, 

 earth's surface ; namely, an insular situation, the attraction of 

 mountains, and strata of unequal density beneath the surface : 

 and either of these may be productive of considerable effects. 



To arrive in the easiest manner at an estimate of the effect 

 upon a plumb-line arising from observations made in an insular 

 situation, let Don Rodriguez imagine the simple case of a 

 triangular island so posited on the surface of an aqueous 

 spheroid, that a meridian shall run along from its vertex, directed 

 northward to the middle of its base : he will perceive that, in 

 such a case, as an observer proceeded from the south towards 

 the north, there would be a constant variation in the deflection 

 of the plumb-line ; in such manner, that there would be only 

 one point on the meridian, where the attractions occasioned by 

 the island itself should be so counterpoised and adjusted, that 

 the true and observed vertical lines should correspond. Pursu- 

 ing this hypothesis, with the requisite modifications for a 

 neighbouring continent on the south, and an immense ocean 

 north, he will find that the singular order exhibited by the 

 English estimates of degrees, though an unexpected, is by no 

 means an unnatural, consequence of our insular situation. Dr. Dr - Hutton on 

 Hutton has treated this very point with his usual perspicuity, from g n «nff^ 

 in a valuable note at page 198, vol. ii. New Abridgment of the situations. 

 Philosophical Transactions , published in 1803. That note is 

 too long to be copied into this place j I shall, therefore, merely 

 transcribe the Doctor's concluding inference : " Hence also 

 it follows, that insular situations must be worst of any j having 

 the plumb-line deviating to the north at the south end of the 

 line, to the south at the north end, to the east at the west side, 

 and to the west at the east side j thus producing errors in all 

 observed latitudes and longitudes." 



Laplace, most probably alludes to this kind of effect, at p. 5Q, Laplace ditto. 

 "Exposition," where he speaks of the much more extensive 

 attractions than those of mountains, of which the effect is 

 sensible in 1 taly, England, &c. 



That the deflections of the plumb-line, and the consequent 

 estimate of the lengths of degrees, must be greatly affected 

 by hills and valleys, is also very manifest. Professor Playfair, 



after 



