186 Dr. Gregory^ s Strictures on Don Rodriguez. 



of the earth and local attractions may occasion considerable 

 discrepancies ;" yet he does not believe they can ever pro- 

 duce a deviation of the magnitude just specified. Here 

 again he is at war with the decisions, I believe, of all pre- 

 ceding philosophers who have directed their attention to 

 this subject. There are, obviously, three causes which may 

 jointly or separately occasion a deflection of the plumb-line 

 from the true perpendicular to the 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 eflects. 



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

 upon a plumb-linearising from observations made in an in- 

 sular 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 j he will per- 

 ceive that, in such a case, as an observer proceeded from 

 the south towards the north, there would be a constant va- 

 riation 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 ver- 

 tical lines should correspond. Pursuing this hypothesis, 

 with the requisite modifications, for a neighbouriug coii- 

 tinent on the south and an imtriense ocean north, he will 

 find that the singular order exhibited by the English esti- 

 mates of degrees, though an unexpected, is by no means 

 an unnatural, consequence of our insular situation. Dr, 

 Hutton has treated this very point with his usual perspi- 

 cuity, in a valuable note at page IgS, vol. ii. Neiv Abridge- 

 ment of the Philosophical Transactions, published in 1803. 

 That note is too long to be copied into this place; I shall 

 therefore merely transcribe the Doctor's concluding in- 

 ference : "Hence also it follows that insular situations 

 must be worst of any, having the plumb-line deviating to 

 the north at the south end of the l-.ne, to the south at the 

 north end, to the east at the west side, and to the west at 

 the east side ; thus producing errors in all observed latitudes 

 and longitudes." 



Laplace most probably alludes to this kind of effect, at 

 p. 39, ^'Exposition," where he speaks of the much more 

 extcmivc attractions than those of mounlains, of which the 

 effect is sensible in Italy, England, &c. 



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

 quent estimate of the lengths of degrees, must be greatly 



affected 



