ti%UAXtVa TO, THE T.IGTJilE O^, THE KARTH. 103 



denfity that varies with any fundlion of the diftance from the 

 centre, the two fraftions, expreffing the compreflion at the 

 poles, and the diminution of gravity at the equator, when 

 added together, muft be of the fame amount as in the homo- 

 geneous fpheroid, that is, muft be = ^^ or -j-tt- Now, the 

 fecond pendulum is conceded, from tlie beft and moft recent 

 obfervations, to be longer at the pole than at the equator by 

 T-ly, and this, taken from -j-jy, leaves y^^ for the compreHion 

 at the poles. 



2. But though t4-s, or fome fra6tion not very different from Why have not 



, , , °, . , , -, , , , , ,. ., the obfervations 



it, (hould be admitted as the moft probable value of the com- ^^ ^^^^ agreed 

 predion, or ellipticity, as it is called, of the terreftrial fphe- better ? 

 roid, it ftill remains to be explained, why all the obfervations^ 

 "Confidering the care with which they have been made, do not 

 agree more nearly with this conclufion. Among the cau(es 

 ^ that may be affigned for this inconfiftency, though unavoidable 

 ' miftakes, and the imperfection of inftruments, muft come in 

 'for a part, there can be little doubt that local irregularities in 

 Uhe direction of gravity have had the greateft fliare in producing 

 'it. Of thefe irregularities, that which arifes from the attrac- Anf.— Prind- 

 "tion of mountains has had its exiftence proved, and its quan- gt-raafon" V * 

 ttity, in one cafe, afcertained, by the very accurate obferva- mountains have. 

 *tionsof th« prefent aftronom«r-royal at Schehallien in Perth- jjg^^f."f°thr 

 "(liire. We may trace the operation of this caufe ia many of plumb-line, 

 'the degrees that have been adtually meafiired. Thu??^ in the 

 ''degree at Turin, when^ divided into two parts, and each efti- 

 'mated feparately, that which was to the north of the city, and 

 * pointed toward Monte Rofa, the fecond of the Alps in efeva- 

 } ""'tion, and the firft perhaps in magnitude, was found greatef in 

 ^■'* proportion than that toward the fouth, the plummet having 

 been attracted by the mountain above mentioned, and the ^ze- 

 , iiith made of confequence to recede toward the fouth. There 

 » ^are no doubt lituations in which the meafurement of a fmall 

 air<^ might, from a fimilar caufe, give the radius of curvature 

 of the meridian infinite, or even negative. 



But there is another kind of local irregularity in the dIre6tion Another more 

 of gravity, that may alfo have had a great effea in difturbipg ^J'J"^'*^?'* ""^* 

 the accuracy of the meafurement of degrees. The irregularity 

 I mean is onearifing from the unequal denfity of the materials 

 under and not far from the furface of the earth ; and this caufe 

 of error is formidable, not only becaufe it may go to a great 



extent, 



