CATA t.OCD E.— I’UACTXCAt ASTROKOXIV
Giioo r Arny.
353
latitude.
Toiscs,
Fathoms
according
3 8" 18'S.
3703/
to Roy.
Klostcrmann.
'La CaiUe, 17 52.
/or 57070
FerncliusA
b 502 1
56S80
Nouet. Ph. M. XII. 208.
The excess of the degrees of the meridian in an ellipticE Pheroid is very nearly in the ratio of the square of thes,, 'e of the latitude: and the length of the degree at anyP°mt, is to the length at the equator, accurately, as thec uhe of a line drawn parallel to the plumb line from a point111 the axis equidistant from the centre with the equator,B ud terminating in a point of the plane of the equator, to‘he cube of the line drawn from this point to the true pole :^ r > if c be the ellipticity, and a’ the sine of the latitude, the' cn gth of thedegree will vary, as (l -f^e-fee).™?)^.
Por loo ooo vibrations at Paris , 98770 were made by theSa,I >e pendulum at the side of the river of Amazons , 98740
Quito , 08720 on Pichincha . Condamine and Bouguer.
The length of the pendulum at the equator was found by® 0, ’gucr38 ,g 9 'lQ English inches ; at Spitzberpcn 39 ,107 ft iacceleration being 150" from the equator to Eondon,a «d 08 ".5 from London to Spitzbergen . Roy. Ph. tr.> 787 .
"’be length of the pendulum at St. Helena , lat. 15 ° ss'S.,s to that at Greenwich, as 1 to 10 . 0248 . Maskelyne. Ph.* r ‘ 1 7 0 a. 434 .
’'he pendulum at Paris is 1.5 line longer than at thee SUator: at Petersburg .4 5 longer than at Paris , and atP ° n °i, lat. 07° 4 ', .65 longer. In proportion to the squarenf the sine of the latitude it should be .4 8 longer at Petcrs-btir S than at Paris . Mallet. Ph. tr. 1770- 365.
According to the observations of the pendulum calculatedRoy, as well as some others, it appears that the lengththe pendulum is about 39 inches at the equator, andc ’ s ewhere 39 + .221 (s. lat.) *, or 1 + .00567 (s. lat.) 8Ift 5tead of .00507 Dr. Maskelyne’s observations give .004 6for a multiplier: the observations mentioned by Mallet•b <>523 : the earth’s ellipticity being supposed ^ 5 , the mul-bplier becomes, on Clairaut ’s principles . 00547 , or, if ^- 5 ,,Q ° 5 36. Perhaps .0055 is a good mean, and 39 + ' 2 l 5
(s. lut.) 1 for the length in inches, Robison makes the va-riation of the pendulum 1 | t , or .00555, andthe ellipticity ri ' v .
EIL'pticity, or excess of the equator above theaxis.
If the earth’s density were uniform, theellipticity would be Newton.
If infinite at the centre and evanescent 22 ' J
elsewhere, it would be _!_ Laplace.
57 7
In the actual circumstances of a den-sity greater towards the centre than at thecircumferences, the polar increase of gra-
.... 1 1 1 Laplace after
vity being —, it must be- 1
fRoy’s first elliptic spheroid deducedfrom observations on the pendulum only,without regard to Clairaut 's theory 1
i?H
Roy's second spheroid, from a compa-rison of the six best result s of measure
ments, —1-
191-5
Roy’s third spheroid, from the degreesof the equator and the old measurement
of the polar circle,
Roy’s fourthellipticspheroid, approach-
ing the nearest to Bouguer’s theory,
Roy’s fifth is Newton’s.
Roy’s sixth spheroid, from the degreesat the equator and in latitude 45°
Roy’s seventh spheroid, having theleast possible ellipticity,
Roy's eighth spheroid is not elliptic, theexcesses of the degrees varying as thesquares of the sines of the latitude; this,however, nearly resembles the fourth.
221.5
1
309 31
539
Roy’s ninth spheroid is formed uponBouguer’s theory of rhe excesses of thedegrees varying as the fourth power of thesines. This falls within the ellipsis, andaccording to Roy, agrees best with obser-vation; he finds the power 3.4 2 nearerthe truth than 3 which Bouguer men-tions as more accurate than the fourth ;the eccentricity is made