CATALOGUE.— PRACTICAL ASTRONOJIV, GEOGRAPHY. 



363 



Fathoms 

 Latitude. ■ Toises. according 



to Roy. 

 38" 18' S. 57037 Klostermann. 



56740 I^ Caillc, 1752. 



(or 57070 Fernclius.N 



55021 Snellius. / 



In Egypt. 56880 Nouet. Ph. M.Xn. 208. 



The excess of Ihe degrees of the meridian in an elliptic 

 spheroid is very nearly in the ratio of the square of the 

 sine of the latitude : and the length of the degree at any 

 point, is to the length at the equator, accurately, as the 

 cube of a line drawn parallel to the plumb line from a point 

 in the axis equidistant from the centre with the equator, 

 and terminating in a point of the plane of the equator, to 

 the cube of the line drawn from this point to the true pole : 

 Or, if e be the ellipticity, and x the sine of the latitude, the 

 length ofthedegree will vary, as (1 +(2e+ee)T.r}|. 



Length of the Pendulum, 



For 100 000 vibrations at Paris, g8770 were made by the 

 same pendulum at the side of the river of Amazons, 98740 

 at Quito, 98720 on Pichincha. Condamine and Bouguer. 



The length of the pendulum at the equator was found by 

 Bouguer 38,0949 English inches ; at Spitzbergen 39,1978 ; 

 the acceleration being 156" from the equator to London, 

 and 68".5 from London to Spitzbergen. Roy. Ph. tr. 

 1787'. 



The length of the pendulum at St. Helena, lat. 15° 55'S. 

 is to that at Greenwich, as 1 to 10.0246. Maskelyne. Ph. 

 tr. 1762. 434. 



The pendulum at Paris is 1.5 line longer than at the 

 equator: at Petersburg .45 longer than at Paris, and at 

 Ponoi, lat. 67° 4', .65 longer. In proportion to the square 

 of the sine of the latitude it should be .4 8 longer at Peters- 

 burg than at Paris. Mallet. Ph. tr. 1770. 365. 



According to the observations of the pendulum calculated 

 by Roy, as well as some others, it appears that the length 

 of the pendulum is about 39 inches at the equator, and 

 elsewhere 39 + -221 (s. lat.) % or 1 + .00567 (s. lat.) « 

 Instead of .00567 Dr. Maskelyne's observations give .0046 

 for a multiplier: the observations mentioned by Mallet 

 .00523 : the earth's ellipticity being supposed j^j, the mul- 

 tiplier becomes, on Clairaut's principles .00547, or, if ^, 

 .0053S. Perhaps ".0055 is a good mean, and 39 + .215 



(s. lat.) ' for the length in inches. Robison makes the va- 

 riation of the pendulum ^5, or .00555, and the ellipticity ji,. 



Ellipticity, or excess of the equator above the 

 axis. 



If the earth's density were uniform, the 

 ellipticity would be Newton. 



If infinite at the centre and evanescent 

 elsewhere, it would be Laplace. 



In the actual circumstances of a den- 

 sity greater towards the centre than at the 

 circumferences, the polar increase of gra- 

 vity being — , it must be 



114.2 r 

 f Roy's first elliptic spheroid deduced 

 from observations on the pendulum only, 

 without regard to Clairaut's theory _ 



Roy's second spheroid, from a compa- 

 rison of the six best results of measure 

 ments, 



Laplace after 

 Clairaut, 



1 



178 



191-5 



Rsy's third spheroid, from the degrees 

 of the equator and the old measurement 



of the polar circle, 



Roy's fourth ellipticspheroid, approach- 

 ing the nearest to Bouguer's theory, — 



2 



Roy's fifth is Newton's. 



Roy's sixth spheroid, from the degrees 

 at the equator and in latitude 45° 



Roy's seventh spheroid, having the 

 least possible ellipticity, 



Roy's eighth spheroid is not elliptic, the 

 excesses of the degrees varying as the 

 squares of the sines of the latitude ; this, 

 however, nearly resembles the fourth. 



Roy's ninth spheroid is formed upon 

 Bouguer's theory of the excesses of the 

 degrees varying as the fourth power of the 

 sines. This falls within the ellipsis, and 

 according to Roy, agrees best with obser- 

 vation ; he finds the power 3.42 nearer 

 the truth than 3 yj which Bouguer men- 

 tions as more accurate than the fourth ; 

 the eccentricity is made 



1 , 



178.4 



