337 



In July of the next year, 1823, the theodolite belonging to the 

 Ordnance was placed at the station at Chingford, and the series of 

 observations, which had been left imperfect the preceding autumn, 

 were completed. Pains were taken by sinking stones of proper size, 

 with the word " station " marked upon them, and also by observing 

 the angles formed by steeples and other permanent objects in the vi- 

 cinity, to preserve the identity of the stations, for the use of future 

 observers. 



In the second section, an account is given of the methods of com- 

 putation that were adopted. The methods which have been employed 

 for geodetical calculations, may be reduced to three ; the first con- 

 sists in considering the observed triangles as spherical triangles, of 

 which the sides are to be computed by spherical trigonometry ; the 

 second is to deduce from the spherical angles, the angles formed by 

 the chords, and thus reduce the spherical triangle to a plane triangle ; 

 the third consists in deducting from each of the observed spherical 

 angles, one third of the spherical excess, which reduces the triangle 

 to a plane triangle, in which the computations may be made by plane 

 trigonometry. This last method, devised by Le Gendre, and which 

 is recommended by its elegance and simplicity, was the one employed 

 on the present occasion. 



The third section comprises the details of the observations of the 

 several triangles, and the computations made from them of the actual 

 distances of the several stations. As the standard of linear measure 

 employed by General Roy for the measurement of the base upon 

 Hounslow Heath differs by a small fraction from the Imperial stand- 

 ard yard, it was found necessary to add 5 '82 feet as a correction 

 to that distance. Corresponding corrections to all General Roy's 

 measurements may be obtained by using the constant multiplier of 

 0000691. 



The fourth section is occupied with computations of the distances 

 from the meridian, and from the perpendicular to the meridian of 

 Greenwich. 



The fifth section contains the investigations of the latitudes and 

 longitudes of the several stations. In these computations the ellip- 

 ticity of the earth has been assumed at one 300dth, as being nearly 

 the mean between -s-J-o and T i T , the limits between which the ellip- 

 .ticity is generally supposed to be comprised. 



The sixth section contains remarks on the observations of the pole 

 star for determining the direction of the meridian, showing the small 

 degree of reliance to which, with reference to that object, such ob- 

 servations are entitled, and also on the determination of the length 

 of the degree upon a circle perpendicular to the meridian, which is 

 liable to similar causes of error. 



The seventh section is on the measurement of the heights of the 

 stations above the level of the sea ; and the influence of terrestrial 

 .refraction on the accuracy of these measurements. 



As the results of M. Arago's observations in France have not yet 

 been published, the longitude of Calais must be taken, as given in the 



VOL. II. Z 



