28 Prof. Encke on Itiierpolatiori. 



From this formula we obtain, 



P = i (sin^ ^ + sin^ X') - -^ 



y—'ia sin . _ 

 ^ _ 2 



in which e* and a are to be considered as unknown quantities. 

 Now the length of a degree of the meridian, or which is better, 

 any measured arc of the meridian, will give another equation 

 between the same unknown quantities, which is sufficient to 

 determine them both. It would serve no purpose to apply 

 this method to the stations at Beachy Head and Dunnose, be- 

 cause it seems certain that there is a great error in the ob- 

 served azimuths and the diflPerence of longitude. 



Taking the difference of longitude as in the Survey, and 

 assuming the value of « as determined by the measurement of 

 meridional arcs, in which there can be no great uncertainty, 

 we shall find by the foregoing formula, 



e'^ = -01807. 

 This is nearly three times the excentricity of the meridians ; 

 which seems so great an irregularity that we are forcibly led 

 to suspect that the difference of longitude errs in defect, which 

 makes the chord of the sphei'e too short, and, in consequence, 

 e^ too great. 



On the other hand, if we make the difference of longitude 

 1° 27' 5"'6, which, there is reason to think, is not far from the 

 truth, we shall then have, 



e^ = -00653, 

 which coincides with the excentricity of the meridian. In 

 this case therefore the surface of the earth at the two stations 

 would coincide with the figure formed by the regular revolu- 

 tion of the meridian about the earth's axis. Now it is vei'y pro- 

 bable that this is nearly true ; and it is confirmed by the ex- 

 actness with which the same figure represents all the longi- 

 tudes that have been accurately determined in the neighbour- 

 ing region. t t 

 Bee. 13,1828. J. IvORY. 



IV. On Interpolation*. 

 {From Prof. Encke's Astronom. Jahrbuchfor 1830,/). 265.) 



TNTERPOLATION means in general the proceeding by 

 * which is derived from the given numerical values of any 

 function of a quantity, (or, according to astronomical language, 



an 

 • The substance of this paper is taken from the lectures of Prof. Gauss, 



which 



