4^ MEASmE 0)P A DEGREE ON THE COROMANDEL COAST. 



divide the excess! or defect 'between the other two, and then 

 compute from the given side the other two sides ; and after 

 doing the same thing with each of the angles successively, 

 a mean of the sides thus brought out was taken, which, to 

 certain limits, will always be near the truth. I then varied 

 the selection of the observed angles, rejecting such as I had 

 reason to doubt ; and by correcting them, and computing 

 'the two required sides of the triangle, those which gave the 

 iiides nearest to what had been brought out by the other 

 method were adopted, let the errour be what it would. This, 

 however, lias rarely happened; and when it did, great pre- 

 caution was used; and no angle was rejected, without some 

 reason appeared to render it doubtful. 



In correcting the observed angles to obtain those made 

 by the chords, I have vised the formula given by the Astro- 

 nomer Royal, in his demonstration of M. de Lambre's pro- 

 blem, which appears in the Philosophical Transactions for 

 I797. The spherical excess is of course had from the well 

 knoVvn methorl of dividing the area of the triangle in square 

 seconds, by the number of seconds in the arc equal to ra- 

 dius, where the number of feet in a second may be had by 

 vising the degree as has been commonly applied to the mean 

 sphere, or the mean between the degree on the meridian and 

 its perpendicular. This being of no farther use than to 

 check any errour that might happen in computing the 'cor- 

 rections for the angles. 



Observations hy the Zenith Sector for the latitude c/Paudree 

 station^ and the station near Trivandeporum ; and the 

 length of the celestial arc. 



Zenith sector. The zenith sector, with which these observations have 

 been taken, was made by Mr. Ramsden, and is the one al- 

 luded to by General Roy^in the Philosophical Transactions 

 for 1790, being then untinished. The radius of the arc is 

 five feet, and the arc itself is of that extent to take in nine 

 degrees on each side of the zenith. It is divided into de- 

 grees, and smaller divisions of 20' each, which are num- 

 bered, Each of these last is again subdivided into four, of 

 5' each. Tiie micrometer, which moves the telescope and 

 ftrc, is graduated to seconds, and one revolution moves the 



arc 



