270 Mr Galbraith on the English Arc of the Meridian. 



to be consistent ; tluat is, they ought to be proportional to the 



radii of their I'espective parallels. 

 From this analogy 4787.69 feet become . . 6047.71 feet 



But the calculatfon from the azimuths is, . . 4909.95 ... 



Difference, 137.70 feet 



Now, from Clifton, at the distance of Dunnose 137.76 feet, 

 would subtend an angle of 27". 42. But the accurate deter- 

 mination of the azimuth by the pole star with the great theo- 

 dolite, is an operation difficult to be performed in the manner 

 described by General Mudge in the first volume of the Tri- 

 gonometrical Survey, page 243. Captain Kater remarks in the 

 new Survey for connecting the observatories of Greenwich and 

 Paris, Philosophical Transactions for 1828, page 183: " There 

 is, however, another source of inaccuracy to which azimuths by 

 the pole-star are liable, and which seems to have been wholly 

 disregarded — I allude to an error in the line of collimation. 

 This error may, however, be destroyed by inverting the tele- 

 scope, or placing that end of the axis which was on the east 

 to the west ; and taking a mean of the observations of the 

 star in both positions." Certainly, if this inversion of the axis 

 was omitted, a considerable error might ensue, as Captain 

 Kater justly remarks ; and though General Mudge does not 

 directly say the axis was inverted, yet it is difficult to believe 

 that so experienced an observer was likely to neglect it, 

 though it is not impossible, unless he rectified it completely by 

 the usual adjustments. But even though complete adjustment 

 be attempted, yet the expei'ienced observer will never impli- 

 citly trust to this, but will regularly invert the axis, as 1 am 

 constantly in the habit of doing in all my detemninations of 

 angles, whether in altitude or azimuth. If this precaution, how- 

 ever, was really neglected, then it would seem to follow, from 

 our computations above, that that error had amounted to one- 

 half of 27".42, or 13".71, at each of the stations of Dunnose 

 and Clifton. Indeed, from a computation which I have made, 

 if the azimuth at Beachy Head be supposed correct, that at 

 Dunnose would, by computation, differ from the observed 

 quantity, by 13".93 ; and conversely, if the azimuth at Dun- 

 nose be considered accm-ate, that at Beachy Head would, by 

 calculation, differ from the observed quantity by 13".93, or 



