Mr Giialbi-aith on the English Arc of the Meridian. 273 



which is accounted the true latitude, and agrees very closely 

 with the preceding result. There is, however/ between the 

 two last, a difference of 9 '.54, one-half of which, or 4".77, is 

 here, at the zenith distance of about 27° 20', reckoned the er- 

 ror. Hence, for a change of zenith distance of IS"" 20', there 

 is a corresponding change of error of 3".13. Some observers 

 find, or think they find, that these errors vary as the sine of 

 the zenith distance ;* while others can detect no such law, 

 though a mean of judiciously chosen observations give remark- 

 ably consistent results, when the observations are very numer- 

 ously repeated. Still, however, in this country, observers ac- 

 customed to British instruments, would greatly suspect their 

 final accuracy, even from vei'y numerous olservations, however 

 consistent the individual results might be, whenever they in- 

 volved such remarkable discrepancies. The opposite error 

 seems applicable to our observers. Generally provided with 

 large instruments, having powerful telescopes, they trust per- 

 haps rather too confidently, in a very few observations which 

 they consider good, and neglect to repeat them sufficiently to 

 counteract atmospheric irregularities, for which no power of 

 telescope will compensate. Even the power of the telescope 

 of Roy''s theodolite, by Ramsden, was not great, as he himself 

 states, in the Trigonometrical Survey, vol. i. page 123 ; it only 

 magnified about forty or fifty times, as commonly employed. 

 I have not seen the power of that belonging to the Board of 

 Ordnance anywhere stated. 



In taking horizontal angles, " the errors," says Captain 

 Kater, Phil. Transactions for 1828, page 197, " which mcay 

 arise from lateral refraction, have often been suspected, but 

 never clearly ascertained. In the course of our work, how- 

 ever, we had such evidence of the fact as to leave no doubt of 

 its existence. The angle (measured) between the same ob- 

 jects would differ (when taken) under the most favourable cir- 

 cumstances, about Jive seconds on different days, and perhaps 

 a second and a-half, or two seconds, may be considered as the 

 error which may effect an angle from lateral refraction in an 

 ordinary state of the atmosphere.'' 



• This coincides nearly with these examples, the difforenco being only 

 0".70 from this bypothcsis. 



