4'32 Mr. Nixon on the Measurement {by Trigonometry) of the 



telescope being taken out of its Ys, and replaced reversed in 

 position, the bubble of the left-index level, and afterwards, on 

 inverting the telescope, that of the right-index level, were read 

 off as before. . The reversing point of the middle of the bub- 

 ble of either level being evidently equal to one-fourth of the 

 sum of the readings of the position of its ends in the direct 

 and reversed positions of the telescope, two marks were made 

 with a camel-hair pencil dipped in white paint on the tube of 

 each level, one on each side of, and equidistant from the re- 

 versing point by half the length of the bubble. 



The sector had been transported in the course of the sur- 

 vey in vehicles of every description over the roughest roads 

 imaginable; yet the great levels, as will be evident from the 

 subjoined statement of the position of their reversing points at 

 the several stations, had retained their first adjustments to the 

 accuracy of a second or two. 



Right Index. Left Index. Mean. 



Reversing point at Bear's Head 67° 74° 70°'5 



Shunnor Fell . . . 66 72 69 



Bakestone Edge . 62-5 76 69 



Penhill 65 76-5 71 



(July 9th) Settronside 61*5 76-5 69 



(July 10th) 65-5 75 70 



Mean 70° 



Heretofore the vertical angle could not be measured until 

 the ends of the bubble were made to coincide exactly with the 

 reversing marks ; but on the addition of scales to the levels, 

 the angle read off could be corrected for any slight deviation 

 of the bubble from its marks, by noting the contemporary po- 

 sition of the ends of the bubble. To understand the nature of 

 this correction, it is to be observed, that when the telescope 

 is pointed at an elevated object, and the index moved until 

 the bubble of its level comes to rest at its marks, the zero of 

 the index will be lower than that of the graduated arch (fixed 

 to the telescope) by the arc of elevation. Consequcntlj^, on 

 subsequently elevating the index in a slight degree, the two 

 zeros will be brought nearer to each other ; the displaced bub- 

 ble, advancing in the direction of the object-glass, will come 

 to rest with its middle point opposite a number in the scale 

 exceeding that of the reversing point ; and the angle of eleva- 

 tion now read off on the graduated arc, will be in defect by 

 the angular displacement of the bubble. Hence the registered 

 angles of elevation will require correcting by the difference in 

 seconds of the half-sum of the readings of the position of the 

 ends of the bubble and that of the reversing point ; additive or 



subtractive 



