122 Mr. Nixon on the Measurement {by Trigonometry) of the 



ness of the metal, were too discordant to be worthy of confi- 

 dence. When a proper support has been procured, still it 

 will frequently occur that a careful observation has been ruin- 

 ed on reversing the instrument, by disturbing the stand ; — by 

 lowering the telescope so rapidly or incautiously as to bring 

 it forcibly in contact with the Ys; — or by a spontaneous de- 

 viation of coincidence in the zeros of the arc and index. From 

 the subjoined statement of the position of the reversing points 

 of the two levels, derived in every instance from numerous 

 observations, it will be seen that their mean places were con- 

 fined to a range of about 2". Unfortunately this high degree 

 of constancy in the adjustments is not to be acquired until the 

 instrument has been exposed for a long period to extremes 

 of temperature, and frequently transported in rude vehicles 

 along uneven roads. On commencing some subsequent opera- 

 tions in another quarter, it was unavoidably necessary to dis- 

 turb the adjusting screws; a step which rendered the position 

 of the reversing points as fluctuating as they had hitherto been 

 constant. As to measurements made by instruments requir- 

 ing the adjustment, on the spot, of the level, or even of the 

 line of collimation, it is difficult to conceive how the most skil- 

 ful observer can satisfy himself of their uniform accuracy. 



Positions of the Reversing Points. 



Right Index. Left. Mean. 



1829. o o o 



May 16. At Great Whernside, on a rock.... 59 76 67*5 



June 8. Reeth, on stone steps 61 74 67*5 



10. Muker, on a wall 62 75 68*5 



12. Kirkby Stephen, on a mantel-piece 61 75 68-0 



15. Hawes, on a window-ledge 62 75 68*5 



17. Ditto ditto 61 76 68-5 



Mean 68° 

 At Great Whernside, Shunnor Fell, and Bakestone Edge, 

 the sector was placed on firm piles of stone set up within a 

 yard or two of the signal. At the other stations the tripod of 

 the theodolite, surmounted by a large level board, was made 

 use of. 



The observed refractions, with their deviation from the 

 formula adopted in the calculation of the heights, are stated in 

 the following table. With the exception of the two instances to 

 which asterisks are prefixed, the quantities were all derived 

 from reciprocal observation. The former are calculated from 

 the vertical angle obtained at one station only ; yet the con- 

 tained arcs were so great, and the differences of altitude so 

 well established, that they may fairly rank with the latter. 



Stations. 



