2 1 2 Determination of the Altitude of Great Wher aside ; 



the refractions will be less or greater than usual. The reason 

 is sufficiently obvious. 



I now add the result of my own observations, made with 

 an instrument of which the description has already been 

 given. 



The eye-tube and object-glass being reversed in position in 

 the hollow cylinder of the horizon-sector, the angular error of 

 the parallellism of the sides is correctly ascertained. This is 

 a constant quantity (the effect of expansion, which is nearly 

 insensible, excepted), and being once determined the experi- 

 ment needs not to be repeated. The error of coUimation is then 

 ecjual to half the difference of the zenith distances as given by 

 the two indices, and, like to the repeating circle, is determined 

 at evei'y pair of observations. This is an object of no little mo- 

 ment, the error frequently increasing in the course of a few 

 hours from 2" or 3" to four times the quantity. It has already 

 been remarked, that an increase of temperature affects the 

 levels, and causes an augmentation of the observed zenith di- 

 stances. From 34° to 54° the correction was 10"; but from 

 40° to 73° it was scarcely so much : Mr. Troughton conceives 

 tJie alteration to be occasioned by one end of the glass-tube 

 being thicker than the other. Were this the sole source of 

 the evil, a remedy presents itself in the tiao indices of the sec- 

 tor. The tubes might be so placed as to coxmteract their 

 irregularities (on this subject consult Biot's description of the 

 repeating circle). It is proper to remark that two thermo- 

 meters, one shaded and the other not, were noted, and the 

 average made use of to correct the levels for expansion. 



As to the range of the refraction, I admit to have found it 

 nearly as extensive as any recorded ; but have had the good 

 fortune to stumble upon methods of reducing its variations to 

 limits so circumscribed as to render it no longer a formidable 

 impediment to accurate computation. 



The refraction in its variations from its mean quantity may 

 affect the ray in its total extent, or only partially ; for instance, 

 at either or both extremities, or at one or more intermediate 

 portions. 



Of the former class is the variation influenced by the change 

 of the refringent force of the air, as indicated at the place of 

 observation by the barometer, thermometer and hygrometer. 

 This variation, as is demonstrated by theory and confirmed 

 by my own numerous experiments, is too ti'ivial to be percep- 

 tible in arcs not greater than 30'. The diminution of tem-. 

 perature in terms of the ascent, when taking place in the same 

 ratio throughout the arc, must, as we have already been ap- 

 prized, most jnaterially regulate the degree of refraction. The- 

 orists 



