Heights of the principal Hills of Dent, $c. Yorkshire, 193 



of the cone will be perpendicular. This constant error might 

 be ascertained, were there no refraction, by reciprocal obser- 

 vations of the elevations and depressions. Let d e denote the 

 true depression and elevation; d 1 e 9 , their values affected by 

 the error of collimation y 9 and a the contained arc ; then, as it 



has been shown that (e + a) = d, consequently 1 = 



~ J " -^- will be equal to the error of collimation, to 

 be added to the observed depressions, and — — - the er- 

 ror subtractive. When both angles dT> are depressions, their 

 sum, it has been demonstrated, will equal the contained arc ; 



hence - 9 or ° „ — — will give the error of colli- 



2 2 



mation ; the depressions being observed in excess in the former 

 case, and in defect in the latter. 



When the line of gravity, disturbed by local attraction, is 

 not in the direction of the centre of the earth, the line of col- 

 limation supposed to be horizontal, describes in its revolution 

 a plane inclined to the true horizon at an angle equal to the 

 deflection, and cutting it at right angles to the direction of the 

 disturbing cause. The elevations must therefore be in defect 

 in the direction of the attraction, and in excess in the op- 

 posite quarter of the horizon by a quantity equal to the incli- 

 nation of the planes to each other ; but in the direction of 

 their intersection the error of collimation will be null. When 

 the deflection ( g ) as measured on the vertical plane passing 

 through two stations, is the same at both and in one direction 

 (or parallel), the elevation and corresponding depression will 



be equally in excess or defect, and Lzil_ Jf — £ w iU exceed 



~^~ by gl but should the deflections be in opposite direc- 

 tions (or inclined to each other), a compensation of error takes 

 place, (d ' fg 2 +(g ~ — being equal to ^—-. Admitting the line 



of gravity to be disturbed at one station only, LjL|£_jL1 w \\\ 

 differ from ~J~ e by — . 



2 f 2 



Refraction. — In the general state of the atmosphere the ele- 

 vations may be considered as increased, and the depressions 

 equally diminished by a constant ratio of the contained arc (a). 

 In this case, if d and e represent, as before, the true de- 

 pression and elevation, their values d! and e 1 as affected by 



New Series. Vol. 3. No. 15. March 1828. 2 C the 



