22 



the maker ; and few artists can be furnished with the exqui- 

 site apparatus, which must be employed for effecting tiic 

 former); I think it may be to many desirable to have an 



to the object is not changed, nor consequently the incidences of the rays on it ; yet in 

 observing very near objects, as the height or angular distances of buildings, offsets in 

 surveys, bearings^ &c. a .great thickness of the index glass will produce a variable error, 

 which though trifling, is unsatisfactory in an instrument, whose general excellence would 

 make one wish it to be exempt from even the smallest imperfection. And this error can 

 be diminished only by choosing such a certain position for the index glass with respect to 

 its centre of motion, as would cause a part of the field of view to be lost in measuring 

 angles but little exceeding 90°, when the rays fall very obliquely on the index glass, and 

 when also the error eucreases, as does the complement of the observed angle to 180 

 degrees. For the point e (in fig. 5.), can be made to approach to the point j», only as the 

 triangle e d h, which is of given dimensions, shifts toward the mirror H, by its angle b 

 advancing toward it in the line h H, the triangle being moved parallel to itself; by w hich 

 the point h would fall beyond the end of the mirror i g at g, and the field would be 

 contracted. But the face of the mirror et, and consequently the triangle e b d, will 

 be elevated, by advancing toward H, more or less, as the centre of motion of the in- 

 dex is placed farther from, or nearer to, the line p B the face of the index glass : so 

 that the point of incidence of the ray t e cannot fall nearer to that of the ray R p, with- 

 out causing a part of the field to be lost, and this where it is most contracted. 



It has been made evident here, that if the thickness of die index and horizon glasses be 

 equal, or as formerly in use, there will be an interval between the beams of light re- 

 flected from the opposite surfaces of the Jatfer ; and in this interval the reflected image 

 is not visible to the observer; who can only see there the object directly through the 

 glass: and if he is to view both images coincident, he can only do so in the space filled 

 by the beams ; as in x or 3 fig. 3 ; for if he attempted to make the extremities of the 

 images to coincide at the internal edge of either of the reflected beams, he could not 

 hold the quadrant steady enough to keep them there ; for which purpose it would require 

 to be absolutely immoveable. 



On these accounts, if advantage is to be taken of the double reflection, (without 

 which the narrowness of either beam of light, and the evanescence of the reflected 



