VOL. LXII.] * PHILOSOPHICAL, TRANSACTIONS. 301 



this reason, Mr. Hadley very properly directed the thickest and thinnest edges of 

 the index glass to be placed parallel to the plane of the quadrant. But, as it 

 may well be questioned whether this care is always taken by the instrument 

 maker, and it cannot be supposed that tlie glasses can be ground perfect parallel 

 planes, it would certainly be an advantage acquired to the instrument, could the 

 error arising from a want of parallelism of the planes be removed, in whatever 

 position the common section of the planes should be placed, with respect to the 

 plane of the quadrant. This will be effected for celestial observations, if the 

 upper part of the index glass be left unsilvered on the back, and made rough 

 and blacked, the lower part of the glass being silvered as usual, which must be 

 covered whenever any celestial observations are made. Then, if the telescope 

 be sutficiently raised above the quadrant, it is evident that the observations will 

 be made by the rays reflected from the fore surface of the upper part of the index 

 glass, and consequently, if the quadrant be adjusted by making use of the same 

 part of the index glass, the observations will be true, whether the two surfaces 

 of the index glass are parallel planes or not. The sun or moon may be thus 

 observed by reflection from the unsilvered parts of the index glass and horizon 

 glass, so that a paler darkening glass will suffice, and they will appear much 

 distincter than from an index glass wholly silvered with a deeper darkening glass ; 

 for though the surfaces of a glass may be parallel, yet there always arises some 

 little confusion from the double reflection. Neither will the moon appear too 

 weak by 2 unsilvered reflections, even when her crescent is very small, unless she 

 should be hazy or clouded ; and then the light may be increased by lowering the 

 telescope, so as to take in part of the silvered reflection of the index glass, which 

 in this case must be uncovered: the same is also to be understood with respect 

 to the sun, should his light be too much weakened by haziness or thin clouds. 

 The horizon glasses should be adjusted, or the error of adjustment found by the 

 sun or moon ; the first will be in general the best object for the purpose ; and, 

 as the sun or moon seen directly through the unsilvered part of the horizon 

 glass, will be much brighter than the image of the same seen by 2 unsilvered 

 reflections, it must be weakened by a darkening glass placed beyond the horizon 

 glass, the reflected image being further weakened, if necessary, by a paler dark- 

 ening glass placed, in the usual manner, between the index glass and the horizon 

 glass. 



If a quadrant was designed principally for taking the distance of the moon 

 from the sun and fixed stars, and was not wanted for observing terrestrial angles, 

 it would be the best way to have none of the glasses silvered, but to leave the 

 horizon glasses entirely transparent, and to put a red glass for an index glass of 

 the same matter with the darkening glasses, which would reflect light from the 

 fore surface only. 



