218 Mr Sang on an Improvement in the 



with that reflected from the plate glass. When this coincidence 

 is obtained, the one reflecting surface is parallel to the other, at 

 least if we neglect the parallax. The next coincidence will place 

 the second plane in the same situation, and thus the inclination 

 will be at once obtained, provided the parallaxes in the two cases 

 are alike. 



By means of the permanent reflector, we can make all our 

 observations on images of one object, which we can take as dis- 

 tant as convenient ; the coincidences will thus be more easily 

 observed than those of one object with another. The parallax 

 can always be rendered so small as not to influence the results ; 

 indeed, by using an object at the distance of half a mile, it will 

 be entirely avoided. But, even although circumstances should 

 compel us to use a proximate object, the parallax can be readily 

 and advantageously eliminated from the observations ; before, 

 however, any observations are made, the permanent reflector 

 must have its plane rendered parallel to the axis of the instru- 

 ment. The limited motion of the brass arm enables us to make 

 this adjustment. A substance with a pretty extensive and well- 

 polished face is cemented to the goniometer, and the image of 

 a distant object in it is made to coincide with that seen in the 

 permanent reflector. The limb of the goniometer is then turn- 

 ed half round, when, unless the adjustment happen to have been 

 hit at first, the instrument, when used as a sextant, by receiving 

 the direct light from the object and the twice-reflected light from 

 it at the same time, will not exhibit again that coincidence. 

 The two images will appear in a plane passing along the axis of 

 the motion, and, by the motion of the permanent reflector, one- 

 half of the distance must be corrected ; the other half by the 

 motion of the adjusting apparatus on the goniometer. After 

 this, the operation is to be repeated until no error appear ; the 

 permanent reflector is then placed parallel to the axis. 



The possibility of obtaining a coincidence will now be suffi- 

 cient to shew that the face of a crystal is placed properly on the 

 goniometer. During all these operations the instrument may 

 be held in the hand like a reflecting circle, the coincidences be- 

 ing entirely independent of the absolute, and depending only on 

 the relative positions of the parts. Indeed, if the observer were 



