20 



pleasant to adjust by Mr. Blair's method, when the eyo 

 takes in a sufficient field of view ; and moreover as not every 

 where a quadrant can be procured, furnished with an index 



tlie horizon glass D, iu tlie same manner, and with the same incidences, refractions and 

 reflections as in fig. 3 ; on the mirror C it will occupy a space / /, equal to the breadth of 

 the edge of the mirror A ; and will cover the equal space It r, on the back surface of the 

 mirror B ; after reflection from which, it will be refracted in the surface Ik, enier,r;ing 

 in the beam z; the several rays iu this beam issuing at distances from / toward k, equal 

 to the distances of their first incidence from i toward 1; the last ray b i emerging 

 coincident with the ray I a: so that if the beam x did not fill the space i I, the beam s 

 would not fill the space k I, but would leave an interval next to /equal to the deficiency 

 toward i. Let the line p r be drawn perpendicular to the mirror, bisecting the line / 1, and 

 the angle of incidence and reflection / r i, and parallel to c # the cosine of the angle of re- 

 fraction n I s, which angle is equal to c s I. In the similar triangles s c I, r p i, the side 

 r p, the thickness of the mirror B, is to p i half the thickness of the mirror ^, as « c the 

 cosine of the angle of refraction, to c i or s n the sine of the same ; so that when the thick- 

 ness of the mirror B, is p r the cosine of refraction, the thickness of the mirror A must 

 be double of p i the sine of the same angle. Now to make the index mirror of so great 

 thickness may produce a small inaccuracy, when angular distances are to be taken bc- 

 ,tween very near objects, at which a small part of the length of this mirror would subtend 

 a perceptible angle; for the thicker the glass is, and the greater the complement of the 

 angle observed, the greater intervals on its surface will there be between the places of 

 iucidence and emergence of the rays forming the reflected images; which will therefore 

 be seen, sometimes by rays issuing from the middle of this mirror, and sometimes by rays 

 distant from the same : from which variation I have above stated the errors that may 

 arise: and because every minutia in the construction or use of this admirable instrument 

 is deserving attention, it may be worth while to shew the manner in which this hap- 

 pens. 



Let I G (fig. .5.) be the index glass, in its position when the index is at o, and //the 

 ttorizon glass at right angles to it ; its adjustment being made by the reflected image of an 

 object .V, seen by the eye at E to coincide with another opposite object visible in the 

 direction E //. The image of S is conveyed to the eye by the ray S A refracted in A C, 



