298 PHILOSOPHICAL TRANSACTIONS. [anNO \7T1. 



motion of the quadrant is all that is wanted, it will never differ much in practice 

 from a vertical axis ; therefore the observer, by properly combining and pro- 

 portioning two motions, one of the quadrant on the axis of vision, and the other 

 of himself on his heel, keeping himself upright (which gives the quadrant a 

 motion on a vertical axis) will cause the image of the sun to describe a small arch 

 of a parallel circle about the sun in the heavens, without departing considerably 

 from the axis of vision. 



If it should be asked, why the observer should be directed to perform two 

 motions, rather than the single one equivalent to them, on a line drawn from 

 the eye to the sun, as an axis ? I answer, that we are not capable, while looking 

 towards the horizon, of judging how to turn the quadrant about on the elevated 

 line going to the sun as an axis, by any other means, than by combining the two 

 motions abovementioned, so as to keep the sun's image always in the proper part 

 of the horizon glass. When the sun is near the horizon, the line going from 

 the eye to the sun will not be far removed from the axis of vision ; and con- 

 sequently the principal motion of the quadrant will be performed on the axis of 

 vision, and the part of the motion made on the vertical axis will be but small. 

 On the contrary, when the sun is near the zenith, the line going to the sun is 

 not far removed from a vertical line, and consequently the principal motion of 

 the quadrant will be performed on a vertical axis, by the observer's turning 

 himself about, and the part of the motion made on the axis of vision will be but 

 small. In intermediate altitudes of the sun, the motions of the quadrant, on 

 the axis of vision and on a vertical axis, will be more equally divided. Hence 

 appears the reason of the method used by the best observers, in taking the sun's 

 altitude, when near the zenith, by holding the quadrant vertical and turning 

 about on the heel, and the defects of the rules that have been commonly given 

 for observing altitudes in other cases. 



As it may conduce to the setting this matter in a still clearer light, I shall here 

 describe in order the several motions that will be given to the reflected image, by 

 turning the quadrant about on the axis of vision, a vertical axis, or the line 

 drawn from the eye to the sun, successively. 1. If the quadrant is turned about 

 on the axis of vision, the same being directed to the point of the horizon 

 exactly beneath or opposite the sun, the image of the sun will move from right 

 to left, or from left to right, across the horizon glass, the same way as the arch of 

 the quadrant is carried, both in the fore and back observations, with a velocity, 

 which is to the angular velocity of the quadrant, as the sine of the sun's altitude to 

 the radius, describing an arch convex downwards in both cases; and when the 

 motion of the sun in this arch is parallel to the horizon, the quadrant is held truly 

 perpendicular to the horizon, and consequently in a proper position for taking the 

 sun's altitude. But if the axis of vision be directed to, and turned round, a point in 



