VOL. LXn.3 PHILOSOPHICAL TRANSACTIONS. ' iQQ 



the horizon beside the vertical circle passing through the sun, the sun's image, 

 when its motion is parallel to the horizon, will be neither in the axis of vision 

 nor the sun's vertical, but between both ; at the same time the plane of the 

 quadrant will not be vertical, and the altitude found by bringing the sun's image 

 to touch the horizon, will not be the true altitude. 



1. If the quadrant be held perpendicular to the horizon, and turned about on 

 a vertical axis, or one nearly so, the sun will describe an arch convex downwards 

 in the fore observation, and upwards in the back observation, the motion of the 

 sun being the same way as the axis of vision is carried in both cases, and being 

 to the angular motion of the quadrant, as the verse-sine of the sun's altitude to 

 radius in the fore observation, but as the verse-sine of the supplement of the 

 sun's altitude to 180°, to the radius, in the back observation. The sun therefore 

 will move slower than the axis of vision in the fore observation, and consequently 

 will be left behind, with respect to the axis of vision, or seem to move back- 

 wards ; and the sun will move quicker than the axis of vision in the back obser- 

 vation, or will seem to get before iL When the motion of the sun in this arch 

 is parallel to the horizon, the plane of the quadrant coincides with the vertical 

 circle passing through the sun, and consequently the quadrant is in a proper 

 position for taking the sun's altitude. But if the quadrant be held a little 

 deviating from the perpendicular position to the horizon, and turned about on 

 an axis, either vertical or nearly so, the arch described by the sun apparently will 

 cut the horizon, but will never move parallel to it, and consequently the 

 quadrant will not be brought into a proper position for observing the sun's 

 altitude. 



3. If the quadrant be turned on the line going to the sun, as an axis, the 

 reflected sun will be kept constantly in the axis of vision, and will describe an 

 arch of a parallel circle about the real sun, with a velocity which is to the 

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

 radius; and when the motion of the reflected sun is parallel to the horizon, the 

 quadrant is vertical. 



Hence naturally arise the 3 methods of taking an altitude, which have been 

 mentioned before. In the first, the axis of vision is supposed always directed to 

 one and the same part of the horizon, namely that which is in the sun's vertical. 

 In the 2d, the observer is required to hold the quadrant truly vertical, and to 

 turn himself on a vertical axis ; but it is evident neither of these motions can 

 be accurately performed. In the 3d method, the observer is only required to 

 move both himself and the quadrant, so as to keep the sun always in or near the 

 axis of vision, which may be performed very well, because the <ixis of vision is 

 a visible and certain direction for it. One exception, however, should be made 

 to this general rule, namely, in taking the sun's altitude when very low, by the 



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