[ 112 ] 



the horizon-glafs, the fame way as the arch of 

 the quadrant is carried, both in the fore and 

 back-obfervations, with a velocity which is to the 

 angular velocity of the quadrant as the fine of the 

 Sun's altitude to the radius, defcribing an arch 

 convex downwards in both cafes ; and when the 

 motion of the Sun in this arch js parallel to the 

 horizon, the quadrant is held truely perpendicular 

 to the horizon, and confequently in a proper 

 polition for taking the Sun's altitude. But, if 

 the axis of viiion be directed to, and turned 

 round a point in the horizon befide the vertical 

 circle paffing through the Sun, the Sun's image, 

 when its motion is parallel to the horizon, will 

 be neither in the axis of vifion nor the Sun's 

 vertical, but between both ; at the fame 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. 

 II. If the quadrant be held perpendicular to the 

 horizon, and turned about upon a vertical axis, or 

 one nearly fo, the Sun will defcribe an arch con- 

 vex downwards in the fore-obfervation, and up- 

 wards in the back-obfervation, the motion of the 

 Sun being the fame way as the axis of vifion is 

 carried in both cafes, and being to the angular 

 motion of the quadrant, as the verfe-fine of the 

 Sun's altitude to the radius in the fore-obferva- 

 tion, but as the verfe-fine of the fupplement of 

 the Sun's altitude to 1 8 o° to the radius in the 

 back-obfervation. The Sun therefore will move 

 flower than the axis of vifion is the fore-obfer- 

 vation, and confequently will be left behind, 



with 



