VOL. LXII.] PHILOSOPHICAL TRANSACTIONS. 3^ 



would be true, if a person could by sight certainly know the part of the horizon 

 exactly beneath the sun; but, as this is impossible, the precept is incomplete. 

 Moreover, in taking the sun's altitude in or near the zenith, this rule entirely 

 fails, and the best observers advise to hold the quadrant vertical, and turn one's- 

 self about upon the heel, stopping when the sun glides along the horizon with- 

 out cutting it : and it is certain that this is a good rule in this case, and capable 

 with care of answering the intended purpose. We have thus two rules for the 

 same thing, which is a proof that neither of them is a universal one, or sufficient 

 in all cases alone. 



In taking the observation, observers have been advised either to turn the 

 quadrant about upon the axis of vision, or, holding the quadrant upright, to 

 turn themselves about upon the heel, indifferently. The true state of the case 

 is this ; that, in taking the sun's altitude, whether by the fore or back 

 observation, these two methods must be combined together ; that is to say, the 

 observer must turn the quadrant on the axis of vision, and at the same time turn 

 . himself about on his heel, so as to keep the sun always in that part of the 

 horizon glass which is at the same distance as the eye from the plane of the qua- 

 drant: for, unless the caution of observing the objects in the proper part of the 

 horizon glass be attended to, it is evident that the angles measured cannot be true 

 ones. In this way the reflected sun will describe an arch of a parallel circle 

 round the true sun, whose convex side will be downwards in the fore observation, 

 and upwards in the back observation, and, consequently, when, by moving the 

 index, the lowest point of the arch in the fore observation, or the uppermost point 

 of the arch in the back observation, is made to touch the horizon, the quadrant 

 will stand in a vertical plane, and the altitude above the visible horizon will be 

 properly observed. 



The reason of these operations may be thus explained ; the image of the sun 

 being always kept in the axis of vision, the index will always show on the 

 quadrant the distance between the sun and any object seen directly which its 

 image appears to touch ; therefore, as long as the index remains unmoved, the 

 image of the sun will describe an arch every where equidistant from the sun in 

 the heavens, and consequently a parallel circle about the sun, as a pole ; such a 

 translation of the sun's image can only be produced by the quadrant being turned 

 about on a line drawn from the eye to the sun, as an axis; a motion of rotation 

 on this line may be resolved into two, one on the axis of vision, and the other 

 on a line on the quadrant perpendicular to the axis of vision ; and consequently 

 a proper combination of these two motions will keep the image of the sun con- 

 stantly in the axis of vision, and cause both jointly to run over a parallel circle 

 about the sun in the heavens; but when the quadrant is vertical, a line on it 

 perpendicular to the axis of vision becomes a vertical axis ; and, as a small 

 VOL. XIII. Q a 



