476 Additional Notes. 



applied my thoughts, upwards of two years, to find a more 

 certain instrument, and contrived the following improvement, 

 as I think, in the make and use of the bow; viz. 



The quadrant is to be numbered from each end to .90 at 

 the other, as in the figure. The sight and glass vanes are the 

 same with the common, excepting that the glass should be 

 larger, and 1 think it would be better if ground to the seg- 

 ment of the cyhnder. The horizon-vane should be like that 

 in tlie figure thereof; having three holes, IK L; one hole, I, 

 to fit on the centre of the Quadrant, A ; the other two, K L, 

 to see the horizon through, whose length across the vane may 

 be one-eighth of the radius A B, or more ; the horizon-vane 

 should be a little hollowed, answerable to the curvature of 

 the circle DAE, or cylinder, whose semi-diameter A H is 

 about seven-elevenths of A B, the radius o£ the quadrant. 



In observing with this Quadrant at sea, let the sight and glass 

 vanes be kept nearly on the same numbers, or at equal dis- 

 tances from the ends of the arch, and then it v^-ill be suffi- 

 ciently exact to bring the spot and horizon in a right line, op 

 anv part of the horizon-vane, by moving the vanes nearer 

 together or further apart, the middle of the horizon-vane be- 

 ing parallel to the horizon, then the zenith distance will 

 be the sum of the distances of the vanes from the end of the 

 Quadrant arch. For, putting r=the radius of the Quadrant, 

 c=the distance of the spot from the middle of the horizon- 

 vane, 5^=the sine, and 6*=the cosine of half the sun's alti- 

 tude, unity being radius, tlie sine of the error will be nearly 

 equal to c \^x'^-^\ and, therefore, when greatest (which is 

 when the zenith distance is 00.00, or 47deg. 45min.), of the 

 distance of -^ of the radius of the Quadrant from the middle 

 of the horizon-vane, it is but 1.30; I would advise to bring 



