380 FERGUSON'S LECTURES. 



LECT In the universal ring-dial, for instance, the divisions 

 L^V-^> on the axis are the tangents of the angles, of the sun's 

 declination placed on either side of the center. But 

 instead of laying them down from a line of tangents, I 

 would make a scale of equal parts, whereof 1000 should 

 answer exactly to the length of the semi-axis, from the 

 center to the inside of the equinoctial ring ; and then 

 lay down 434 of these parts toward each end from the 

 center, which would limit all the divisions on the axis, 

 because 434 are the natural tangent of 23o 29*. And 

 thus, by a nonius affixed to the sliding piece, and taking 

 the sun's declination from an Ephemeris, and the tan- 

 gent of that declination from the table of natural tan- 

 gents, the slider might be always set true to within two 

 minutes of a degree. 



And this scale of 434 equal parts might be placed 

 right against the 23, degrees of the sun's declination, 

 on the axis, instead of the sun's place, which is there of 

 very little use. For then, the slider might be set in the 

 usual way, to the day of the month, for common use ; 

 but to the natural tangent of the declination, when great 

 accuracy is required. 



The like may be done wherever a scale of sines or 

 tangents is required on any instrument. 



RULE II. 



The latitude of the place, the sun's declination, and his 

 hour distance from the meridian, being given ; to find, 

 (1.) his altitude ,- (2.) his azimuth. 



Let d (see engraving, page 372) be the sun's place, 

 d R, his declination ; and in the triangle P Z d, P d 

 the sum, or the difference, of d R, and the quadrant 

 P R, being given by the supposition, as also the com- 

 plement of the latitude P Z, and the angle d P Z, which 

 measures the horary distance of d from the meridian ; 



