. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. ight, or from sunset till sunrise. Note. The time of apparent sunrise or sunset may befound in a similar manner, if the parallel circle ts be drawnat the distance of 33 below the horizon HO. PROBLEM. VII. Given the suns altitude, and declination, with the latitude ofthe place ; to find the hour, and the suns azimuth. Example. Suppose the suns altitude, observed at Cam-bridge, to be 46° 20, on the 21st of June, its declina
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. ight, or from sunset till sunrise. Note. The time of apparent sunrise or sunset may befound in a similar manner, if the parallel circle ts be drawnat the distance of 33 below the horizon HO. PROBLEM. VII. Given the suns altitude, and declination, with the latitude ofthe place ; to find the hour, and the suns azimuth. Example. Suppose the suns altitude, observed at Cam-bridge, to be 46° 20, on the 21st of June, its declination be-ing 23° 27 57 N ; required the time, and the suns azimuth. projection. Draw the meridian, hor-izon, prime vertical, axis,equinoctial, and parallel ofdeclination, as the parallel circle rs,at the distance of 4b° 20above the horizon HO, andit will intersect mn in Z, 0, N, describethe azimuth circle ZjN,and through P, Q, S, thehour circle P©3. CALCULATION. In the oblique spheric triangle P0Z, PZ = the co-lati-tude, Z© = the co-altitude, PO = the co-declination orpolar distance, OPZ = the hour anyie from noon, and OZP= the azimuth SPHERIC ASTRONOMY. 479 The arc 0m is measured by Ex, the measure of the angle3LPx, or ZPQ j and yO measures the angle yZO, or ©ZP. 1. To jind the hour angle from noon 0PZ. PZ = 47° 36 32PO = 66 32 3Z© = 43 40 2)157 48 35 | sum 78 54 17| 47 36 32 | sum—PZ 31 17 45| | sum 78 54 i 7|PO 6b 32 3 sine 9* 7155513 jsum—P012 22 141 sine 9*3308919 Co-ar. sin. 47° 36 32 0*1316143 Co-ar. sin. 66 32 3 0*0374897 23° 54 352 sine 2)19*2155472 9*6077736 47 49 10=ZQPZ. The hour angle 47° 49 10, reduced to time, is 3h. 11 1640. Therefore the time required is 8h. 48 43| in the fore-noon, or 3h. 11 16| in the afternoon, if {.he given declinationke that of the sun at each of those times. 2. To find the azimuth rem. 31° 17 45! sine 9*7155513 * sum 78 54 17|ZO 43 40 2d rem. 35 14 17| sine 9*7611584 480 Mathematics. C
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