Sun's declination at noon, January 10th, = 21:57:50 S. 21:55:10 S. Sun's reduced declination = Obs. alt. of sun's 1. limb 14:31:47"; hence, its true cent. alt. is 14:41:36" Sun's dist. from the mer. the app. time=3115: Log.rising=5.47241.5 = January 20th, 1825, in latitude 37:20: S. and longitude 49:45 E., the mean of several altitudes of the sun's lower limb was 26:39:15", that of the corresponding times, per watch, 19:11:45, and the height of the eye above the level of the horizon 16 feet; required the apparent time of observation, and the error of the watch? Sun's declination at noon, January 20th, 209 7:11 S. = Obs. alt. of sun's 1. limb = 26:39:15%; hence, its true cent.alt. is 26:49:58" Sun's true zenith distance at the time of observation = Sun's horary distance from the merid.=443" 42: Log.rising=5.82813.2 Of computing the horary Distance of a celestial Object from the Meridian. If the latitude of the place of observation and the declination of the celestial object are of different names, let their sum be taken,-otherwise, their difference,-and the meridional zenith distance of the object will be obtained; the natural versed sine of which, being subtracted from the natural co-versed sine of the object's true altitude, will leave a remainder. Now, to the logarithm of this remainder add the log. secants of the latitude and the declination, and the sum will be the log. rising of the object's horary distance from the meridian; and if this object be the sun, the apparent time will be known, and, hence, the error of the watch, if required, as shown in the first method, page 384. Example 1. May 1st, 1825, in latitude 40:35. S., and longitude 63:15 E., the mean of several altitudes of the sun's lower limb was 19:43:58", that of the corresponding times, per watch, 20:57 45, and the height of the eye above the level of the sea 14 feet; required the apparent time of observation, and the error of the watch? Obs. alt. of sun's 1. limb 19:43:58"; hence, the true cent. alt. is 19:53:47" Sun's mer. z.dis.= 55:51:53′′Nat.V.S. = 438851 Remainder = 220829 Log. = 5.344056 Sun's horary distance from the merid.= 3 245 Log.rising=5.47918.5 November 10th, 1825, in latitude 49°13' S., and longitude 36:50′ W., the mean of several altitudes of the sun's lower limb was 22:28:30", the mean of the corresponding times, per watch, 5425, and the height of the eye above the level of the horizon 20 feet; required the apparent time of observation, and the error of the watch? Obs. alt. of sun's 1. limb=22:28:30"; hence, its true cent. alt. is 22:38′17′′ Remainder = 463460 Log. = 5.666012 Sun's dist. from the mer. the appar. time=5 025: Log.ris. 5.87095.7 Time of observation, per watch, = . . 5. 4.25 Watch fast for apparent time = . 4" 0: METHOD IV. Of computing the horary Distance of a celestial Object from the Meridian. RULE. If the latitude of the place of observation and the declination of the celestial object be of different names, let their sum be taken,-otherwise, their difference, and the meridional zenith distance of the object will be obtained; from the natural co-sine of which, subtract the natural sine of the object's true altitude, and to the logarithm of the remainder add the log. secants of the latitude and the declination; and the sum will be the log, rising of the object's horary distance from the meridian. Now, if this object be the sun, the apparent time is known, and, hence, the error of the watch, if required, as shown in the first method, page 384. Example 1. July 4th, 1825, in latitude 39:47:S., and longitude 60:50. E., the mean of several altitudes of the sun's lower limb was 13:2:30%, that of the corresponding times, per watch, 310" 45, and the height of the eye above the level of the horizon 22 feet; required the apparent time, and the error of the watch? Greenwich time past noon of July 3d 23 725' Obs. alt. of the sun's 1. limb=13:2:30"; hence, its true cent. alt. is 13:9.53" Sun's mer. z. dist.=62:41.42′′Nat, co-sine=458727 Sun's dist. from the mer. the appar. time=3, 1035: Log.ris.=5.51363.0 Time of observation, per watch, = Watch fast for apparent time = Example 2. 3. 10.45 010: July 19th, 1825, in latitude 40:10:50" N., and longitude 53:20: W., the mean of several altitudes of the sun's lower limb was 33:23:15", that of the corresponding times, per watch, 19:47 30, and the height of the eye above the level of the horizon 15 feet; required the apparent time, and the error of the watch? Obs. alt. of sun's 1. limb=33:23:15"; hence, the true cent. alt. is 33:34:1" Remainder = 389887 Log.=5.590939 Sun's horary distance from the merid.=411-53: Log, rising 5. 73684. 1 |