MR. JAMES WOOD, MASTER MARINER, WHITBY.

On June 3rd, 1868, in lat. 54° 30', the sun's declination being 22° 23′ N., the obliquity of the ecliptic being 23° 27′; I require to know the sun's right ascension, longitude, ascensional difference with the time of his rising and setting; also his true amplitude with the variation of the compass (his mag. amp. being E. 19° N.) and also his true azimuth at 6 hours from the meridian, with his true altitude at that time, which the following proportions

will give.

Log. tang. dec. 22° 23′ N. + co-tang. oblq. 23-27—10=log. sine rt. asc.
Log. sine dec. 22° 23′ N. +10—log. sine oblq. 23°-27′=log. sine O's longitude.
Log. tang. dec. 22° 23′ N. + log. tang. lat. 54° 30-10=log. sine ascenl. diff.

This ascensional difference added to 6 hours will give the app. time of O's setting, and subtracted from 6 hours will give time of rising. Log. sine dec. 22° 23′ N+log. secant lat. 54° 30′ N.-10= log. sine O's amp. from E. at rising, and from W. at setting towards the North. Co. sine lat. 544°+10-co. tang. dec. 22° 23′ = log. co. tang. of true azi. at 6 h. Co. sine dec. 22° 23′+10-sine true azim. = log. co. sine of true alt. at 6 h. To find the Sun's Longitude.

To find Sun's Right Ascension.

Log. tang. decl. 22° 23′

9.614718 Sine +10=19.580699

co. tang. oblq. 23° 27′-10-0.362735 Sine

9.599827

or II 13° 7'

9.980872=sine long. 73° 7'

To find the True Azimuth and True Altitude at 6 o'clock.

To find the Time or Meridian Distance, and the Sun's Altitude, when true

East or West.

4h. 51' 40.

Log. co. tang. lat. 54° 30'+tang. dec. 22° 23′-10= log. co. sine mer. dist. 72° 55′ co. sine dec. 22° 23′+ log. sine mer. dist. 72° 55'-sine azim. 90° or 10 = co

Sun's Declination and Ascensional Difference given to find the Latitude and

Amplitude.

Log. sine ascl. 35° 16'+10-tang. decl. 22° 23′

co. tang. lat. 54° 30′ N. co. sine decl: 22° 23′+co. sine ascl. diff. 35° 16′-10=co. sine amp. 40° 50′ N.

Sime ase, diff, 35, 16′ log. + 10 = 19.761464 Co. sine-10{

-Tang. dec. 22° 23′ N.

Co. tang. lat. 54° 30′ N. (Prob. 6.)

True amp. N.

9.911942 9.965981 Prob. 1.

40 59: co. s. 9.877923 from E. at rising and W. at setting towards the North.

Sun's Declination and Altitude at the hour of 6 given, to find the Latitude and

his Azimuth.

Log. sine alt. 18° 4' + 10-sine of decl. 22° 23′ N. =log. co. sine decl. + 10-co. sine 18° 4′-log, sine of

sine of lat. 54° 30′ N. 's azim. N. 76° 33′ E. in the

(Prob. 3.)

Co. sine

9.978042

morning.

Co. sine +10= 19.965981

9.987939 sine azim.

N. 76° 33′ E. A.M.

The Sun's Declination 22° 23′ N. and his Altitude 27° 53′ being due East; required the hour distance from 6 o'clock, and the Latitude the Elevation of the Pole.

The Sun East or West, the Time from 6h. = 1h. 8′ 20′′ 17° 5′, and the Sun's Declination 22° 23′ N.; Required the Altitude at that time, and also the Latitude.

June 3rd, 1868, in Latitude 54° 30′ N., Longitude 0° 33′ W.; the Planet Venus was on the Meridian at 3h. P. M. (civil mean time), consequently at 9h. P.M. she would be 6h. West of the Meridian, her Declination 23° 30′ N,; I require to know her true Altitude and Azimuth, also her Amplitude and time of Rising and Setting.

Log. co. sine lat. 54° 30′+10, 19.763954

co. tang. dec. 23' 30' 10.361698 Co. sine +10, 19.962398

Co. tang, azim. N. 75° 50′ W. 9.402256 Sine

9.986587

9.600700

Sine amp. 43° 22′ N. = 9.836746

To be reckoned from East at rising and from West at setting towards the North or

South according as the Declination is North or South.