ASTRONOMY AND METEOKOLOGY. 371 



latitude of the place, and the observed altitude of the moon. Lieut. 

 Ashe first computes the zenith distance of the moon on the supposi- 

 sition that the observer is on the meridian of Greenwich. As the 

 Greenwich sidereal time is known, the arc of the equinoctial between 

 the moon's node and the meridian may be computed from the " Nau- 

 tical Almanac," and the angle which the moon's orbit makes with the 

 equinoctial may be assumed to be equal to the moon's greatest declina- 

 tion. Hence the solution of a right-angled triangle will give the arc 

 on the moon's orbit, from her node to the meridian, or arc a ; the arc 

 on the meridian between the orbit and the equinoctial, or arc b ; and 

 the angle included between these arcs, or /. Again, if a perpendic- 

 ular be let fall from the zenith upon the moon's orbit, the angle in 

 this triangle opposite the perpendicular will be y, and the hypothenuse 

 is the latitude of the place when increased or diminished by arc b ; 

 hence the value of the perpendicular arc d is found, and also the 

 distance of the foot of the perpendicular from the meridians; the 

 addition or substraction of e to a gives the longitude of the foot of the 

 perpendicular, reckoned on the moon's orbit from the node. Finally, 

 having the values of the perpendicular on the orbit, and of the moon's 

 zenith distance calculated for the meridian of Greenwich, the third 

 side is computed, which when applied to the last found arc gives the 

 longitude of the moon on her orbit reckoned from the node, on the 

 hypothesis that the observer is on the meridian of Greenwich at the 

 sidereal time supposed. Lieut. Ashe then assumes that the change of 

 meridian from Greenwich to the place of observation will not alter 

 the relation of these circles to each other, and that the moon will 

 merely occupy another situation in her orbit. As the zenith dis- 

 tance at the place of observation is supposed to be known, there are, 

 in the right-angled triangle requiring solution, the perpendicular on 

 the moon's orbit, and the observed distance of the moon from the 

 zenith ; and from these data the longitude of the moon on her orbit, 

 reckoned from the node, is found for the time and meridian of the 

 place. The difference of the two arcs thus found, divided by the 

 moon's motion, will give the difference in longitude between Green- 

 wich and the place of observation. Lieut. Ashe suggests a second 

 mode of determining the longitude by an altitude of the moon, when 

 compared with an altitude of the sun or a star. " For the sake of 

 simplicity, take an example with a star. Let the altitude of a star 

 near the prime vertical be taken, and compute its hour-angle. As 

 soon after as many be convenient, take the altitude of the moon, and 

 find her hour-angle ; the elapsed sidereal time, and run of the ship (if 

 necessary,) being applied to the hour-angle of the star, the hour-angles 

 of the moon and star are known at the instant of last observation, and 

 consequently the right ascension of the moon is known from the 

 right ascension of the star. A simple proportion will show what is the 

 Greenwich time corresponding to this right ascension of the moon. 

 When the observations are made on the same side of the meridian, an 

 error in latitude, or instrument, or that caused by bad horizon, or re- 

 fraction, or personal equation, will not materially affect the ' difference ' 

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