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time, subtract the former from the latter, and call the Greenwich date the same as the ship's date; but if the longitude in time is greater than the ship's astrono- mical time, add 24 hours to the latter, then subtract, and call the Greenwich date one day less than the ship's date. Hour angle or Meridian distance, as it is sometimes called, is another term that we need know. It may be defined as the angle at the Pole, included between the meridian of the observer and the cel- estial meridian of the body referred to. Like the right ascension, the hour angle is measured on the celestial equator in the same way that longitude is measured on the terrestrial equator. Hour angle may also be defined as the distance of a body east or west of the observer's meri- dian, expressed either in time or angle. Thus at 11 a. m. the sun's hour angle is 1 hour east of the meridian, Since the sun revolves. (apparently) around the earth once in 24 hours, pass- ing through 15° of longitude every hour, if we can ascertain how many hours and minutes east or west of Greenwich the sun is, and how many hours and minutes east or west of the sun we are, we shall know our longitude. When the longitude is not known, then the problem is to find the hout angle of the sun. At sea the chronometer always indi- cates Greenwich time, and that of course, is simply the hour angle there. If we can now find the hour angle at our own meridian, the difference between the two will be the number of hours, minutes and. seconds we are east or west of the Greenwich meridian, and this quan- tity is, as we have seen, convertible into the degrees, minutes and seconds of lon- gitude of arc. With respect to circumpolar stars it will be noticed that during the lower half: of the star's journey their motion is from west to east. Attention is par- ticularly called to this, because in ob- serving star azimuths, unless acquainted with it, a beginner is likely to fancy he has made a mistake on discovering that, as his western hour angles grow larger after they have exceeded six hours, the star's bearing becomes more easterly, which at first sight seems opposed to what one would expect. The annexed diagram makes the explanation clear. A of. Pole 62 B LTorwzeoxnr Last Wes TAE Marine REVIEW AWBE is the daily circle of a north- ern circumpolar star, and the line AB represents the meridian of the observer. At A the star is at its upper transit or in other words, it is on the meridian above the pole, and bears true north. During *the following six hours, while traveling from A to W, it falls toward the westward; at W, therefore, the hour angle of the star is 6 hours west. Dur- ing the next six hours, between W and B, it falls toward the eastward. At B it is at its lowest transit, or, in other words, it is on the meridian below the pole, and again bears true north. Dur- ing the third six hours, between B and E, it rises toward the eastward; at E the star's hour angle may be expressed eith- er at 18 hours west or six hours east of the meridian. And during the last six hours its course is upwards, and towards the westward, till, after a lapse of 24 sidereal hours, it again transits at A. If the night be cloudless, it is easy in the northern hemisphere--without refer- ence to the compass--to tell when a star is near the meridian below the pole, by its being vertically under, the Pole star, which latter is now a trifle better than one degree from the true pole itself. Now it is obvious that the hour an- gle of Polaris may be very great with- out any serious change in the altitude. Let the center of the circle.be the true north pole of the heavens, and the cir- cumference the apparent orbit of Polaris. At .D /and B the altitude of the. star equals the altitude of the pole, which equals the latitude. For the north pole being 90° from the equator, will be in the horizon of an observer at equator. If you go 10° north of the equator, your northerly horizon will drop - by 10°, and hence the pole will be 10° high, and so on up to 90°, when the pole would be over head, or 90° high. With the Pole star at A you would have to subtract 1° 11' from its altitude to get the altitude of the pole, which eauals the latitude; at' C you would have to add 1° 11', Now as the right ascension of the meridian advances from o to 24 hours in exactly the same time as the pole star appears to revolve around the the - : on pole, the astronomers have made a table by which we can make the proper addi- tion or subtraction to the latitude of Po- laris at any hour. The true meridian of a place is there- fore approximately, if not actually, marked by a bearing of the North Star at' any time, that is, the direction of the star. from you at any place is the true meridian. The most that you can. be out of the way is a trifle better than one de- gree. : To tell when the North Star is on the meridian can be performed roughly by means of a plumb line held out at arm's length. When the star Mizar (the second star from the end of the handle, or from Benetnasch) and the Pole Star are vertically in line as shown by the plumb . line, Polaris is on the meridian above the pole, and therefore bears true north. The Big Dipper will be below 'the Pole Star as if resting on the end of its handle and the lower edge of its bottom next to where the handle joins the dip- per part, indicated by the star Phecda. The position of the Pole Star is also in- dicated by the position of the Big Dip- per. If the Dipper is east of the meri- dian the Pole star will be west. of the meridian, and east of the -meri- dian when the Pole Star is west. The imaginary point representing the pole of) the heavens may be found by drawing a line from Mizar to within a degree and a quarter of the North Star. These two stars are consequently on di- ametrically opposite sides of the Pole. When Mizar is six hours from the meri- dian, the North Star will be so also, and its altitude in that position will be nearly -the same as the elevation of the pole. It will be known when this is the' case. by a line through Mizar and Polaris be- ing parallel with the horizon. The eye can guess this pretty accurately. ' Since the stars come to the meridian about 4 minutes earlier every night ac- cording to our time, we can, after once determining the time by watch that Po- laris is on the meridian, find it at any. time thereafter by subtracting 4 minutes from our time for every day elapsed from the date first noted. When Polaris is on the meridian below the pole the star Spica is on the meri- dian above the pole. This indicates at once that Spica has a right ascension equal to the right ascension of Polaris, 'but on looking in the star tables we find . that Polaris has a R. A. of th. 24m. and Spica's R. A. is 13h. 20m., about 12 hours difference... This is because Polaris has two R. A:, one for its transit above the pole, the other for below the pole. When a sidereal clock shows 13h. 25m. Polaris will be on the meridian below the pole. Polaris has a declination of 88° 49' N. while Spica has a declination of about -10%° S, Hence, when Polaris is on the