ference of the north and south readings of the level scale, we have for latitude by observing a star south of the zenith, λ — 90° — (A® —z") + ro +( N (6 REDUCTION TO MERIDIAN." (6) If a star were observed before it reached, or after it had passed the meridian, the observation made would require a third correction, called the "Reduction to Meridian." In the figure suppose the star seen at в to be observed on the meridian, and after it has passed the meridian, to be again observed at B', then the difference between ZB' and ZB BD = "Reduction to Meridian." The formula for "Reduction to Meridian" is in which m = L= = tabular quantity taken from the table of "Reduction to Meridian," Table XXXVI. by sin 1', the argument being the hour angle or time the star is from the meridian. (See p. 304.) (Lee p. 46) Latitude of Station. A North Polar Distance of Star. It is evident, without demonstration, that the zenith distance of any star will be the smallest when it is on the meridian (the telescope being moved in azimuth), therefore the algebraic sign of the correction for "Reduction to Meridian" to the latitude resulting from an observation of a star north of the zenith will be +, and for the latitude resulting from the observation of a star south of the zenith, the algebraic sign of the correction will be. Hence for a star north of zenith By adding (7) and (8) we have for twice the latitude, in which a represents the arc value of one division of micrometer, and b the arc value of one division of the level scale. In the preceding example the 1st column contains the date of the observation, the 2d column the numbers of the stars observed in the British Association Catalogue, the 3d column indicates whether the star is north or south of the zenith; the 4th and 5th columns give the number of turns and fractions of a turn of the micrometer screw, necessary to bring the wire from zero to coincide with the star; the 6th column gives the difference of the micrometer reading, the 7th the value of the same in are depending, of course, on the value of one turn of the micrometer screw ;* the 8th column the polar distances of two stars observed on each day, their sum "+A, and 180° — (A" + A), according the formula, from which subtracting† the number in the 7th column, which is the difference of their zenith distances in are, or z"-z, according to the formula, p. 345, the remainder will be by the formula equal to twice the approximate latitude which is written in the 9th column. The 10th and 11th columns contain the n level readings at the north and south ends of the scale, in both positions of the instrument, together with the values of Ño + Ñ3, and sa + s', the 12th column shows the difference of these results, or the value of (y" + N°) (ss), according to the formula; the 13th column contains the hour angle of the star when not observed exactly on the meridian in minutes and seconds of time; the 14th column contains the correction for error of level, which is obtained by dividing the result in the 12th by 4, and multiplying by the value of one division of the level scale, according to the formula; the 15th column contains the result obtained by the computation in the 19th column, of the correction for the star's not being observed exactly upon the meridian by a method similar to that at top of p. 304, using a more accurate table, in which the constant sin 1" is incorporated; the 16th column contains the correction for refraction; the 17th column, the double latitude after the corrections in the 16th and 14th have been applied to the 9th; the 18th column, the latitude which is half the result contained in the 17th; the 19th column is for miscellaneous purposes, used in this example for the computation already mentioned. LONGITUDE BY CELESTIAL OBSERVATIONS. The best mode of determining longitude ordinarily is by means of moon culminations. The Nautical Almanac gives p. 504 et seq. in the edition of 1850, the apparent R. A. of the bright limb of the moon at the instant of its transit at Greenwich, both for the upper culmination marked u A good way of finding the value of one division of the screw head of the micrometer is to note the time by chronometer of the transit of Polaris over the movable wire placed vertically, and set successively to every division of the screw head. Representing by x the angular distance from the meridian at which any reading was taken, by p the hour angle, and by ▲ the polar distance of the star, we have sin sin A sin p The value of being computed for each reading, the difference of these values, divided by the difference of the corresponding micrometer readings, gives the value of one division. + Really adding in this example, because z is less than z. |