hi the following figure (6), therefore, c A, or C at, or c n = moon's horizontal parallax ; k c s = apparent distance between the sun and moon, m being the moon's place in the figure and a the sun's ; or the are m s = apparent distance. at E = the moon's zenith distance, or, as every part of the small parallel of altitude, r E, is equally distant from ki,c n on the line of sines will oval the moon's altitude.
And again, s 1' will be the sun a zenith distance, and therefore (3 I( on the line of eines will equal the sun's altitude, A D being the moon's horizon and A r the sun's ; n E will be the moon's parallax in altitude ; and in: c n : : cos. E D : radius, or the moon's parallax in altitude = her. pax. x cos. moon's alt.
• radius And in the orthographic projection of tho lunar triangle at 8 z on a scale where radius is = moon's her. parallax, or C D, the angle at is the angle at the moon corresponding with the angle c in the usual lunar construction, as in Ay. 7; and c N (the distance of the orthographic great circle m N passing through z, where the sun's and moon's horizons coincide) is the cosine of this compared with radius c n. But C D : C v ::HE:DE; or tr 7. is the correction for parallax= CNX II E' and is radius measured from tt z by the scale of chords from the nature of the pro jection. (In fig. 7, Cc' : cD : : tad.: cos. c, c e' being the moon's parallax in altitude, and C n the correction for parallax.) In fig. 6, moreover, x n = tangent of moon's zenith distance, in seconds for alt. 45'; is r, correction for moon's refraction in seconds ; s v = correction for sun's refraction in seconds. Such being the principles ou which
this part of the apherograph is constructed, the following is the form of each of the parts :— The under sphere has its line at c crossed by parallel circles drawn to the scale of sines, or on the orthographic projection ; these are again crossed by lines parallel to Si C, C D being divided into 60 parts by the lino of chords (being very nearly of refraction at as above).
The practical use of the ephcrograph in correcting a lunar distance may be thus briefly illustrated : suppose, for example, the apparent distance given =72', the moon's altitude the sun's altitude= and reduced horizontal parallax = 59'. Moving the circles concen trically until m and a are moved apart in fig. 6;= the apparent distance, where the two horizons A E and 0 T cut each other, will give a point which, counting the vertical lines from at c, each will be one minute of correction (as read upon en); this correction, multiplied by a number taken from a small table printed on the back of the instru ment, gives at once a correction for the distance, thus :— When the intersection of the horizons falls on the right of m c, the correction is subtractive ; when to the left, it is additive. The spherograph is especially useful to check observations when worked out by logarithms, and imparts confidence to a navigator. A little work published by Longman and Co., Calculation and Projection of the Sphere, plainly illustrates the general mode of spheric con struction.