SPHER'OGRAPH, a simple and exceedingly efficient instrument for the mechanical solution of such problems in spherical trigonometry as navigation, geography, etc., present, was invented in 1856 by Mr. Stephen Martin Saxby, nix. It consists of two circular pieces of paper, the whole of the under and the rim of the upper being made of stout card-board, and the interior portion of the upper one of strong transparent tracing-paper; these two circles are attached by a pin through their common center, the pin being made to work in an ivory collar, so as to prevent any lateral motion of either circle. Round the pin as center, equal circles are drawn, one on each sheet; each circle is then filled in with lines representing meridians and parallels according to the stereo graphic projection, and the instrument is completed, As one of the chief uses of the spherograph is to show the course, distance, and differences of latitude and longitude in "great circle sailing" (q.v.), we shall give a problem of this sort in illustration of the working of the instrument. Fig. 1 represents the ap pearance presented by the spherograph when the two poles are separated from each other by an angular distance of 40°; the lines drawn on the under circle (represented by dotted lines in the fig.) showing through the transparent paper which forms the upper circle, on which the continuous lines are delineated. Suppose, then, that a ship is in lat. 50° n., long. 29' w., and is bound for a point in lat. 10' n. and long. 80° w., and that its great circle track, etc., are required: let P, the pole of the under circle, represent the place of the ship (the circle Z['D always representing the meridian of the point of departure, and the upper circle, whose pole is Z, representing the earth's hemisphere), which is done by turning the upper circle till P appears at let. 50° n.; X represents the point to be arrived at, and consequently PX, the arc of a great circle passing through P and X, is the great circle track, PD is the difference of latitude, Er the difference of longitude; the spherical angle XPD, measured by GIL an arc of a great circle, of which P is the pole, is the course; and the length of PX is measured by PT, the portion of PS which is cut off by a parallel of the under circle through X, in degrees. The data, then, being as above, we find by inspection of the instrument the
difference of lat. = 40° s., the difference of long. = 60° w., the course =,s. 72i° w., and the distance = 634°= 3,800 nautical miles. Besides the saving of time and labor by the use of this instrument—the whole work being the setting of the instrument, and then the reading off of the required elements—it is evident that the substitution of a mechanical solution for calculation greatly lessens the probability of error. It is found that spherographs of 5 in. radius give results of sufficient accuracy for all the purposes of the navigator.
All other spherical problems can be solved with equal facility by this instru ment, but one more example will suffice.
Let Z (fig. 2) now represent the zenith of a place, ZHNR its meridian, P the north pole of the heavens; the other lines are then circles of declination, altitude, azi muth, and hour circles; and let 0 repre sent the place of the sun in given declina tion and altitude at a certain time. The instrument is now set by turning round the upper card till the point 0 (determined by its circle of declination and hour circle) on the under card falls upon the circle of given altitude on the upper card, then d is the sun's place at noon, lid being his meridian altitude, PR the latitude of the place, the angle RPS (measured in degrees along QE) the time of sunset, ds half the length of the day, se half the length of the night, etc. The spherograph is also use ful in finding latitude when the horizon is hid by fogs, right ascensions at night, and in correcting lunar observations; but for these purposes, spherographs are specially constructed, as some slight variations in the form given above are necessary.