It is well known that one common source of error in working, sea observations taken at night, is the liability to mistake the name of a star. This instrument provides a very handy method of correctly finding the name of of the first magnitude, even when others around it are obscured. The inventor of the spherograph, Mr. Stephen Martin Saxby, R.N., had noticed that no two stars of the first magni tude had equal declinations in either hemisphere, or were within two or three degrees of each other in that respect. By having a list of such stars and their declinations on the face of the instrument, the name of any star of first magnitude is easily obtained in the following manner :—Using merely approximate data, such as latitude, altitude, and azimuth, we apply them thus : suppose a star has an altitude of about 10°, its time bearing [Built:in] being N.E., the estimated lati tude of the place being 43° N.; setting the instrument to the latitude, the intersection of these three elements would on the line of declina tion be 38i° N. Reference to the " list of stars on the instrument would at once show that this declination could only apply to the star a Lyra.
In working a night observation; the finding of the right ascension is rendered in the spherograph peculiarly simple, and is divested of all liability to error from the occasional fault of adding instead of sub tracting, &c. A form of spherograph is prepared for this. (See fig. 5.) the lines that are not necesaary to the working of this question, we ;ffiall, in fig. 4, have a view of the spheric triangle under consideration, which, had it been merely projected on a plane, must have been worked by computation, thus : in the spheric triangle z o r we have o z =zenith distance, 0 r the polar distance, and z r o the hour angle, to find z r the colatitude, and thence PR the latitude. By the spherograph this question of Latitude is answered (simultaneously with numerous other results not asked for in this) by simply turning the upper sphere on the under, until the place where the time and declination on the under sphere coincide with some part of the parallel of given altitude on the upper. The instrument is thus said to be set, and the measures of altitude, azimuth, time of sun setting, rising, &c., are at once read off; while without the spherograph the latitude alone would require the following work (and ono illustration of its saving of time and labour will suffice) :— After letting fall a perpendicular in fig. 4 from the centre g through o to x [Sruesicat TRIOONOWETRY], 0 d r will be a right angle, then by circular parts in triangle r z o find angle z, thus,— The spherograph is of different forms, to suit special purposes Figures 2 and 3 combined, 2 being the upper sphere, represent Its general form for latitude, time, azimuth, altitudes, and declina.
The inner circle a revolves upon a:centre-pin connecting it with b the under part. On this circle the principal stars are delineated according to their right ascensions, which are measured on its circumference, and their declinations as measured upon a radius. To avoid confusion, we omit, in the above figure, all but Regulus. Suppose at 2b 12. a.m., on the 5th of November, a navigator was desirous of using Regulus as a means of obtaining his latitude, dm On turning the cirelo till the data 5th November, marked on it, coincided with marked upon the outer part b, he would find that a line through Regulus would cut a point on the part b at the distance of 5b 5° from the part of the circle marked Noon. This, then, would be the star's distance from the meridian, and would be used in the common form of spherograph made up of figs. 2 and 3, as if it were time by the sun. Thus night observations are rendered as easy as those taken by day.
There is another peculiarity of the instrument. Heavy southerly gales in the English Channel, when they clear up, generally do so by the clouds breaking in the N.W. to N., so that the polar star is generally about the first star visible. At such times, the mariner eagerly attempts to obtain his latitude, and the form of spherograph fig. 5, is a very great Suppose he have obtained an altitude of the polar star = 50° 5' at 12' a.m. of 5th November ; baying set the date to the hour as before, the polar index engraved on the circle will point to some one of the figures engraved round the circle on the part b ; in this instance it would be to 47' subtractive : then 50° 5' —47'= 49° 18', the true latitude, to the nearest mile. The readiness of the method admits of increased number of observations ; and, consequently, by using the means of such observations, the present prevailing error from the indistinctness of the horizon is greatly diminished.
We shall only notice one other use of the spherograph as greatly curtailing labour of computation—namely, in lunar observations. The lines on fig. 6 are thus obtained (and here, again, a knowledge of the principles on which ths lines are constructed is not at all necessary to the successful use of it) :— Taking advantage of the circumstance that refraction varies nearly as the tangent of the zenith distance, and as tan. 45° = radius, we take, in the projection for refraction, the radius as the refraction at 45° zenith distance. It fortunately happens that 58'4, the number of seconds In the refraction at nearly corresponds with the number of minutes in the mean horizontal parallax. Tho same diagram does therefore for both parallax and refraction, aubetituting seconds for minutes.