717 



SPHEROGRAPH. 



SPHEROGRAPH. 



718 



one (Jl'j. 3) has hour circles and parallels of declination : for of the 

 three parts always given in every spheric triangle, two will fall on 



either one of the cards, and their intersection is made to touch the 

 third datum as found in the other. We will suppose, in illustration, 

 that we have given the sun's altitude 48, the declination 10 N., and 

 the apparent time 11 h. A.M., to find the latitude. If we discard all 



' 



the lints that are not necessary to the working of this question, we 

 shall, infy. 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, thuw : in the spheric triangle z o p we have o z = zenith 

 the polar distance, and zro the hour angle, to find 7, r the 

 co-latitude, and thence r B 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 coin' : me part of the parallel of given altitude on the 



upper. The ir.^truraent is thus said to be set, and the measures of 

 altitude, azimuth, time of sun setting, rising, &c., are at once read off; 

 wliil- without the spherograph the latitude alone would require the 

 following work (and one illustration of its saving of time and labour 

 will suffice) : 



After letting fall a perpendicular in fg. 4 from the centre g 

 through o to jrTSpiiKiuc.vL TRIGONOMETRY], odr will be a right angle, 

 then by circular p.-irts iu triangle P z o find angle z, thus, 



As line zenith distance o i, 42' 

 Is to sine hour-angle p, 1 5' . 

 So is tin: polar distance o r, 80"' . 



co. ar. 0-174189 



. 9-412996 



. . 9-993351 



To inc angle z, 180' 22' 23' 

 In A de o find dr. 



157" 37' =9-580836 



At coUn?. polar distance, 80 . CO. ar. 0-793681 

 1 to co<me hour-angle, 1 5 ' . . . 9-984944 

 So i radius ..... .30- 



To tangent side rfr, 79' 39' 

 In A d z o find d z. 



. =10-738625=79' 39' 



A^ cotang. zenith distance, 42 . co. ar. 0"J54437 

 Ii to cosine 180" 1 J7 1 3;'=2J 23' . 0-905981 

 60 It radioi ... . . lo- 



To tangent of <Jz, 



= 9-920418=39' 47' 



Co-latitude = 39 52 

 00 



I.atitude = 5 



The spherograph is of different forms, to suit special purposes 

 Figures 2 and 3 combined, 2 being the upper sphere, represent 

 it general form for latitude, time, azimuth, altitudes, and declina 



ion ; and it has introduced a new mode of navigating ships in 

 jlaces subject to fogs and haze : for instance, the Montreal traders 

 use it on the Banks of Newfoundland, by substituting azimuth for 

 altitude, in the three things given, when the horizon is entirely 

 nvisible, the sun being in sight. It also dispenses with double alti- 

 .udes, inasmuch as latitude can be as well determined by it from a 

 single observation as from two, rendering all elapsed time uncalled for. 

 3ut it is not our purpose to describe these methods in detail. It seems, 

 lowever, that a means of so readily finding the position of a fast-sailing 

 steamer when approaching the laud is important. 



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 

 inding the name of any "star 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 tliree 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 true bearing [BCAUIXG] 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 38J N. Reference to the list of stars on the instrument 

 would at once show that this decimation could only apply to the star 

 a Lyrac. 



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 fg. 5.) 



Fig. 5. 



If a art 



The innercirclea 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 2 h 12"' a.m., on the 5th of 

 November, a navigator was desirous of using Hegulus as a means of 

 obtaining his latitude, &c. On turning the circle till the date 5th 

 November, marked on it, coincided with 2'' 12 marked upon the outer 

 part 6, he would find that a line through Regulus would cut a point 

 on the part b at the distance of 5 k 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 /</. 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 spherograpli 

 /</. 5, is a very great convenience. Suppose he have obtained an 

 altitude of the polar star = 50 5' at 2' 1 12'" a.m. of 5th November; 

 having 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 6 ; 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, iu lunar observations. Tho 

 lines on Jiy. 6 are thus obtained (and here, again, a knowledge of the 

 principles on which the 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, tve take, 

 in the projection for refraction, the radius as the refraction at 45 



