UC-NRLF 
 
PUBLISHED UNDER THE SUPBRIN TENDS HfCS OF THE SOCIETY FOR THE 
 DIFFUSION OF USEFUL KNOWLEDGE. 
 
 AN EXPLANATION 
 
 OF THE 
 
 GNOMONIC PROJECTION 
 
 THE SPHERE; 
 
 AND OF SUCH POINTS OF ASTRONOMY AS ARE MOST NECESSARY 
 IN THE USE OF ASTRONOMICAL MAPS: 
 
 A DESCRIPTION OF THE CONSTRUCTION AND USE OF THE LAUGEU AND SMALLER 
 
 MAPS OF THE STARS; 
 
 AS ALSO OF THE 
 
 SIX MAPS OF THE EARTH. 
 
 BY 
 
 AUGUSTUS DE MORGAN, 
 
 OF TRIN. COLL., CAMS., SECRETARY OF THE HOYAL ASTR. SOC. 
 
 LONDON: BALDWIN AND CRADOCK. 
 
 183(5. 
 
LONDON: 
 
 Printed by WILLIAM CLOWES and SONS, 
 Stamford Street. 
 
ADVERTISEMENT. 
 
 THIS Treatise, though particularly intended for those who use 
 either of the maps mentioned in the title-page, will, I hope, be 
 found useful to all who wish to acquire a distinct idea of the con- 
 nexion between projections in general, and the surface of the 
 sphere which they represent. The leading principles derived from 
 an accurate consideration of any one instance, are those which 
 apply to every other hitherto used, with the exception only of what 
 is called Mercator's Projection. But of all the methods in question, 
 I should decidedly prefer the Gnomonic Projection for any purpose 
 of general instruction, on account of its superior simplicity, and 
 the ease with which the transition may be made from the sphere 
 to its inclosing cube. 
 
 Simple as a globe may be in its principle, there are many 
 facilities afforded by a map ; and on the other hand, there are 
 some points in which the former has decided advantages over the 
 latter. A map may be considered either as a catalogue for the 
 practical astronomer, or as a picture of the heavens for a learner. 
 In the former point of view, it is of little consequence what pro- 
 jection is employed : in the latter, the primary property of the 
 Gnomonic Projection, namely, that three stars which are in a line 
 in the apparent heavens, are also in a line in the map, renders it, 
 
 106008 
 
ADVERTISEMENT. 
 
 I may say, the only projection by which the celestial objects can 
 be easily identified. A movable planisphere, similar to that de- 
 scribed in pages 51, 52 3 (and more especially if the boundaries 
 of the gnomonic maps were projected on it,) would, in conjunction 
 with the maps in question, give every advantage possessed by the 
 largest globe. 
 
 The account of the selection of objects in the maps, of the au- 
 thorities, and of the notation employed, is to be found in page 107, 
 &c. For the materials of this part of the work I am indebted to 
 Mr. Lubbock, under whose superintendence the maps have been 
 constructed and filled up. 
 
EXPLANATION, &c, 
 
 CHAPTER I. 
 
 BEFORE proceeding to describe the maps of the heavens, which this 
 treatise is intended to accompany, we shall devote some space to the 
 consideration of maps in general, and of the gnomonic projection in 
 particular, the latter being the name of the method followed in draw- 
 ing the maps which it is our business to explain. 
 
 When a ray of light reaches the eye, the impression received is 
 that of an object somewhere in the line traversed by the ray, and if 
 the object be at any great distance, we can say no more than this 
 When we see a star, though we can point out the direction in which \ 
 it lies, there is nothing to guide us in determining its distance. The 
 brightness of the star is no test, for in comparing one star with another 
 of equal brightness, we can only conclude that they are at the same 
 distance, if we previously know that they emit the same quantity of / 
 light. It may happen that one of the stars is twice as bright as the 
 other, or would appear so to an eye placed at the same distance from 
 both, and that the first or brighter star is farther from us than the 
 second, by which means its apparent brilliancy is no greater than 
 that of the second. It is only when objects are previously known to 
 us, that we can thus compare their distances ; which we do partly by 
 their apparent magnitude, and partly by their apparent brightness. 
 
 The term distance has, therefore, no definite meaning as applied / 
 to two stars, unless by it we mean angular distance : that is, sup-y 
 pose two telescopes, of which the eyepieces are brought close to- 
 gether, to be pointed towards two different stars ; all the separa- 
 tion of which we form any idea, is the opening or angle which those 
 telescopes make with one another; for, since we form no estimate 
 of the absolute distance of either star, we should perceive no altera- 
 tion if either were to move directly towards or from its telescope. 
 But if either were to move out of the line of its telescope, we should 
 be warned of the change by its vanishing from the field of view, 
 
6 EXPLANATION OF MAPS OF THE STARS. 
 
 which would oblige us to follow it with one telescope, and alter the 
 angle which the two make with one another. 
 
 If we imagine a transparent surface of glass, of any form whatever, 
 to be interposed between the eye and the objects which are to be 
 pictured, and if straight lines be drawn through the various points of 
 any object, all meeting at the eye, which may represent rays of light, 
 the points at which these rays intersect the glass will together mark 
 on the glass the picture of the object chosen. This is represented in 
 the following diagram, where A is the position of the eye, B C D E a 
 part of the map or picture, and P Q R a triangle to be represented. 
 The space p q r is that through some point of which every ray of 
 light coming from any point of the tri- 
 angle must pass, in order to reach the 
 eye ; so that if the part p q r were 
 opaque, the triangle could not be seen. 
 It is the object of a mop, simply to 
 mark out this space ; of a picture, to 
 mark it out in such a way, by colour- 
 ing and shading, that the rays which come from the various points 
 of p q r shall resemble in colour and brilliancy those which would 
 pass through p q r, if the transparency were restored and the object 
 allowed to be seen. 
 
 Let us now suppose a spectator situated at any point of the earth. 
 So long as he looks at the fixed stars only, it is indifferent in what 
 part of her orbit the earth may be, since the distance of the fixed 
 stars is so great, that there is no apparent change of place arising out 
 of the motion of the earth in her orbit. Thus in travelling, objects 
 which are near to us change their directions perceptibly in a very 
 short time ; and we leave behind us the things which shortly before 
 were at our right or left hands. This sort of change is perceived in 
 instrumental observation with regard to the planets, which are suffi- 
 ciently near to show the earth's change of place as well as their own. 
 But, just as in the former case it may be hours or days before the direc- 
 tion in which we see a distant hill is perceptibly altered, or as the sea- 
 men say, before its bearing is changed ; so on the heavens, the whole 
 yearly track of the earth does not enclose a space which is perceptible 
 from the nearest fixed star, so that the position of the latter will not 
 
EXPLANATION OF MAPS OF THE STARS. 3 
 
 be sensibly altered by the orbital motion of the earth. The reader 7 
 must attend to this point, because to this it is owing that we do not S 
 want different maps of the stars for different periods of the year. } 
 
 If a glass globe of considerable dimensions were constructed 
 around the spectator, of which his eye was in the centre, and if we 
 imagine, for the sake of illustration, that the spectator is not on the 
 earth, but in void space, where he can see the whole of the heavens, 
 \ve may conceive a number of dark spots to be placed upon this globe, 
 in such a way as to hide from him the several stars which before were 
 visible. Here would be a picture of the relative positions of the stars, 
 which would be a lasting one, since the apparent change of place 
 arising out of the diurnal motion of the earth is not taken into ac- 
 count, the spectator being fixed. If, however, we imagine the ap- 
 parent revolution of the stars caused by the tesfcqseaiton ad motion to 
 be real, and to carry all the stars round the spectator in twenty-four 
 hours, the globe may be supposed to turn in the same time, and in 
 the same direction, by which means each spot will continue to keep 
 the same star out of view which it did at first. 
 
 The visible part of the heavens has the appearance of half such a 
 globe ; for since we form no idea of the relative distances of the dif- 
 ferent stars from ourselves, the latter seem like bright spots all situated 
 at the same distance from us ; at least it requires no effort of imagi- 
 nation to suppose them such. They give us, therefore, the idea of being 
 placed upon an immense sphere, of which the glass globejust alluded \ 
 to is a small copy. We see from many terrestrial appearances, 
 that when distances become considerable, we lose the power of dis- 
 tinguishing one from another : thus when a large part of the hori- 
 zon is bounded by a chain of hills, very far from us, it seems as if 
 they were arranged in a part of a circle, though perhaps they may be 
 in a straight line interrupted by continued and irregular variations. 
 
 This circular form of the horizon is a proof of the tendency to esti- 
 mate those distances as equal, between which, from their magnitude, 
 we have lost the power of discriminating. However irregular the 
 
 ground may be, the boundary of the view, if in any degree extended 
 
 i, j. . . . , rf**j^^$cr^^ii^i^^ , . 
 in all directions, is circular. 1 As this phenomenon t is cited in many ^ 
 
 popular works on astronomy as a proof of the rotundity of the earth, 
 we will call attention to the fact that it would still remain, if the earth 
 
 were a plane, indefinitely extended on every side. For, such being 
 
 B 2 
 
4 EXPLANATION OF MAPS OF THE STARS. 
 
 the case, suppose a spectator at sea, with an open view in all directions ; 
 there would still be an apparent boundary,, since all above the line/. 
 A B would be sky, and all below it 
 water. There would therefore be in 
 every direction a visible line in which 
 the sky and water meet, which would 
 appear at the same distance in every 
 direction, and would assume the 
 
 form of a circle, at the height of the eye. The proof of the rotun- 
 dity of the earth, from the appearance of the horizon at sea, 
 ought to be derived from the line in which the sky and water meet 
 not being of the same height as the eye ; which appears in the follow- 
 ing diagram to be the property of a spherical or other round surface. 
 This phenomenon is very clearly 
 visible when the horizon is viewed 
 from the top of a high hill. 
 
 From the actual survey of the heavens, the stars were divided 
 into groups, which were fancifully likened to figures of men 
 and animals, before any globes or maps were constructed. Thus 
 the astronomer had certain fixed notions of the positions which 
 the constellations occupied relatively to one another, and to him- 
 self, that is, to the centre of the apparent celestial sphere. The 
 stars were distinguished from one another by the positions they 
 occupied upon the body of the constellation to which they be- 
 longed ; one was in the right arm, another in the left, a third 
 in the leg, and so on. The formation of artificial globes in- 
 volved a difficulty, as the spectator of the globe was not in the 
 same position relatively to the pictured constellations as that in 
 which he stood to the apparent celestial sphere ; being on the out- 
 side, and not at the centre. If we conceive an artist, painting 
 
 i ! , '"''' *'"'' ^"v , c^ i ,- 
 
 UMigliirc ift the mterior^according to his own notions of the relative 
 
 position of the constellations, another person viewing Ike figures 
 from the exterior, through the glass, would see them all reversed ; 
 that is, the hand which the interior observer would call the right, is 
 the left in the opinion of the exterior observer. The same effect is 
 produced by looking through a picture from the back. Most persons 
 must be aware of the manner in which it is necessary to arrange the 
 letters in the printer's composing-stick, in order that the impression 
 
EXPLANATION OF MAPS OF THE STARS. O 
 
 may be direct, or from left to right. If the types could be arranged 
 as follows, 
 
 Maps of the Stars; 
 
 the impression taken from them would be the following, 
 
 ;8i)2 srftlo acpsM 
 
 and vice versa; so that types set up in the second way exhibit an im- 
 pression like the first. The reason why the printers' types cannot be 
 set up in the first position, is that they cannot be completely re- 
 versed ; since in that case they would only present the unlettered end 
 of the metal to the paper unless stamped at both ends. The partial 
 reversal that the common'types would bear, would simply amount 
 to writing the sentence backwards, and upsidedown ; as follows, 
 
 '. sJB^g aq; jo sde j\[ 
 
 this is the appearance presented, not to a spectator outside the globe, 
 but to one who stands upsidedown inside the globe. 
 
 If the first arrangement were made on thin paper, the second 
 would appear on looking at it through the paper ; and the same 
 alteration takes place when that which has been written or drawn 
 on the inside of a transparent globe, is looked at from the outside. 
 A spectator on the outside sees the figures as he ought to draw them 
 on wood or copper, in order that the impression may represent the 
 appearances presented to a spectator on the inside. 
 
 Let us now suppose that the artist in the interior, instead of draw- 
 ing figures upon the globe, forms thin and flexible statues, in which 
 the front and back, or the two sides if the figure is placed sideways, 
 are perfectly formed, the thickness only being diminished. These 
 he fastens on the interior .of the globe, with the fronts towards him- 
 self. Hence wher6 ke sees uie front of a figure, the spectator on the 
 outside will see the back ; where one sees the right hand side, the 
 other will see the left ; both will see the same outline, but differently 
 filled up in the two cases, as in the following picture, which ex- 
 hibits the appearance of a figure from the interior and exterior. 
 
 There will now be no confusion between the right hand and the 
 left, since both will fix upon the same hand when asked for either ; 
 but those stars which to the spectator in the interior appear in the \ 
 breast of a figure, will to a spectator at the outside appear in the r 
 back. We shall hereafter resume this subject in discussing the rea- J 
 
EXPLANATION OF MAPS OF THE STARS, 
 
 sons which have been thought sufficient for the adoption of the 
 scheme followed in the maps we are describing. 
 
 The globe having been thus obtained, and the position of the 
 spectator settled, we come to the definition and construction of a 
 map of the globe. By the word map is generally understood a re- 
 presentation of part of a curved surface on a plane, or flat surface. 
 If we wanted a map of a cone or cylinder,, the surfaces of which 
 admit of being unrolled without the relative position of any points 
 on the surface being altered, that is without any expansion, con- 
 traction, or tearing, a perfect map would be obtained by simply 
 unrolling the surface. But a sphere has not this property of develop- 
 ment, and whatever contrivance we may employ, the representation 
 of a sphere upon a plane must produce some distortion ; that is, 
 stars which are at equal distances on the globe, cannot always be 
 placed at equal distances on the map. This is however an ob- 
 jection only when a map is considered as a perfect picture or 
 resemblance of the whole heavens, but none whatever when 
 we consider a map as no more than a method of registering 
 the different stars and nebulae, which shall preserve contiguous 
 portions of the heavens, when not very large, in something like 
 their relative positions. It is sufficient for the purpose of registry, to 
 have a plane or planes, so connected with the sphere by a simple 
 mathematical law, that every point of the globe has one point, and 
 no more, corresponding to it upon the planes ; and for the purposes of 
 general similitude, it is enough that objects which are very near 
 upon the globe are very near upon the map, the proportions of dis- 
 
EXPLANATION OF MAPS OF THE STARS. 7 
 
 tance upon the latter not very much differing from those upon the 
 former : for example, if the star A upon the globe is twice as far 
 from B as from C, it is sufficient that on the map the distance of 
 A from B does not differ much from twice the distance of A from 
 C. Rejecting the latter condition, we may conceive various ways of 
 constructing a map either upon planes or other surfaces, which shall 
 answer the principal condition of having one point and no more on 
 the map, corresponding to each point upon the globe. For illustra- 
 tion, conceive the stars, constellations, &c., to be drawn upon a globe 
 with ink, which, as soon as it is laid on any point, sinks directly to 
 the centre, without spreading in any other direction ; so that each 
 point, so soon as it is marked, is connected with the centre by a dark 
 line. Let parts of the globe be now cut away regularly or irregularly, 
 with this condition only, that the centre is never to be laid open, and 
 no excavation is to be made which shall, after one of the dark lines 
 has been divided from the centre, allow any higher part of that 
 line to continue in the piece which contains the centre. In this case, 
 whatever may be the form of the remaining piece, it is, theoretically 
 speaking, as complete a representation of the heavens as the globe 
 itself: for though any star be cut away, some other point of the 
 black line which ran from it to the centre will be laid open, and the 
 star will not be lost. If the sphere were placed upon a turning lathe, 
 and turned into another and smaller sphere with the same centre, 
 there would be no distortion, since all figures and distances would 
 be lessened in the same proportion. This would hardly be a map, in 
 the common sense of the word, for it could not be unrolled and laid 
 upon a plane, the sphere, as already explained, not being developable. 
 But if a cone or cylinder, or a cube or other surface composed en- 
 tirely of plane faces, were cut out of the sphere, the surface thus 
 obtained might be unrolled, as in the following diagrams ; in which 
 
 the cube forms six squares placed together, the cylinder a rectangle, 
 and the cone a sector of a circle. 
 
8 EXPLANATION OF MAPS OF THE STARS. 
 
 We now exhibit one sort of map*, which we have purposely 
 
 r 
 
 Veru. 
 
 X.TL/1, 
 
 is 
 
 X 
 
 Vem. Eg. E Vern. E&y 
 
 * This species of projection has been put in practice. See Lalande, Bibliographie 
 pp. 352 and 561. 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 9 
 
 chosen because it is not much like any of those which are most 
 commonly seen. Differing entirely from a common picture in prin- 
 ciple, and being altogether unlike any representation of a globe, it 
 will the better illustrate our definition that any figure will serve for a 
 map, which has a point corresponding to every point on the globe. 
 
 It consists of two circular sectors, ECEFE and EDEFE, 
 each containing more than a semicircle, or about 254^. Each of 
 these sectors is a developed cone, and the cones may be restored by 
 cutting out the sectors, and bringing together the pairs of lines 
 marked D E, D E, and C E, C E. The two cones thus formed will 
 have the diameters of their bases double of their heights, and when 
 put together base to base, will form a double cone or spindle, 
 having the distance between its opposite vertices (that is, twice the 
 height of either cone) equal to the diameter of the common base. 
 If we suppose a sphere made by the revolution of the circle C E D F 
 about its diameter C D, such a spindle-shaped surface will be 
 
 E 
 
 described by the periphery or outline of the square C D E F. We 
 may conceive the stars represented on the globe as already de- 
 scribed, and the sphere then cut away, all except the double cone, 
 which will, on our preceding suppositions, when unrolled, exhibit 
 the map we have chosen. The only points which are twice repre- 
 sented, are those on C E, C E, and D E, D E, as these lines are 
 made to coincide when the cones are formed. 
 
 We recommend the reader who is not used to such considerations, 
 not to leave this diagram until he can well account for the various 
 appearances exhibited on the map, and reconcile them with the 
 globe. As this construction is not the one which we have to explain, 
 we will not dwell upon it further, except to point out the distortion 
 
10 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 which must take place. Looking at C E, we see that the length 
 from 30 to 60 is much less than that from to 30, or from 60 to 
 90, whereas on the globe these are equal lengths. 
 
 Abandoning the illustration hitherto used, we will now suppose 
 the reader able to carry in his mind the idea of a sphere with the 
 great and small circles drawn on it, together with the stars and con- 
 stellations, and having straight lines drawn from the centre through 
 every star, and through every point in the great and small circles. 
 These lines must be supposed to be produced beyond the surface of 
 the sphere as far as may be necessary. A great circle of the sphere 
 is one which passes through the centre, and divides the whole into 
 two equal hemispheres. Any other circle is called a small circle. 
 These names are certainly not very expressive, since a small circle 
 may be as nearly equal in magnitude as we please to a great circle. 
 It would be better, perhaps, to call them centric and excentric circles ; 
 but custom has sanctioned the preceding appellations. 
 
 Let us call the line drawn through any point of the sphere from 
 the centre, the projecting line of that point. A great circle, with all 
 its projecting lines, forms a plane; a small circle, with all its pro- 
 
 jecting lines, a cone. If any plane be placed outside a sphere, so as 
 to be cut by the projecting lines coming from any part of the sphere, 
 a map of that part of the sphere will be formed upon the plane, and 
 the point of the map which corresponds to any star, is the point in 
 which the projecting line of the star cuts the plane. If the globe 
 were transparent, and the stars placed upon it opaque, and if a small 
 lamp were placed in the centre, the shadows of the several stars 
 would fall upon the corresponding points of the map. 
 
 * 
 
EXPLANATION OF MAPS OF THE STARS. 11 
 
 The line or point on the map which represents any line or point 
 on the globe, is called its projection. The projection of a great 
 circle is a straight line, since all its projecting lines are in one plane, 
 and a plane cuts a plane in a straight line. The form of the pro- 
 jection of a small circle depends upon its position relatively to the 
 centre, and to the map. To determine the different forms which 
 this projection may assume, we must recollect that the projecting 
 lines which pass through the centre of the globe, and the various 
 points in the circumference of a small circle, form a cone. If we, 
 therefore, let the circle remain in its place, and move the plane in 
 which the map is to be drawn, the various figures in which the 
 moving plane of the map cuts the cone will be those of which we are 
 in search, namely, all the possible projections of the small circle. 
 
 Let O be the centre of the globe, and A B the small circle which 
 is to be represented on the map. The various lines of the conical 
 surface O AB are therefore those which convey, so to speak, each 
 point of the circle to its appropriate place on the map. If the latter 
 be held parallel to the position of the small circle, as at C D E F, 
 the representation of the circle will be another circle, differing from 
 the former in size. If the map be held obliquely to the circle, as at 
 G H, but still in such a position as to cut the cone completely 
 through, the representation will be a flattened figure, called, in geo- 
 metry, an ellipse. To get a clear idea of the other figures, we must 
 
 x 
 
 make another conical surface O M, behind the surface OAB, by 
 
12 EXPLANATION OF MAPS OF THE STARS. 
 
 lengthening all the projecting lines in the cone O A B, backwards 
 towards the left. If the map be so held, as at K L N, that it shall 
 never completely pass through the cone O A B, but yet at the same 
 time shall never cut the opposite cone O M, though ever so far 
 lengthened either way, the representation of the circle will be a figure, 
 which, though resembling an oval at or near the point P, spreads out 
 without limit on both sides of it, so that it has no point opposite to P. 
 The point A has therefore no representative upon the map ; for O A, 
 being parallel to the plane K L N, will never meet it. The figure 
 in which K L N cuts the cone in this case, is called a parabola. 
 Now let the map be held still more obliquely to the circle, as at 
 R S T V, so that having cut the cone at W, it also cuts the opposite 
 cone at X, instead of passing through the other side of the first cone, 
 as in H G, or remaining always equidistant from the opposite parts 
 of both cones, as in K N. The representation of the circle will 
 therefore consist of two figures proceeding from W and X, the first 
 towards the right, the second towards the left. Through O conceive 
 two lines, O Y and O Z, to be drawn, parallel to the plane R S T V, 
 and cutting the circle in Z and Y. It is evident that all the figure 
 to the right of W is the representation of so much of the circle as 
 falls below Z and Y, or is contained in the arc Z B Y, while the 
 figure to the left of X represents the arc Z AY. For if from any 
 point of the circle which is above Z Y, we draw a line through 
 O, it will fall towards the left of the plane R S T V, beyond X. This 
 double figure is called an hyperbola, of which the two separate parts 
 containing W and X are called the branches. We shall not have 
 occasion to consider more than one branch of an hyperbola, namely, 
 that in which the point represented falls between its projection and 
 the centre ; that is, we shall only want the part which contains ,W, 
 and corresponds to the lower arc Z B Y in our figure. 
 
 The general conclusion is as follows : Let a point, a circle, and 
 a plane, be all situated in space, and let a straight line, which always 
 passes through the point, and runs along the circumference of the 
 circle, be produced in both directions, till it meets the plane either 
 on one side of the point or the other, thus tracing out a curve on the 
 plane, while it moves round the circle. If the straight line always 
 meets the plane, that is, never becomes parallel to it, an ellipse is 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 13 
 
 marked out on the plane. If the straight line is parallel to the plane 
 in one position, and one position only, it traces out a parabola, and 
 if it becomes parallel to the plane in two different positions, it traces 
 out an hyperbola. The curve is called the projection of the circle 
 upon the plane, the point is called the pole of projection, and the 
 plane, the plane of projection. 
 
 M 
 
 The simplest way of applying the preceding rule is as follows : 
 Let O be the pole of projection, ABC the plane of projection, and 
 through O draw a plane K LM parallel to AB C. The planes are 
 to be considered as indefinitely extended in all directions. It is a 
 theorem in geometry, that all the lines which can be drawn through 
 O, parallel to the plane ABC, lie entirely in the plane K L M, and 
 the converse ; that is, if a line passing through O lie upon K L M, 
 it will never meet ABC, while, if it do not lie upon K L M, it will 
 meet A B C, if produced far enough. If then a circle cut the plane 
 K L M, meeting it therefore in two points P and Q, there are two 
 lines which can be drawn through O, and the circumference, parallel 
 to the plane ABC, namely O P and OQ ; if the circle only rests 
 upon the plane K L M, or touches it in one point only, as R, there 
 is only one line which can be drawn through O and the circum- 
 ference parallel to the plane A B C, namely, O R ; while if the 
 circle be entirely off the plane K L M S, as S, no line can be drawn 
 through O and the circumference parallel to ABC. In the first 
 case, the projection of the circle upon the plane ABC from the 
 pole O is an hyperbola; in the second, a parabola ; in the third, an 
 ellipse. Therefore, draw a plane through the pole of projection 
 
14 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 parallel to the map or plane of projection : if this plane cuts the 
 circle, the projection is an hyperbola ; if the circle only meets the 
 second plane, the projection is a parabola; if the circle does not 
 meet the second plane, the projection is an ellipse. 
 
 We now come to the description of the method which has been 
 employed in the maps to be explained. The pole of projection is the 
 centre of the globe. The maps are planes, six in number, touching 
 the globe so as to form the circumscribed cube. The figure called a 
 
 cube, which is that of a die, or of a box, the length, breadth, and 
 depth of which are equal, is bounded by six equal square surfaces, 
 which are opposite, two and two. It has twelve sides or edges, and 
 eight* corners or angles. Each side (as Ca) has another side (c A) 
 opposite and parallel to it, and two other sides (B d and D 6) adja- 
 cent and parallel. In future, we shall denote four of the angles or 
 corners by the letters A, B, C, D, and the opposite angles by the 
 small letters a, b, c, d. Thus to find, mechanically, the side, surface, 
 or angle which is opposite to any given one, change large letters into 
 small, and small letters into large. For instance, the corner opposite 
 to A is a, the side opposite to B c? is 6 D, and the surface opposite 
 to B C a d is b c A D. 
 
 The cube has a centre, in which ftie lines A a, B b, C c, and D d, 
 meet, and this centre, which we call O, is also the centre of the 
 sphere, when the latter is placed inside the cube. The point O is 
 equally distant from every corner, though, owing to the perspective, 
 
 * The number of surfaces and solid angles in a solid bounded by planes will always 
 together exceed the number of edges by two : thus in the cube, there are six surfaces/eight 
 angles and twelve edges, and 
 
 6+8 = 12 + 2. 
 In a pyramid, there are four surfaces, four angles and six edges. 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 15 
 
 this does not appear to be so in the figure. Any line drawn through the 
 centre cuts two opposite surfaces in points which are situated in the 
 same parts of each. Thus the line XOa? drawn through O cuts 
 B C a d in X, and b c A D in x ; and if the square B C a d were laid 
 upon 6 c A D, so that d, R, and C should coincide with D, b, and c, 
 X would coincide with x. The line X O a? is also bisected in O. 
 A plane passing through the centre O, and cutting the cube, may 
 c D v 
 
 pass through four of the faces, not meeting the other two, as P Q p q, 
 or may cut all the six faces, as T R S t rs. In the first case, the in- 
 tersection of the plane with the faces of the cube is a parallelogram ; 
 thus P Q is parallel to p q, and P q to p Q. The rest of this figure 
 may be easily found, when one side only is known. Suppose, for 
 example, p Q remains, and the other sides are rubbed out. To re- 
 store P q, we go to the opposite map*, and finding the points D 
 and C opposite to d and c, we take D P and C q respectively equal 
 to dp and c Q. The points P and q being thus found, we join p 
 and q, q and P, and P and Q. In the second case, where the plane 
 cuts the cube in all six maps, the figure TRSrsisa hexagon, or 
 six-sided figure, with its opposite sides T R and t r parallel and equal, 
 as also R S and r s, and T s and t S. Each side cuts off a corner 
 from the map in which it is found, instead of passing through opposite 
 edges. 
 
 Supposing all the sides of this figure to be rubbed out, except T R, 
 it is not so obvious how to replace them. We can immediately lay 
 down tr, by taking at equal to AT, and ar equal to AR; but 
 
 * This word is here introduced, as the six faces of the cube are the six maps to be ex- 
 plained. 
 
16 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 before the section can be completed, we must find either S or s. 
 Having found t, as just described, lengthen TR and C D till they 
 meet in V. Join V and t 9 meeting D b in S, which is the point 
 required, arid t S one of the remaining sides. But this obliges us 
 to travel out of the map, and perhaps beyond the limits of the paper. 
 The following arithmetical method is preferable. Suppose, for ex- 
 ample, that each side of the map is twelve inches, and that AT is 
 three inches, and A R five inches. 
 
 Multiply the whole side AD 12 inches, 
 
 by what is left after taking away A R, 7 
 and by AT 3 
 
 which gives 252 
 
 Multiply each of the two A R and 5 x 9 = 45 
 AT, by the remainder arising from 
 
 subtracting the other from AD, 3 x 7 = 21 
 
 and add the products, which gives 66 
 
 Divide the first by the second, which gives DS=3|| inches, or 
 a little more than 3 T *L inches. This is also the length of ds, whence 
 all the points of the hexagon are determined. 
 
 It remains to lay down the section when no side of it is given, but 
 one point only in each of two different maps. When the two points 
 are in opposite maps, as in A B C D and abed, let them be E and P. 
 On A B C D find p the opposite point to P, then the line p E pro- 
 duced to meet the sides, will be one of the sides of the section re- 
 quired ; to complete which one of the preceding rules must be applied. 
 When the points are on adjacent maps, as on A B C D and A B, cd, 
 
EXPLANATION OF MAPS OF THE STARS. 17 
 
 let X and Y be the points, and X S Y a part of the section which 
 passes through them and the centre. Draw X M and Y N perpen- 
 dicular to the common side A B ; bisect A B in H, and let L and K 
 be the centres of the maps in question, whence H K or H L is half 
 the side of the cube. Measure H N and N Y, H M and M X, and 
 also H K or H L, the half-side of the cube. Form the four follow- 
 ing products. 
 
 (1.) HM multiplied by NY. 
 
 (2.) HN multiplied by MX. 
 
 (3.) The sum of M X and N Y multiplied by H K. 
 
 (4.) NY multiplied by MX. 
 
 The length of H S and its direction may now be found as follows : 
 
 1. When N and M fall on the same side of H. Add together the 
 products (1) and (2), multiply by H K, and divide by the difference 
 of the products (3) and (4). The quotient is H S. 
 
 When it happens that H S is greater than H A or H B, as on the 
 left side of the figure, T may be determined as follows : Find S B 
 and S N, by subtracting HB and H N from H S just found. Mul- 
 tiply S B by Y N, and divide by S N. The answer is B T, and B V 
 may be found by proceeding in the same manner with M X and S M. 
 
 2. When M and N fall on different sides of H, take the difference 
 of the products (1) and (2), multiply by H K, and divide by the 
 difference of the products (3) and (4). The quotient is H S, which 
 must fall on the same side of H as N, if the greater of the products 
 (1) and (2) contains H N, or as M, if the greater product contains 
 HM. 
 
 We should recommend the reader who wishes to get a clear idea 
 of these and similar processes, to provide himself with a cube of soft 
 wood, of about three inches in height, and to lay down several sec- 
 tions by the preceding rules. A common foot ruler will serve for the 
 measurements, which may be made correctly enough for every prac- 
 tical purpose to twentieths of inches. 
 
 We now proceed to consider in what way a cone, whose vertex is 
 at the centre of the cube, will intersect the several maps. We may 
 see from page 13, that if a circle be placed inside the cube, which 
 does not pass through its centre, the projection, if any, upon each 
 single face of the cube will be the whole or part of an ellipse, or part 
 
18 
 
 EXPLANATION OF MAPS OF THE STARS, 
 
 of a parabola or hyperbola. Imagine a cubical room, in the centre 
 of which a small lamp is placed, while an opaque circle is moved into 
 various positions, throwing a well-defined shadow upon the walls or 
 ceiling, or both. If the shadow be thrown entirely upon one wall, or 
 upon the ceiling, it is an ellipse; for the ellipse is the only one of 
 the three figures which is bounded, or contained in a finite space. 
 But the shadow may be thrown partly on the wall or walls, and partly 
 on the ceiling, so as to throw a part of one ellipse on the ceiling, 
 and a part of another on the wall ; or a part of an ellipse on the 
 ceiling, and of an hyperbola on the wall, and so on. The rule given 
 in page 13 will distinguish the cases immediately. Draw through 
 the centre of the cube (the pole of projection), planes parallel to its 
 several faces (the planes of projection), as in the following diagram ; 
 the left hand figure of which represents the cube with the planes 
 
 drawn inside it, and the right hand the planes by themselves. To take 
 an instance, there is a circle of which we see the part m. It does not 
 cut the central plane Q q R r, and therefore the projection of the 
 circle on A B C D is an ellipse, or the part of it which falls on 
 A B C D is part of an ellipse. In this case we ought to say the pro- 
 jection is itself a circle, because the circle m is parallel to the plane 
 A B C D. But the term ellipse includes circle, because the circle is 
 itself a particular species of ellipse. In the case of m as drawn in 
 the figure, the projection is completely thrown on A B C D, because 
 the cone drawn through O and the circle m passes out from the cube 
 through A B C D before it has widened enough to meet the other 
 faces. But if the circle m be increased, (as seen in the figure,) 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 19 
 
 some part of the projection may be thrown on the sides, as in the 
 left-hand figure, and the parts of it which lap over will not be parts 
 of ellipses, but of hyperbolas, because the circle m cuts the central 
 planes which are parallel to the lateral faces in question. By 
 increasing the circle m still more, it will soon happen that none of 
 the projection is contained in A B C D, but is thrown entirely on 
 the four lateral maps, where it will appear as four arcs of hyperbolas. 
 All three cases are distinctly shown in the figure of page 20, over 
 leaf. 
 
 Let us now suppose a sphere, whose diameter is equal to AB, to 
 be placed inside the cube, with its centre at O. It will therefore rest 
 upon the cube at p, and will besides touch it in P, Q, q, R, and r. 
 The various stars and constellations may now be projected upon the 
 cube by right lines drawn through the centre O. There is no need 
 to project the six points P, p, Q, q, R, and r, since they are both 
 upon the sphere and the cube ; and if through any other point of the 
 sphere we draw a straight line from O, this line will meet the cube 
 in some one or other of the six faces, and we then know to what 
 map, and to what part of it, the star which is at that point of the 
 globe must be referred. Each face of the cube receives the represen- 
 tation of a sixth part of the sphere, the form of which will be better 
 understood from the following diagrams. 
 
 JL 
 
 In the middle figure, O is the centre of the cube and sphere, and 
 is the vertex of a pyramid, of which A B C D, a face of the cube, is 
 the base. This pyramid contains a part of the sphere, and separates 
 it from the rest. A B is the projection of L M, A C of LP, C D of 
 P N, and D B of N M. The arcs N M, &c., are each about 70| of 
 the whole circumference, and the arc which extends from corner to 
 corner is what remains of 180 or 1091. The arc which runs 
 through the middle of the map is 90. The visible hemisphere on 
 the left contains the portion which corresponds to one complete map, 
 
 c 2 
 
20 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 surrounded by the halves of the four contiguous maps : the invisible 
 hemisphere on the other side contains the remaining halves of the 
 four latter, together with the sixth map, which completes the whole 
 sphere. The visible part of the globe on the right contains two com- 
 plete maps, and the halves of two others. 
 
 Returning to the figure in page 18, the globe of the heavens is so 
 placed within the cube, that P is the north pole, and p the south 
 pole. Hence Q R q r is the representation of the equator. This 
 will remain if .we suppose the globe to turn inside the cube on the 
 axis Pp; we stop it when the equinoxes, or points in which the 
 ecliptic meets the equator, have come to R and r. Hence the poles, 
 the projections of the equator and ecliptic, together with those of 
 the circles of right ascension and declination, will assume the fol- 
 lowing form, of which the visible half only is drawn. 
 
 Returning to a preceding illustration, if we were to suppose every 
 particle of ink laid upon this cube to sink direct to the centre, leaving 
 a dark line to mark its progress, and if the solid were then placed 
 upon a lathe, with P and its opposite point p (not seen) for pivots 
 
EXPLANATION OF MAPS OF THE STARS. 21 
 
 of rotation, and then turned into a sphere, the latter would be 
 marked like a common globe as follows. P and p would be the 
 poles, GB.gh would leave the equator on the globe, and LM/m 
 the ecliptic. VWvw would become the equinoctial colure, and 
 X Y xy the solstitial colure. The lines marked 1234, vyhich are 
 circles on the higher map, and parts of hyperbolas on the lateral 
 maps, will all become circles of declination. Again, 5 P 6 78, and 
 all similar sections of the cube, together with C Ac a, D Edb, and 
 XYzy, VW-uio already mentioned, will become circles of right 
 ascension or horary circles. 
 
 Before supposing the maps to be separated, it will be convenient 
 to have some distinct name for each. These at the top and bottom 
 we shall call the north polar and south polar maps, from the poles 
 which they contain. The letters at the corners of these will be 
 A B C D and abed. Each of the lateral maps contains one of the 
 principal points of the ecliptic, from which it may take its name. 
 The denominations will therefore be as follows. 
 
 A B C D North Polar Map 
 
 A B c d Vernal Equinox Map 
 
 BCt/a Summer Solstice Map 
 
 CDa6 Autumnal Equinox Map 
 
 D A b c Winter Solstice Map 
 
 abed South Polar Map 
 
 No difficulty will arise from our using letters not seen in the dia- 
 gram, if it be recollected that the small letter corresponding to any 
 great letter is always on the point of the cube directly opposite. 
 
 We should recommend the reader to write the letters A, B, C, D, 
 &c., at the corners of his maps. The following diagram exhibits the 
 whole six, separated, the manner in which they are placed in the 
 book being shown by the heading of each, which is written at the 
 top of the map. Those points or lines in which maps come toge- 
 ther on the cube are denoted by the same letters ; and to aid the 
 conception of the positions of different points on the maps, when the 
 latter are placed on the cube, a number is placed in every quarter of 
 three of the maps, and the same number is placed in the opposite 
 quarter of the opposite map : for example, the quarter marked 9 in 
 the winter solstice map, is opposite to the quarter marked 9 in the 
 summer solstice map. 
 
22 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 The hinges by which the maps are connected will enable us to see 
 how the cube may be restored. Suppose them so small as not to 
 
 \ 
 
 
 p 
 
 \ f 
 
 
 14 /! 
 
 \ 
 
 
 j| 
 
 I * 
 
 
 i 5- 
 
 
 
 \ ?' 
 
 1 
 
 
 ii 
 
 1 te 
 
 
 ^ 
 
 
 
 1 
 
 separate the edges of adjacent maps by any perceptible quantity ; 
 and let the whole system be supported at the point P. The four 
 adjacent maps will then fall into the four sides of the cube,, which 
 will be completed by bringing up the south polar map, and fixing it 
 to that of the vernal equinox by the clasps shown in the diagram. 
 The points of different maps which have the same letters will now 
 have fallen together. Thus L on the vernal equinox map, will meet 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 23 
 
 L on the winter solstice map ; and the points marked c on the 
 vernal equinox, winter solstice, and south polar maps, will come 
 together. 
 
 As we cannot here pretend to give a complete doctrine of the 
 sphere, we presume our reader to have the common knowledge of 
 that subject, and shall endeavour, by applying all our explanations to 
 the maps, and not to the globe, to elucidate the former by those 
 ideas with which he is supposed to be familiar on the latter. 
 
 1. P, p. The north and south poles, or points about which the 
 diurnal motion of the earth makes the heavens appear to turn. They 
 are the only fixed points in the heavens. Any fixed star is always 
 at the same distance from P. This distance, or angle contained 
 between P and a star, is the north polar distance of the latter. 
 
 2. The line G H, Hg, g h, h G. The representation of the great 
 circle called the equator, every point of which is equally distant 
 from the north and south poles. It is a square which divides the 
 
 cube into two hemi-cubcs, each exactly like the oilier. The angular 
 distance at which a star is from the point nearest to it of the equator 
 
24 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 is its declination, which is north or south, according as the star is in 
 the hemi-cube which contains the north or south pole. The decli- 
 nation and polar distance together make up the distance between 
 the pole and the equator, which is 90. In the diagram of 
 page 23, the north polar distance of S is the angle represented by 
 P S ; its declination, which is north, is the sum of the angles repre- 
 sented by T a and a 3. The north polar distance of X is the sum 
 of the angles represented byP6 and 6X; ils declination is that 
 represented by Z X. And Y has the south declination represented 
 byVY. 
 
 Decimation on the globe of the heavens answers to latitude on 
 the globe of the earth, or, as we must now call it for distinction, 
 geographical latitude. Thus when a spectator sees a star directly 
 over his head, he knows that the declination of that star is the same 
 as the latitude of his own position. The reader may now find those 
 stars which will in the course of the day pass over his head, he being 
 in London in latitude 51^. The polar distances of all such stars 
 will therefore be about 38J, and he will find among the most con- 
 siderable of those which pass nearly over head, /3 and y in Draco, 
 95 and 7 in Ursa Minor, and a in Perseus. 
 
 3. The double line L M, M I, I m, m L_, is the representation of 
 the ecliptic, or the great circle through which the sun appears to move 
 in the course of a year. It is represented on the cube by an ob- 
 long figure or rectangle, the shorter sides of which are m L and M L 
 Its principal points are 
 
 Sign. 
 
 At the first point of 
 
 Position of the Sun. 
 
 Name. 
 
 cp 
 
 Aries 
 
 In the equator, and about to 
 pass into the northern hemi- 
 sphere. 
 
 Vernal Equinox, 
 
 25 
 
 Caucer 
 
 At its greatest distance above 
 the equator, and about to 
 descend. 
 
 Summer Solstice. 
 
 == 
 
 Libra 
 
 In the equator, and about to 
 pass into the southern hemi- 
 sphere. 
 
 Autumnal Equinox. 
 
 VS 
 
 Capricornus 
 
 At its greatest distance below 
 the equator, and about to 
 ascend. 
 
 Winter Solstice. 
 
EXPLANATION OF MAPS OF THE STARS. 25 
 
 The opposite points E, e, are the poles of the ecliptic, that is, the 
 points from which the sun always keeps the same distance. The 
 pnccssion of the equinoxes, or the gradual change in the relative 
 position of the ecliptic and equator, causes these poles to move 
 slowly round in the direction contrary to that of the annual motion 
 of the sun, completing a revolution in about twenty-six thousand 
 years. The equinoctial points qr> and ^ therefore move backwards, 
 that is from H towards G, and from h towards g, at the rate of about 
 50 T y in a year. Properly speaking, therefore, these maps (and all 
 others) become incorrect in time ; but owing to the smallness of 
 the precession, it will be more than a century before they are practi- 
 cally useless. 
 
 4. As yet we have only mentioned the distance of a star from 
 the pole, or from the equator, as a means of fixing its position. But 
 a star might move round the pole, without changing its distance from 
 it, and while it did so would ^be said to change its right ascension. 
 The right ascension of a star is the following. Let a great circle be 
 drawn through the place of the star, and through both the poles P 
 and p. Such a circle is called the hour circle of the star. In the 
 figure of page 23, various hour circles are represented as they appear 
 on the disjointed maps. Anyone may be found by keeping the same 
 letter in view. Each one on the cube is a rectangle, and any one may 
 be obtained by cutting the cube by a plane which passes through the 
 axis. Those parts of the hour circles which are found in the north 
 or south polar maps are represented by straight lines passing through 
 P and p ; those parts which are found on any of the other maps 
 are lines parallel to two of the sides of the map. The right ascension 
 of the star is the angle made by its hour circle with that hour circle 
 which passes through the intersections of the equator and ecliptic, 
 which points, called the Equinoxes, are chosen as convenient stations 
 from which to measure, in the same way as on the earth the meridian 
 which passes through Greenwich is adopted as a convenient beginning 
 for the measure of terrestrial longitude. This first hour circle is no 
 other than the equinoctial colure; so that the solstitial colure, which 
 is at right angles to the equinoctial colure, has 90 of right ascension. 
 
 It must, however, be observed, that the parts of the same hour 
 circles which lie on different sides of the pole have right ascen- 
 
26 EXPLANATION OF MAFS OF THE STARS. 
 
 sions differing by 180. Thus though the part of the solstitial 
 colure which lies on the side P 25 has the right ascension of 90, 
 that which lies on the side P "\tf has the right ascension of 270 
 So that the right ascension of a star depends on which half of the 
 hour circle it is found in. The circles of right ascension are sup- 
 posed to move with the stars,, so as to keep their position relatively 
 to the latter. If it were not so, a star would have every possible 
 right ascension in the course of the twenty-four hours. 
 
 The term right ascension answers to longitude on the terrestrial 
 globe, or geographical longitude, in the same way as declination to 
 latitude. Thus if the star a is on the meridian of Berlin at the mo- 
 ment when the star b is on that of Paris, the difference of the right 
 ascensions of a and b is the same as the difference of longitude of 
 Berlin and Paris. It is customary to measure right ascension all 
 round the globe, and not, as in measuring geographical longitude, 
 to divide the globe into two halves, one east and the other west of 
 the first meridian. So that to make the globe of the heavens and 
 earth correspond in the methods of measurement, we ought to say 
 that 1 west of Greenwich is 359 of longitude, always measuring 
 eastward till we come to the place the longitude of which is ex- 
 pressed. 
 
 The circle in the north polar diagram, which is not on the real 
 map, is that under the points of which the zenith of Greenwich Obser- 
 vatory successively comes in the course of the diurnal motion. The 
 direction of the arrows is that of the real motion of the earth, to which 
 the apparent motion of the heavens is contrary. The hour circle, 
 in which the zenith of Greenwich is found for the moment, is the 
 meridian of Greenwich at that instant. 
 
 On a globe, it is most convenient to suppose the meridian fixed, 
 and the hour circles to come successively under it, moving from east 
 to west. But on these maps, the different parts of the day are most 
 easily represented by supposing the whole cube to remain fixed, 
 while the meridian of Greenwich successively moves over the hour 
 circles from west to east; the first supposition representing the 
 apparent motion of the stars to an observer who imagines himself 
 fixed, while the second arises out of the real motion of the earth. 
 
 The meridian of Greenwich goes round the whole cube in twenty- 
 
EXPLANATION OF MAPS OF THE STARS. 27 
 
 four hours. In the same time it takes every possible right ascen- 
 sion, or moves through 360 of right ascension. This is at the 
 rate of 15 to an hour, 15' to a minute of time, and 15" to a second 
 of time. There is some confusion arising out of the use of the 
 words minute and second in two different senses. The circle is 
 divided into 360 degrees, each degree into 60 minutes, and each 
 minute into 60 seconds. The latter two are called minutes and 
 seconds of space it should rather be of angle. The division of the 
 day need not be repeated; its minutes and seconds are called, for 
 distinction, minutes and seconds of time. The degrees, minutes, and 
 seconds of space, are marked ' "; the hours, minutes, and seconds 
 of time, are marked h. m. s. 
 
 Thus when we say that the star a Tauri or Aldebaran, on January 
 1, 1830, had the right' ascension 4 h 26 m 10 s of time, or 66 32' 30" 
 of space, we may verify the assertion as follows : 
 
 4 hours answers to 4 x 15 degrees or 60 0' 0" 
 
 26 minutes of time . . . 26 x 15 minutes of space 6 30 
 10 seconds of time . . . 10 x 15 seconds of space 2 30 
 
 4 h 26 m 10 s of time ... 66 32 30 
 
 We may regard the proposition as equivalent to either of the fol- 
 lowing, in which it will immediately be recognized by the reader 
 who has a clear notion of the term right ascension. 
 
 1. If we pass along the equator from the vernal equinox, in 
 the direction of the sun's annual motion, we shall pass through 
 66 32' 30" of the equator before we come under the star Alde- 
 baran, or before we reach the point from which we might travel on 
 a great circle through Aldebaran to the pole. 
 
 2. The angle which the hour circle of Aldebaran, or the plane 
 of that circle, makes with the plane of the equinoctial colure, is 
 66 32' 30". 
 
 3. The meridian passes through the vernal equinox 4 h 26 m 10 s 
 before it passes through Aldebaran ; or, supposing the meridian fixed, 
 Aldebaran comes upon the meridian 4 h 26 m 10 s after the vernal 
 equinox. 
 
 If instead of the equator we substitute the ecliptic, and instead of 
 the poles (by which word, when used alone, the poles of the equator 
 
28 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 are intended) we substitute the poles of the ecliptic, then the terms 
 latitude and longitude are used instead of right ascension and decli- 
 nation. They should be called celestial latitude and longitude, to 
 distinguish them from geographical latitude and longitude, with 
 which they have no connexion. The following general explanation 
 will apply to these and other terms. Let A B be any great circle on 
 the globe, and let Q and q be its poles. Let S be a star, and draw 
 
 Q, 
 
 the great circle Q S q passing through the star, and the poles of A B, 
 cutting A B in y. Then the following table connects the names 
 given to the arcs AY and Y S with the various names that may be 
 given to A B. 
 
 AB 
 
 Q 
 
 1 
 
 A 
 
 B 
 
 AY 
 
 Y S 
 
 Equator 
 
 North Pole 
 
 South Pole 
 
 Vernal 
 Equinox 
 
 _ Autumnal 
 Equinox 
 
 Right Ascen- 
 sion 
 
 Declination 
 
 Ecliptic 
 
 North Pole 
 of do. 
 
 South Pole 
 of do. 
 
 do. do. 
 
 do. do. 
 
 Longitude 
 
 Latitude 
 
 Horizon 
 
 Zenith 
 
 Nadir 
 
 North Point 
 of Horizon 
 
 South Point 
 of do. 
 
 Azimuth 
 
 Altitude 
 
 In the diagram of page 22 the dotted line which is partly in the 
 north polar map and partly at the top of the adjacent maps encloses 
 that portion of the heavens which is always visible at Greenwich; 
 while the similarly dotted portion in the lower hemisphere cuts off that 
 part which is never visible at Greenwich. The elevation of the pole 
 above the horizon is always equal to the geographical latitude of 
 the place of observation. Thus at Greenwich the angle made by the 
 lines drawn from the spectator to the pole and the point of the horizon 
 directly beneath it, or the north point, is about 51^-. Hence no star 
 will set, unless its distance from the pole, or north polar distance, be 
 more than 51 1. Similarly no star will rise unless its distance from 
 the south pole be more than 
 
"EXPLANATION OF MAPS OF THE STARS. 29 
 
 The name given to the projection of the sphere which \ve have 
 been describing, is the ynomonic projection. It is peculiarly adapted 
 for the construction of sun-dials, or gnomons. A dial is made by 
 erecting any opaque object, and marking out the line along which the 
 edge of the shadow ought to fall at every hour of the day; so that, 
 by observing the shadow, the hour of the day may be observed at the 
 same time. The opaque object has usually a rectilinear edge, which 
 throws a rectilinear shadow, revolving round the base of the object 
 with the sun, and the object is usually called the style of the dial. 
 
 If the style do not point towards the pole, there must be a different dial 
 constructed for every different day of the year. For though the sun is 
 always on the same hour circle at any one hour of the day, noon for 
 example, he is on different parts of that hour circle at different noons, 
 in consequence of the motion to or from the equator, that is from or 
 to the pole, which he has from his motion in the ecliptic. Let O P be 
 the direction of the axis of the heavens, and let the proposed dial be 
 horizontal, the circle A B representing the spectator's horizon. Then 
 A and B being the north and south points, A P B is the spectator's 
 meridian, in some part of which the sun must be at noon. If the sun 
 were to move up and down the arc P B, the shadow of a style drawn 
 through O would change its direction, unless that style were in 
 the plane of the circle B P A. In this case it will always be in 
 the direction O A, shortening or lengthening, according as the sun 
 moves up or down, but always forming part of the line O A. There- 
 fore, in order that noon may be always denoted by one and the same 
 direction of the shadow, the style must be in the plane of the meri- 
 dian, or noon hour circle. Similarly, in order that one o'clock P.M. 
 may be denoted by the same direction of the shadow, the style must 
 be somewhere in the one o'clock hour circle, and so on. Therefore 
 the dial which serves for one day will not serve for another, unless 
 
30 EXPLANATION OP MAPS OF THE STARS. 
 
 the style be placed in some line which passes through all the hour 
 circles. The only such line is the axis of the heavens, in the direc- 
 tion of which the style is therefore placed. 
 
 In the preceding figure we see the hour circles for 10 and 11 
 o'clock in the forenoon. The directions of the shadows of O P at 
 those hours, on the horizontal dial, are the lines opposite to O 10 and 
 O 11, or those lines continued backwards. The question therefore 
 of constructing a sun-dial on a given plane,, is reduced to the follow- 
 ing. If the point where the style meets the dial be made the centre 
 of the globe, in what points will the different hour circles cut the 
 dial ? This question is very easily solved on such maps as those we 
 are describing, because all the great circles are represented by 
 straight lines, and all the hour circles are readily drawn. If then, 
 as in page 16, we draw the section in which any plane passing 
 through the centre cuts the cube, and also lay down the points in 
 which the representations of the hour circles cut that section^ we 
 can, by joining the centre of the sphere and cube with these points, 
 and continuing the several lines through the centre, find the direc- 
 tions of the shadows on that plane corresponding to the various 
 hours of the day. This would not be the best practical method, 
 but we have mentioned it as illustrative of the name given to the 
 projection in question. 
 
 In the map of page 8, we observed the distortion, that is, we 
 saw that lines which are of equal length on the globe, are not repre- 
 sented by equal lengths on the map. On our present maps there 
 is some distortion, but not much, and that principally at the edges 
 and corners. This may be seen by looking at the north and south 
 polar maps, in which the distance between the circles of declination 
 evidently increases as we proceed from the pole, these circles being 
 separated by equal arcs on the sphere. But in our projection, a line 
 drawn from the centre of the map differs from the arc which it re- 
 presents by the same quantity, in whatever direction it may be drawn ; 
 that is, the distortion of lines measured from the centre, is the same 
 in all directions. Thus in the north polar map, though Capella, or 
 the star, a in Auriga and Deneb, or a in Cygnus, are both farther 
 from the pole than they would be in the globe which lies in- 
 
EXPLANATION OP MAPS OF THE STARS. 
 
 31 
 
 side the cube formed by the maps, yet being both very nearly on 
 the same circle of declination, they will both receive the same in- 
 crease of their polar distance. The following table will give an idea 
 of the progressive increase of the distortion as we approach the cor- 
 ner of the map. A globe is supposed of 10,000 inches radius, or 
 20,000 inches in diameter. The corresponding cube will, therefore, 
 have a side of 20,000 inches. A line is drawn from the centre of the 
 map, of the number of degrees marked in the first column ; on the 
 second is the length of the globular arc represented by that line; on 
 the third is the real length of that line on the map ; while the fourth 
 gives the difference of the second and third columns, or the distortion. 
 The nearest inch is given, and fractions of inches are rejected. 
 
 No. of De- 
 grees. 
 
 Length on 
 the Globe. 
 
 Length on 
 the Map. 
 
 Difference. 
 
 No. of De- 
 grees. 
 
 Length on 
 the Globe. 
 
 Length on 
 the Map. 
 
 Difference. 
 
 5 
 
 873 
 
 875 
 
 2 
 
 35 
 
 6109 
 
 7002 
 
 893 
 
 10 
 
 1745 
 
 1763 
 
 18 
 
 40 
 
 6981 
 
 8391 
 
 1410 
 
 15 
 
 2618 
 
 2679 
 
 61 
 
 45 
 
 7854 
 
 10000 
 
 2146 
 
 20 
 
 3491 
 
 3640 
 
 149 
 
 50 
 
 8727 
 
 11918 
 
 3191 
 
 25 
 
 4363 
 
 4663 
 
 300 
 
 55 
 
 9599 
 
 14281 
 
 4682 
 
 30 
 
 5236 
 
 5774 
 
 538 
 
 60 
 
 10472 
 
 17321 
 
 6849 
 
 Instead of supposing so large a cube, we may imagine the half 
 side of a map to be divided into ten thousand parts, and the preced- 
 ing table will then apply to that map, the unit being, not an inch, 
 but the twenty-thousandth part of the whole side of the map. 
 
 Now if we suppose that in a crowded design, composed of objects 
 on which the eye is not much used to dwell, (which remark is im- 
 portant, as what we here say would not hold of a picture of houses 
 or scenery,) the eye would not well estimate the length of any line 
 within about its sixth part, the preceding distortion is immaterial 
 until it amounts to about the sixth part of each line that is seen. 
 From the above table it appears that a line drawn from the centre of 
 the map, representing 40, contains 8391 parts, of which 1410 are 
 due to distortion. The latter is about the sixth part of the former ; 
 hence we may conclude that for 40 every way from the centre of the 
 map, the latter is a good representation of the corresponding part of 
 
32 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 the globe, so far as simple appearances and linear distortion measured 
 from the centre are concerned. Indeed, in no part of the map is 
 this distortion so considerable as to render it a bad representation of 
 what is seen in the corresponding part of the heavens. 
 
 With regard to angular distortion, there is none in lines drawn 
 from the centre of the map ; that is, if through the centre of the 
 map lines be drawn to two stars in it, the angle made by these lines is 
 the same as that made by the planes of the circles which they repre- 
 sent. But two straight lines drawn through any other part of the 
 map, make in some cases a smaller, in some cases a larger, angle 
 than the circles they represent. At the corner of the map, the dif- 
 ference amounts to 30 ; so that the circles bounding the part of a 
 globe which falls into one of the maps in the diagram of page 19, 
 make an angle of 120, whereas the lines which represent them 
 make an angle of 90, or a right angle. 
 
 If we divide the half side of a map into ten parts, as in the pre- 
 ceding diagram, and describe the squares there drawn, the right 
 angles in the corners opposite to K nearly represent the following 
 angles on a globe, the square called the first being the smallest. 
 
 First 
 
 Second 
 
 Third 
 
 Fourth 
 
 Fifth 
 
 90 T V 
 
 T 
 97 T V 
 
 ioi T v 
 
 Sixth 
 
 Seventh 
 
 Eighth 
 
 Ninth 
 
 Tenth 
 
 105 T V 
 109 T V 
 113 
 
 116 T V 
 120 
 
 The angular distortion is therefore a much more considerable de- 
 fect than the linear distortion treated above, and must be recollected 
 and allowed for in finding the stars in the heavens, by means of our 
 projection. For example, looking at the north polar map, it would 
 appear that lines drawn through the star a in Cygnus to y in 
 
EXPLANATION OF MAPS OF THE STARS. 33 
 
 Draco and /3 in Cassiopeia, are as nearly as possible at right angles. 
 On the heavens, however, these lines will appear at an angle sen- 
 sibly greater than a right angle. 
 
 We will close this chapter by a remark on the general appearance 
 of the heavens. When we turn the eyes round, we cannot avoid the 
 impression of being in the centre, we will not say exactly of a sphere, 
 but of a rounded vault, compressed towards the top. When, how- 
 ever, we look at a small part of this vault, such as can be taken 
 in at a fixed glance, we see nothing but the appearance of a flat 
 surface ; which, by the common rules of perspective, should be repre- 
 sented by a part of such a map as we have been describing, the cen- 
 tre of which is in the point to which the eye is most immediately 
 directed. The best points, therefore, on which to begin the study of 
 the heavens from our projection, so far as tracing resemblances is 
 concerned, are the centres of the different maps, or points near to 
 them. The following stars will be near enough to those points for 
 the purpose. 
 
 North Polar Map . . . Pole Star 
 Vernal Equinox y Pegasi 
 
 Summer Solstice . . . The Belt of Orion 
 Autumnal Equinox . . Spica Virginis 
 Winter Solstice ... a Ophiuchi. 
 
34 
 
 CHAPTER II. 
 
 WE shall now proceed to such astronomical details as will enable 
 the reader to adapt the map to the heavens at any hour of any day. 
 
 In all that follows, we shall suppose the spectator situated at the 
 Observatory of Greenwich, the astronomical capital of England, as 
 well on account of the constant allusion made to that place in works 
 on the subject, as for the convenience of reference to the Nautical 
 Almanac, which is calculated for the meridian of Greenwich. The 
 general appearances of the heavens (telescopes and graduated in- 
 struments apart) will be the same in all parts of the United King- 
 dom, with this exception, that a few low stars, which rise but little 
 above the horizon at the Land's End, will not be seen in the northern 
 parts of the island. The utmost difference in the meridian altitudes 
 of the same star will be about eight degrees about as much as the 
 distance between the two lower stars of Charles's Wain (/3 and y of 
 Ursa Major) ; and the utmost difference between the times of the 
 same star passing the meridian of the most easterly and westerly 
 points of the United Kingdom, will be about forty-five minutes. 
 
 The diurnal motion of the earth, which is from west to east, or in 
 the same order as the signs of the zodiac, carries the meridian of 
 Greenwich with it. The part of this meridian which is on the north 
 and south polar maps is, as already stated, a straight line passing 
 through the pole, and which moves round the map in the direction 
 in which the degrees and hours are written at the edges. The parts 
 of the meridian which lie in the ecliptic maps are straight lines 
 perpendicular to the equator, and the daily motion of the meridian 
 will therefore be represented on these maps by a straight line moving 
 parallel to itself and the sides of the cube, over four faces succes- 
 sively, from right to left of each. This will be more clearly seen in 
 the figure of page 20, and the daily course of the zenith of Green- 
 wich is marked by the circle in the north polar map of the figure 
 of page 22. The difference between the method of using a com- 
 mon globe and our maps is this : in the globes, the meridian is 
 fixed, and the appearances of the diurnal motion are represented 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 35 
 
 by turning the globe under the meridian from east to west : in the 
 maps, it is the real motion of the meridian from west to east 
 which is supposed to take place; so that instead of talking of a 
 star coming upon the meridian, we ought to speak of the meridian 
 arriving at a star; or if we speak of the sun or any planet which is 
 in motion, we should say that the meridian overtakes the planet. 
 
 To supply something analogous to the meridian on a common 
 globe, believing that such illustrations are always useful, we describe 
 the following apparatus. 
 
 Returning to the figure of page 20, let two pins project from the 
 poles P and p (not seen). The frame 1234 has its sides 12 and 
 34 a little longer than B D ; but 13 and 24 equal to D b or A c. 
 The interior sides 56 and 78 are moveable in grooves cut in 12 and 
 34, and are repelled from 13 and 24 by the springs 11 and 12, by 
 which they would be driven till they meet, were no resistance in- 
 terposed. This frame is placed upon the cube, page 20, the pins 
 at P and p passing through holes at 9 and 10, so that when the 
 frame is moved round in the direction ABCD, the force of the 
 springs always keeps 56 and 78 close to theTcube. Thus 5678 will 
 always represent the meridian, 57 and 68 being on the north and 
 south polar maps, and 56 and 78 on two opposite ecliptic maps. 
 
 The day is a general term for the complete time of revolution of 
 the meridian from any body, fixed or moveable, to the same body 
 again. The days in common use among astronomers are the fol- 
 lowing : 
 
 1. The sidereal day, or time of the earth's revolution, so that any 
 fixed star which was on the meridian at the beginning of this day, is 
 again on the meridian at the end. Instead of dating from any par- 
 ticular star, it is customary to begin from the time when the meridian 
 is on the equinoctial point of Aries, or the intersection of the ecliptic 
 
 02 
 
36 EXPLANATION OF MAPS OF THE STARS. 
 
 with the equator, marked <Y>, and from thence to count, not two 
 periods of 12 hours, but one only of 24 hours. Thus p. 20, when 
 the meridian is within 15 of cp, it is 23 hours sidereal time ; when 
 the meridian has passed the equinoctial point cp, by 15, it is one 
 hour sidereal time. 
 
 2. The real solar day. In this case the sun is the body from which 
 the day derives its name, the latter being the period elapsed between 
 two successive times when the meridian overtakes the sun's centre,, 
 or two real noons. It begins when the meridian passes through the 
 sun, and is a little longer than the sidereal day, because since the 
 sun is also slowly moving forward at about the 365th part of the 
 rate at which the meridian moves, the latter must not only com- 
 plete the circuit of the heavens, but must also overtake the sun. 
 
 The real solar days are not precisely equal in length all the year 
 round ; for the daily motion of the sun is not the same throughout 
 the year, being more than 61' of longitude at the beginning of the 
 year, when it is greatest, and less than 58' at the beginning of June, 
 when it is least. 
 
 3. The mean solar day. To avoid the inequality above alluded 
 to, a fictitious sun has been supposed to move, not in the ecliptic, 
 but in the equator, which setting out with the real sun, when the 
 latter is at P f proceeds uniformly along the equator so as to arrive 
 again at ry> when the real sun is there again. The mean solar day 
 is the interval between two successive passages of the meridian over 
 this fictitious body, and is longer than the sidereal day for the same 
 reason as before. The difference of the two may be easily calcu- 
 lated. It is found that the year (or revolution of the sun) is 365J 
 mean solar days, and there must be one more sidereal revolution 
 in that time than there are mean solar days, because in turning 
 the sidereal into solar revolutions, there must be one whole revolu- 
 tion of the former broken up and wasted, so to speak, in making up 
 the daily differences between the solar and sidereal revolution. 
 A more familiar illustration may be found in the hands of a watch. 
 If we call the complete rotation of the minute hand an hour, as 
 usual, and the time between two conjunctions of the minute and hour 
 hand by any other name, say a period, then twelve hours will be as 
 long as eleven periods, and in that time, one hour will, altogether, 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 37 
 
 be employed by the minute hand in making up the differences be- 
 tween hours and periods. Consequently, a period exceeds an hour 
 by the eleventh part of an hour. Apply the same principle, and 
 divide a mean solar day, or 24 hours, i. e. 1440 minutes, by 365^, we 
 have a little less than 4 mean solar minutes for the excess of the 
 mean solar above the sidereal day. More correctly 
 
 Mean solar day =: 24 h 3 m 56% 6 sidereal time. 
 Sidereal day = 23 h 56 m 4 s , 1 mean solar time. 
 The distinction of day and night is unknown in astronomical 
 reckoning. The mean solar day begins when the meridian overtakes 
 the fictitious sun in the equator, which moment is O h O 5 mean 
 solar time. The civil and astronomical reckonings then agree till 
 midnight, which is 12 h in both ; but one o'clock the succeeding 
 morning (civil reckoning), is 13 h mean solar time (astronomical 
 reckoning) ; eight in the morning is 20 h , astronomical reckoning. 
 Consequently, six o'clock on Sunday morning, is 18 h of the day 
 which commenced on Saturday at noon. The following examples 
 will illustrate this : 
 
 Civil Reckoning. Astronomical Reckoning. 
 
 May 1, noon. May 1, O h O m s 
 
 Sept. 17, 6 A.M. Sept. 16, 18 h O m s 
 
 Jan. 1, 11 A.M. Dec. 31, 23 h O ra O 3 
 
 Aug. 12, 9 P.M. Aug. 12, 9 h O m s 
 
 The cause of the difference between the mean and real solar day 
 is two-fold : first, the real sun moves irregularly, which the fictitious 
 sun is not supposed to do ; secondly, the real sun moves in the 
 ecliptic, and the fictitious sun in the equator. Even if the real sun 
 moved uniformly in the ecliptic, the meridian would not be on the 
 real and fictitious sun at the same time, as will be evident on look- 
 ing, for example, at the vernal equinox map. Suppose the real and 
 fictitious suns each to have moved through 30, in which case the 
 former will be at y on the ecliptic, and the latter at 30 on the 
 equator ; but the meridian must move through more than two de- 
 grees from the latter before it overtakes (or falls under) the former. 
 The equation of time is the quantity of mean solar time in which 
 the meridian moves from the real to the fictitious, or from the ficti- 
 tious to the real sun, according to which is the foremost: it is 
 given for every day at noon in the Nautical Almanac. It may, 
 
38 EXPLANATION OF MAPS OF THE STARS. 
 
 however, be observed, that the difference between the two is rarely 
 so great as to be of importance in questions for which these maps 
 may be made useful. 
 
 We proceed now to the actual employment of the maps. 
 
 The following table will show at a glance in what map to look for 
 any point whose right ascension and declination are given. 
 
 Opposite to each map is the whole range of right ascension con- 
 tained in it, the numerals signifying degrees, the Roman figures 
 hours, and underneath, in a line marked ' Limit of Declination,' is 
 the greatest declination which must be looked for in the hour circles 
 where right ascensions are above. All points having higher de- 
 clinations, must be sought in the north or south polar maps, ac- 
 cording as the declination is north or south. For instance, in what 
 map is the star whose right ascension is 16 h 56 m , and declination 
 44 19' south ? Recollect that 20 minutes of right ascension is 5 
 degrees. We find 16 h in the winter solstice map, and under 17 h 
 (the nearest to 16 h 56 m ) we find 44 0', as the limit of declination. 
 We must, therefore, look for the star in the south polar map. If 
 the declination be upwards of 45, north or south, the star is cer- 
 tainly in the corresponding polar map. 
 
 The method of laying down a star or planet, when its right ascen- 
 sion and declination are known, hardly needs explanation. If the 
 declination be so great, that the star must be in one of the polar 
 maps, look for the right ascension on the edge of the map, and 
 having found it, proceed along the straight line drawn from the part 
 of the edge just found, until you come to the circle of declination of 
 the star, which may be found by looking at the diagonals of the 
 square, on which the declinations are marked. If the star be on 
 one of the ecliptic maps, the right ascension must be looked for on 
 the equator, or on the upper or lower edge, and the declination on 
 either side. 
 
 The positions of the sun, moon, and planets, for every day in the 
 year, may be found in the " Nautical Almanac," which work will be 
 necessary to'all who make much use of the maps. Of the sun, the lon- 
 gitude only need be found, which must be looked for on the ecliptic. 
 The places of the planets may be taken from the same work, either 
 as seen from the earth, or from the sun. For the first, the geocen- 
 tric right ascensions and declinations must be taken; for the second, 
 
EXPLANATION OF MAPS OF THE STARS 
 
 8* 
 
 r . - 
 
 8 
 
 39 
 
 10 . 
 
 rH * 
 
 O 
 rH 
 
 10 
 
 o d 
 
 s 
 
 CO 
 
 s 
 
 CO 
 
 CO g 
 
 CO 
 
 CO 
 
 CO 
 
 M 
 
 o 
 
 - 
 
 
 ^^ 
 
 S 
 
 I 
 
 O 
 
 rH 
 
 10 
 
 
 
 8 
 2 
 
 S 
 
 8 
 
 B 
 -7* 
 
 o >: 
 
 rH 
 
 W X 
 
 8 
 
 rH 
 
 s 
 
 P 
 
 
 10 
 
 CO 
 
 
 
 CO 
 
 
 CM 
 
 s 
 
 CM 
 
 CM 
 
 I 
 
 c 
 
 "^ 
 
 CO rH 
 
 SQ^. 
 
 CO 
 
 CO 
 
 ?-t- 
 
 CO N 
 
40 
 
 EXPLANATION OF MAPS OF THE STARS, 
 
 the heliocentric. The orbit of any planet may be found with suffi- 
 cient nearness by laying down two positions of the planet in the 
 same map, and drawing a line through the two. This may be con- 
 tinued on the other maps by the methods explained in p. 15 and 16. 
 
 The time at which any part of the heavens comes on the meridian 
 at Greenwich, may be found from the same work by means of the 
 column headed ie mean time of transit of the first point of Aries" 
 (page 22 of each month). To the time at which the equinox passes 
 the meridian, as thus found, add the right ascension of a star in 
 time, and the result will be (correctly enough) the time of transit of 
 that star. But if the sum exceed twenty- four hours, subtract twenty- 
 four hours, and the remainder is the time of transit. The day be- 
 gins from noon, as explained in page 3/. 
 
 For ascertaining phenomena with a less degree of precision, but 
 sufficient for the purposes of amusement or elementary instruction, 
 the following table will be sufficient, in which the sun's longitude at 
 noon is given for every ten days within a quarter of a degree, and the 
 right ascension within a minute. 
 
 Longitude and Right Ascension of the Sun at Noon. 
 
 Jan. J 
 
 Deg. Qu. 
 280 3 
 
 Hrs. Mns. 
 18 46 
 
 July 10 
 
 Deg. Qu. 
 107 3 
 
 Hrs. Mns. 
 7 17 
 
 11 
 
 290 3 
 
 19 30 
 
 20 
 
 117 1 
 
 7 57 
 
 21 
 
 301 
 
 20 13 
 
 30 
 
 126 3 
 
 8 37 
 
 31 
 
 311 1 
 
 20 55 
 
 Aug. 9 
 
 136 1 
 
 9 15 
 
 Feb. 10 
 
 321 1 
 
 21 35 
 
 19 
 
 146 
 
 9 53 
 
 20 
 
 331 2 
 
 22 14 
 
 29 
 
 155 2 
 
 10 30 
 
 March 2 
 
 341 2 
 
 22 52 
 
 Sept. 8 
 
 165 1 
 
 11 6 
 
 12 
 
 351 2 
 
 23 29 
 
 18 
 
 175 
 
 11 42 
 
 22 
 
 1 2 
 
 5 
 
 28 
 
 184 3 
 
 12 18 
 
 April 1 
 
 11 1 
 
 41 
 
 Oct. 8 
 
 194 3 
 
 12 54 
 
 11 
 
 21 
 
 1 18 
 
 18 
 
 204 3 
 
 13 31 
 
 21 
 
 31 
 
 .Utt. 
 
 28 
 
 214 2 
 
 14 9 
 
 May 1 
 
 40 2 
 
 2 33 
 
 Nov. 7 : 224 3 
 
 14 49 
 
 11 
 
 50 1 
 
 3 11 
 
 17 234 3 
 
 15 29 
 
 21 
 
 60 
 
 3 51 
 
 27 
 
 244 3 
 
 16 11 
 
 31 
 
 69 2 
 
 4 31 
 
 Dec. 7 
 
 255 
 
 16 55 
 
 June 10 
 
 79 
 
 5 12 
 
 17 
 
 265 1 
 
 17 39 
 
 20 
 
 88 2 
 
 5 54 
 
 27 
 
 275 1 
 
 18 23 
 
 30 
 
 98 1 
 
 - 6 35 
 
 
 
 
EXPLANATION OF MAPS OF THK STARS. 41 
 
 The degrees of longitude are laid down on the ecliptic, and thus we 
 may find the position of the meridian at noon, and, what is of more 
 importance for our present purpose, at midnight ; for half a degree 
 added to the sun's longitude at noon, will give the longitude at mid- 
 night sufficiently near ; and 180 added to the longitude, or sub- 
 tracted from it if it be greater than 180, will give the longitude of 
 that point of the ecliptic which is opposite to the sun at midnight, or 
 which is then visible. Having found this point, take notice what con- 
 spicuous stars are on, or nearly on, the meridian. 
 
 The degrees on the ecliptic are counted by thirties, each 30 being 
 a sign of the zodiac. The following table shows the degree of longi- 
 tude at the beginning of each sign, and the symbol by which it is 
 denoted. The astronomical sign must not be confounded with the 
 constellation, for a reason which we shall afterwards see. 
 
 Astronomical name 
 of the sign. 
 
 Symbol. 
 
 Degree of Longitude 
 at the commence- 
 ment of the sign. 
 
 Map in which the com- 
 mencement of the 
 sign is to be found. 
 
 Aries 
 
 Y 
 
 "0 
 
 Vernal Equinox 
 
 Taurus 
 
 8 
 
 30 
 
 
 
 Gemini 
 
 n 
 
 60 
 
 Summer Solstice 
 
 Cancer 
 
 23 
 
 90 
 
 
 
 Leo 
 
 SI 
 
 120 
 
 , 
 
 Virgo 
 
 w 
 
 150 
 
 Autumnal Equine 
 
 Libra 
 
 d& 
 
 ISO 
 
 
 
 Scorpio 
 
 til 
 
 210 
 
 5) 
 
 Sagittarius 
 
 / 
 
 240 
 
 Winter Solstice 
 
 Capricornus 
 
 Yf 
 
 270 
 
 u 
 
 Aquarius 
 
 gg 
 
 300 
 
 t i> 
 
 Pisces 
 
 X 
 
 330 
 
 Vernal Equinox 
 
 For example, required the state of the heavens at midnight, on 
 the 1st of January. The sun's longitude is half a degree more than 
 2SOJ, or 2811. Subtracting 180 from this, we have 101i, the 
 longitude of the point of the ecliptic, which is on^the visible part of 
 the meridian at midnight. This point is 11J past the first point 
 of Cancer, marked 25 in the summer solstice map. Finding this 
 point, we see that the visible part of the meridian towards the south, 
 has at midnight, January 1st, a little more than 102 of right ascen- 
 sion ; or in the more common phraseology, the hour-circle of 102 
 
42 EXPLANATION OF MAPS OF THE STARS. 
 
 is nearly on the meridian. The constellations Canis Major and 
 Gemini are on it, and the bright star of the former, Sirius, has 
 been passed by the meridian, or has appeared to cross the meridian 
 about ten minutes before midnight. Orion is to the westward, the 
 belt having passed the meridian at about a quarter to eleven 
 o'clock. Pollux,, one of the principal stars in Gemini, will be 
 overtaken by the meridian, or will appear to cross it, in about 50 
 minutes. Looking to the north polar map, in which the continua- 
 tion of the meridian is a line nearly close to the radius drawn from 
 102 to the pole, we find Lynx and Camelopardus on the meri- 
 dian, but no remarkable star. The Great Bear is in the east, and 
 Cassiopeia in the west. Very low down, between the north and north- 
 west, is the bright star in Cygnus; while low in the north are the 
 stars in the head of the Dragon. If we want the position of the hea- 
 vens at eight o'clock the same evening, or four hours before midnight, 
 we must put the meridian back four times 15, or 60, which gives it 
 a little more than 42 of right ascension. Place the vernal equinox 
 and summer solstice maps side by side, the former on the right, and 
 look at the hour-circle of 42. We see the bright star Menkar, 
 in the whale, just coming on the meridian ; the head of Aries passes 
 about fifty minutes before eight, and the Pleiades will pass about 
 nine, P.M. 
 
 Looking at the north polar map, we find Algol in the head of 
 Medusa just past the meridian, where Capella will be in two hours, 
 and Andromeda was two hours ago. The Great Bear has passed 
 the meridian below, or on the north side of, the pole, about three hours. 
 
 The visible part of the meridian is determined in the northern 
 hemisphere as follows. Measure from the pole, on the north side, 
 the latitude of the place, which gives the northern point of the hori- 
 zon ; measure from the equator towards the south, the angle by 
 which the latitude of the place falls short of 90, which gives the 
 south point of the horizon. 
 
 Resuming the first of the preceding examples, the latitude of 
 Greenwich being 51J, we find the bright star a in Lyra, very nearly 
 at the north point of the horizon at midnight, January 1. At or 
 near the south point of the horizon, there is no remarkable star, 
 but e in Canis Minor is about 10 above it. 
 
EXPLANATION OF MAPS OF THE STARS. 43 
 
 The whole heavens may be divided into three portions, with regard 
 to any place of observation: 1. a portion which is never below 
 the horizon ; 2. a portion which never rises above the horizon ; 
 3. a portion which rises and sets. 
 
 Since the pole is always elevated above the horizon by an arc 
 equal to the latitude of the place, a small circle drawn round the 
 pole, and distant from it at every point, by the latitude of the place, 
 will contain the circumpolar polar of the heavens, as it is called, 
 which is visible throughout the whole of the twenty-four hours. All 
 stars contained in this are called circumpolar stars. Similarly, since 
 the other pole (that is in our hemisphere, the south pole) is de- 
 pressed below the horizon by an arc, equal to the latitude of the 
 place, a circle equal to the former drawn round the south pole contains 
 a part of the heavens which never rises, equal in magnitude to that 
 which never sets. The rule, in the northern hemisphere, for deter- 
 mining whether a star falls in either of these portions, is ; if the de- 
 clination of the star be greater than the complement* of the lati- 
 tude of the place, (for Greenwich this is 38 31', the latitude being 
 51 29',) it never sets if the declination be north, or never rises if 
 the declination be south. 
 
 The remaining part of the sphere, containing every point which 
 has less declination (north or south) than the complement of the 
 latitude of the place, rises and sets alternately. 
 
 .Looking at our maps, we find that the circumpolar portion at 
 Greenwich includes the whole of the north polar map, with the ex- 
 ception of very small segments at the corners, containing no large 
 star. It also includes four small portions of the ecliptic maps, as 
 previously described in page 28. Also, the portion which never 
 rises at Greenwich contains the whole of the south polar map, the 
 corners only excepted, and four similar southern portions of the 
 ecliptic maps. 
 
 Our maps (and indeed all others) are very ill suited to determine 
 the actual time of rising or setting of any star. The best instru- 
 ment for this purpose, is a planisphere hereafter to be noticed, while 
 
 * The complement is what remains after subtracting" an arc from 90. Thus 30 is 
 the complement of 60. 
 
44 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 the correct method of ascertaining any such point must be left for 
 those who are acquainted with spherical trigonometry. We give 
 here a rough table of the times at which some of the most remark- 
 able stars, visible at Greenwich, come upon the meridian of that 
 place, for the first day of every month. Where the star is 
 circumpolar, the meridian passage chosen is that south of the 
 pole. A few stars of inferior magnitudes are added in the case 
 where a remarkable constellation has no star of the first magnitude. 
 
 Letter and Con- T 
 stellation. Name 
 
 Jan. 
 
 Feb. 
 
 March. 
 
 April. 
 
 May. 
 
 June. 
 
 July. 
 
 August. 
 
 a Cassiopeise 
 
 of 
 
 3| 
 
 2 
 
 *Hf 
 
 * 9| 
 
 * 7f 
 
 * 5f 
 
 *3f 
 
 a Arietis 
 
 74 
 
 51 
 
 34 
 
 li 
 
 *114 
 
 * 94 
 
 * 7 
 
 * 54 
 
 a Ceti Menkar 
 
 si 
 
 6 4 
 
 <i 
 
 2 i 
 
 124 
 
 *10 
 
 * 8J 
 
 * 64 
 
 * Persei 
 
 8| 
 
 64 
 
 4| 
 
 24 
 
 121 
 
 * 1 - 
 
 * 8i 
 
 * 64 
 
 a Tauri Aldebaran 
 
 9 f 
 
 n 
 
 5| 
 
 H 
 
 II 
 
 *ni 
 
 * 9| 
 
 * 7f 
 
 a. Aurigae Capella 
 
 ioi 
 
 8 i 
 
 61 
 
 44 
 
 24 
 
 121 
 
 *10| 
 
 * 8 
 
 a Orionis Bete/gcux 
 
 11 
 
 9 
 
 7? 
 
 5 
 
 3 
 
 i 
 
 *11 
 
 * 9 
 
 a, Canis Maj. Sirius 
 
 *12 
 
 10 
 
 8 
 
 6 
 
 4 
 
 2 
 
 12 
 
 *10 
 
 ex. Canis Min. Procyon 
 
 *12| 
 
 lOf 
 
 8| 
 
 H 
 
 4| 
 
 2 I 
 
 12| 
 
 *10f 
 
 )3 Gemiaorum Pollux 
 
 *12f 
 
 10| 
 
 9 
 
 7 
 
 5 
 
 3 
 
 1 
 
 *11 
 
 a. Hydrae Cor Hydra 
 
 * 24 
 
 *12i 
 
 10f 
 
 8| 
 
 6! 
 
 4| 
 
 2 5 
 
 12| 
 
 a Leonis Regulus 
 
 * 3 
 
 * u 
 
 Hi 
 
 9 i 
 
 7i 
 
 5 i 
 
 3i 
 
 li 
 
 a Ursae Maj. Dubhe 
 
 * 44 
 
 * 21 
 
 *12 
 
 li 
 
 8 i 
 
 6 I 
 
 4 i 
 
 24 
 
 a. Virginia Spica Virginis 
 
 * 64 
 
 44 
 
 * 2^ 
 
 *124 
 
 101 
 
 8 
 
 61 
 
 4 i 
 
 ex. Bootis Arcturus 
 
 * 1\ 
 
 * 5 
 
 * 3 
 
 * ]i 
 
 n i 
 
 9i 
 
 H 
 
 54 
 
 a Serpentis 
 
 *S 
 
 * Gf 
 
 * 5 
 
 * 3 
 
 * 1 
 
 11 
 
 9 
 
 7 
 
 a Scorpii Antares 
 
 * 91 
 
 * 74 
 
 * 5| 
 
 * 3| 
 
 li 
 
 Hf 
 
 9| 
 
 7 f 
 
 a Ophiuchi Rus Alhagus 
 
 *10f 
 
 * 8f 
 
 * 6} 
 
 * 4f 
 
 * 2| 
 
 *123 
 
 10| 
 
 8f 
 
 y Draconis 
 
 *11J 
 
 * 91 
 
 * 7-1 
 
 * 54 
 
 * 3^ 
 
 * u 
 
 11? 
 
 9 i 
 
 a Lyrae Vega 
 
 *H| 
 
 * 9J 
 
 * 8 
 
 * 5} 
 
 * 3| 
 
 * li 
 
 iif 
 
 9f 
 
 a. Aquilae Atair 
 
 1 
 
 *11 
 
 * 9i 
 
 * 7 
 
 * 5 
 
 * 3 
 
 * i 
 
 11 
 
 a Cygni Deneb 
 
 If 
 
 *llf 
 
 *10 
 
 * 8 
 
 * 6 
 
 * 4 
 
 * 2 
 
 *12 
 
 a Cephei Alderamin 
 
 2 4 
 
 12* 
 
 *10f 
 
 * 84 
 
 * 6i 
 
 *4i 
 
 * 2 4 
 
 *124 
 
 a, Aquarii 
 
 3 i 
 
 li 
 
 *11J 
 
 * 9i 
 
 4- 
 
 * 54 
 
 * 3i 
 
 * 14 
 
 a Piscis Aust. Fomalhaut 
 
 4 
 
 2 
 
 12 4 
 
 *ioi 
 
 * 8 
 
 * 64 
 
 * 44 
 
 * 24 
 
 a. Pegasi Markab 
 
 4 i 
 
 2 i 
 
 12 i 
 
 *ioj 
 
 * 8 1 
 
 * 6 
 
 * 44 
 
 * 24 
 
 a Andromedae Alpheratz 
 
 H 
 
 34 
 
 ii 
 
 *ni 
 
 * 9- 
 
 * 74 
 
 * 54 
 
 *34 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 45 
 
 Letter and Con" ,., 
 stellation. Name " 
 
 Sept. 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 Time between 
 rising and 
 coining to the 
 meridian. 
 
 Point of the 
 heavens in 
 which it rises. 
 
 Cassiopeiae 
 
 * If 
 
 11| 
 
 9| 
 
 7| 
 
 
 
 
 
 a. Arietis 
 
 * 3* 
 
 * 1* 
 
 H| 
 
 9| 
 
 8i 
 
 ,N.EAE. 
 
 Ceti Menhar 
 
 *4* 
 
 *2i 
 
 *12 
 
 10| 
 
 H 
 
 E. 
 
 a. Persei 
 
 *4i 
 
 * 24 
 
 *12i 
 
 101 
 
 
 
 
 
 a Tauri Aldebaran 
 
 * 5| 
 
 *3f 
 
 *lf 
 
 11| 
 
 7i 
 
 E.N.E. 
 
 a Aurigae Capella 
 
 *6 
 
 * 44 
 
 *2i 
 
 *12i 
 
 
 
 
 
 a. Orionis Betefyeux 
 
 * 7 
 
 * 5 
 
 * 3 
 
 * 1 
 
 6 4 . 
 
 E.6.N. 
 
 a Canis Maj. Sirius 
 
 * 8 
 
 * 6 
 
 * 4 
 
 * 2 
 
 4| 
 
 E.S.E. 
 
 Canis Min. Procyon 
 
 *Sf 
 
 * 6| 
 
 * 4 3 
 
 *2| 
 
 64 
 
 E.b.N. 
 
 /S Geminorum Pollux 
 
 *H 
 
 * 7 
 
 *4f 
 
 * 3 
 
 9 
 
 N.E.6.N. 
 
 a Hydrae Cor Hydrae 
 
 *10 
 
 *8S 
 
 * 64 
 
 *4| 
 
 H 
 
 E.6.S. 
 
 a. Leonis Regulus 
 
 nj 
 
 *9i 
 
 *7 
 
 * H 
 
 7* 
 
 E.N.E. 
 
 a Ursae Maj. Dubhe 
 
 12^ 
 
 *10i 
 
 *i 
 
 *6i 
 
 
 
 
 
 a. Virginia Spica Virginis 
 
 24 
 
 lf| 
 
 *10i 
 
 *8i 
 
 H 
 
 E6S. 
 
 Bootis Arcturus 
 
 34 
 
 li 
 
 *lli 
 
 * 94 
 
 7| 
 
 N.E.6.E. 
 
 a Serpeutis 
 
 4| 
 
 3 
 
 I2f 
 
 *11 
 
 64 
 
 E6.N". 
 
 a Scorpii Antares 
 
 5 
 
 3| 
 
 U 
 
 *11| 
 
 3i 
 
 S.E. 
 
 Ophiuchi Ras Alhagus 
 
 6| 
 
 4| 
 
 2| 
 
 12| 
 
 7i 
 
 E.N.E. 
 
 y Draconis 
 
 7f 
 
 54 
 
 3^ 
 
 H 
 
 
 
 
 
 a Lyrae Vega 
 
 7f 
 
 5^ 
 
 3| 
 
 If 
 
 
 
 
 
 a. Aquilae At air 
 
 9 
 
 7 
 
 5 
 
 3 
 
 6| 
 
 E.6.N. 
 
 Cygni Deneb 
 
 H 
 
 8 
 
 51 
 
 4 
 
 
 
 
 
 a. Cephei Alderamin 
 
 104 
 
 8^ 
 
 N 
 
 44 
 
 
 
 
 
 a Aquarii 
 
 i 
 
 i 
 
 7 i 
 
 5| 
 
 6 
 
 E. 
 
 Piscis Aust. Fomalhaut 
 
 *12 
 
 101 
 
 8 
 
 6* 
 
 24 
 
 S.E.6.S. 
 
 a Pegasi Markab 
 
 *12J 
 
 10i 
 
 8J 
 
 64 
 
 7 
 
 E.N.E. 
 
 a Andromedae Alpheratz 
 
 *H 
 
 1U 
 
 9| 
 
 7i 
 
 8| 
 
 N.E. 
 
 The first column contains the usual method of naming the star, 
 by its constellation and letter. The second contains the peculiar 
 name of the star, where it has one ; but when the name is seldom 
 if ever used, it is put in italics : thus a Lyrse is hardly ever called 
 Vega, while a Canis Majoris is usually called Sirius. The succeed- 
 ing twelve columns show, within about a quarter of an hour, the 
 times when the various stars will be on the meridian of Greenwich 
 on the first day of the various months of the year. The asterisk 
 denotes midnight or after midnight, the figure without asterisks 
 
46 EXPLANATION OF MAPS OF THE STARS. 
 
 noon or afternoon. Thus (* 12) is midnight, and (12) is noon; 
 (*2f) is a quarter to three in the morning, (2j) the same in the 
 afternoon ; (* 10) is ten in the morning, (10) ten in the evening. 
 The last column but one shows the interval of time between the 
 star's rising and coming on the meridian, or between the latter 
 and its setting; and the last column shows near which point of the 
 compass it rises ; while the substitution of W. for E. throughout 
 will show the same for the setting. Where the last two columns 
 are vacant, the star is circumpolar, that is, not sufficiently distant 
 from the pole to rise or set. 
 
 For instance, we wish to know the position of the constellation 
 Orion on the 1st of March. Opposite to a Orionis, and under 
 March, we find (7J), or this star comes on the meridian at about a 
 quarter past seven in the evening. In the last column but one 5 we 
 see 6|, or the star has risen six hours and a half before it comes on 
 the meridian, and will set six hours and a half after coming to the 
 meridian. That is, it rose at about a quarter to one, P.M., and will 
 set at about a quarter to two, A.M. It rises east by north, and sets 
 west by north.* 
 
 To correct the preceding table for the intermediate days, abate a 
 quarter of an hour for every four days from the first of the month. 
 Thus on the 18th of December, seventeen days from the first, the 
 stars will be on the meridian about an hour earlier than the time 
 marked in the table for the first. Thus the learner may judge in 
 what part of the heavens to look for any remarkable constellation 
 at any time of the year ; and may find the smaller stars by more 
 particular comparison of the map with the portion of the heavens so 
 found. 
 
 The most useful problem for which our maps offer no great facili- 
 ties, is the finding of the distance between two stars. But when 
 
 * Very few persons (except seamen) have distinct ideas upon the meaning of the more 
 complicated points of the compass. The following two rules embrace all the cases. 
 When the letters indicating two points are joined together, the point which is half way 
 between the two is meant : thus N.E. is half way between north and east; and N.N.E. 
 is half way between north and north-east. When the letters of two points are joined 
 together with the intermediate word by, or the letter b, it means the point which comes 
 next after the first, in going towards the second : thus, N.6.E. is the point which fol- 
 lows north towards the east; S,E,6,S. is the next point to south-east, looking towards 
 the south. 
 
EXPLANATION OP MAPS OF THE STARS. 
 
 47 
 
 the right ascensions and declinations of the stars are known, a 
 simple geometrical construction will overcome the difficulty ; which 
 we insert more readily, as the same may also be applied to the find- 
 ing of the distance between two given places on the earth's surface. 
 
 Of the two methods which we now give, the first is the construc- 
 tion of a problem in spherical trigonometry, is independent of the 
 map, and is meant to be applied when the stars the distance of which 
 is to be measured, lie upon different maps. It is taken from Sir 
 Jonas Moore's system of mathematics, and requires only a scale or 
 table of chords. The second method is conveniently applied when 
 the stars are upon the same map, and requires only a scale of equal 
 parts. 
 
 To find the distance between two stars, proceed as follows : 
 
 1. Find the right ascensions and declinations of the stars. 
 
 Case First. Case Second. 
 
 1st star R.A. 358 Dec. 57JN. 1st star R. A. 94* Dec. 16 N. 
 2d starR.A.307iDec.44iN. 2d star R. A. 344 Dec. 30 S. 
 
 2. Take the difference of the right ascensions ; or if this difference 
 be greater than 180, subtract it from 360, and take the remainder. 
 Call this A. 
 
 A = 50f A = 110J 
 
 3. If the declinations be both north, or both south, subtract both 
 from 90 ; if one be north and the other south, add either to 90 and 
 subtract the other from 90. Call the results B and C. 
 
 B = 32* B = 106 
 
 C = 45| C = 59i 
 
 4. Take a circle whose radius is the chord of 60, and from the 
 centre O draw any radius O X. 
 
 D 
 
48 EXPLANATION OF MAPS OF THE STARS. 
 
 XJ) 
 
 5. Set off X Y with the chord either of B or C, and Y D, Y D' 
 with the chord of the other. 
 
 6. Set off D S, D S', with the chord of A. 
 
 7. Draw O D, D D', S S'. 
 
 8. From M the intersection of O D and S S', draw M P perpendi- 
 dicular upon D D' : from P draw P Q perpendicular upon O X or 
 O X produced, and produce P Q to meet the circle in R. 
 
 9. Measure XR with the compasses, and find the angle of which 
 it is the chord ; that angle is the distance of the atars required. 
 
 The answer in the first case is 33J, and in the second 115|. 
 
 To apply this to finding the distance between two places on the 
 earth, use lotfgitudes instead of right ascensions, latitudes instead of 
 declinations, but take the difference of longitudes for A, only when 
 both are east or both west, and their sum when one is east and the 
 other west. In all other respects, the rules are precisely the same. 
 When the angular distance is found, allow 70 miles to a degree, and 
 subtract from the result, its hundreth part, which will be sufficiently 
 exact. 
 
 The second method of finding the angular distance of two stars 
 
 is as follows : 
 
 -u 
 
 M 
 
 K. 
 
 Let P and Q be the stars, K the centre of the map, and D V a half- 
 
EXPLANATION OF MAPS OF THE STARS. 49 
 
 side. Set off D p, D </, respectively equal to K P and K Q, and 
 draw V p, V q. On P Q, or on a line M N, equal to P Q, construct 
 a triangle, of which the remaining sides R M, R N, are respectively 
 equal to V p, V q. Then the angle at R is the angular distance of 
 the stars P and Q on the globe. 
 
 If the side of the map be considered too large a scale, any con- 
 venient length may be taken to represent an inch, and a scale of 
 equal parts may be used. 
 
50 
 
 CHAPTER III. 
 
 WE now proceed to some historical and critical account of the gno- 
 monic projection. 
 
 It has been usual to distinguish maps of the stars from those of the 
 earth, by the name of planispheres ; or representations of the sphere 
 upon a plane. This name is rejected because both species equally 
 merit the latter title. The first planispheres of which we have any 
 distinct account are those of Ptolemy, or rather of Hipparchus and 
 Ptolemy. It appears that the former knew the stereographic pro- 
 jection, in which the eye is placed at a point of the sphere, and the 
 plane of projection is perpendicular to the diameter which passes 
 through the eye. Hipparchus is said, by constructing such a pro- 
 jection, and laying down sixteen principal stars, to have provided an 
 instrument for determining the hour of the night. But Ptolemy is 
 the first writer on the stereographic projection, whose work has come 
 down to us ; not indeed in Greek, but only by an Arabic version, 
 which latter was rendered into Latin by Commandine. 
 
 The distinguishing properties of the stereographic projection are, 
 1. that every circle of the sphere, great and small, is represented by 
 a circle ; 2. that the angle made by the projections of two circles 
 which intersect, is the same as that made by the circles themselves. 
 But neither appear to have been known either to Hipparchus or 
 Ptolemy, except the first property in the case of great circles ; which 
 is the more curious, as in the conic sections of Apollonius, pub- 
 lished long before the time of the latter, a proposition is given which 
 very nearly amounts to the same thing as the first-mentioned pro- 
 perty. The first who distinctly announced it for every circle was 
 Jordanus, in a treatise on the planisphere, written at the beginning 
 of the thirteenth century, but not published till 1507. The oldest 
 known demonstration of the second property is in Leadbetter's 
 Astronomy, London, 1728. 
 
 For the projection of a whole hemisphere, the stereographic has 
 
EXPLANATION OF MAPS OF THE STARS. 51 
 
 some considerable advantages ; but not so for smaller portions of 
 the sphere. At and near the point opposite to the eye it is nearly 
 the same as the gnomonic projection, but farther from the centre 
 of the map the distortion becomes considerable. For common use 
 in the finding of stars, it is altogether inadmissible, since stars which 
 lie on the same line, or nearly so, in the apparent heavens, are 
 placed in a circle in the stereographic map, to which circle the eye 
 has no guide. For example, it is seen in our summer solstice map, 
 that Procyon, Rigel, and y Eridani are nearly in a line with each 
 other, as are also Columbae, Sirius, and Procyon. Neither of 
 these would be suspected, on looking at a stereographic projection. 
 
 There is, however, one very useful application of the stereogra- 
 phic projection, (as of all others which suppose the eye to be in the 
 axis, and the plane of projection parallel to the equator,) which we 
 notice because it is most effective in the point where our maps are 
 weakest; namely, in laying down the various positions of the 
 horizon. If a common globe be rectified for the latitude of any 
 place, it is then indifferent whether we suppose the globe fastened 
 to the axis, and turning with it, while the horizon remains fixed, 
 or whether we suppose the horizon to be attached to the axis, 
 which turns it the contrary way, while the globe remains fixed. 
 If we lay this down on a stereographic projection, of which the place 
 of the eye is the south pole of the axis, the horizon will continue 
 throughout its whole motion to be represented by the same circle, 
 moving in the plane of the equator, round a point, the position of 
 which depends upon the latitude of the place, being nearer the cir- 
 cumference the less is the latitude. This was applied by Apian,* 
 in his Cosmographia, to a planisphere for geographical purposes, 
 and by the late Dr. Wollastonf to a similar one for the heavens. 
 By it can be found immediately the stars visible at the place for 
 any hour of any day in the year, together with the position on the 
 visible hemisphere occupied by each ; as also the time of rising, 
 
 * For a short account of whom, see Penny Cyclopaedia. 
 
 f Possibly the Usus Astronomicus, &c., of Bartschius, published in 1661, may have pre- 
 viously contained the same thing. See Lalande, Bibliographic Astronomique, page 249. 
 The same may be said of the planisphere of Stampioen, which had a moveable horizon. 
 See page 3 11, 
 
 E 2 
 
52 EXPLANATION OF MAPS OF THE STARS. 
 
 setting, and coming on the meridian of each, to within about five 
 minutes*. 
 
 The remaining projection which was known to Ptolemy, is that 
 now known by the name of orthographic, called by him the 
 Analemma, and described in his work of that name, which has 
 descended to us in a Latin translation. Its principle is not re- 
 ducible to that of a picture, unless we suppose the eye placed at 
 an infinite distance. It may be more easily conceived as follows. 
 Let the hemisphere to be projected be placed with its circular base 
 horizontal ; the place of each star is the point of the ground-plane 
 which is directly under the star. The distortion of this projection is 
 very considerable towards the edges, and all circles are represented 
 by ellipses, except those which are parallel to the plane of projection. 
 It has however, like all other projections, its own peculiar advan- 
 tages ; one of which is, that, supposing the plane of projection to be 
 the equator, a star is very easily laid down, when its right ascension 
 and declination are given. 
 
 Delambref attributes to Ptolemy a knowledge of the gnomonic 
 projection, which he appears to us to infer from very slight premises. 
 We do not know that he laid down any map of the heavens which 
 supposed the eye to be at the centre of the sphere. 
 
 The first modern work on the sphere which enjoyed any consider- 
 able reputation, was that of John de Sacro Bosco, or Sacro Busto, 
 an Englishman, probably, from his name, either called Holywood or 
 Halifax, or else born at one of those places. He studied, first at 
 Oxford, afterwards at Paris, and died in 125G, leaving behind him a 
 Latin treatise on the sphere, which for more than three hundred 
 years continued to be the principal one in use. Being written in 
 Latin, it was as well known on the continent as in England, and 
 probably much better ; for among the many commentators on the 
 aforesaid work, there is not the name of any Englishman of note. 
 
 The first work which we can find, professing to treat of the 
 sphere, and written in English, is the " Castle of Knowledge," by 
 
 * By much the best planisphere of this kind which we have found, is that constructed 
 by Messrs. Smith and Son, 172, Strand. It is, of course, adapted to Greenwich, but will 
 not be very wrong, and may be easily corrected, for any part of England. 
 
 i Hist. Ast, Anc, vol. ii, p. 486. 
 
EXPLANATION OF MAPS OF THE STARS. 53 
 
 Robert Recorde, physician, best known as the first introducer of 
 algebra into this country. It was published in 1556, and dedicated 
 in English to Queen Mary, and in Latin to Cardinal Pole. It is an 
 unfavourable specimen both of typography, uniformity of spelling, 
 and accuracy of reasoning, but contains much curious information 
 on the then existing notions of astronomy.* It does not refer to 
 any English work on the subject, but only to Sacro Bosco and 
 foreign commentators. It does not contain any distinct account of 
 either projection, but the orthographic projection is employed in the 
 figures. 
 
 In 1590, Thomas Hood published " The Use of the Celestial Globe 
 in Piano, set forth in two Hemispheres," the first work in English, 
 which appears in the Bibliographic Astronomique of Lalande, and of 
 which he remarks, '' L J Astronomic commencait a percer en Angle- 
 terre." This work consisted of a very meagre account of the stereo- 
 graphic projection, together with an explanation of the mythological 
 constellations, embellished with some surmises f of the author. 
 
 The first work on the gnomonic projection appeared at Rome 
 in 1612, with the following title : 
 
 " Prospective nova Coelestis, seu Tabulae peculiares ad Asterismos 
 in Piano delineandos, auctore R. P. Christophoro GRIENBERGER, 
 Soc. Jesu." 
 
 The author was born, according to Lalande, in 1561, at Halle 
 in the Tyrol, and died at Rome, in 1636. Another edition appeared 
 in 1679, edited by H. A. Langenmantel, a Benedictine canon, 
 which is in the British Museum. It consists principally of tables 
 for laying down the various constellations in this projection. 
 
 In 1674, folio maps, similar to those of which this work treats, 
 appeared at Paris, under the following title : 
 
 * It is slated in this work, but no where else that we have found, that the milky way 
 was anciently called " Watling Street," and the seven stars of Ursa Major, ' the brood 
 hen." 
 
 f We quote the following, as part of one of our old "Explanations of Maps of the Stars." 
 
 " Scholar. I marvell why, seeing she (Ursa Major) hath the forme of a beare, her 
 taile should be so long. 
 
 " Master. Imagine that Jupiter, fearing to come too nigh unto her teeth, layde holde 
 on her tayle, and thereby drewe her up into the heaven; so that shee of her selfe being 
 very weightie, and the distance from the earth to the heavens very great, there was great 
 likelihood that her taile must stretch. Other reason know I none." 
 
54 EXPLANATION OF MAPS OF THE STARS. 
 
 " Globi Coelestis in Tabulas Planas reducti Descriptio, auctore 
 P. Ignatio Gastone PARDIES, Soc. Jesti Mathematico, opus post- 
 fa timum." 
 
 These were six maps, representing the six sides of a cube circum- 
 scribed about the sphere, as described in the first Chapter of this 
 treatise. 
 
 There were one or two other editions. The first is in the British 
 Museum, and presents six maps corresponding to those on which 
 this work treats, and in particular we must notice that the figures 
 of the constellations are turned with their backs towards the spec- 
 tator, in the manner represented in our plates, though the maps 
 represent the interior of the globe. On this point we shall presently 
 speak. 
 
 In the course of mathematics projected by Sir Jonas Moore, for 
 the Mathematical School at Christ's Hospital, and published after 
 his death in 1681, he has placed, at the end of the Cosmography, 
 six maps reduced from those of Father Pardies, but in other respects 
 a perfect copy of them. These are, as far as we know, the only 
 maps of the kind yet published in England. Another projection of 
 the same species, but which does not appear to have been copied, is 
 to be found in the Atlas of Doppelmaier, published at Nuremburg, 
 in 1742. The constellations are arranged in the same manner with 
 regard to fronts and backs. 
 
 We now come to the reasons which have recommended the 
 adoption of the gnomonic projection, in preference to any other. 
 Generally speaking, the practical astronomer has no need of maps, 
 since catalogues have entirely superseded both these and globes. 
 In such catalogues the stars are arranged in the order of their right 
 ascensions, which are given, as also their declinations. The degree 
 of accuracy required is such, that unless maps were at least five hun- 
 dred times as long and as broad as ours, and made of some material 
 which does not shrink, they could not supersede a catalogue ; and 
 even then, there would be many inconveniences independent of their 
 size. The only case in which a map might be useful is where some 
 new object, such as a comet, having been observed for several days, 
 and then lost, a rough approximation to its track is wanted, which 
 may tell the observer in what direction to look for it again. But for 
 
EXPLANATION OF MAPS OF THE STARS. 55 
 
 this purpose, a map containing a sixth part of the heavens could 
 never be wanted, and the Atlases of Flamsteed or Bode, which are 
 well known to astronomers, and in which single constellations are laid 
 down on a large scale, would better serve the purpose. Conse- 
 quently, the astronomer has no use for our maps, other than that 
 which is common to him with the rest of the world. 
 
 The common reader is desirous of seeing the relative position o 
 the constellations, and seldom or never wants any large development 
 of a single portion of the heavens. Therefore maps of individual 
 constellations would only perplex him by their minuteness, as well as 
 by their detached character. At the same time, the possessor of 
 a moderately good telescope, who pursues star-gazing as an amuse- 
 ment, requires more exact detail than could be furnished in a very 
 small space. To the first description of persons, every projection is 
 practically useless, which does not preserve the main character of 
 the relative positions ; that is, which does not place those stars 
 in the same line, which appear in the same line in the heavens. All 
 purposes are better served in the gnomonic projection upon the cir- 
 cumscribed cube, than in any other with which we are acquainted ; 
 for as each map contains a sixth part of the whole celestial sphere, 
 the most important groups are to be found in the same map ; and 
 as the straight line, which joins two stars on the same map, is the re- 
 presentative of the apparent shortest distance between them, all the 
 stars which appear on the same line in the heavens are found on the 
 same line in the map. This is the particular advantage of the method 
 of projection ; and by it, a person who has no idea of arithmetic or 
 geometry, or even of astronomy, except knowing the names of the 
 principal stars, might possibly substantiate his claim to be the dis- 
 coverer of a new comet ; or, if he were very lucky, of an old one 
 whose return is expected. 
 
 Suppose that a person, so circumstanced, were to see, in an 
 evening's walk, some faint and cometary-looking appearance in a 
 particular portion of the sky, near the constellation Orion. Upon 
 looking at neighbouring stars, he sees that it appears exactly in a 
 line with the two shoulder stars of Orion (a and y), and also with 
 the star in the foot (/3), and the star above, and nearest to it in a 
 line parallel with the belt, which is in Eridanus, and is marked . 
 
56 EXPLANATION OF MAPS OF THE STARS. 
 
 Having made these observations, he has, on his return home, the 
 power of obtaining the approximate place of the body, with a facility, 
 and we may almost say, with a correctness, which Ptolemy might 
 have envied. On drawing straight lines through the stars above 
 named, in the summer solstice map, it will be seen that the right 
 ascension of the appearance observed must have been 69, and its 
 declination above 4J North. 
 
 The same method will of course apply to finding out the appella- 
 tion of any particular star, which is not known, by means of two 
 which are known. Draw a line in the winter solstice map through 
 # Aquilae, and a Lyrse, and it will then become very easy to detect 
 a and /3 Capricorn i, 0, /3, y, , and s Aquilse, the three stars in 
 Sagitta, /3 Cygni, and y Lyrse. 
 
 It will be better for the beginner to observe, for himself, stars which 
 appear in one line, and to proceed to compare them with the map, 
 than to follow the directions laid down in any book. 
 
 The relative position of the constellations is not easily recollected ; 
 their forms, and the manner in which they are dispersed on the globe, 
 are too irregular. To fix in the mind the first rough idea of their 
 position, perhaps the best way would be to refer them to corre- 
 sponding portions of the terrestrial globe, in the following manner ; 
 or at least, it may be worth while for the reader to try whether he can 
 derive any advantage from such a comparison. Let the instant 
 chosen be the commencement of the sidereal day at Greenwich, that 
 is, let the vernal equinox be on the visible part of the meridian at 
 that place. Then the following constellations will be vertical to, or 
 over the heads of, the countries which are marked opposite to them. 
 We have chosen as often as possible the central part of the constel- 
 lation, or boundaries where they were more convenient; and it must 
 be recollected that the notion so given is the rudest possible. 
 Ursa Minor From N. Pole to Mackenzie River. 
 Draco British and Russian N. America. 
 
 Cepheus Greenland, Iceland. 
 
 Cygnus N. Atlantic, between coast of America and Azores. 
 
 Hercules W. of N. America, Gulf of Mexico. 
 
 Andromeda Mediterranean, Austria, Spain. 
 Pegassus Cape Verd Islands. 
 
EXPLANATION OF MAPS OF THE STARS. 57 
 
 Cassiopeia N. and W. Europe, Spitzbergen. 
 
 Perseus Caspian, Black Sea, Persia. 
 
 Auriga W. Tartary. 
 
 Lynx E. Tartary, Japan. 
 
 Ursa Major E. Siberia, Sea of Kamscatka, N. Pacific. 
 
 Caraelopardus W. Siberia. 
 
 Orion Ceylon. 
 
 Eridanus Madagascar. 
 
 Canis Major Ocean W. of New Holland. 
 
 Canis Minor Borneo. 
 
 Hydra New Guinea. 
 
 Leo Minor Ocean E. of Japan. 
 
 Centaurus New Zealand and Ocean S. and E. 
 
 Bootes Sandwich Isles, and Ocean N. and E. 
 
 Serpens Pacific Ocean off Mexico. 
 
 Ophiuchus Pacific Ocean off Peru and Columbia. 
 
 Aquila Columbia, Peru, River Amazon. 
 
 Lyra United States. 
 
 Corona Borealis Off California. 
 
 Cetus Congo, Mozambique. 
 
 Aries Egypt, Ethiopia, W. Arabia. 
 
 Taurus E. Arabia, Hindostan. 
 
 Gemini China, East peninsula of India. 
 
 Cancer Philippines, Ocean off China. 
 
 Leo Lad rone Islands. 
 
 Virgo Society Islands, and Ocean N. W. 
 
 Libra Marquesas to Pitcairn's Island. 
 
 Scorpio Easter Island and Ocean S. 
 
 Sagittarius Ocean off Chili, Buenos Ayres. 
 
 Capricornus Brazil. 
 
 Aquarius Ocean off Brazil. 
 
 Pisces Guinea and interior of Africa. 
 
 To return to the projection ; it has been objected that the con- 
 stellations which are near the corners and sides of the cube are 
 
 divided among different maps. This is certainly the failing of the 
 projection : but it must be remembered that every choice which 
 could have been made has some remarkable defect. And the ob- 
 
58 EXPLANATION OF MAPS OF THE STARS. 
 
 jection lies,, not so much against the species of projection, as against 
 the choice of the cube for the exterior figure on which to project 
 But the cube, which is a solid of the least number of faces, renders 
 the disadvantage as small as is possible. Had the maps been 
 broken up into constellations, the same objection would have applied 
 still more strongly, unless each design had been large enough to in- 
 clude not only its constellation, but all around it ; so that each 
 constellation should appear in one map as the principal figure, 
 and in several others as contiguous to the principal figure. This 
 is what is done in the atlases of Flamsteed and Bode ; and for small 
 portions of the heavens answers very well ; but it would very much 
 have increased the expense of these maps. Any projection of the two 
 hemispheres separately would have been out of the question on so 
 large a scale. There appear to be only two ways of meeting the 
 difficulty, and both of them expensive. The first, to suppose the 
 faces of the cube extended, and the projection to be carried farther 
 on each face, so as to get the contiguous portions, which would thus 
 be repeated, some on two, some on three maps ; the second, to have 
 another gnomonic projection, in which the sides of the cube should 
 be parallel to the diagonals of the first projection. As the matter 
 stands, wehave the ad vantages; 1. of having great circles represented 
 by straight lines ; 2. of getting the circumpolar portion of the hea- 
 vens very nearly into one map ; 3. of representing a whole sixth of 
 the sphere in each map ; 4. of drawing the most important part of 
 the zodiac with very little distortion. These must be placed against 
 the disadvantage of not being able to present to the eye all the most 
 remarkable groups ; which is a defect only for finding the stars by 
 means of one another, and none whatever for most of the other 
 practical uses of the map. We need hardly observe, that there is 
 in each map a sufficient number of groups to diminish the incon- 
 venience materially. 
 
 We now come to the question of the constellations. The writings 
 of Ptolemy (who lived about the year 140 of our era) which preserved 
 a full account of all that had been done before him, were the most 
 classical works on astronomy, till the time of Tycho Brahe, or about 
 A.D. 1600. In forming his catalogue of the longitudes and lati- 
 tudes of the stars, he fixed the relative position of the constellations, 
 
EXPLANATION OF MAPS OF THE STARS. 59 
 
 and rendered it necessary to keep to his arrangement, because he 
 described each star, not by letters or numbers, but by its position in 
 the constellation. Thus, what we call /3 Orionis or Rigel, was de- 
 nominated by Ptolemy, " the bright star in the left foot." 
 
 The figures of the constellations are of no use to the astronomer, 
 as such ; a star is sufficiently well known, when its right ascension 
 and declination are given ; and if letters referring to the constellation 
 are used, such as /3 in Orion, y in Draco, &c., it is not now to direct 
 the attention to any imaginary figure of an armed man or a dragon, 
 but to a particular region of the heavens, which might with equal 
 propriety have been called region A or region B. It is to the 
 mythological antiquary that the figures are useful, as sometimes 
 throwing light upon his pursuits. Every ancient people has written 
 its own version of the singular fables which are common to all 
 mythologies, upon groups of stars in the heavens ; and it might 
 have been thought that some feeling of congruity, if taste were too 
 much to expect, would have prevented the burlesque of mixing the 
 utensils of modern life with the stories of the heroic age,, presenting 
 much such an appearance as the model of a locomotive steam-en- 
 gine on the top of the Parthenon. But the Lacailles, the Halleys, 
 and the Hevelii, have arranged it otherwise ; the waterbearer pours 
 a part of the stream which should wash the southern fish into a 
 sculptor's workshop ; a carpenter's rule has got between old Chiron 
 and the altar on which he was going to sacrifice a wolf; and the 
 Lion and the Hydra, whose juxtaposition has made more than one 
 speculator imagine he had found the key to the whole allegory, are 
 in truth two astronomers fighting for a sextant, w.hich Hevelius has 
 placed at their disposal. A great part of the southern hemisphere is 
 laid out in mathematical instruments. 
 
 If figures are to be drawn at all, it is, as we have said, for the his- 
 torian, not for the astronomer ; and we imagine the former will think 
 it no loss that in our maps the heavens of Ptolemy have been re- 
 stored, and in no one drawing exceeded. The names only, and 
 boundaries of the modern constellations, are given; but all the 
 figures are those of Ptolemy, so arranged as to represent his cata- 
 logue. Mr. Howard, who drew the figures, has favoured us with 
 the following account of the alterations, which he found it necessary 
 
60 EXPLANATION OF MAPS OF THE STARS. 
 
 to make in the usual distribution of the stars, in order to represent 
 the catalogue of Ptolemy. 
 
 ft The star /u, Ceti has been transferred to Aries ; it was described 
 by Ptolemy as at the extremity of the hind foot." 
 
 " a and 9 Ci ucis have been appropriated to the foot of Centaurus, 
 agreeably to Ptolemy's description of them.' 1 
 
 "The river Eridanus is not carried so far to the south-west as the 
 star now bearing the name of Achernar, because the star described 
 by Ptolemy as the last of the river,, is placed by him in longitude 
 cp 7 \ J, and south latitude 53^, giving a difference of nearly 50 in 
 longitude (with full allowance for precession) and 7 or 8 degrees in 
 latitude." 
 
 " The variations I have found necessary in drawing the figures 
 according to Ptolemy's description, are unimportant. A reference to 
 his catalogue will set any question respecting them at rest, as I have 
 adhered closely to it in every instance. 7 ' 
 
 The maps which we are describing, represent the interior of the 
 heavens ; that is, the spectator is supposed to stand at the centre of 
 the cube. The difference between a map and a globe, generally 
 speaking, is, that in the former the spectator is supposed to be in 
 the inside, and in the latter, at the outside. The consequence of this 
 difference is, that when the north pole is uppermost, a spectator 
 who places himself directly opposite to the vernal equinox., sees Aries 
 upon the left hand in the map, and upon the right hand in the globe. 
 When a spectator looks at the equinox (which suppose to be at the 
 south, on the meridian), from east to west is from left to right, and 
 the apparent daily motion is in that direction : but this apparent 
 daily motion brings the zodiac on the meridian according to the 
 order of the signs ; and therefore Aries follows the equinox, and must 
 appear on the left. On the outside of the globe the effect is reversed, 
 (see page 5) unless we suppose the backs of figures to be presented. 
 The question now arises, did Ptolemy conceive himself to be looking 
 at the constellations from before or behind, from the inside or outside 
 of the sphere ? Four different hypotheses are possible, between 
 which, at first sight, it might appear easy to decide, by inspection of 
 the catalogue ; but, as we shall presently see, a question has been 
 raised. This much appears certain, that before the time of Bayer, 
 
EXPLANATION OF MAPS OF THE STARS. 61 
 
 A,D. 1600, all maps were drawn so that the spectator either looked 
 at the backs from the outside, or at the fronts from the inside of the 
 sphere. To this we have not met with any exception, though we can- 
 not of course undertake to verify such a proposition. Apian's Cos- 
 mographia (edition of Frisius, 1553) contains an example of the 
 firsthand Postellus'* signorum coelestium vera configuration published 
 also in 1553, of the second. Bayer adopted another plan, described 
 and reasoned upon by Flamsteed in the following paragraph, which 
 is translated from the preface to the third volume of the Historia 
 Calestis, p. 156. 
 
 " Tycho Brahe died in the year 1601, two years after Bayer pub- 
 lished his Uranometria, wherein he gives us maps of all the constella- 
 tions ; his figures are tolerable, and the stars well enough laid down 
 according to their places in Tycho's catalogue, and many other 
 small stars are added, which are not in the catalogue of Tycho, and 
 which, it appears, he (Bayer) laid down by the unassisted eye, by 
 comparing them with the fixed stars inserted in his maps from 
 Tycho's catalogue, whose nomenclature is the same. But having 
 drawn all his human forms, except Bootes, Andromeda, and Virgo, 
 with their backs towards us, those stars which all before him place 
 in the right shoulders, sides, hands, legs, or feet, fall in the left, and 
 the contrary, in his figures ; with which, therefore, whosoever goes 
 about to examine the ancient observations, or the catalogues of the 
 fixed stars printed or published in any language, will find himself 
 much perplexed, if he be not beforehand apprized of this. The 
 reason probably of Bayer's error, was, that often finding the words 
 gy vuTct) and ev pterappevw in Ptolemy's catalogue, and consulting the 
 Greek Lexicons for the sense of them, he always found vuros ren- 
 dered bydorsum, and ptera^svov by inter scapilium , and concluded that 
 infer scapilium was the space betwixt the shoulder-blades on the back; 
 and whenever he met with either of these words in the description 
 of any constellation, except Virgo and Andromeda, he drew it with 
 the back towards us. Whence he makes all those stars that Ptolemy 
 (and the ancients, and all since them to himself) placed in right 
 
 * To our disappointment, this work contains nothing on the point in question, except 
 what is to be found iu the map. This Was afterwards copied into Morel's edition of 
 Aratus, 1559. 
 
O^ EXPLANATION OF MAPS OF THE STARS. 
 
 shoulders, arms, sides, legs, and feet, &c., of their forms, to stand 
 on their left, whereby he renders the oldest observations false and 
 absurd. To remedy this fault, when he mentions any eminent fixed 
 star to be in dextro humero 9 or dextrd tibia, he adds alias in sinistrd, 
 &c. ; which, indeed, seems to correct the misconception, but being 
 done but seldom, will perplex those that make use of his maps, and 
 render them useless. Had Bayer but drawn the map of Sagittarius, 
 or any other of the human forms, so that the stars placed in the right 
 hands, shoulders, sides, and feet of Ptolemy's catalogue might stand 
 on the same in his figures, he would have seen that they would all 
 have their faces towards us, and thereby would have learned, that in 
 Ptolemy's Greek, vwros- signifies the crates corporis, or the ribs, and 
 /xET#(pev6v, the space betwixt the shoulders, not only on the back, but 
 also on the forepart of the body or upper part of the breast, and 
 there would then have been no incongruity between his figures and 
 ancient descriptions. I am convinced that not only Ptolemy but 
 Homer himself uses those words in a more comprehensive sense 
 than the Lexicons commonly allow. Nevertheless, in most of 
 the maps of the fixed stars that have been engraved since those of 
 Bayer, the forms are taken from him, and have the same faults 
 with his." 
 
 It so happens, that owing to stars being frequently referred to the 
 shoulders, or to some part of the dress, as Orion's belt, which will 
 equally apply to the front or hind part, the back is very seldom directly 
 mentioned ; but when such a necessity does arise, the word vwror or 
 /xerafp/jsvos- is used, which (though Flamsteed, without citing any autho- 
 rity, curiously enough supposes them to mean the front, being led away 
 by his hypothesis) are always used, the first for the back generally, the 
 second for the part of the back between the shoulders. To draw a 
 correct inference, we must remark, that since the supposition of an 
 inside view of front figures makes the heavens agree with Ptolemy's 
 description as to the right hand or left hand position of any star, it is 
 plain that Ptolemy placed the figures fronting inwards on the sphere. 
 Whether he supposed himself to look from the inside or outside, 
 must be settled by ascertaining whether he places stars which are in 
 the middle of the figure in the front or in the back ; and the pre- 
 ceding words prove that he did the latter. Bayer, therefore, should 
 
EXPLANATION OF MAPS OF THE STARS. 63 
 
 have reversed the order of the constellations, making the signs of the 
 zodiac proceed from left to right, instead of from right to left, at the 
 same time when he made the other change. We have already men- 
 tioned that in the gnomonic projections which have preceded the 
 present, and we may add, in most maps of the seventeenth century, 
 the plan of Bayer has been followed ; that is, an inside view of 
 figures fronting outwards. The same plan has been adopted in our 
 maps j not with any view to correctness, but with an avowed de- 
 parture from it, and for this reason, that an inside view of the 
 sphere was too essential to astronomical purposes to be sacrificed 
 to historical and mythological truth. But at the same time, in 
 choosing between the reversal of right and left, or front and back, 
 the former has been preferred, as being a less violent departure from 
 the actual appearances which Ptolemy supposed himself to observe 
 when he formed his catalogue. We may sum up the result in the 
 following memoranda : 
 
 I. Ptolemy took an outside view of figures fronting inwards ; our 
 maps are an inside view of figures fronting outwards ; therefore the 
 left hand of a figure in our map is the right hand according to 
 Ptolemy, and vice versa. 
 
 II. To obtain a representation of the sphere of Ptolemy* in every 
 respect, look at the maps through the paper. 
 
 In the cube of page 20, that we might present to the student 
 
 * It has been suggested to us, that Ptolemy himself placed some constellations dif- 
 ferently from others, that is, some presenting the front and some the back: and Virgo 
 is particularly instanced, in which one star (a) is described by him as being in the coun- 
 tenance (xporuxoS). But in this constellation, as in all others, the "right" and "left" 
 of Ptolemy can only be drawn upon a figure fronting inwards ; while the star (o) can be 
 placed in the countenance, to a person looking from behind, if the face be turned side- 
 ways, as in the map. The placing of stars in the wings of Virgo is to us a strong pre- 
 sumption that the back of the figure was looked at : our readers must have observed 
 the awkward manner in which those appendages are obliged to be brought forward 
 when the front of the figure is drawn in the usual way. On this very point, Ptolemy 
 mentions his having removed some stars from the wiugs to the sides, to preserve the- 
 natural appearance of the figure. Would he have thought one position more natural 
 than another had the wings been in front ? The reader may decide for himself, and 
 perhaps the more safely (if we may say it), that the question is not how ladies would 
 have worn their wings, had they them, but how a mathematician would have thought 
 they ought to have worn them. 
 
 Hipparchus expressly says, that every body turns all the constellations towards the 
 inside of the universe (Petavius, Ura?tofogion } p. 181). But we cannot ascertain how he 
 supposes them to be looked at, whether from the outside or inside. 
 
64 EXPLANATION OF MAPS OF THE STARS. 
 
 maps in every respect like those which this treatise accompanies, 
 without raising a question which was there of no importance,, we have 
 drawn such maps on the outside of the cube. To set this right, and 
 to make the cube there given a perfect outside representation of the 
 sphere, write =G= where cy is now, all the rest of the figure remain- 
 ing the same. 
 
 The longitudes of the stars have been altered more than 20 by 
 precession since the time of Ptolemy, by which means their position 
 with respect to the equinox, is very different from what it was in his 
 day. In noticing this inequality, we shall also include those of 
 nutation, aberration, and refraction, by which the apparent places 
 of the stars are also affected, as well as parallax, which alters the 
 places of the planets. That is, we shall explain the nature of the 
 phenomena without entering into their causes. 
 
 Let the stars only be laid down on an immoveable wooden globe, 
 which is placed inside a glass globe. On the glass globe draw the 
 circles of right ascension and declination, and let an axis pass 
 through the poles of the ecliptic. On this axis let the glass globe 
 turn slowly and uniformly round, in the direction contrary to that 
 in which the constellations of the zodiac are reckoned, at the rate of 
 about 1 in seventy-two years. This motion of the circles by which 
 right ascension is measured, is the effect of a slow conical motion of 
 the earth's axis. It changes the right ascension and declination of 
 stars, and also their longitude, but not their latitude ; because the pole 
 of the ecliptic keeps its position, and the latitude is what the angular 
 distance from the pole of the ecliptic wants of 90. If we suppose 
 the exterior glass globe to remain fixed, the same relative change 
 will be produced by causing the interior globe to revolve round the 
 pole of the ecliptic in a contrary direction, that is, according to the 
 order of the signs. This will make every star move slowly forward 
 along its parallel of latitude, which is the most simple way of stating 
 the phenomenon. This is called the precession. 
 
 While the glass globe above mentioned is revolving round an axis 
 which passes through the poles of the ecliptic, let this axis itself 
 (its centre remaining fixed) make a very minute conical oscillation 
 of about nineteen years in duration. The effect will be that the 
 parallel of latitude will not merely move along over the star, but will 
 
EXPLANATION OF MAPS OF THE STARS. 65 
 
 have a lateral motion, which will make it oscillate to and fro, being 
 first on one side of the star, then on the other. If the motion be 
 caused by the interior globe, the effect will be that the star, instead 
 of moving along its parallel of latitude, will describe a waving curve, 
 to which the parallel of latitude is a sort of axis. The effect of 
 this is called nutation, and the utmost departure of the pole of the 
 ecliptic from its mean place is about 17''. It arises from the axis 
 of the earth not describing merely a cone, but a cone fluted from 
 the vertex to the base. 
 
 While the exterior glass globe is performing the two motions 
 above described, let the stars on the interior wooden globe move on 
 that globe in the following manner : 
 
 ECHOIC ^ 00000 O p ieofEciiptic - 
 
 Let a star in the ecliptic oscillate backwards and forwards in the 
 ecliptic, through an arc of about 40'' in the course of a year. At the 
 pole of the ecliptic let the star which has hitherto been in the pole, 
 describe a yearly circle of 20" of radius about the pole. Between 
 the two let the star describe a yearly ellipse whose greater radius is 
 20", and is parallel to the ecliptic, and more or less flattened ac- 
 cording as the star is nearer to, or farther from the ecliptic ; as is 
 shown in the preceding figure. The alteration of place arising from 
 this motion is called aberration, and arises from the motion of the 
 earth, which produces an alteration of the apparent direction of 
 the rays of light which meet the eye ; being a phenomenon of the 
 same kind as the alteration of the apparent direction of a ship's 
 course, when seen from another ship which is in motion. If we 
 suppose the star to move in consequence of precession and nuta- 
 tion, as in the second supposition of the preceding descriptions, the 
 effect may be represented as follows. Instead of supposing the star 
 to describe the waving curve alluded to along its parallel of latitude, 
 let the centre of the ellipse of aberration describe that curve. Let 
 the ellipse always present its flat part to the pole of the ecliptic, and 
 let the star describe the ellipse in the course of a year. 
 
 Refraction is the effect of the atmosphere upon the rays of light, 
 by which they are bent a little towards the earth, in consequence of 
 which the star appears somewhat higher than it really is. At the 
 
 F 
 
66 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 horizon, where it is greatest, it is somewhat more than half a degree; 
 at the zenith it is nothing ; and of any two stars 3 that is the most 
 altered by refraction which has the least altitude. Owing to the 
 difficulty of laying down the horizon on our maps, it is not easy to 
 represent the effect of refraction upon them. 
 
 The preceding complicated motions cannot be well understood 
 by any but a mathematician ; it is evident that the three, precession, 
 nutation, and aberration,, will sometimes conspire, or each increase 
 the effect of the other, and sometimes destroy each other's effects 
 either wholly or partially. The following figures show the species of 
 waving curve in which four different stars describe their parallels of 
 latitude. The first is that of Orionis, the second that of Leonis 
 or Regulus, the third that of the Pole star, and the fourth that of 
 y Draconis. 
 
 The nutation, from its smallness, and the length of its period, is 
 insensible on the scale which we have chosen. The effect is there- 
 fore entirely that of aberration and precession. In 7 Draconis, 
 which is near the pole of the ecliptic, and, in which, consequently, 
 the precessional motion is small, and the aberrational nearly circu- 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 G7 
 
 lar, we see the effect of a circular motion, where the circle is slowly 
 carried forward. But in Regulus, which is nearly on the ecliptic, 
 and on which the effect of precession is large when compared with 
 that of aberration, the latter being little more than a linear oscilla- 
 tion, the effect is very different. In 3 Orionis, which is not near 
 either to the ecliptic or its pole, we see a mixture of the preceding 
 characteristics. The first two stars have three years' motion repre- 
 sented, and the latter two, four years. 
 
 Parallax is one of those effects which are not easily laid down on 
 the maps, owing to their dependence upon the horizon. All astro- 
 nomical tables are made to represent the appearances of the heavens 
 from the centre of the globe, whereas the spectator is at its circum- 
 ference. Imagine two persons with telescopes, one at the centre, the 
 other on the surface, the intervening ground being supposed transpa- 
 rent. To see a star in the zenith, both must point their telescopes 
 the same way, viz., directly upwards; but to look at a star in the 
 horizon of the surface, or between that horizon and the zenith, the 
 spectator at the centre must point his telescope higher than the one 
 at the circumference. The difference of the directions of the two 
 telescopes is the parallax of the star. It is greater, the nearer the 
 object looked at ; for the fixed stars, it is totally insensible, on 
 account of their distance ; and equally so on our maps, for all the 
 bodies of the solar system except the moon, for which it is some- 
 times greater than a degree. For the sun it is about eight seconds 
 and a half. 
 
68 
 
 CHAPTER IV. 
 
 HAVING explained the construction on which these maps of the stars 
 are drawn, we now proceed with the description of the manner in 
 which they have been filled up, and subjects connected with it. 
 
 When we speak of maps of the heavens, it must be, in some way 
 or other, under limitations such as accompany our notions of maps 
 of the earth. To make an absolute delineation of the latter is im- 
 possible : the size of the paper imposes the necessity of introducing 
 only such objects as are of a visible magnitude in the scale which is 
 chosen. If we had to consider physical geography only, the best 
 principle which we could adopt, supposing there were means of 
 carrying it into practice, would be to suppose the spectator placed 
 at such a height above the surface, that the country which he is to 
 map should be as much under his eye, and appear of about the same 
 size, as the paper on which he is to draw it. If in such a case 
 tolerably distinct vision could be procured, the minor features of the 
 landscape would disappear, and the relative importance of those 
 which remain could be estimated. We have a map of this sort in 
 the drawing of the face of the moon, as seen through a powerful 
 telescope. 
 
 But for the purposes of political geography, such a map would 
 require considerable additions. Rivers too small to be seen are the 
 boundaries of powerful states, and towns which could not be omitted 
 would be altogether imperceptible. These two considerations have 
 their analogies when we come to maps of the heavens. If we were 
 to propose maps of the visible heavens, it would be necessary first to 
 ascertain what they are. On a hazy night they are not the same as 
 on a clear night ; and even at the same hour and place, the eye of 
 one man will distinguish objects which have no existence in that of 
 another. Still greater will be the difference, if we suppose one to 
 have a telescope, which the other has not : the heaven of a twenty- 
 foot reflector is toto ccelo different from that of the naked eye, or even 
 of a tolerable refractor. It might be, and has been, proposed, to adapt 
 maps of the heavens to some given telescope say, for example, a 
 
EXPLANATION OF MAPS OF THE STARS. 69 
 
 refractor of five-feet focal length, with a magnifying power, say of 
 two hundred times. But even this would be no certain criterion, for 
 instruments of different makers, and different instruments by the 
 same maker, have different degrees of goodness ; while different 
 people will discern more or less with the same instrument. As a 
 rough guide to the selection requisite for utility, such a test might 
 be taken ; but it would be far from accurate near the limits. 
 
 Again, historical or practical considerations may invest a very 
 faint object with an interest which does not attach to much brighter 
 ones ; and the position of a small star in the heavens may render it 
 of more importance than many of greater popular fame. Were the 
 astronomer to choose, he would rather the whole constellation of 
 Orion were annihilated than lose the pole star ; and y Draconis, 
 both as passing near the zenith of Greenwich, and as being the star 
 by means of which aberration was discovered, is of much greater 
 interest than Sirius, the brightest star in our heaven. Let it happen 
 that a little star of the eighth magnitude is predicted to lie almost 
 directly in the apparent track of a coming comet : it immediately 
 becomes of much greater importance to determine the place of that 
 star very accurately, than of dozens which could be named, and 
 which are always visible ; for the most powerful telescopes are 
 seldom furnished with any very exact means of finding the place of 
 a star in the heavens, but are provided with micrometers, which 
 serve to ascertain the relative position of two objects so near each 
 other, that they appear in the field of the telescope together. Hence 
 the place of the small star being settled, and that of the comet with 
 respect to it, the absolute place of the latter is found. 
 
 From such considerations, it appears that some test must be 
 found of a more practical character than any yet named ; and when 
 we consider that any method will include the stars visible to the 
 naked eye, and even to inferior telescopes, it is obvious that the 
 difficulty at the limits is a matter which entirely concerns the pos- 
 sessor of a good telescope, and no other person, except inasmuch 
 as he may not like to have his maps crowded with objects which he 
 cannot see. But even of these there are many of which he must 
 read : so that the only question is 1. How to lay down a suffi- 
 cient number of objects of interest or high curiosity : 2. How to 
 
70 EXPLANATION OF MAPS OF THE STARS. 
 
 enable him to draw a line between those which exist with reference 
 to his astronomical means, and those which do not ? 
 
 But for the astronomer, it is necessary to lay down, for the most 
 part at least, such objects as have been observed, and actually find 
 a place in his books of reference. A new object is seen, and the first 
 question is, of all those which lie near it, which have had their places 
 well determined? where is he to look for information respecting 
 them ? This is much the same as asking By whom have they 
 been observed ? in what catalogue are they found ? Hence it 
 becomes most requisite that all maps of the stars should be based 
 upon some one or more of the best catalogues. Tf there should 
 even be visible stars (of which there are several) which do not find 
 a place in any of the standards of astronomy, they would be of little 
 use. Nothing could be very accurately determined by them, for 
 they are not very accurately known themselves. The interest which 
 belongs to peculiar portions of the heavens the zodiac, for example, 
 which always contains most of the planetary bodies has caused them 
 to be more carefully noted than the rest. This will make catalogues 
 rather standards of astronomical importance in reference to stars 
 which they insert or omit, than of comparative visibility. But this 
 is precisely what is desirable on account of the astronomer ; and, as 
 we have observed, it is of little consequence to any one else what 
 method is chosen. 
 
 Astronomical catalogues are of three kinds : 
 
 1. Those which are intended to give the places of the stars con- 
 tained in them with the utmost degree of accuracy which the existing 
 state of astronomy will admit : these, as may be supposed, cannot 
 contain a great many stars. That of Dr. Maskelyne, published in 
 1805 (and then considered the most correct which had appeared), 
 contained only thirty-six stars. This number was afterwards in- 
 creased in the Nautical Almanac ; and at present the places of one 
 hundred stars are yearly given in that work, of which fifty-four have 
 the standard character here described. As these must be consi- 
 dered, for every practical purpose, what they are called in the 
 Nautical Almanac, the " principal fixed stars/' we give a list of 
 them, the standard stars being in italics. They are in order of right 
 ascension, and the numbers refer to the hours of right ascension : 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 71 
 
 
 
 IX. 
 
 XVII. 
 
 y Prgasi (Algenib). 
 
 * Argus. 
 
 Ursae Minoris. 
 
 J3 Hydri. 
 
 a, Hydras. 
 
 <r Octantis. 
 
 a CassiopeoB. 
 
 Ursae Majoris. 
 
 a Herculis. 
 
 /3 Ceti. 
 
 Leonis. 
 
 (3 Draconis. 
 
 I. 
 
 a Leonis (Regulus.) 
 
 a Ophiuchi. 
 
 a t/rs# 3/m. (Polaris.) 
 
 X. 
 
 y Draconis. 
 
 6 l Ceti. 
 
 yy Argus. 
 
 XVIII. 
 
 a Eridani (Achernar.) 
 
 a Ursce Majoris. 
 
 /x l Sagittarii. 
 
 a Arietis. 
 
 XI. 
 
 8 Ursce Minoris. 
 
 II. 
 
 y Ceti. 
 
 & Leonis. 
 
 a, Lyrce (Vega.) 
 
 
 8 Hydrae et Crateris. 
 
 /3 Lyrce. 
 
 5t (^/Ctl, 
 
 j3 Leonis. 
 
 Aquila. 
 
 III. 
 
 a Perse i. 
 
 y t/r?*e Majoris. 
 
 XIX. 
 
 t\ Tauri. 
 
 XII. 
 
 8 Aquilce. 
 
 y 1 Eridani. 
 
 |3 Camaeleontis. 
 
 y Aquilce. 
 
 IV. 
 
 a 1 Crucis. 
 
 a Aquilce (Altair.) 
 
 a Tauri (Aldebaran.) 
 
 /3 Corvi. 
 
 /3 Aquilce. 
 
 V. 
 
 12 CanumVenaticorum. 
 
 XX. 
 
 CL Auriga (Capella.) 
 
 XIII. 
 
 a 2 Capricorni. 
 
 /3 Onoraj (Rigel.) 
 
 a Virginis (Spica.) 
 
 a Pavonis. 
 
 |3 Tauri. 
 
 Ti) Ursce Majoris. 
 
 X Ursae Minoris. 
 
 o Orionis. 
 
 Y t Bootis. 
 
 a Cygni. 
 
 a, Leporis. 
 
 /3 Centauri. 
 
 6V Cygni. 
 
 Orionis. 
 
 XIV. 
 
 'XXI. 
 
 a Columbse. 
 a Orionis. 
 
 a Bootis (Arcturus.) 
 a 2 Centauri. 
 
 Cygni. 
 a Cephei. 
 
 VI. 
 
 Bootis. 
 
 |3 Aquarii. 
 
 /a, Geminorum. 
 
 a? Librce. 
 
 /3 Ce^Aei. 
 
 a Argus (Can opus.) 
 
 |3 C7r^ Minoris. 
 
 Pegasi. 
 
 51 (Hev.) Cephei. 
 
 YV 
 
 a Aquarii. 
 
 a Cam* Jlfa/. (Sirius.) 
 
 A. V . 
 
 /^ T *1 
 
 a Gruis. 
 
 Canis Maj. 
 
 TTT T 
 
 /3 Librae, 
 a Coronce Borealis. 
 
 XXII. 
 
 VII. 
 
 8 Geminorum. 
 a 2 Geminorum( Castor) 
 a Caw. 3/m.(Procyon) 
 
 a, Serpentis. 
 Ursae Minoris. 
 /3 1 Scorpii. 
 XVI. 
 
 Pegasi. 
 a PiscisAustralis(o- 
 malhaut.) 
 a Pegasi (Markab.) 
 
 VIII. 
 
 5 Ophiuchi. 
 
 XXIII. 
 
 15 Argus. 
 
 a Scorpii (Antares.) 
 
 / Piscium. 
 
 Hydras. 
 
 >j Draconis. 
 
 y Cephei. 
 
 Ursse Majoris. 
 
 a Trianguli Austral ie. 
 
 a Androinedce. 
 
72 EXPLANATION OF MAPS OF THF, STARS. 
 
 With the difference between the more exact catalogue and the 
 second-rate one, the maps have nothing to do, for the quantity in 
 question is inappreciable. A few hundredths of a second in the 
 time of coming on the meridian, is all the difference of errors that 
 is found by observation to exist between the first and second-rate 
 stars of the preceding list. 
 
 2. Catalogues which are intended to represent a large portion of 
 the heavens with considerable accuracy, but not with that high 
 degree which it is possible to obtain by multiplying observations of 
 the same star. Such catalogues are always more than sufficiently 
 exact for the purposes of a map. 
 
 3. Catalogues of objects which are interesting, not as marking 
 out definite points in the heavens, but on account of the phenomena 
 which they present, whether of a fixed, periodical, or indefinitely 
 changing character. Such are double and triple stars, variable 
 stars, and all the class of nebulae. The exact places of these being 
 a matter of no great importance, only such right ascensions and 
 declinations are given as will enable the observer to find what he 
 wishes to look at. But even these are sufficiently exact for the 
 purposes of a map, in which the whole field of a telescope is but a 
 very small circle. 
 
 So soon as the order of the maps has been settled, as to what 
 stars or other objects they shall contain or omit, it becomes ne- 
 cessary to fix upon an epoch. The small motion of precession, 
 described in p. 64, is continually varying the absolute positions of 
 the stars with respect to the equinox, or of the equinox with respect 
 to the stars. But this motion, amounting to only a degree in seventy- 
 two years, does not affect the utility of the map, as a map, for that 
 time at least ; and even at subsequent periods may cause it to be a 
 useful history of the past state of the heavens. The time will come 
 when the pole-star is no pole-star at all, for any of the purposes 
 which it now assists; but such a change must be the work of thou- 
 sands of years, and need not be taken into account. In some 
 degree, to obviate future inconveniences, the maps in question re- 
 present the heavens as they will be in the year 1840 so that till 
 that time they are in fact changing towards exactness. In 1858 
 the equinox will be wrongly placed by about a quarter of a degree; 
 in 1912 by about a whole degree. 
 
EXPLANATION OF MAPS OF THE STARS. 73 
 
 The identification of the several stars is the next point to be con- 
 sidered. If the student in astronomy should imagine that every 
 possible star is distinctly laid down in some catalogue or other, he 
 would be very much mistaken. The stars he finds catalogued 
 are for the most part those which are visible to the naked eye, 
 or to telescopes of moderate aperture.* But every accession of 
 optical power makes the heavens present new stars and nebulae, to 
 an extent which human industry can hardly be expected to classify. 
 The Berlin Academy, in 1825, invited all such astronomers as were 
 inclined, to share among them the task of making minute maps of 
 the heavens. It was proposed that each of twenty-four observers 
 should take one hour of right ascension ; and " that, having formed 
 a chart including all the stars of the Histoire Celeste and Bessel's 
 Zones, he should put in, by estimation only, all the stars that could 
 be seen by one of Fraunhofer's telescopes of thirty-four lines aper- 
 ture." A few of these charts have been published : the stars of 
 course have no names, nor any other method of identification, except 
 their place in the map, which looks like a spoiled skeleton of a map 
 plentifully spirted with small drops of ink. We have thus> besides 
 the stars which are in catalogues, a large reserve of additional points 
 of reference, which come, one and another, into use when a comet or 
 a planetary body passes by them. An observer compares a comet or 
 planet with a small star, which he finds conveniently in the field of 
 his telescope with the comet or planet. He can, with the micro- 
 meter, settle the position of the comet with respect to the star, much 
 better than he can settle that of either star or comet in the heavens. 
 To make this clearer, observe that most astronomical instruments 
 may now be considered as divided into two classesf meridian and 
 equatorial. The first have telescopes which move in the plane 
 of the meridian only, as their name imports : they are incapable of 
 any lateral or azimuth motion (except a very small quantity, to 
 allow of the proper adjustment of the instrument), and consequently 
 
 * The focal length of a telescope is the distance of the focus of the object-glass from 
 the glass itself; but as the eye-glass is very near the focus of the object-glass, the focal 
 length may be taken for the length of the telescope itself. 
 
 I The zenith sector, for observing stars near the zenith, and the altitude and azimuth 
 instrument, which resembles ihe theodolite in principle, are now not so much used. 
 
74 EXPLANATION OF MAPS OF THE STARS. 
 
 only see a star for about a minute before and after it comes to the 
 meridian. The object of this fixed character is stability, it being found 
 that every motion of which a telescope admits opens two or. three 
 sources of error. Even with such precautions, no meridian instru- 
 ment can, without verification, be considered as perfectly the same 
 for twenty-four hours together ; and it is the business of the astro- 
 nomer to make such observations as will, by comparison or com- 
 bination, point out or do away with the instrumental errors. And 
 if even meridian instruments are thus to be in a continual state of 
 correction, which are of the most simple construction, mechanically 
 speaking, still less can equatorial instruments be made the direct 
 means of setting the places of heavenly bodies. These are to be so 
 constructed, that the telescope may, by the mere motion of the 
 hand (or which is now preferred, by clockwork), be made to follow 
 any star in the heavens throughout the whole time during which it 
 is visible. There must be then an axis parallel to the axis of the 
 heavens, both ends being pivots of rotation. Off this axis must 
 come another axis perpendicular to it, on which the telescope must 
 turn. An hour-circle must be connected with the principal axis, 
 which may point out nearly at what period of the rotation the tele- 
 scope is for the time being ; and a declination circle must be fixed to 
 the cross axis, on which it may be seen how much the telescope is 
 elevated above the position in which (if the instrument be true) it 
 should look at a point in the equator. If all the preceding con- 
 ditions be fulfilled, and the telescope be once pointed on a star, a 
 slow motion given to the principal axis will make the star remain 
 visible. But these instruments cannot be so constructed that they 
 shall accurately give the absolute right ascension and declination of 
 a star, on account of the variety of conditions to be fulfilled, and 
 other circumstances; but they can be so constructed, that the hour 
 and declination circles shall be sufficiently exact to find a star, 
 and place it somewhere in the field of the telescope. When two 
 objects are together in the field, a micrometer may be applied, to 
 give very accurately the relative positions of the two. 
 
 The accurate determination of the places of stars and planets by 
 large fixed instruments is the proper work of public observatories 
 while the determination of such relative measurements as can be 
 
EXPLANATION OF MAPS OF THE STARS. 75 
 
 made by equatorial instruments is 'not only the course in which a 
 private observer can make himself most useful, but also that in 
 which astronomy presents itself in the most interesting light to the 
 greater part of mankind. But the object of this digression has 
 been the manner in which the uncounted class of unknown stars 
 become useful. An observer, perhaps many thousand miles from 
 a first-class observatory say in South America makes a series 
 of observations upon a comet with an equatorial instrument, not by 
 absolutely determining its place, but by comparing it with a number 
 of unknown stars, whose places he finds with sufficient nearness lo 
 enable others to identify them. Say, for instance, that August 13, 
 at 22 m 47 s past ten in the evening, he has found that a comet is in 
 the field with a small star, whose right ascension is* (as near as his 
 instrument will show) 13 h 26 m 8 s , and its declination 20 15' 48" N. 
 By accurate micrometrical observations, it is ascertained that the 
 comet has 17% 3 more of right ascension than the star, and 23" 
 less of declination. This is transmitted to Europe; and by the 
 more powerful aids which large observatories contain, a small star is 
 detected very near the place in question (such as would be visible to 
 the foreign observer, according to his own description of his optical 
 means), and this same small star, being accurately measured, is found 
 to have a right ascension of 13 h 20 m 41 s 5, and a declination 
 of 20 C 16' 2". Consequently, the apparent right ascension of the 
 comet, at the time and place in question, was 13 h 20 m 58 s , 8, and 
 its declination 20 15' 39". The use of the Berlin maps, when 
 completed, will be, 1. That the disappearance of any stars will be 
 detected, if the process be repeated at intervals ; 2. That when 
 any unknown star is made a point of reference, as in the pre- 
 ceding supposed observation, a look at the map may at once give 
 the observatory astronomer assurance of the star being really there, 
 and not so contiguous to another as to make it doubtful which to 
 observe. 
 
 * Such right ascensions and declinations are usually put down with as much ap- 
 pearance of accuracy as if it was really meant to be implied that the instrument used 
 was fit for such close determinations. The reason is, that since all which is known is that 
 the instrument will be wrong, but not which way it will be wrong, whether in excess or 
 defect, any alteration for the sake of round numbers might be an increase of the error. 
 
76 EXPLANATION OF MAPS OF THE STARS. 
 
 In the last-mentioned point will lie a difficulty to many readers. 
 If the stars be in reality so thickly placed in the heavens^ is it 
 possible to specify which is meant by an instrument capable of very 
 rough determination only ? In the first place, if a cluster of stars 
 had been observed with the comet, the relative positions of the 
 cluster would have been drawn and sent with the observation, while 
 it would have been distinctly specified which star was meant (if 
 only one of the collection had been observed). But to get a further 
 notion of the relative thickness with which stars appear in the 
 heavens, we shall enter upon the following consideration : 
 
 The field of a telescope, even under a low magnifying power, is a 
 very minute portion of the heavens. A telescope of five foot focal 
 length, with a magnifying power of about 60, will just contain the 
 whole sun in the field. The sun is a circle of about half a degree in 
 diameter (a little more). If we suppose telescopes and observers 
 enough to look at the whole visible hemisphere at the same moment, 
 upwards of 92,000 would be necessary. The Histoire Celeste of La- 
 lande (the largest single catalogue ever published) would certainly 
 not allow a star to every three observers at any one moment. And 
 if we consider not the whole extent of the field, but the portion of it 
 by which an observer might be supposed liable to mistake the place 
 of a star, we cannot suppose it less than thirty to one that a star 
 afterwards observed near the place will be that in question. 
 
 The identification of stars which are thus described by their ap- 
 proximate right ascensions and declinations is not a matter of diffi- 
 culty ; and it is not necessary to assign specific names to them. 
 Those which are in any catalogue, are sufficiently described by their 
 number in that catalogue. The oldest method of distinguishing 
 visible stars is that of Hipparchus and Ptolemy, which points out 
 the place of the star in the picture of the constellation : thus we 
 have the first in the belt of Orion, meaning that which comes first 
 on the meridian, or which has least right ascension, the first in the 
 left wing of Virgo, and so on. This cumbrous method was first 
 departed from (as is commonly asserted) by Bayer in 1603, who, 
 as Delambre remarks, gained immortality at a cheap rate, by 
 affixing the Greek and Roman letters, each to a star. But Bayer 
 
EXPLANATION OF MAPS OF THE STARS. 77 
 
 had been preceded by Alexander Piccolomini,* who in his book 
 Delia Sfera e delle Stelle fisse, has carried the principle which 
 Bayer's fame is founded upon further than his successor : for he 
 has abandoned the pictures in favour of letters. As this is an his- 
 torical point f of some curiosity, we shall in the note extract the 
 passage in which he explains his views. Bayer himself afterwards 
 abandoned letters in favour of numbers, in the joint edition J of 
 himself and Julius Schiller; but notwithstanding this rejection, 
 (which indeed was not known, as it has never been very distinctly 
 stated in modern times that Schiller's edition was in reality the 
 work of Bayer, as to the astronomical part, ) Flamsteed and the 
 more modern astronomers have agreed in using the letters of Bayer, 
 though not without some mistakes and misapprehensions. 
 
 * Alexander Piccolomini, bora at Sienna, 1508; died there, 1578. He was Arch- 
 bishop of Patras, and coadjutor of Sienna, and was the first Italian who wrote on 
 mathematical and philosophical subjects in his native language. He has also some 
 reputation as a comic writer. The first edition of the book cited in the text bears, in 
 the preface, Da la Villa di Valzanzibio. II di X di Agosto nel MDXXXIX. See Riccioli, 
 Vossius, Bayle, &c. There is a full account in the Elogi degli Uomini illustri Toscani, 
 Lucca, 1771. 
 
 f Voglio che sappiate ancora che queste stelle, che io u'ho detto, piu principali, e 
 piu chiare, che io considero fino alia quarta grandezza ; tutte ho notate a i piedi de le 
 fauole di qual si uoglia immagine. ho notato dico, ciascheduna con una lettera de 
 1' alfabeto : e questo ho fatto, accioche poi lie le figure le riconosciate, e sappiate distin- 
 guere 1' una da 1' altra. poniam caso, quella che sara ne la testa, de quella che sara nel 
 braccio, e cosi de 1' altre parimente. Ben e uero, che poi ne le figure ho posto molte 
 uolte alcune stelle piu, lequali a i piedi de le fauole non ho numerate : e couseguente- 
 mente tali stelle non son notate con lettera d' alfabeto. e questo ho fatto perche per la 
 breuita de la carta, tanta moltitudfne di carattere de 1' alfabeto farebbe in molte figure 
 non poca confusione. ma ho auertito di far questo in quelle stelle, lequali facilmente 
 possa considerarsi in che parte sieno de 1* immagine, per la uicinanza di alcune altre 
 con il caratter notate : come il tutto benissimo comprenderete, senza che io piu in cio 
 mi distenda. Ancora non ho uoluto come fa Iginio ne le dette figure dipingere i mem- 
 bri di quegli animali, che i Poeti han finto esser nel Cielo, perche ancor che cio facesse 
 alquanto di uaghezza a 1' occhio ; nondimeno offuscarebbe ancor parimente le stelle, e 
 farebbe non poca coufusione : ed io ho piutosto uoluto haver riguardo a la chiarezza 
 de la figura, che a la uaghezza de 1' occhio ; essendo il mio primo intento, mostrar 
 quelle figure piu distintamente ch' io posso, e nel modo che le sono, sendo elle sol di 
 stelle adornate senza braccia ne piedi, come ciaschedun puo uedere. 
 
 J See PENNY CYCLOPAEDIA, Article BAYER. 
 
 Schiller himself, Riccioli and Gassendi, state it distinctly. See PENNY CYCL, cited 
 above. 
 
78 EXPLANATION OF MAPS OF THE STARS. 
 
 After the catalogue of Flamsteed was published, which contained 
 both the old nomenclature of Ptolemy, and that of Bayer, it be- 
 came the practice to adopt a numbering for the stars in different 
 constellations, derived from the position in which they stood in 
 Flamsteed's catalogue. Thus the star y Geminorum, described by 
 Ptolemy as in the left foot of the second twin, happens to be the 
 twenty-fourth star in the constellation in Flamsteed's catalogue. 
 It is therefore called 24 Geminorum, and generally speaking, when 
 a number precedes a star, the number in Flamsteed's list of the 
 constellation is intended. In Piazzi's catalogue a different method 
 is adopted: the stars in each hour of right ascension are numbered 
 according to the order in which they come on the meridian, without 
 reference to the constellation in which they are. Thus if the 25th 
 of all the stars of Piazzi which are in the fourth hour should happen 
 to be a star in Gemini, it would be the 25 Geminorum of Piazzi, 
 namely, a star in Gemini, not the 25th of the constellation, but the 
 25th of the stars which have (or had) between three and four hours 
 of right ascension. The stars in the catalogues of Hevelius, 
 Bradley, and Lacaille, have also their numbers, and the conse- 
 quence is, that the whole system of nomenclature of the stars is in 
 a state of great confusion, with the agreeable certainty of its being 
 almost impossible to introduce one general and uniform system 
 throughout Europe. The only method at present appears to be to 
 attach to the numbering some abbreviation or other conventional 
 distinction for the name of the numberer. In the Index to the 
 Astronomical Society's Catalogue, an easily remembered alliteration 
 is adopted : Bradley s numbers are in brackets* and Piazzi's in 
 parentheses* Those of Lacaille have the letter C ; those of the late 
 Mr. Fallows have Fa. It is not difficult to foresee that all this con- 
 fusion of nomenclature must increase until it becomes a matter of 
 first-rate astronomical importance to agree upon the use of some 
 general method ; and then, laborious as the task will be, it must be 
 accomplished. To add to the difficulty, constellations which are 
 used and alluded to by some, are not recognized by others. 
 
 With the maps, however, these difficulties have nothing to do, 
 except as they render extreme accuracy of description very difficult, 
 and multiply the chances of error. An inquirer who has occasion 
 
EXPLANATION OF MAPS OF THE STARS. 79 
 
 to look for a star in the map which he has found in the heavens, 
 will, when he finds it, see its proper description annexed. It 
 matters nothing to him what 24 of Hevelius, or 29 of Flamsteed, 
 really means : it is sufficient that there is a star which will be un- 
 derstood by astronomers under that name, and that he knows 
 which star it is. Another, who wants to find out in the heavens 
 the star called 24 Geminorum of Flamsteed, must have settled, 
 previously to coming to the map, the way in which he is to denote 
 his star ; and though he may have encountered a difficulty, he will, 
 of course, have met with it in a manner for which no map can be 
 responsible. 
 
 The magnitude of a star is a term used to denote its apparent 
 brilliancy. Before the invention of the telescope, the stars were 
 imagined to be bodies of sensible apparent magnitude, as indeed it 
 is obvious they seem to be. And it was an unanswerable argument 
 against the probability of the Copernican system, that, admitting 
 (which was necessary to be supposed) the fixed stars to be so dis- 
 tant that the earth's whole orbit would appear no larger than a point 
 to them, their apparent magnitude made it necessary also to sup- 
 pose that the largest of them, at least, were many times the diameter 
 of the earth's orbit in diameter. The telescope showed that the 
 appearance of magnitude was altogether illusory, and dependent 
 upon atmospherical phenomena ; for though upon hazy or troubled 
 nights stars may appear large, their magnitude is not permanent, 
 but accompanied with a tremulous, boiling, or bubbling outline. 
 And in good climates and 4Still nights, no micrometer will give a 
 sensible outline and apparent diameter to any but large stars. 
 That these do appear of some slight sensible magnitude in large 
 telescopes may be true ; but it may be shown from the laws of 
 optics, that not even a mere point, supposed to emit light, could be 
 made to appear as nothing but a point, in a lens with spherical 
 glasses at least. The term magnitude then merely denotes brilliancy 
 to the eye, and is itself perfectly indefinite. We see without a glass 
 some five or six gradations of light in the several stars. Those of 
 the brightest class are said to be of the first magnitude ; those in 
 the next set, which differ sensibly from those of the first magnitude, 
 
80 EXPLANATION OF MAPS OF THE STARS. 
 
 are said to be of the second, and so on. Telescopic research has 
 detected stars which should be called of the sixteenth magnitude ; 
 but as to the fainter objects, it must be observed that not only will 
 different observers assign different magnitudes to the same star, but 
 even the same observer on different nights. And many stars which . 
 to Bayer appeared brighter than others, do not do so now ; but 
 owing to the uncertainty of the denominations employed, it is im- 
 possible to say whether this proceeds from a slow change in the 
 brilliancy of the star, or from difference of circumstances and habits 
 of perception in the observers. There are now various means of 
 estimating the apparent brilliancy of different stars, that is, their 
 relative brilliancy. Sir J. Herschel 5 from his father's experiments, 
 estimates the quantity of light received from the several stars 
 which bear the first six magnitudes to be in the proportions of 
 100, 25, 12, 6, 2, 1 : from his own, he rates the light of Sirius at 
 about 324 times that of a star of the sixth magnitude. (Astronomy, 
 Cabinet Cycl, p. 375.) 
 
 It is sometimes attempted to subdivide at least the greater mag- 
 nitudes, and to talk of a star of the 2\ magnitude, and so on. It 
 was usual to call a star which was considered as half-way between 
 the second and third magnitudes, one of the 2.3 magnitude: but 
 Mr. Baily, in his edition of Flamsteed's Catalogue, lately published, 
 has adopted the fractions of magnitudes, and it -is to be desired that 
 the example should be followed. The following will show that 
 it is not likely two observers with different telescopes * could expect 
 to agree within half a magnitude by mere estimation. Sir J. Her- 
 schel (Mem. Astron. Soc. vol. iii. p. 180) compared a large number 
 of the magnitudes assigned by himself to stars with those assigned to 
 the same stars by Professor Struve in his Dorpat Catalogue. 
 Taking an average for each sort of magnitude, it would appear that 
 the stars designated as having the magnitudes in the first column 
 by Professor Struve, would be styled as in the second by Sir J. 
 Herschel ; (the second column is in magnitudes, and tenths of mag- 
 nitudes.) 
 
 * It is found that two different persons with the same telescope make up two different 
 instruments ; and the discrepancy is still more increased when different telescopes are 
 used, in different climates, or on different nights, 
 
EXPLANATION OF MAPS OF THE STARS. 81 
 
 S. H. S. H. 
 
 4 5-4 84 9-5 
 
 5 6-5 9 10-3 
 5J 7 94 10-8 
 
 6 7-1 l(f 11-1 
 6J 7-4 104 12 
 
 7 8-1 11 11-5 
 74 8-8 114 11 
 
 8 9-0 12 12-7 
 
 It appears, therefore, that a mass of estimations by two observers, 
 both accustomed above others to this class of researches, not only 
 produces results considerably different in quantity, but presents ab- 
 solute inversions of order in the case of the smaller objects. That 
 the difference depends on climate is not probable, since it would 
 also affect the well-known and admitted stars to which the others 
 are referred : for example, Sirius is of the first magnitude all the 
 world over, whether in an English or Italian sky. But whether 
 climate does act or no, this much appears clear, that the method 
 of naming magnitudes by estimation is not a sure method of ob- 
 taining a universal classification. 
 
 The reader would probably not be wrong in considering the 
 matter thus. If a person used to look at the heavens were to 
 assert that he had seen a comet like a star of the first or second 
 magnitude, it is probable that he would be correct. If of the third, 
 the comet might be concluded to be somewhere between the 24 and 
 the 34 of all the recognized 1 stars in the heavens ; if of the fourth, 
 between the 3 and the 5 ; if of the fifth, between the 4 and the 6, 
 and so on. With regard to the maps, we need only observe that 
 the stars are designated after the best catalogues. The only 
 experimental methods of determining the relative quantity of light 
 transmitted by different stars give vague determinations, not fit 
 for settling the questions above treated with any degree of ac- 
 curacy. In the telescope, a contingent circumstance affords a 
 method of comparing faint objects somewhat better than naked 
 estimation. The measuring instrument itself is not the telescope, 
 but certain very fine threads, (frequently of spider's web,) fixed or 
 movable, according to the nature of the observations to be made, 
 
 G 
 
82 EXPLANATION OF MAPS OF THE STARS. 
 
 and placed in or near the focus of the object-glass. The image of 
 the star is formed in the focus of the object-glass, in or near the 
 plane of the threads ; and the eye-glass may be considered as a 
 microscope, for magnifying the image, and (a defect which cannot 
 be helped) the threads,, or wires, as they are termed. These wires 
 cannot be made visible without more light than comes from a small 
 star ; to remedy which there is an orifice near the middle of the 
 tube, close to which a lamp is placed, the light of which is re- 
 flected upon the wires, and the field is thus illuminated. The 
 orifice can be expanded or contracted, or closed altogether, and 
 thus the quantity of illumination may be varied. Now when two 
 objects are so faint that the illumination of the field may be made 
 to extinguish them altogether, it may be ascertained what quantity 
 of illumination is just sufficient to destroy each, and thus a notion 
 (not a very perfect one) may be formed of the quantities of light 
 received from each. But it must be observed, that it is not only 
 difficult to get a lamp which shall always yield light of the same 
 intensity, and to know whether any given lamp be such or not ; but 
 as the various lights of the heavens are almost always more or less 
 of different tints, the same lamp will extinguish one star of one 
 colour sooner than another of the same brightness but different 
 colour. Thus a red light would entirely extinguish a star of the 
 same tint, before a weaker, but bluish star, had disappeared. It 
 is by no means impossible that a diligent employment of lights of 
 different colours might be made to add to our knowledge of this 
 part of astronomy, and it is in such fields as the preceding that the 
 private observer may become a useful assistant to the public one. 
 It would be of little use for an individual to erect an observatory 
 with fixed instruments, for the purpose of obtaining right ascensions 
 and declinations, unless he could give up so much time, and procure 
 such a quantity of assistance in reducing observations, as would 
 place him on a level with national observatories. The following ac- 
 count of the late Mr. Groombridge* will illustrate our meaning : 
 " In the year 1806, he became possessed of a splendid transit 
 circle of four feet diameter, (the workmanship of our celebrated 
 
 * Annual Report of the Royal Astronomical Society for 1834. His catalogue is 
 stated to be in course of publication by the Lords of the Admiralty. 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 83 
 
 Troughton,) so well known by his name, and the excellent use to 
 which he applied it ; and he immediately commenced the task of 
 forming an exact catalogue of the stars as low as the 8.9 magni- 
 tude, within 50 of the North Pole. 
 
 " In this arduous undertaking he persevered with singular assiduity 
 for ten years, and in the year 1816 had completed about 30,000 
 observations in right ascension, and the same number in declination, 
 on this part of the heavens a series almost without a parallel in 
 the annals of modern astronomy. But Mr. Groombridge was not 
 inclined to be satisfied with merely registering his observations ; he 
 applied himself with equal industry to the harassing labour of re- 
 duction, on which ten years more were exhausted ; until, in 1827, 
 he suffered a severe attack of paralysis, from which he never per- 
 fectly recovered. During this period he had applied the reductions 
 which depend upon refraction, as well as instrumental and clock 
 errors, to all the observations, and had obtained the mean places of 
 about one-third of the whole number, so that nothing more was re- 
 quired for obtaining the catalogue, precisely as it would have ap- 
 peared from his own hands, except to apply the corrections for 
 aberration, nutation, &c., according to his own tables." 
 
 Such is the sort of labour by which an unassisted individual 
 performs work which will vie with that of a large and permanent 
 observatory ; but the amateur has another line of utility. All 
 questions connected with stars or planets except the apparently 
 simple one of making such observations as shall aid the prediction 
 of their future places with, if*possible, increasing accuracy from year 
 to year belong to the private observer, at least until such time as 
 Governments shall found observatories for purposes expressly equa- 
 torial, as it would be convenient to call them. (See p. 73.) We 
 shall devote some pages to a very short account of the various ways 
 in which a person fond of looking at the heavens, provided with a 
 moderately good telescope and micrometer, may make himself 
 useful, even without mathematical knowledge. 
 
 Let us take first the variations of the fixed stars in magnitude 
 and colour. It is evident that the question, whether a fixed star 
 revolve on an axis or not, can never be settled except by somo 
 variations of appearance presented by its different parts, as they 
 come one after another under the eye of the observer, and also that 
 
 02 
 
84 EXPLANATION OF MAPS OF THE STARS. 
 
 a regular succession of repeated appearances in a star is a very 
 strong presumption of the existence of a rotation round an axis. 
 For instance, the star /8 Persei will to-day, at 8 P.M., appear of the 
 second magnitude ; to-morrow, at midnight, it will be decidedly 
 smaller ; and in another day, it will nearly have recovered its first 
 appearance. This succession of changes can be observed re- 
 peatedly, time after time ; and the inference is, that the said star 
 revolves round an axis in 2 days, 20 hours, 48 minutes. The only 
 question is, how such pretensions to accuracy can be sustained, 
 since it is most evident that no one can pretend to say, to a minute 
 or an hour, when the star is most or least brilliant. This question 
 is one of a large number which every thinking person must ask, 
 when he hears that prediction and accomplishment differ from each 
 other by such portions of time as the twentieth part of a second ; 
 and in this particular instance it happens that an answer can be 
 given which will satisfy the most scrupulous. To take a very simple 
 case, let us suppose the length of the year is to be determined, that 
 is, the time elapsed between the sun being twice successively in the 
 summer solstice. Let it be supposed that any one single observer is 
 liable to a mistake say of five minutes one way or the other, in 
 determining the exact time when the sun is in the solstice ; so that, 
 by possibility, the observations of two successive solstices may give a 
 year ten minutes too long or too short. But remember that the 
 error possibly to be encountered is an absolute quantity, not con- 
 nected with the time elapsed between two observations. Suppose 
 then that the time of the sun's solstice is obtained in June 1830, and 
 June 1831. The year thus obtained may be ten minutes too long 
 or ten minutes too short. Let us suppose that we have already a 
 rough notion of the length of the year say exactly 365 days. 
 Instead of observing the solstice of 1831, let us wait till that of 1832. 
 Then being liable to an error of five minutes, one way or the other, 
 at each extremity, the two years so estimated may be ten minutes 
 too long or too short. Consequently, the single year obtained by 
 halving the period of two years cannot be more than five minutes 
 too long or too short. If we had waited till June 1833, and taken 
 the third part of the whole period (possibly wrong by ten minutes) 
 for the actual length of the year, the error of a single year could not 
 have been more than the third part of ten minutes ; and if a hundred 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 85 
 
 years had been so taken, the error could not have been more than 
 the hundredth part of ten minutes, and so on. Thus the art of 
 astronomical observation consists, in great part, in taking results 
 obtained at times so far distant from each other, that the error of the 
 two extremities shall be divided among a great number of the 
 periods in question, instead of being borne by one only; and the 
 correctness of modern astronomy is thus in some degree due to 
 Hipparchus, who lived about a century and a half before Christ. 
 This constitutes the great difference between astronomy and all 
 other sciences, pure or mixed except perhaps geology, in a small 
 degree. If Euclid could be discovered to-morrow to be a forgery of 
 twenty years' date, it would matter nothing, in any sense, however 
 remote, to the truth of any one proposition in geometry. But 
 establish the fact that Tycho Brahe wrote in 1700 instead of 1600, 
 and several of the fundamental results of astronomy are thereby 
 proved to be wrong, more or less. 
 
 The catalogue of variable stars, considered as well established by 
 Sir J. Herschel*, in 1833, is as follows. A few resolute private 
 observers would probably increase it considerably : 
 
 Star's Name. 
 
 Period of 
 Revolution. 
 
 Variation of 
 Magnitude. 
 
 Discoverers. 
 
 Persei 
 
 D. H. M. 
 
 2 20 48 
 
 2 to 4 
 
 J Goodricke . .1782 
 1 Palizch . . 1783 
 
 B Cephei , 
 
 5 8 37 
 
 3$ 5 
 
 Goodricke . .1784 
 
 Lyrae . . 
 
 690 
 
 3 4i 
 
 Goodricke . 1784 
 
 i) Antinoi . . 
 
 7< 4 15 
 
 34 41 
 
 Pigott . . .1784 
 
 a, Herculis . . 
 
 60 6 
 
 3 4 
 
 W. Herschel . 1796 
 
 X Serpentis ^ 
 
 
 
 
 R.A. 15 h 41 I 
 
 180 
 
 7? 
 
 Harding . . 1826 
 
 p. D. 74 \y } 
 
 
 
 
 o Ceti 
 
 384 
 
 2 
 
 Fabricius . . 1596 
 
 x c yg ni 
 
 396 21 
 
 6 11 
 
 Kirch . . . 1687 
 
 367 (Bode) Hydrae 
 
 494 
 
 4 10 
 
 Maraldi . . 1704 
 
 34 (Flamsteed) Cygni 
 
 18 years. 
 
 6 
 
 Janson . . fc 1600 
 
 -120 (Mayer) Leonis 
 
 Many years. 
 
 7 
 
 Koch . . . 1782 
 
 K Sagittarii . 
 
 do. do. 
 
 3 6 
 
 Halley . . .1676 
 
 y Leonis . . . 
 
 do. do. 
 
 6 
 
 Montanari . 1667 
 
 * The reader will find the Treatise on Astronomy, in the Cabinet Cyclopaedia, the most 
 instructive and correct in the English language ; and for the history of astronomical 
 
86 EXPLANATION OF MAPS OF THE STARS. 
 
 To these may be added the sudden appearance and disappearance 
 of stars without any apparent cause, such as the star of Hipparchus, 
 which led him to draw up the first catalogue on record, and that 
 recorded by Tycho Brahe, in 1572. From the appearance of a new 
 star, in the same part of the heavens, near Cassiopea, in the years* 
 945, 1264, and 15J2, it seems possible that a few years after 1872 
 the same appearance may again be presented. 
 
 The disappearance of stars is a well-recorded fact ; nor is the lost 
 Pleiad of mythology the only instance. One cause of the loss of a 
 star out of a catalogue has been this, that the supposed star was in 
 fact a planet, which of course continued moving in its orbit, instead 
 of remaining to be verified by those who afterwards examined the 
 catalogue. In this way the planet Uranus appears once or twice 
 in old catalogues as a star. And this considerably enhances the 
 merit of Sir William Herschel, who, it must be observed, was not 
 merely gazing through a telescope, without any object but to pick 
 up chance curiosities, but was examining the whole visible heavens 
 bit by bit, and time after time, that by successive investigations, 
 with the same telescope, he might note any changes of magni- 
 tude, colour, or motion ; and a very recent communication of Signer 
 Cacciatoref , of Palermo, shows the use of continued investigation. 
 
 discoveries, he may consult the Treatise in the Library of Useful Knowledge (History 
 of Astronomy), or the Historical Account of the Progress of Astronomy, by Mr. Narrien 
 Baldwin, 1833. But we do not cite the treatise above-mentioned merely because it is a 
 good treatise on astronomy, but because Sir J. Herschel is one of the first authorities 
 on extra-observatorial astronomy which exist at present. 
 
 * It must be observed, however, that both the first years are stated as having been 
 those of comets by Lubinietski, on various authorities; and as this writer mentions the 
 star of 1572, we do not know on what evidence the first two are founded. On looking 
 into Tycho Brahe", De Nova Stella, p. 331, we find that the authority for the two first 
 stellce (we say this, because the Latin word may stand for star, planet, or comet) is his 
 own contemporary, Cyprian of Leovitia; and of the star of 945 (or more probably 944) 
 Tycho remarks, sed a quo Historiographo id haleat, non adducit. On the star of 1264 
 Tycho says, Annotamt ille descriptionem ex quodam manuscripto codice desumsisse. Now 
 neither evidences will do at the present day, even to establish a comet, much less to dis- 
 tinguish a supposed new star from a comet, which other authorities tend to establish. 
 Tycho Brahe himself seems to think, that if he does not doubt the evidence, others may ; 
 for he adds, Nee facile crediderim ilium haec falsa pro veris nobis obtntsisse. Quorsumne 
 idfaceret ? 
 
 f In a letter to Captain Smyth, R.N. Read to the Astronomical Society, Dec. 11, 1835. 
 
EXPLANATION OF MAPS OF THE STARS. 87 
 
 " In the month of May I was observing the stars that have proper 
 motion a labour that has occupied me several years. Near the 
 17th star, 12th hour, of Piazzi's catalogue, I saw another, also of the 
 7*8th magnitude, and noted the approximate distance between them. 
 The weather not having permitted me to observe the two following 
 nights, it was not till the third night that I saw it again, when it had 
 advanced a good deal, having gone farther to the eastward, and 
 towards the equator. But clouds obliged me to trust to the fol- 
 lowing night. . . . When at last the weather permitted observations 
 at the end of a fortnight, the star was already in the evening twilight, 
 and all my attempts to recover it were fruitless stars of that magni- 
 tude being no longer visible. Meantime, the estimated movement 
 in three days was 10" in right ascension, and about a minute, or 
 rather less, towards the north. So slow a motion would make me 
 suspect the situation to be beyond Uranus." 
 
 Here, then, is somewhat more than a suspicion of a new planetary 
 body. It may be a century before it is recovered again, or it may 
 have been found again at this moment. But it will always be easy 
 to establish by calculation, as to any new planet, whether it was or 
 was not the star observed, at the time and in the place specified, by 
 the worthy successor of Piazzi. 
 
 Changes in the place of 'stars are well known, though not of so 
 great magnitude as the one in the preceding paragraph. When a 
 star still appears to have motion, over and above that which is due 
 to precession, nutation, and aberration, it is called a proper motion, 
 or one really existing in the star. The three motions just cited, 
 being common to all the stars, according to their different laws, have 
 been traced to different motions of the earth. But when one star 
 appears to have other motion, which another close to it has not, it is 
 then necessary to attribute the apparent motion of the first to a real 
 motion in the star. If we could discover a new motion, common to 
 all the stars, and amounting to this, that all the stars in one part of 
 the heaven increased their distance a little, while all those in the 
 opposite part came nearer together, it would then be evident that the 
 cause was a motion of the whole solar system towards the point at 
 which the stars opened most. Considering the solar system ac- 
 cording to the laws of mechanics, which have been so successfully 
 
88 EXPLANATION OF MAPS OF THE STARS. 
 
 applied to the derivation of the relative motions of the sun and 
 planets, .it is millions to one against the sun being absolutely at 
 rest in space. But the questions which way the whole system is 
 moving together, with what velocity, and how soon we may expect 
 to ascertain these points ? are wholly unanswerable. All we know 
 of the distance of any fixed star from us is negative namely, that it 
 is not less than about five thousand million of times the distance 
 from the surface to the centre of the earth : it may be this only, or 
 near it, or it may be a hundred times as much, or even more. In the 
 mean time, the proper motions of such stars as have them do not 
 exhibit any such degree of relation as will justify our supposing that 
 they arise from a motion of our system, as will more distinctly appear 
 in the following list* of such stars as have more than half a second 
 of motion, either in right ascension or declination. The first column 
 contains the name of the stars ; if with a single number, it is Flam- 
 steed's if, with a number in parentheses, it is Piazzi's ; or in brackets, 
 Bradley's. A number of Hevelius has (Hev.) The second column 
 contains the magnitude of the star ; the third, the proper motion in 
 right ascension, being the average of the yearly motion from 1800 
 to 1830 ; the sign , denoting that the right ascension is dimi- 
 nished, while in all other cases it is increased. The fourth column 
 contains the average yearly motion in declination for the same period, 
 denoting a southward motion, all the others being northward. The 
 stars are arranged in the order of right ascension, so that it will be 
 seen that the quantities and directions of the motions appear to be 
 perfectly irregular, or proper to the individual stars, without any 
 dependence on their places in the heavens. The motions are ex- 
 pressed in hundredths of a second (of space), so that 59 means 59 
 hundredths of a second, or 59 per cent, of a second. Observe, as to 
 the quantity of the motion, that the sun's diameter contains about 
 nineteen hundred seconds. In the columns which have been left 
 vacant, no result has yet been obtained. 
 
 * Abridged from a paper by Mr. Baily, in the fifth volume of the Memoirs of the 
 Royal Astronomical Society. A catalogue of proper motions, by M. Argelamler, of 
 Abo, has very recently been published, which, if requisite, we shall notice in the Ap- 
 pendiXt 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 89 
 
 Star. 
 
 lag. 
 
 R.A. 
 
 Dec. 
 
 Star. 
 
 Mag. 
 
 R.A. 
 
 Dec. 
 
 6 Cassiope<e . 
 
 24 
 
 125 
 
 
 Ursce Majoris . 
 
 3 
 
 58 
 
 - 5 
 
 54 Piscium . . 
 
 64 
 
 - 64 
 
 
 6 Centauri . . 
 
 2 
 
 - 84 
 
 - 98 
 
 (130) Ceti . . . 
 
 6 
 
 155 
 
 
 Bodtis . . . 
 
 1 
 
 -114 
 
 -199 
 
 (177) Ursae Minoris . 
 
 7 
 
 590 
 
 
 (127) Librae . . . 
 
 64 
 
 60 
 
 
 n Cassiopece . 
 
 4 
 
 218 
 
 - 50 
 
 % Herculis . 
 
 6 
 
 65 
 
 
 (189) Piscium . . 
 
 6 
 
 84 
 
 
 y Serpentis . . 
 
 3 
 
 7 
 
 -129 
 
 43 (Hev.) Cephei 
 
 5 
 
 206 
 
 
 49 Librae . . . 
 
 5 4 
 
 - 73 
 
 
 (234) Ursse Minoris . 
 
 64 
 
 245 
 
 
 Ursae Minoris . 
 
 4 
 
 93 
 
 - 8 
 
 a Ursce Minoris . 
 
 24 
 
 146 
 
 
 
 A Ophiuchi . 
 
 44 
 
 - 69 
 
 109 
 
 p, Cassiopeae . 
 
 54 
 
 601 
 
 
 30 Scorpii . . . 
 
 7 
 
 - 83 
 
 
 I Cassiopeae . 
 
 3 
 
 65 
 
 - 16 
 
 ft, Herculis . 
 
 4 
 
 - 23 
 
 - 72 
 
 f Ceti . . . 
 
 34 
 
 -172 
 
 83 
 
 p Ophiuchi . 
 
 44 
 
 18 
 
 -106 
 
 (123) Ceti . . . 
 
 6 
 
 154 
 
 
 (380) Draconis . . 
 
 5 
 
 77 
 
 
 18 (Hev.)Persei . 
 
 4 
 
 203 
 
 1 
 
 9i Serpentis 
 
 4 
 
 - 55 
 
 - 73 
 
 12 Eridaui . . 
 
 3 
 
 15 
 
 63 
 
 36 Draconis . 
 
 5 
 
 73 
 
 
 (47) Eridani . . 
 
 4 
 
 253 
 
 52 
 
 X, Draconis . 
 
 44 
 
 59 
 
 - 37 
 
 Eridani , . 
 
 4 
 
 - 94 
 
 - 1 
 
 I Ursse Minoris . 
 
 3 
 
 241 
 
 1 
 
 I Eridani . . 
 
 34 
 
 - 24 
 
 64 
 
 50 Draconis . 
 
 5 4 
 
 , 65 
 
 
 40 Eridani . . 
 
 5 
 
 -214 
 
 
 b Aquilae . . 
 
 5 
 
 83 
 
 
 104 Tauri . . . 
 
 5 
 
 54 
 
 
 f Draconis . 
 
 5 
 
 184 
 
 
 43 Camelopardali 
 
 5 
 
 - 67 
 
 
 Aquilas . . 
 
 U 
 
 55 
 
 32 
 
 C anis Majoris . 
 
 1 
 
 - 61 
 
 -124 
 
 (29) Sagittar . . 
 
 6 
 
 127 
 
 
 Canis Minoris. 
 
 H 
 
 - 66 
 
 -112 
 
 69 Draconis . 
 
 6 
 
 118 
 
 
 /3 Geminorum 
 
 2 
 
 - 62 
 
 1 
 
 x Cephei . . 
 
 44 
 
 147 
 
 9 
 
 11 Argus . . . 
 
 54 
 
 78 
 
 
 9i Cephei . . 
 
 34 
 
 52 
 
 80 
 
 2 Cancri 
 
 6 
 
 - 52 
 
 
 75 Draconis . 
 
 54 
 
 112 
 
 
 i Ursse Majoris . 
 
 34 
 
 - 55 
 
 - 24 
 
 24 (Hev.) Cephei 
 
 54 
 
 313 
 
 
 sr 1 Cancri . . 
 
 61 
 
 - 56 
 
 
 61 Cygni . . . 
 
 54 
 
 546 
 
 319 
 
 6 Ursae Majoris . 
 
 3 
 
 -140 
 
 -i 53 
 
 77 Draconis . 
 
 6 
 
 125 
 
 
 v Ursae Majoris . 
 
 44 
 
 - 73 
 
 10 
 
 70 Cygni . . . 
 
 6 
 
 91 
 
 
 36 Ursae Majoris . 
 
 5 
 
 - 65 
 
 - 7 
 
 T Cephei . 
 
 44 
 
 82 
 
 14 
 
 | Ursce Majoris . 
 
 4 
 
 - 32 
 
 - 56 
 
 Cephei 
 
 44 
 
 93 
 
 5 
 
 83 Leonis . 
 
 8 
 
 - 69 
 
 
 28 Cephei . . 
 
 6 
 
 68 
 
 
 (> Virginis . . 
 
 34 
 
 87 
 
 - 47 
 
 Cephei . . 
 
 6 
 
 81 
 
 
 4 (Hev.) Draconi 
 
 5 
 
 - 83 
 
 
 31 Cephei . . 
 
 5 
 
 59 
 
 
 14 Virginis . 
 
 64 
 
 - 71 
 
 
 ff Pegasi . 
 
 5 4 
 
 63 
 
 
 9i Corvi . . 
 
 44 
 
 - 53 
 
 - 10 
 
 51 Pegasi . . 
 
 6 
 
 50 
 
 
 8 Canum Ven. . 
 
 44 
 
 -104 
 
 17 
 
 34 (Hev.) Cephei 
 
 54 
 
 55 
 
 
 y Virginis . 
 
 4 
 
 - 50 
 
 - 3 
 
 y Piscium . . 
 
 44 
 
 73 
 
 2 
 
 Virginis . 
 
 34 
 
 - 54 
 
 - 25 
 
 o Cephei . 
 
 7 
 
 105 
 
 
 43 Comae Ber. 
 
 6 
 
 - 66 
 
 
 39 (Hev.) Cephei 
 
 6 
 
 398 
 
 
 61 Virginis 
 
 44 
 
 - 84 
 
 -101 
 
 85 Pegasi . . 
 
 6 
 
 117 
 
 
90 EXPLANATION OF MAPS OF THE STARS. 
 
 In the preceding list,, the first thing which will strike the observer 
 is, that the proper motions in right ascension are, on the whole, 
 much greater than those in declination. But since right ascension 
 and declination are the results of measurements, which depend only 
 on the position of the earth's axis, and the plane of the ecliptic, or 
 plane in which the earth moves round the sun, it cannot be supposed 
 that there is any physical connexion between these circumstances 
 and the motion of stars which appear totally unconnected with the 
 earth. Such might be the surmise of any one ; but it may be very 
 soon shown that there is a simple geometrical reason why it must 
 necessarily be, ceferis paribus, that the motions of stars are greater 
 in right ascension than in declination. 
 
 Let P be the North Pole, CYD M ^ the equator, and S and S' the 
 places at the beginning and end of a year, of a star which has the 
 proper motion S S'. Let A S C B be the circle of the apparent 
 diurnal motion of the star at the beginning, and PS, PS', the 
 horary circles. Then the whole of the star's motion is S S' ; the 
 motion in declination is C S' : while the motion in right ascension 
 is, not S C, but the part of the equator corresponding to S C, 
 namely, M M', greater than S C. If all the stars were in the 
 equator, then the several SCs (if we may invent such a plural) 
 would coincide with their respective M M' s ; and if there were all 
 kinds of proper motions, we should upon the whole see no reason 
 to call the variations of right ascension greater than those of decli- 
 nation. But if all the stars were very near the pole, very small 
 proper motions would make differences of right ascension of several 
 
EXPLANATION OF MAPS OF THE STARS. 91 
 
 hours. To take the extreme case, suppose a star very near the 
 pole to pass actually through the pole in the course of the year. 
 Then there would be twelve hours difference between its right 
 ascension on the two sides of the pole, and by supposing it to 
 pass as near the pole as we please, we may thus make a yearly 
 difference of right ascension as near as we please to twelve 
 hours. 
 
 The stars in the preceding list which have their names in Italics 
 are double stars : that is, though appearing only single to the naked 
 eye, they are separated by telescopes of more or less power, into 
 two stars close to each other. There might easily be conceived 
 one star which should hide another, owing to the line of their 
 junction passing, when sufficiently lengthened towards us, through 
 the earth's orbit^ which in comparison of the distance of the stars 
 from us is a mere point. But it would be against all probability to 
 suppose that in an infinite extent of space so thinly spread with 
 stars, in comparison with what might have been the case, a great 
 number of hundreds of stars should thus appear couples, owing to 
 the mere position of their lines of junction. If twenty thousand 
 grains of sand were thrown up before the eyes of a spectator, at ten 
 yards off him, and all deprived of further motion at one given mo- 
 ment, the chances are enormously against five hundred of them 
 being so placed as to hide another five hundred in whole, or in part, 
 and still more would be the probabilities against mere accident 
 of position, as we must call it, making so large a proportion of dis- 
 cernible stars double. The inference to which the mind would be 
 strongly led, is that this juxtaposition is a part of a real connexion 
 between the two stars, which constitutes them one system having 
 mutual relation between their motions, and very probably that which 
 is found to exist between the sun and planets in our system. It 
 needed no very long consideration of the planetary system (when it 
 began to be known) to draw the inference that in all probability the 
 fixed stars were themselves the suns of other systems, each con- 
 trolling the motions of its own train of planets and satellites. But 
 experience has shown that this supposition lacked boldness, and 
 was but a restriction instead of an extension. No one was suffi- 
 ciently hardy to imagine two suns demonstrated, and in some in- 
 
92 EXPLANATION OF MAPS OF THE STARS. 
 
 stances three or four strongly suspected, with all the probabilities of 
 each having its own train of planets remaining just as before. But 
 we must explain what we mean by two suns. 
 
 The suns of a system must be defined to be those bodies which 
 shine by their own light, and which are masses of matter com- 
 parable to each other in size, so that neither must be considered 
 as a mere speck, when the other is likened to an orange.* This 
 definition may require extension from future discoveries, to make 
 it include all bodies to which it shall or may be convenient to give 
 the name of suns, but at present it answers every purpose. If we 
 could suppose Jupiter to have light of its own, just enough to be 
 seen with the most powerful telescopes from a fixed star, or if we 
 could suppose its reflected light to produce such a phenomenon, 
 then the observers in that star would see our sun and Jupiter, as a 
 bright star accompanied by another, extremely faint, which revolves 
 round it, the two being inseparable by the naked eye. But as it 
 stands, we have in our heavens stars of not very different degrees 
 of brilliancy, and of which there is no reason for supposing that 
 either is the only source of illumination to the other, but the con- 
 trary, since their lights are generally of nearly the same intensity, 
 
 * We are quite serious in saying that the following extract from Sir J. HerschePs 
 Astronomy, (Cab. Cycl.) contains a better view of the solar system than a great many 
 volumes which preceded, with their clap-traps of millions of millions of miles. See 
 the Work, p. 287. 
 
 ' Choose any well-levelled field or bowling-green. On it place a globe, two feet in 
 diameter; this will represent the sun: Mercury will be represented by a grain of mus- 
 tard seed, on the circumference of a circle 164 feet in diameter for its orbit ; Venus, a 
 pea on a circle 284 feet in diameter ; the Earth also a pea, on a circle of 430 feet ; Mars, 
 a rather large pin's head, on a circle of 654 feet; Juno, Ceres, Vesta, and Pallas, grains 
 of sand, in orbits of from 1000 to 1200 feet; Jupiter, a moderate-sized orange, in a 
 circle nearly half a mile across ; Saturn, a small orange, on a circle of four-fifths of a 
 mile ; and Uranus, a full-sized cherry, or small plum, upon the circumference of a circle 
 more than a mile and a half in diameter. As to getting correct notions on this subject 
 by drawing circles on paper, or still worse, from those very childish toys called orreries, 
 it is out of the question. To imitate the motions of the planets, in the above-mentioned 
 orbits, Mercury must describe its own diameter in 41 seconds; Venus in 4 minutes 14 
 seconds ; the Earth in 7 minutes ; Mars in 4 minutes 48 seconds ; Jupiter in 2 hours 
 56 minutes; Saturn in 3 hours 13 minutes; and Uranus in 2 hours 16 minutes.' To 
 complete the above, we must add, that the model of the nearest fixed star must be at 
 least 5000 miles distant from the bowling-green. 
 
EXPLANATION OF MAPS OF THE STARS. 93 
 
 and of different colours (though this is not conclusive). These 
 stars revolve round each other, in ellipses , like the planets. But 
 before proceeding farther, we have some remarks to make on 
 the manner in which this subject concerns several, perhaps many, 
 of our readers. The first motion mentioned, namely, the proper 
 motion in the heavens, concerns the observatory astronomer entirely, 
 both as to the phenomenon in question and the difficulty of de- 
 tecting it. For not only is it his office to assign by prediction every- 
 thing that affects the stars considered as reference points in the 
 heavens, but the quantity in question is so small, that nothing but 
 the most powerful instrumental aids and the greatest skill in obser- 
 vation will detect it. But the means of many private observers 
 might be made useful in the delicate task of detecting the relative 
 motions of double stars, nor need any one be deterred by the idea 
 that he cannot himself make use of his observations after they are 
 made, or apply them to determine what are called the elements of 
 the orbit There are several steps in astronomical work: firstly, the 
 determination and selection of the phenomenon to be observed, and 
 of the proper instrument ; the investigation of the defects which are 
 peculiar to that instrument, (and every one has its own,) and of the 
 proper method of making the observation, so as to avoid as much 
 as possible of the error, and have the means of removing the rest by 
 subsequent computations; secondly, the observation itself ; thirdly, 
 the reduction of the observations, or the clearing them from the 
 effects of one phenomenon and another, which must not be taken 
 into account ; fourthly, the discovery and selection of such methods 
 and formulae as will, when applied to the observations, pro- 
 duce those general data which are called elements, and when 
 known, form the most convenient quantities with which to set out 
 in the attempt to predict the future from the past ; fifthly, the 
 actual deduction of the future phenomenon. The first is the work 
 of a mathematician and mechanician ; the second, of any person who 
 will give a short time to the practice of the rules and maxims de- 
 duced by the first, with or without understanding the principles on 
 which they have proceeded : the third, of a very ordinary computer ; 
 the fourth, of a mathematician and natural philosopher neither 
 Newton nor Laplace was more than equal to his task in this de- 
 
94 EXPLANATION OF MAPS OF THE STARS. 
 
 partment of the science; the fifth, of a skilful computer, well versed 
 in the results of the fourth. We need not enlarge on the advan- 
 tages which would result, have resulted, and do result, from the 
 same person being competent to every part of the preceding duty: 
 what we have here to say is, that the desire of being useful may be 
 accomplished in any one of the preceding paths, without much 
 attention to the others. But our business is here with the actual 
 observer, who has what is to most minds the most pleasant and 
 easy task of the whole, though as indispensable to the success of 
 the united operation as any other. Indeed it is impossible to say 
 which of the preceding should be dispensed with first. 
 
 A person with a moderately good instrument, and some attention 
 to its use, will not find the results he may produce neglected. His 
 fellow-labourers will take the raw material he furnishes, and apply 
 all the successive steps of the manufacture to it. Nor will he lose 
 the credit which is due to him ; for to omit mentioning the name of 
 an observer, the nature of his instrument, and the place where the 
 original observations are to be found, would be to ensure the re- 
 jection of the results of such observations both abroad and at home. 
 The particular case in question, namely, the fundamental obser- 
 vations of double stars, are peculiarly pointed out as the most cer- 
 tain field of the private observer, because they require no clock, 
 unless one be used as a convenient method of moving an equatorial 
 telescope. The day of observation is all that is necessary to be 
 known ; and a time-piece, with its necessary accompaniment, a 
 transit instrument, is not wanted. An equatorial telescope of suffi- 
 cient power to separate the two stars, and a wire micrometer) are 
 the necessary apparatus : of the principle of the latter we shall give 
 a general description, not entering into any of the niceties of its 
 construction, and supposing throughout that the instrument is 
 perfect. 
 
 The wire micrometer consists in the addition of an apparatus to 
 the eye-glass of a telescope, such that, on being inserted into the 
 tube, the field presents the usual appearance of a luminous circle, 
 cut by four very fine wires, parallel, two and two, the first pair being 
 at right angles to the second. It is found that the apparatus can 
 be turned round, so as to place either pair of wires in any direction. 
 
EXPLANATION OF MAPS OF THE STARS. 95 
 
 One pair of wires is fixed, but the other pair consists of one fixed 
 and one movable wire ; the latter always remaining parallel to the 
 fixed wire, but capable of having its distance increased or dimi- 
 nished by a screw, which carries round a small circle graduated on 
 the edge, into (say) 100 parts. The threads of the screw are so 
 small, that a whole revolution of the graduated circle carries the 
 thread to or from its parallel thread by a very small space ; and as 
 we have supposed 100 divisions on the circle, and as the gradua- 
 tions of this latter are so distant that the position of a fixed index 
 may be read on the circle within a quarter of a division, we have 
 thus the four-hundredth part of the effect of a whole revolution 
 easily ascertainable. We might suppose the other wire moved by a 
 screw at the other end, but this is not necessary. We can now 
 easily see that one wire may be made to cover one star, (which is 
 very easily continued if the instrument be carried by clock work* 
 at the same rate as the heavens,) and the movable wire may then 
 be adjusted to cover another star, both being in the field together. 
 The observation is then made, and is to be read off. See how 
 many revolutions, and parts of revolutions will bring the movable 
 wire home to the fixed wire : the distance of the two stars is then 
 known in terms of the divisions of the micrometer. 
 
 The question now is, what do the divisions of the micrometer 
 stand for? If the artist attempted to construct the instrument so 
 that each revolution of the screw should answer exactly, say to 20 
 seconds of distance, he would certainly lose his labour. Screw- 
 cutting is in a very high state of perfection, all things considered, 
 but the errors of the screw are, of course, magnified in the tele- 
 scope, perhaps 250 times. The artist can cut the divisions of the 
 screw sufficiently near to equality with each other, but cannot de- 
 termine with sufficient nearness how many seconds of space in a 
 given telescope will answer to each revolution. The observer, 
 therefore, being only furnished with an instrument, each division of 
 which means something, must find out from the heavens what that 
 
 * An equatorial telescope is an awkward instrument if the hands must be continually 
 employed in keeping the star in the field. Clock-work is uow made at a cheap rate, 
 when compared with the price of a good telescope. 
 
96 EXPLANATION OF MAPS OF THE STARS. 
 
 something is. And this notion of an astronomical instrument, so 
 different from the common one, namely, that it is an awkward mass 
 of wood, glass, &c., which must be taught by one star what to say 
 of another, will be here easily illustrated. The fundamental unit 
 of measurement throughout astronomy is the diurnal revolution, 
 which is made to be 24 hours. If a star be exactly in the equator, 
 every second of this 24 hours (page 27) answers to 15 seconds 
 of space. The observer separates the wires by (say) exactly 10 
 revolutions of the screw, and putting the telescope upon a star in 
 the equator, (if not, a correction must be applied, which is not 
 here to be considered,) he finds that the star takes 22^- seconds by 
 a sidereal clock to move from one wire to the other, or 22 s -5, an- 
 swering to 15 times as many seconds of space, or to 337" 5. The 
 tenth part of this, or 33" -75, is the value of each revolution of the 
 screw, and the hundredth part of this, or 0"*3375, is the value of 
 each of the hundred graduations. A common clock or watch 
 will here be sufficient ; but even without this, he may measure the 
 diameter of the sun on the meridian, at which time the diameter in 
 question is given in the Nautical Almanac (predicted). Suppose, 
 for instance, he finds it to be 60 revolutions, and 12 of the divisions 
 of a revolution, or 6012 divisions ; and that the Nautical Almanac 
 gives 31' 56" for the diameter of the sun, or 1916". Then 1916, 
 divided by 6012, gives 0"-3186 for each division, or 3 1" -86 for 
 each revolution. 
 
 By such a rough description, it may be imagined that an indi- 
 vidual with leisure to follow his own views, some means of pro- 
 viding instruments, and a moderate zeal for the prosecution of 
 details, need not be deterred by any idea of difficulty from endea- 
 vouring to be of use in practical astronomy. We now proceed with 
 the subject of double stars. 
 
 It was observed by Sir W. Herschel that some of these double 
 stars revolved slowly round each other, by measuring what is called 
 their angle of position, that is, the angle made with the meridian, 
 by the line joining the stars, which, were there no rotation, ought 
 to remain always the same. In 1803, Sir W. Herschel announced 
 to the Royal Society the motions of 7 Leonis, e Bootis, Her- 
 culis, S Serpentis, and 7 Virginis, all of which have been subse- 
 
EXPLANATION OF MAPS OF THE STARS. 97 
 
 quently confirmed. Many hundreds of stars have since been added 
 to the list ; every accession of power to the telescope separates new 
 single stars into double stars, and there is no denying the possibility 
 of every star in the heavens being double, though it is a strong cir- 
 cumstance in favour of single stars, that our own sun appears to be 
 one. Forcible as are the presumptions that every double star is a 
 connected system, and not a result of the position of the line of 
 junction, it is yet proper to distinguish between stars which are 
 proved to be connected, and those which are not (as yet). The 
 latter are therefore simply called double stars, and the former binary 
 stars, or more properly binary systems. It is found by observation 
 that certain double stars revolve round each other, and it was natu- 
 rally the first inquiry, whether they revolved round each other 
 according to the same laws as our planets round the sun, or satel- 
 lites round their primaries. The method of testing any astro- 
 nomical theory, is to assume it, and deduce its consequences, and 
 then to see whether those consequences are written in the heavens. 
 This method is completely misunderstood by almost all the various 
 speculators who have tried to overthrow the Newtonian system. 
 They seem to imagine for the most part that Newton reasoned as 
 follows : if such and such attractive forces exist, certain motions 
 must ensue ; but those specified motions are found to exist, there- 
 fore the attractions laid down must exist also. This would not be 
 good reasoning ; for the only deducible result is, that there is a 
 consequent probability in favour of attraction. The real state of 
 the case is contained in the 4 following demonstrated propositions. 
 1. That bodies on the earth are pulled towards the earth by a force 
 to which the name of attraction is given; 2. That this does not 
 depend upon the air, since it holds of bodies in an exhausted re- 
 ceiver ; 3. That detached portions of matter attract each other on 
 the earth* ; 4. That all the motions of the solar system do take 
 place just as, it can be shown, they would take place if all matter 
 attracted all other matter according to the Newtonian law. All 
 these propositions are demonstrable and demonstrated : it is a 
 question for the mind of the reader, how far it is likely that the 
 
 * Proved by Maskelync's and CaYendish's experiment. See PENNY CYCL., article 
 ATTRACTION. 
 
 H 
 
98 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 first three should be true, and the last also from any other cause 
 except attraction. 
 
 To carry this inquiry as far as the fixed stars, it is necessary that 
 the consequences of the Newtonian law should be deduced and 
 compared with observation. The only difficulty is one which the 
 mathematician does not feel, but which must strike a reader with 
 some force who reflects on these things with an elementary know- 
 ledge of mathematics. All the celestial spaces are to us nothing 
 but projections on a sphere in the manner described in p. 3. Thus 
 the distance between two stars does not depend upon their real dis- 
 tance only, but also upon the degree of obliquity under which that 
 distance is seen : and if one star revolve round another, it is very 
 obvious that we do not see the real orbit, but the projection of the 
 real orbit upon the sphere. Now this appears at first sight to be 
 only the change of one orbit into another: what we want to make 
 apparent is, that it will be a change into an orbit described accord- 
 ing to laws quite different from those observed in the solar system, 
 so that if the foreshor tening of the real orbit were neglected, it might 
 be inferred that the theory of mutual attraction does not hold of 
 binary systems as a sufficient explanation of observed phenomena. 
 
 Let S be one of the stars, and let A B C D be the real orbit in 
 which the other moves relatively to it ; but let its obliquity to the 
 sphere be such, that it is foreshortened into abed. Supposing the 
 orbit to be an ellipse of which S is the focus, it follows as a neces- 
 sary consequence of S constantly attracting the other star, that 
 equal areas must be described in equal times ; that if A B C D 
 be the positions of the second star relatively to the first, at any 
 equal intervals of time, then A S B, B S C, and C S D must be areas 
 
EXPLANATION OF MAPS OF THE STARS. 99 
 
 of equal extent. Now this proposition is practically true for the 
 projected orbit, owing to the angle under which it is seen being so 
 small, that any line drawn to a point in it from the earth may be 
 considered as at right angles to its plane, so that the projection is 
 in truth orthographic, as described in page 52. And it is a pro- 
 perty of the orthographic projection, that areas equal to each other, 
 being parts of the same plane, are projected into other areas differ- 
 ing from the first, but still equal to each other. Consequently, 
 equal areas appear to be described in equal times in the projected 
 orbit, which, therefore, in this particular feature, presents no mark 
 of distinction from the real one. 
 
 Again, the projected orbit is an ellipse, as well as the real orbit. 
 How then, having ascertained the apparent orbit, are we to know 
 whether it is not the real orbit ? How can we proceed to determine 
 the real truth of the probable fact, that the orbits of double stars 
 are not all so arranged that the eye views them without any obli- 
 quity ? The truth is, that though the apparent orbits are ellipses, 
 and described so that equal areas are passed over in equal times, 
 yet the point about ivhich equal areas are described in equal times is 
 not the focus of the ellipse. This is the effect of the projection or 
 foreshortening, and so far as alteration of Kepler's laws is in ques- 
 tion, the only effect. Consequently, it must be ascertained in what 
 position, if any, an actual orbit can be placed, which being itself so 
 posited as to be among the possible originals of the apparent orbit, 
 may have the star in its focus which has been considered as the 
 primary. This difficulty, which is a purely mathematical one, is 
 introduced and overcome ; the result is, that orbits are found obey- 
 ing in every respect the laws of Kepler and therefore assimilating 
 the relative motions of binary systems to those of our sun and 
 planets, and agreeing better with the observations than the obser- 
 vations agree with each other. For it must be observed that the 
 measurement of the angles of position, or angles made by the line 
 of junction of the stars with the meridian, is a very rough and in- 
 exact kind of observation, and a difference of five or six degrees 
 will sometimes be found in the individual measures out of suc- 
 cessive sets taken nearly at the same time. But when the angles 
 of position, as they should be if the deduced orbit were perfectly 
 
 H2 
 
100 EXPLANATION OF MAPS OF THK STARS. 
 
 correct, are compared with those which actually have been observed 
 the differences are found to be mostly under one degree, and very 
 seldom above two. The methods by which a mass of conflicting 
 observations, made discrepant by instrumental and personal errors,, 
 have been thus made to give conglomerate results according with 
 Kepler's laws to a greater degree than could fairly have been ex- 
 pected from the appearance of the observations themselves, are due 
 to Sir J. Herschel ; who, in a paper published in the fifth volume 
 of the Mem. Astron. Soc., has deduced from his own observations 
 and those of others*, the elements of the orbits of y Virginis, Castor, 
 a Corona?, Ursa? Majoris, and 70 Ophiuchi ; and in a subsequent 
 paper, in the sixth volume, Bootis, and 75 Coronse are added, with 
 a new determination of y Virginis. There can be nothing con- 
 nected with astronomy of more interest to a general reader, than to 
 see the various steps by which a process is passing through its 
 rough stages, before an uninteresting degree of accuracy is attained. 
 Nobody but a mathematician can sympathize with the director of 
 an observatory, using all his efforts of body and mind, so to improve 
 the lunar theory as to abolish the second of time (or thereabouts) 
 by which she will not t come on the meridian according to pre- 
 diction. But a second in the lunar theory, answers to five years in 
 that of y Virginis, belonging to a department in which from the 
 nature of the case observations are so rough, that instead of cal- 
 
 * The observers who have forwarded this, the most interesting addition to the phe- 
 nomena of astronomy since the time of Galileo, are (in alphabetical order, and the living 
 with their titles) Professor Amici, M. Bessel, Bradley, Rev. W. R. Dawes, W. Herschel, 
 Sir J. Herschel, Maskelyne, Mayer, Pound, Captain Smyth, R.N., Sir J. South, Pro- 
 fessor Struve. 
 
 f The following supposed dialogue between two astronomers is not exaggerated: 
 
 A. Have you seen the volume of observations for this year? 
 
 B. No, but I am told the moon is very much out. 
 
 A. Yes, indeed, almost two seconds in one place. 
 
 B. The small planets altogether wrong, as usual, I suppose ? 
 
 A. Yes, Pallas is out nineteen seconds ! however, some of that is in the epoch. 
 
 B. I wonder whether we shall ever know anything at all about those small planets, 
 &c.? 
 
 This will serve the reader to adjust his notions, when he hears, in one point of view, 
 that modern astronomy is very correct, and in another that it is all wrong. The first 
 looks to what has been obtained ; the second to what remains to be done. 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 101 
 
 culating different portions of the area of an ellipse, it is as much as 
 the data are worth to cut out parts of a paper ellipse, and compare 
 their weights. The following approximations (first and second 
 already alluded to) will show the state of this class of observations. 
 The second is derived from the addition of a large number of new 
 observations, and exhibits that degree of similarity which at once 
 proves that much has been done, and much remains to do. 
 
 Major Semiaxis 
 Eccentricity 
 Perihelion projected 
 Perihelion from node 
 Inclination to plane 
 Node 
 
 Period in tropical years 
 Mean annual motion 
 Perihelion passage, A.D. 
 
 Of the stars mentioned in the preceding list, the approximate 
 elements of the real orbits are as follow : 
 
 Orbit of y Virginis. 
 
 
 First Result. 
 
 Second Result. 
 
 
 . 11" -830 
 
 12"-OSO 
 
 , 
 
 88717 
 
 8335 
 
 
 17 51' 
 
 36 40' 
 
 on 
 
 the orbit . not given 
 
 282 21' 
 
 ftl 
 
 ic heaven . 67 59' 
 
 67 2' 
 
 . 
 
 . 87 50' 
 
 97 23' 
 
 rs 
 
 513-28 
 
 628-90 
 
 
 . 70137 
 
 57242 
 
 .D. 
 
 1834-01 
 
 1834-63 
 
 Star. 
 
 y Yirginis 
 Castor 
 <y Coronse 
 Ursse Maj. 
 70 Ophiuchi 
 % Bootis 
 fi Coronse 
 
 Revolution 
 in years. 
 
 629 
 253 
 
 . 287 
 
 . 61 
 
 . 80 
 117 
 
 Major 
 Semiaxis. 
 
 Eccentricity. 
 
 8335 
 
 Inclination 
 to the 
 projected 
 orbit. 
 
 67 2' 
 
 7582 
 
 70 3' 
 
 6113 
 
 41 15' 
 
 3777 
 
 56 6' 
 
 4667 
 
 48 5' 
 
 5937 
 
 80 5' 
 
 2603 
 
 37 24' 
 
 12" -090 
 
 8" -086 
 
 3" -679 
 
 3" -278 
 
 4" -392 
 12" -560 
 0"-8325 
 
 Cancri is suspected to revolve in an orbit nearly circular, in 
 about fifty-five years. Sir J. Herschel has remarked, with con- 
 siderable probability, that these orbits seem rather cometary than 
 planetary, that is elongated, not nearly circular, oval forms. The 
 last star, 73 Coronse, is the principal triumph of Sir W. Herschel's 
 prediction. It has actually ''completed upwards of a revolution 
 since it was first observed ; and the greatest distance of the two 
 
102 EXPLANATION OF MAPS OF THE STARS. 
 
 stars falls below what was once supposed would ever be matter of 
 observation. 
 
 It must be observed that either star may be taken as fixed : the 
 relative orbit of each round the other being the same for both. 
 Some double stars have, at the same time, proper motion common 
 to both, (which is another proof of connexion,) and thus exhibit 
 the phenomenon of a system in a state of translation through space, 
 which we must, more or less, believe to be the case in our own. 
 Though it may not be directly in our way, we shall take notice of a 
 very remarkable addition, which our present knowledge of the 
 motions of double stars makes to an argument of ancient standing. 
 The practice of making some resemblances the grounds of sus- 
 pecting others, is as old as any attempt to reason, and is justifiable 
 to a certain extent, depending upon the number of resemblances 
 which have been observed. The sun is a mass of matter which 
 gives light ; so far it resembles the stars. But of the sun we know 
 further, that its light and heat are essential to the preservation of an 
 immense organized system, which could not exist without them. The 
 inference has then been drawn, not without probability, that the 
 stars are of the same service to other systems. On the other hand, 
 there have been those who find the use of the stars as subservient 
 to the wants of men, and whose minds do not feel any necessity for 
 further supposition as to the use of their existence. To them it 
 must at least be conceded that their argument is to the point : and 
 that if it be impossible to disbelieve, consistently with all our ter- 
 restrial experience, in the utility for some purpose or other of all that 
 exists, it is incumbent on us, on the other hand, to admit a degree of 
 utility in navigation and geography to the fixed stars, which may 
 justify those who can do so, in refraining from further attempts to 
 create uses from their own imaginations. Nor does it in the least 
 touch this argument that the stars are not all useful, for the same 
 applies to all the products of the earth which have not yet been 
 obtained, to most of the minerals of India for instance; or that the 
 advantages of them are in many instances of comparatively late 
 discovery, for this applies equally to iron considered as the material 
 of a rail-road. But the knowledge which has been lately added to 
 our stock on the subject of double stars, presents an entirely new 
 
EXPLANATION OF MAPS OF THE STARS. 
 
 103 
 
 method of viewing the subject. In our own system we see that the 
 laws under which the planets revolve round the sun are conducive 
 to the maintenance of their existence, and something of the manner 
 in which this is effected. If the motion of the earth were stopped,, 
 nothing would hinder its falling into the sun with a shock which 
 would disorganize the whole, even supposing that life and vegetation 
 could exist up to that moment, under the continually increasing 
 heat and light. Now in the relative motions of the double stars, we 
 see the same method of preventing a mutual shock ; for what pur- 
 pose ? for our geography or navigation ? This is excessively diffi- 
 cult to be supposed of double stars, which are less than a second of 
 apparent diameter apart. The argument in favour of organization in 
 the celestial bodies is very much increased in probability by the 
 discovery of a species of relation which makes a direct provision 
 that, under actually existing laws, one shall not become dangerous 
 to the maintenance of the state of another. 
 
 Among the phenomena which have been observed of binary 
 systems or double stars, one of the most remarkable is their differ- 
 ence of colour, the colour of one being usually near one end of the 
 prismatic spectrum, arid that of the second from the other, the 
 larger being most frequently nearer to the red, and the smaller to 
 the violet. There is an infinite number of varieties of colour among 
 the heavenly bodies ; but so far as can be ascertained, there is no 
 distinction between the optical properties of the light of one star 
 and of another, except that which also belongs to the same differ- 
 ences of colour in terrestriaj objects. 
 
 We shall finish by some notice of the nebula or nebulous bodies, 
 as they are called. The first and great nebula of our heaven 
 is the milky way, extending all round the sphere in the manner 
 pointed out in the maps. Of this phenomenon it is to be remarked, 
 that the nearer we turn our eyes to it, the more do the smaller stars 
 multiply and crowd together. And the milky way is found by 
 powerful telescopes to be itself an enormous collection of minute 
 stars, each yielding too little light to be separately visible, but con- 
 veying altogether the faint impression from which the name is de- 
 rived. The inference drawn is, that we are situated in an immense 
 stratum of stars, the length and breadth of which is very many 
 
104 EXPLANATION OF MAPS OF THE STARS. 
 
 times greater than its thickness, so that when we look through the 
 thin part, \ve see stars in sufficient number ; but when we look along 
 the stratum, we see smaller and smaller stars, more thickly placed 
 than before, and terminating in those which are so distant that their 
 united effect is that of a mere cloud. This was the opinion, or if it 
 be considered as perfectly established, the discovery, of Sir William 
 Herschel, and it opens a wide field of reasonable speculation. For 
 besides the milky way, the heavens are found to be covered with 
 minute patches of light, more or less thickly scattered in every part. 
 These differ from stars in being of finite magnitude; some of them 
 are visible to the naked eye on clear nights. Some, in a telescope, 
 are found to consist of clusters of stars ; in some, the uniformity of 
 appearance under a low power is changed by a higher into that of 
 a varied scene of lights of different degrees of intensity. The pre- 
 sumption is, that every such nebula is & partial universe of itself : 
 that is, composed of a number of stars so great and so distant from 
 our cluster, that the latter would appear from any nebula in some 
 such form as the nebula appears to us. This is, of course, a mere 
 presumption, similar to those which have been already noticed ; but 
 it possesses a degree of probability with which no other hypothesis 
 can compete at present. The number of forms which nebulre 
 assume, and the various appearances which they present in the 
 telescope, it is out of the question to attempt describing. The 
 writings of Sir W. and Sir J. Herschel contain almost all that is 
 known on the subject. The catalogue of the latter, printed in the 
 Phil. Trans, for 1833, contains a list of 2306 such objects visible 
 at Slough : and his journey to the Cape of Good Hope is under- 
 stood to have for one principal object the extension of this list to 
 all the nebulae in the lower part of the southern hemisphere. On 
 this subject* " he is somewhat, surprised at the extraordinary pau- 
 city of close double stars, which cannot arise from want of power 
 in the telescope, or from the nature of the climate : for he con- 
 siders his mirrors as perfect as it is possible to make them ; and 
 he represents the beauty and tranquillity of the climate to be such 
 that the stars are reduced to all but mathematical points, and 
 
 * Ast. Soc. Monthly Notice, Dec., 1835. 
 
EXPLANATION OF MAPS OF THE STARS. 105 
 
 allow of their being viewed like objects under a microscope. But 
 although the number of double stars is so small, considering the rich- 
 ness of the southern heavens in stars, yet he represents the nebulae 
 as very copious, and has accordingly collected a numerous list, &c." 
 
 Nobody can well describe nebulae who is not in the habit of 
 seeing them ; and for this reason we recommend the work on astro- 
 nomy already cited, independently of other merits. The following 
 descriptions of a few objects are taken from the list of nebulae men- 
 tioned above (Phil. Trans. 1833). In interest they will be worth 
 more than any abstract : 
 
 No. 1622. R.A. 13 h 22 m 39* N.P.D. 41 56' 
 
 " This very singular object is thus described by Messier : ' Nebu- 
 " ' leuse sans etoiles.' ' On ne pent la voir que difficilement avec 
 "' une lunette ordinaire de 3^ pieds. Elle est double, ayant cha- 
 "'cuneun centre brillant eloigne 1'un de 1'autre de 4' 35". Les 
 " ' deux atmospheres se touchent.' By this description it is evident 
 " that the peculiar phenomena of the nebulous ring which encircles 
 " the central nucleus had escaped his observation, as might have 
 " been expected from the inferior light of his telescopes. My father 
 " describes it in his observations of Messier's nebulae, (which are not 
 " included in his catalogues,) as a bright round nebula, surrounded 
 " with a halo or glory at a distance from it, and accompanied by a 
 " companion ; but I do not find that the partial subdivision of the 
 <( ring into two branches throughout its south following limb was 
 " noticed by him. This is, however, one of its most remarkable and 
 " interesting features. Supposing it to consist of stars, the appear- 
 " ance it would present to a spectator placed on a planet attendant 
 " on one of them, excentrically situated towards the north preceding 
 " quarter of the central mass, would be exactly similar to that of our 
 " milky way, traversing in a manner precisely analogous the firma- 
 " ment of large stars, into which the central cluster would be seen 
 " projected, and (owing to its greater distance) appearing, like it, to 
 " consist of stars much smaller than those in other parts of the hea- 
 " vens. Can it then be that we have here a real brother system, 
 '* bearing a real physical resemblance and strong analogy of structure 
 " to our own ? The elliptic form of the inner subdivided portion 
 " indicates with extreme probability an elevation of that portion above 
 
106 EXPLANATION OF MAPS OF THE STARS. 
 
 "the plane of the rest, so that the real form must be that of a ring 
 "split through half its circumference,, and having the split portions 
 " set asunder at about an angle of 45 each to the plane of the other." 
 
 No. 2060. R.A. 19 h 52 m 12 s N.P.D. 67 44' 
 
 " In my father's observations the true form, (like that of a double- 
 " headed shot or dumb-bell,) was of course distinctly perceived, and 
 " the small stars it contains are noticed, and taken as an indication 
 " of its resolvibility. I incline, however, to the opinion of their being 
 " accidental stars, (of which multitudes exist in the surrounding re- 
 " gion). But here, as in the former object, the feature which gives a 
 "peculiar interest to the whole nebula, and alters entirely the light in 
 "which its physical constitution must be considered, has been hitherto 
 "overlooked, I mean the faint nebulosity which fills in the lateral 
 " concavities of the body, and converts them, in fact, into protuber- 
 " ances, so as to render the general outline of the whole nebula a 
 "regular ellipse, having for its shorter axis the common axis of the 
 " two bright masses of which the body consists, that is to say, the 
 " longer axis of the oval form under which it was imperfectly seen 
 " by Messier." 
 
 No. 218. R.A. 2 h ll m 58 s N.P.D. 48 25' 
 
 " An extraordinary object. It is of the last degree of faintness, 
 "and may very well be unperceived though full in the field of view. 
 "There can hardly be a doubt of its being a thin flat ring, of enor- 
 " mous dimensions, seen very obliquely." 
 
 The observations of nebulae must be principally interesting on 
 account of the slow changes which appear to be taking place in 
 them. But to the private observer they must be considered, in con- 
 junction with double stars, as affording a valuable means of trying 
 the power of his telescope, and the state of the weather for ob- 
 serving. They may be ranged in classes according to the difficulty 
 of perceiving them, and thus the possessor of a telescope may deter- 
 mine the rank his instrument is entitled to hold. For the very dif- 
 ferent accounts given by observers of the performance of object- 
 glasses, when compared with their stated dimensions, and such 
 other circumstances as to all appearance should give superiority or 
 inferiority, must lead us to conclude that each such glass is an in- 
 strument by itself, not, altogether at least, to be considered as one 
 
EXPLANATION OF MAPS OF THE STARS. 107 
 
 of a class. Such a list, under the title of " A List of Test Objects," 
 was communicated by Sir J. Herschel to the Astronomical Society, 
 and is published in the eighth volume of their memoirs. By per- 
 mission of the Council of that Society, it is republished at the end 
 of this treatise. The references to the catalogues, &c., which serve 
 as the names of the stars, hardly need explanation, since by the 
 approximate right ascensions and north polar distances, the places 
 of the several objects may be found in the maps. (2, Struve ; 
 H, W. Herschel ; h, J. Herschel.) 
 
 We shall finish the chapter with an account of the selection of 
 objects which have been made in the maps. 
 
 The stars in PiazzPs, Bradley's, and Lacaille's catalogues have 
 been chosen, and all those of Flamsteed (Mr. Baily's edition) are 
 included. 
 
 Piazzi's catalogue, published in 1814, contains 7646 stars, all 
 which are inserted in the maps. 
 
 Bradley's stars are taken from the catalogue in Bessel's Funda- 
 menta Astronomice, published in 1818 (the only place in which the 
 results of Bradley's Astronomy exist in a reduced form : see PENNY 
 CYCLOPEDIA, article BRADLEY). 
 
 There are 3222 stars in this catalogue, of which only 216 are 
 not in Piazzi ; all these are inserted in the maps, but are without a 
 reference. Lacaille's Ccelum Australe Stelliferum was published in 
 1763 ; it contains observations of 10,035 stars, of which J942 are 
 formed into a reduced catalogue, all of which are in the maps. 
 
 Piazzi's and Bradley's stars were reduced to the epoch, 1840, by 
 the quantities given in each catalogue; but those of Lacaille were 
 brought up graphically, by moving them, in longitude only, on the 
 maps. 
 
 Lacaille is the authority for the southern hemisphere ; but since 
 the time Nvhen these maps were constructed, a catalogue of 606 
 southern stars has been printed by the East India Company, de- 
 duced by Lieutenant Johnson*, late of the St. Helena Artillery, 
 
 * This catalogue obtained the gold medal of the Astronomical Society, and though 
 the instruments employed were not of the very first description, it was asserted by the 
 committee appointed to examine it, to be capable of vying with those which have 
 issued from the first-rate observatories of Europe. 
 
108 EXPLANATION OF MAPS OF THE STARS. 
 
 from his observations while in charge of the observatory in that 
 island. The difference between the stars' places as given by 
 Lieutenant Johnson and by Lacaille, is not sufficient to be visible 
 in the maps ; but the following new stars, which appear to have 
 been observed by the former only*, are here given, with their 
 numbers in the new catalogue, their magnitudes, right ascensions 
 and declinations for the year 1830 : 
 
 Number in Johnson's 
 
 Catalogue, and name Dec. 1830. 
 
 of constellation. Mag. R.A. 1830. South. 
 
 5 Octans 6 O h 15 ra s 89 18' 32"-0 
 
 327 Octans 7^ 14 13 33,00 87 25 35-9 
 
 388 Octans 6i 15 59 39,70 86 4-7 
 
 395 Norma 5 16 6 49 38 1-1 
 
 423 Octans 6 16 55 6,76 89 14 59-4 
 
 433 Octans 6 17 14 54,90 87 37 12-8 
 
 496 Octans 7 19 26 16,40 89 34 0-8 
 
 549 Octans 6 21 56 10,00 86 49 8-8 
 
 553 Grus 5 22 5 42 11 1-8 
 
 578 Octans 6 22 57 40,30 88 24 38-2 
 
 Flamsteed's number has always been preferred, where it exists, 
 and appears in large print ; Lacaille's number has one line; and 
 that of Hevelius has two lines drawn under it ; that of Piazzi, 
 where it is the distinction of the star, is in small Italic numerals. 
 All Mr. Baily's corrections in his valuable edition of Flamsteed's 
 Catalogue, recently published, have been attended to as to Bayer's 
 letters and Flamsteed's numerals. The former were arranged by 
 Bayer, so that the order of the letters might also be that of the mag- 
 nitudes of the stars ; the latter were attached to the stars in order 
 of right ascension. The stars marked double are taken from Sir 
 W. Herschel's Papers in the Philosophical Transactions for 1782 
 and 1785, and from Struve's Large Catalogue, the Dorpat Cata- 
 logue, as it is frequently termed, published in 1827. Piazzi has 
 separated many of the double stars, and given the positions of both. 
 Where the scale will allow, the two stars are laid down, and Piazzi's 
 numbers given. All Sir W. Herschel's Nebula? (which include 
 
 * They do not appear in the Astronomical Society's Catalogue, nor in Lacaille. 
 
EXPLANATION OF MAPS OF THE STARS. 109 
 
 Messier's,) are laid down with the numbers and classes affixed, 
 namely, 1000 from Phil Trans. 1786 ; 1000 from do. do. 1789 ; 
 and 500 from do. do. 1802 ; 500 are added from Sir J. Herschel's 
 Catalogue already quoted ; and 629 in the southern hemisphere 
 are taken from Mr. Dunlop's Paper in the Philosophical Trans- 
 actions for 1828. From the latter source the Nubecula major and 
 minor are laid down. Sir W. Herschel's nebulae have numbers 
 and classes (for instances, 23. vin.) ; those of Sir J. Herschel have 
 no classes, but have the larger numbering ; while those of Mr. 
 Dunlop are in small print. 
 
 All these stars, as before stated, are reduced to the year 1840, that 
 is, are in the position in which they will be in the year'1840. To 
 form a notion of the way in which precession will appear to carry a 
 star, look at the nearest parallel of latitude, and imagine the star to 
 move parallel to it, in the order of the signs, at the rate of a degree 
 in seventy-two years. The position of the parallel of latitude will 
 enable the reader to estimate whether the motion is greatest in right 
 ascension or in declination. 
 
 The stars which have proper motion are denoted by an arrow an- 
 nexed, which points out the direction of the motion, and gives a 
 notion whether it is great or small. To gain a better idea, look at 
 some of the stars in the preceding list (page 89). 
 
APPENDIX*. 
 
 WITHIN the last few years, the examination and measurement of 
 double stars has been prosecuted with great, activity. We propose 
 to give a slight sketch of the methods hitherto most successfully 
 adopted in measuring double starsf , both on account of the intrinsic 
 value of this branch of astronomical inquiry., and because it is not 
 included in many of the ordinary treatises, though peculiarly within 
 the reach of private observers. The measurement of a double 
 star is the determination of the position of one of the stars with 
 regard to the other,, (assuming the larger as a fixed point,) so as to 
 be able to distinguish and define any change of position between 
 them. At first this was done by noting the differences of right as- 
 cension and declination as the stars passed over the meridian : but 
 the difficulty of observing the difference of right ascension made 
 this (in most cases) an exceedingly inaccurate method. Sir W. 
 Herschel introduced another and much more accurate mode of ob- 
 servation. Placing a wire in the focus of his eye-piece, he turned 
 the eye-piece round until the wire was parallel to the line passing 
 through the centres of the two stars, when they might be threaded 
 as it were in the same moment. Hence, the position of the same 
 wire when perpendicular to the meridian being knownj, the angle 
 between the two positions o/ the wire, which gives the angle which 
 the line joining the stars makes with the parallel of daily motion, 
 was also known. This is Sir William's angle of position, and by 
 the further distinction of preceding or following, north or south, he 
 fixed the situation of the smaller star with respect to the larger 
 without ambiguity. The distance between the stars was at first 
 
 * For this Appendix the author is indebted to his friend the Rev. R. Sheepshanks. 
 
 } The observation of nebula; requires so much light, that only telescopes of the 
 largest aperture can be usefully employed in the pursuit. It is to the two Herschels 
 that science is indebted for almost every thing which is positively and correctly known 
 in this department of astronomy, which, with the researches as to double stars, may 
 be called the Herschelian branch of Astronomy. 
 
 J Simply by turning the eye-piece until one of the stars runs along the wire, 
 
112 
 
 EXPLANATION OF MAPS OF THE STARS. 
 
 estimated in diameters and parts of the larger stars, but afterwards 
 a very ingenious apparatus was used, in which two small moveable 
 lamps were made to subtend in one of the observer's eyes the same 
 angle which the magnified stars did in the other. The distance of 
 the lamps from each other, and from the observer, together with 
 the magnifying power of the telescope, supply sufficient data for 
 determining the distance between the stars. With such imperfect, 
 or rather with such inconvenient means, (for the results are won- 
 derfully accurate,) Sir W. Herschel formed his catalogues of double 
 stars ; and by a comparison between the measures of the same 
 stars (especially of the angles of position) made at considerable 
 intervals, ascertained the fact that double stars are in many in- 
 stances a connected system. 
 
 The discoveries and measurements of Sir W. Herschel were made 
 wholly with reflecting telescopes, mounted so as to move with free- 
 dom vertically and sometimes horizontally : subsequent observers 
 have for the most part employed refractors mounted equatorially*, 
 and the position wire micrometer. When the telescope of an 
 equatorial is pointed on a star, one motion, viz., that of the whole 
 instrument round its axis, with a velocity equal to the apparent 
 motion of the heavens, will keep the star perpetually in the field 
 of view. This motion may be given by one hand turning a handle 
 with a Hook's joint, which works the tangent screw of the hour 
 circle, or still better, by clock-work. The position micrometer, in 
 its newest and best construction, is of this form : 
 
 Fig. 1. Position Wire Micrometer. 
 
 Field of View, fig 2. 
 C' B C 
 
 * '. e. a telescope carried on an axis which is parallel lo the axis of the earth, and 
 hence sometimes called a pctrallactic instrument. 
 
APPENDIX. 
 
 113 
 
 Each of the large exterior divided heads of Fig. 1 is fixed upon a 
 screw, which by its revolution carries one of the spider-web lines 
 B b, C c, Fig. 2, in a parallel direction. The small milled-head 
 screw, which works on an interior toothed wheel, turns the whole 
 system round in the direction of the arrow, or reversely. The ob- 
 servation is made thus : the telescope being set upon the stars, and 
 clamped in declination, is kept upon them by working a handle 
 and Hook's joint ; the small milled-head is turned round until the 
 spider-line, A a, is parallel to the line joining the centres of the 
 stars, which with a little care it may be made to thread at the 
 same moment. The reading of the verniers*, if they have been pre- 
 viously adjusted, will now point out the angle of position of the 
 stars. Now since A a is in the direction of the stars, the lines B 6 
 and C c are perpendicular to that direction ; one of them, as B b, 
 is made to bisect one of the stars by moving the instrument by the 
 handle and Hook's joint ; while the other, C c, by turning the divided 
 head which carries it, is made to bisect the other star. The revo- 
 lutions and parts of the divided head between the coincidence of 
 the two wires and the bisection of the two stars will, with a know- 
 ledge of the scale f, give the distance. 
 
 Fig. 3. Sir W. Herschel. 
 
 Fig. 4. Sir J. Herschel. 
 
 Preceding 
 
 Following 
 
 270 
 
 North 
 
 * In the micrometer here represented, which is graduated according to Sir J. Her- 
 schel's recommendation, the divisions run from 0to 360, aud the verniers read 90 and 
 270, when the star, by its own motion, runs along the fixed wire. For Sir William's 
 nomenclature the circle should be divided into four quadrants, and the readings of the 
 verniers be each when the star runs along the fixed wire. To prevent mistakes, a dia- 
 gram of the stars should always be made at the time of observation. 
 
 f To obtain the value of the scale of the micrometer, set the two moveable wires apart 
 a certain number of revolutions, and place them in the direction of the meridian. Ob- 
 
 I 
 
114 EXPLANATION OF MAPS OF THE STARS. 
 
 Some modifications in this process have lately been introduced, 
 which we will now briefly mention. Sir William Herschel described 
 the position of the small star (see fig. 3, which shows the appear- 
 ance of a double star in an inverting telescope), as being to the 
 north or south, preceding or following the principal star. The 
 angles are reckoned from the parallel of daily motion, from to 
 the north or south point, each of which is marked 90. In the 
 figure, a, is a north following star ; 6, south following ; c, south pre- 
 ceding ; d, north preceding ; and the micrometers constructed for 
 this nomenclature are divided into four quadrants. As this mode of 
 reckoning is complex, and at times leads to errors, Sir J. Herschel 
 proposed in vol. iv. of the Royal Astron. Soc. Mem., p. 333, " to 
 commence the reading of the angle from the meridian at the north 
 point, and to continue it round in the direction nfsp n (north, fol- 
 lowing, south, preceding, north,) from to 360 : so that 1 cor- 
 responds to 89 n/; 91 to 1 */; 181 to 89 sp ; 271 to 1 np*." 
 This proposition has been universally adopted, at least in this 
 country (see Fig. 4, which is the apparent field of view graduated 
 according to Sir John Herschel. In this figure the angle of position 
 for a is about 30 ; for 6, 135 ; for c, 190 ; for d, 330). Another 
 simplification has been pointed out, we believe by Sir John Her- 
 schel (it has certainly been adopted successfully) : viz., to suppress 
 the fixed spider-line A a (Fig. 2) altogether, and to use the lines 
 B by C c, placed near each other, for determining the angle of posi- 
 tion. The micrometer is then adjusted when a star travels along 
 one of the wires, the instrument being at rest, and the verniers show 
 90 and 270. After this verification is made, or what is better 
 the error ascertained, to be hereafter applied as a correction, the 
 
 serve the transits of several stars of known declination over the wires ; then multiplying 
 each interval of seconds of time by 15. cosine of star's declination, and taking the mean, 
 you have the seconds of space which correspond to a known number of revolutions of 
 the screw. 
 
 * If h be the angle of position in Sir J. Herschel's system, and H that according to 
 Sir William's, then 
 
 h = 90 H in the north following quadrant 
 = 90 + H south 
 
 = 270 H in the south preceding quadrant 
 = 270 + H north 
 
APPENDIX. 115 
 
 wires are turned round by the small milled-head screw until the 
 stars are either threaded upon one of the wires, or, being between 
 them, are judged to be parallel to them. The verniers are now 
 read off for the angle of position. This observation is repeated 
 until the result is satisfactory, and then the verniers are turned by 
 the milled-head through 90, when the wires are in the proper 
 position for taking measures of distance. In this way the danger of 
 the wires B 6, C c touching A a, technically called fiddling, is 
 avoided, as well as the indistinctness which with high powers will 
 be found in one of three wires all at different distances * from the 
 eye-glass. There is, besides, the advantage of measuring the dis- 
 tance a little more certainly in the proper direction, and the opera- 
 tion is performed in less time. In measuring the distance of two 
 stars, after the wire B b has been placed upon one of the stars, 
 the larger for instance, and C c on the smaller, it is better to move 
 the whole instrument by the handle and Hook's joint until B b is 
 placed on the smaller, and to move C c by its divided head to a 
 position CY (see Fig. 2) to bisect the larger. The revolutions and 
 parts described by the divided head now give twice the distance of 
 the two stars, and any uncertainty about the zero reading is elimi- 
 natedf. If there be any doubt about the truth of the screws, CV 
 may now be considered to be the fixed wire, and B b the moveable 
 one, and thus the measure may be repeated^, in different parts of 
 each screw. 
 
 Hitherto we have spoken as if the whole instrument was to be 
 moved by the observer, by {land, so as to counteract the effect of the 
 
 * This may be obviated by pushing in or pulling out the eye-piece between the two 
 measures of position and distance ; but besides the trouble and loss of time, there is 
 some risk, if the eye-piece move stiffly, of deranging the apparatus. 
 
 f This zero is thus determined. The wire C c is brought to touch B b first on one 
 side and then on the other, and the mean of the readings of the micrometer head in 
 each position is the reading when the wires coincide. The difference of this reading 
 from is added to or subtracted from all the subsequent readings of C c, according 
 as the zero reading is backwards from or forwards, in the order of the graduation, just as 
 the index-error of a sextant. In this method, B b is a fixed wire. In the method re- 
 commended in the text, (it is due to Sir J. Herschel.) one of the readings of the micro- 
 meter is to be subtracted from the other, but this will cause no embarrassment to an 
 intelligent observer. 
 
 J The Germans call this micrometer the "repeating thread micrometer." 
 
 i2 
 
116 EXPLANATION OP MAPS OF THE STARS, 
 
 diurnal motion. Within the last few years, since the introduction 
 of large refracting telescopes, clock-work has been successfully em- 
 ployed, especially by the celebrated Fraunhofer. The essential 
 quality of a clock for carrying an equatorially mounted telescope, 
 is that it should move smoothly, and not be affected suddenly by 
 any alteration of friction, &c. Fraunhofer's clock is a train of 
 wheels driving an upright spindle on which two small balls are 
 hung. These expand outwards by the rotatory motion of the spindle 
 until they rub against a conical surface above them something 
 like an umbrella, the friction against which destroys the super- 
 abundant power of the clock, and brings it to a uniform motion. 
 There is a contrivance for raising or lowering the point on which 
 the spindle turns, and so regulating the clock to the velocity re- 
 quired. This clock answers very well, and is neither cumbrous 
 nor expensive. Another clock, on a similar principle, but on a 
 larger scale and with more powerful action, has been constructed 
 in this country by Messrs. Troughton and Simms. The upright 
 spindle in this case carries a regular governor, like that attached to 
 steam-engines, which by a double lever presses a powerful break 
 on a wheel attached to one of the arbors of the clock when the 
 balls are expanded to the proper distance*. In Fraunhofer's equa- 
 torials, the bisection of a star is effected by continual alterations 
 of the rate of the clock, by means of a long handle, which is exceed- 
 ingly inconvenient. In the apparatus of Messrs. Troughton and 
 Simms, the micrometer is fitted on a slipping -piece (see Fig. 5) 
 which again fixes on the end of the telescope. 
 
 By the two milled -head screws, a very delicate motion can be 
 given to the micrometer in any required direction, without rotatory 
 motion, so that the bisections which were heretofore performed by 
 moving the whole instrument, are now accomplished much more 
 satisfactorily by touching a screw close to the observer's hands. It 
 is desirable to have the slipping-piece and micrometer as light as is 
 consistent with necessary strength, and the screws of the slipping- 
 
 * For a description and figure of this clock, see the Abstracts of the Proceedings of 
 the Royal Astronomical Society, vol. iii. No. 6. It was subsequently attached to one of 
 the largest equatorials hitherto constructed, which it carried with great truth and 
 perfect smoothness. It is now in the possession of Charles Holford, Esq., F.R.A.S. 
 
APPENDIX. 117 
 
 piece should be very smooth and fine. When the apparatus is pro- 
 perly made, and the clock correctly rated, the observation of such 
 
 Fig. 5. Slipping-Piece. 
 
 double stars as the telescope will separate, is quite as easy as the 
 measurement of two dots on a sheet of paper. The only diffi- 
 culty left, is that of procuring a tangent screw to give motion to 
 the instrument with sufficient accuracy. 
 
 There are many minutiae connected with this subject which it 
 would be tedious to explain at length, though much of the con- 
 venience and comfort of observing depends on them. We will, 
 however, mention one very elegant improvement by the Astronomer 
 Royal in the construction of a splendid equatorial, lately presented 
 by the Duke of Northumberland to the University of Cambridge. 
 In this instrument, the hdur circle, which is carried by clock-work, 
 turns freely on the lower pivot of the polar axis, but can be clamped 
 at pleasure to the bottom frame of the axis which carries the ver- 
 niers or microscopes. If this hour circle be at first properly set, and 
 the clock made to go sidereal time, it is evident that the verniers 
 will show the right ascension of the star directly, without any arith- 
 metical operation whatever. 
 
 When the position-micrometer is used, it is absolutely necessary 
 that the telescope should move without any shake or jar (which is, 
 however, no difficulty since the introduction of clock-work) ; and it 
 is desirable that the mounting should be firm enough to fix a star 
 
118 EXPLANATION OF MAPS OF THE STARS. 
 
 within a few minutes*. If these requisites are obtained, and the 
 tube of the telescope be stiff enough to allow the observer to touch 
 the screws of the slipping-piece and micrometer without shaking, 
 the mounting is sufficient for the measurement of double stars. The 
 difficulty in managing large instruments arises from the mon- 
 strous increase of the moment of inertia, (which is parried by the 
 equable motion given by the clock,) and the tendency of the tele- 
 scope and frame to twist when pressure is applied to a longer lever, 
 viz., at the eye end of the telescope. 
 
 Another instrument for measuring double stars, which requires 
 less steadiness, has recently been most successfully used by Pro- 
 fessor Bessel, of Kb'nigsberg. This is a telescope of which the 
 object glass is cut in two by a plane passing through the diameters 
 of the lenses, and perpendicular to their surfaces. One half can 
 slide by the side of the other, and as each half gives a complete 
 image, a double star appears like four stars, which can be placed in 
 a right line (this gives the angle opposition), and at equal distances 
 (which gives the distance). The observations made by Bessel with 
 the heliometer, as it is called, are greatly superior in accuracy to 
 any other observations hitherto published. As the operation of 
 cutting an object glass in two is a somewhat hazardous one, and 
 the images formed by it never so perfect as those by an undivided 
 glass, it would perhaps be advisable to try what could be effected 
 by dividing one of the lenses of an eye-piece, which would give 
 double images, and might be applied to any telescope what- 
 ever. 
 
 Information on the subject of double stars and nebulae must be 
 gathered from various original memoirs. The following list con- 
 tains those which are most remarkable : 
 
 De Novis in Ccelo sidereo phanomenis Mannheim, 1779. (Chris- 
 tian Mayer.} 
 
 * Any considerable deviation or want of adjustment of the instrument will affect 
 angles of position observed far from the meridian. It must, however, be very large 
 to do any sensible injury; and if the flexure be nearly constant in the same position, 
 it may be allowed for. For the adjustments of the equatorial, see a Memoir by M. 
 Kriel, Mem. Ast. Soc. } vol. iv., p. 495 ; or the Abstracts of the Memoirs, vol. i., No. 29. 
 
APPENDIX. 119 
 
 Phil. Trans., vol. Ixxi., p. 492. Account of measurements of 
 position and distance, with a description of a position micro- 
 meter. (JV. Herschel.) 
 
 vol. Ixxii., p. 112. A catalogue of double stars (269 in 
 
 number). (W. Herschel.) 
 
 vol. Ixxii., p. 163. Description of lamp micrometer. 
 
 ". Herschel.) 
 
 vol. Ixxv., p. 40. Further catalogue of double stars 
 
 (434). (IV. Herschel.) 
 
 1804, p. 353. *Account of changes that have hap- 
 
 pened in the relative situation of double stars; ( W. Herschel.) 
 Mem. Ast. Soc., vol. i., p. 166. Catalogue of 145 new double 
 
 stars. ( W. Herschel.) 
 vol. iv., p. 165. Catalogue of 195 double stars, taken 
 
 from La Lande's Histoire Celeste. 
 Phil. Trans., 1824, Part 2. Catalogue of 380 double stars. 
 
 (J. Herschel and South.) 
 1826, Part If. Catalogue of 458 double stars, with a 
 
 synoptical view. (South.) 
 Mem. of Ast. Soc., vol. ii., p. 459. Observations made with a 
 
 twenty feet reflecting telescope. Descriptions and approximate 
 
 places of 321 double and triple stars. (/. Herschel.) 
 vol. iii., p. 47. Continuation of the above (295 stars). 
 
 (/. Herschel.) 
 
 vol. iii., p. 177. Do. third series (384 stars). (/. Her- 
 
 schel.) 
 
 vol. iv., p. 331. Do. fourth series (1236 stars). (/. Her- 
 
 schel.) 
 
 vol. iv., p. 1. Do. fifth series, with remarks (2007 
 
 stars). (J. Herschel.) 
 
 These five series are not to be considered accurate measures. 
 They are such double stars as were met with by Sir J. Herschel in 
 his sweeps for nebulae, &c. 
 
 Mem. Ast Soc., vol. v., p. 13. Micrometrical measures of 364 
 double stars, with a seven feet equatorial. (/. Herschel) 
 
 * Said to be a continuation of a paper in the vol. for 1803, p. 339, where however no 
 such paper appears, 
 f This paper contains many valuable notes and remarks by Sir J. Herschel. 
 
120 EXPLANATION OF MAPS OF THE STARS. 
 
 Mem. Ast. Soc., vol. v., p. 171*. On the investigation of the orbits 
 of double stars, being a supplement to a paper entitled ' Micro- 
 metrical Measures.' (/. Herschel.} 
 
 Mem. Camb. Phil. Soc., vol. iv., p. 425. Description of a machine 
 for resolving by inspection certain important forms, &c., of 
 transcendental equations. (/. HerscheL) 
 
 Mem. Ast r on. Soc., vol. vi., p. 149. Notice of the elliptic orbits of 
 % Bootis, y Virginis, n Coronse. (/. HerscheL) 
 
 vol. viii., p. 37. Second series of micrometrical mea- 
 surements. (/. HerscheL) 
 
 vol. iii., p. 257. Approximate places of double stars in 
 
 the southern hemisphere. (Dunlop.) 
 
 vol. \.j p. 135. Observations of the triple star Cancri. 
 
 (Dawes.) 
 
 vol. v., p. 139. Observations of double stars. (Dawes.} 
 
 vol. viii., p. 61. --Measurements of 121 double stars. 
 
 (Dawes .) 
 
 Sir J. Herschel is now at the Cape, measuring the double stars of 
 the southern hemisphere, and noting the nebulae. 
 Struve, Cataloyus novus stellarum duplicium (3112 stars). Dor- 
 
 pati, 1827. 
 
 ^stronomische Nachrichten, No. 240, vol. x., p. 392,, contains ob- 
 servations of thirty-nine double stars by Bessel, with a comparison 
 of his results with those of Struve. These are probably the best 
 results in distance yet published. Struve seems to have a constant 
 error of about 0"'3 in his distances, which are too small. Further 
 catalogues may be expected from Bessel and Struve. 
 
 NEBULA. 
 Connoissance des Terns, 1784. 100 nebulse by Messier, 3 by 
 
 Mechain. 
 Phil. Trans., vol. Ixxvi., p. 457. Catalogue of 1000 nebulae and 
 
 clusters. (W. Herschel) 
 
 * This is a description of the easiest, as well as the most elegant and accurate manner 
 of investigating the orbits of double stars, chiefly by a graphical method, which is appli- 
 cable, and indeed has been applied to many physical questions. The following memoir 
 is a sort of supplement to it. M. Savary and Professor Encke have solved the same 
 problem geometrically, but not with equal practical success. 
 
APPENDIX. 121 
 
 Phil. Trans., vol. Ixxix., p. 212. Catalogue of a second thousand 
 new nebulae and clusters, with remarks on the construction of 
 the heavens. (W. Herschel) 
 
 1802, p. 477. Catalogue of 500 new nebulae, nebulous 
 
 stars, planetary nebulae, clusters, with remarks on the con- 
 struction of the heavens. (W. Herschel.) 
 
 1811, p. 269. Astronomical observations relating to the 
 
 construction of the heavens, &c. (IV. Herschel.) 
 
 1814, p. 248. Continuation of the last. (W. Herschel.} 
 
 Many most valuable memoirs, by Sir W. Herschel, which it 
 would be tedious and out of place to specify here, are to be'found in 
 the volumes of the Phil. Trans. Such are his early views on the 
 construction of the heavens vol. Ixxiv., p. 437 ; vol. Ixxv., p. 213 ; 
 1795. p. 46 ; 1796, p. 166. On the comparative brightness of stars, 
 &c. 1796, p. 166; 1797, pp. 142 and 293 ; 1799, p. 121. On his 
 telescopes and power of penetrating into space 1795, p. 347 ; 
 1800, p. 49; 1817, p. 302; 1818, p. 429, &c. It is hoped that a 
 complete collection of Sir W. Herschel's Memoirs may be given to 
 the public at no very distant period. 
 
 Phil Trans., 1828, p. 113. Nebulae and clusters in the southern 
 hemisphere. (Dunlop.) 
 
 Phil Trans., 1833, Part 2, p. 359. A catalogue of nebuli, 
 J. Herschel This most important memoir is the result of a 
 revision of the heavens, by Sir J. Herschel, with a similar in- 
 strument to that used by his immortal father. On the return 
 of Sir J. Herschel from the Cape of Good Hope, we may 
 hope for a like account of the southern hemisphere, thus 
 completing a statistical survey of the heavens at a given epoch. 
 On looking over the list of the memoirs cited, it is obvious how 
 entirely nebulae and double stars may be considered as the 
 acquisition and inheritance of the Herschels, and this notion 
 will be much strengthened by a close examination of the sub- 
 stance of the memoirs. Others may have measured and noted 
 very laudably, but philosophical views and practical details are 
 almost wholly due to them. 
 
122 
 
 A LIST OF TEST OBJECTS, 
 
 Principally Double Stars, arranged in Classes, for the trial of Telescopes 
 in various respects, as to light, distinctness, &c. By Sir J. F. W. 
 HERSCHEL, K. G. H., &c. &c. 
 
 Inserted by permission of the Council of the Royal Astronomical Society. 
 
 N. B. No Double Star is inserted in this list which has not been distinctly separated 
 by the 20-feet Reflector, or 7-feet Equatorial. 
 
 CLASS A. DOUBLE STARS NEARLY EQUAL. 
 
 1st Division : Large Stars. 
 
 6th magnitude, and upwards. 
 
 Object. 
 
 R.A. 1830 + 
 
 N.P.D.1830 + 
 
 Dist. 
 
 Magnitudes. 
 
 Remarks. 
 
 
 h m 
 
 o t 
 
 tr 
 
 
 
 y Arietis . 
 
 1 43,9 
 
 71 33 
 
 9 
 
 4 = 4 
 
 
 Castor . . 
 
 7 23,5 
 
 57 45 
 
 5 
 
 3 3 3 + 
 
 
 Piscium . 
 
 1 53,0 
 
 88 5 
 
 5 
 
 4 , 4 
 
 
 Aquarii . 
 
 22 19,8 
 
 90 55 
 
 4 
 
 5 , 5 
 
 
 p Draconis . 
 
 17 1,8 
 
 35 18 
 
 4 
 
 6 = 6 
 
 
 Androm. 37 (B) 
 44 Bootis (H) 
 
 23 50,7 
 14 58,0 
 
 57 13 
 41 38 
 
 4 
 3 
 
 5=5 
 
 
 I Ursae . . 
 
 11 8,8 
 
 57 30 
 
 2 
 
 5 , 5 + 
 
 
 Bootis . . 
 
 14 32,8 
 
 75 31 
 
 1 
 
 5 , 5 
 
 
 y Virginis . 
 
 12 32,8 
 
 90 29 
 
 1* 
 
 4 = 4 
 
 
 CLASS A. 2nd Division. Small Stars, 7 . . llth mag. 
 
 7th magnitudes. 
 
 2. 2351 . . . 
 
 18 30,6 
 
 48 49 
 
 5 
 
 7 = 7 
 
 
 Androm. 28 (B) . 
 
 23 43,4 
 
 53 4 
 
 4 
 
 7 = 7 
 
 
 2. 1910 . . . 
 
 14 59,1 
 
 80 6 
 
 4 
 
 7 = 7 
 
 
 2. 2947 . . . 
 
 22 43,3 
 
 22 22 
 
 3 
 
 7 = 7 
 
 
 HN. 132 . . 
 
 4 23,5 
 
 72 22 
 
 3 
 
 7 = 7 
 
 
 Coronae 1 (B) . 
 
 15 10,9 
 
 62 30 
 
 2 
 
 7=7 
 
 
 2. 1333 . . 
 
 9 7,7 
 
 53 55 
 
 ]JL 
 
 7=7 
 
 
 7 Coronae 
 
 15 16,1 
 
 59 4 
 
 1 
 
 7 , 7 
 
 The close star. 
 
 36 Androm. Fl. . 
 
 45,6 
 
 67 19 
 
 3. 
 
 7=7 
 
 
 Arietis . 
 
 2 49,4 
 
 69 23 
 
 | 
 
 7 , 7.8 
 
 
 4 Aquarii Fl. 
 
 20 42,1 
 
 96 17 
 
 
 7 , 7.8 
 
 
 8th magnitudes. 
 
 2. 182 ... 
 
 1 44,5 
 
 29 34 
 
 4 
 
 8 , 8 
 
 
 H. II. 52. . . 
 
 3 29,1 
 
 56 26 
 
 4 
 
 8=8 
 
 
 H. I. 69 
 
 6 51,9 
 
 36 59 
 
 4 
 
 8=8 
 
 
 2. 323 . . 
 
 2 43,4 
 
 84 17 
 
 3 
 
 8=8 
 
 
 Lyncis 157 B 
 2. 2845 . . 
 
 9 9,9 
 21 47,5 
 
 51 5 
 
 27 44 
 
 II 
 
 8=8 
 8=8 
 
 
 2. 2701 . . 
 
 20 28,7 
 
 78 33 
 
 2 
 
 8=8 
 
 
 2. 18 . . . 
 
 7,5 
 
 23 20 
 
 1^. 
 
 8 = 8 
 
 
 2. 861 . . 
 
 6 0,3 
 
 59 14 
 
 jl 
 
 8 = 8 
 
 
 2. 158 . . 
 
 1 36,7 
 
 57 42 
 
 1 
 
 8 , 8 
 
 
 2. 1883 . . 
 
 14 40,2 
 
 83 20 
 
 1 
 
 8 = 8 
 
 
 2. 115 
 
 1 12,2 
 
 3"2 46 
 
 i 
 
 8 , 8 
 
 
LIST OF TEST OBJECTS. 
 
 123 
 
 CLASS A. 2nd Division, continued. 
 9th magnitudes. 
 
 Object. 
 
 R.A. 1880 + 
 
 N.P.D. 1830 + 
 
 Dist 
 
 Magnitudes. 
 
 Remarks. 
 
 
 h m 
 
 o > 
 
 n 
 
 
 
 2. 4 . . . . 
 
 0,9 
 
 82 31 
 
 5 
 
 9 = 9 
 
 
 2. 2747 . . . 
 
 20 55.7 
 
 53 
 
 4 
 
 9 = 9 
 
 
 2. 777 ... 
 
 5 33,1 
 
 67 53 
 
 3 
 
 9=9 
 
 
 2. 1564 . . . 
 
 11 30,7 
 
 62 6 
 
 3 
 
 9=9 
 
 
 h. 550 ... 
 
 14 19,8 
 
 53 58 
 
 2 
 
 9 = 9 
 
 
 h. 3074 . . . 
 
 21 49,6 
 
 92 38 
 
 1* 
 
 9 , 9 
 
 
 2. 1626 . . . 
 
 12 8,3 
 
 18 53 
 
 1 
 
 9 = 9 
 
 
 2. 2825 . . . 
 
 21 38,2 
 
 89 56 
 
 1 
 
 9 , 9 
 
 
 2. 2924 . . . 
 
 22 28,3 
 
 20 58 
 
 1 
 
 9 = 9 
 
 
 2. 1093 . . . 
 
 7 17,1 
 
 39 41 
 
 1 
 
 9 , 9 
 
 
 2. 2509 . . . 
 
 19 14,9 
 
 27 7 
 
 1 
 
 9 , 9 
 
 
 1 Oth magnitudes. 
 
 h. 1786 . . . 
 
 23 17,6 
 
 54 6 5 
 
 10 = 10 
 
 
 h. 416 ... 
 
 7 8,8 
 
 66 59 
 
 4 
 
 10 = 10 
 
 
 h. 450 ... 
 
 8 199 
 
 71 29 
 
 3 
 
 10 = 10 
 
 
 h. 1491 . . . 
 
 20 5,2 
 
 49 
 
 8 
 
 10 zr 10 
 
 
 2. 2905 . . . 
 
 22 18,8 
 
 75 43 
 
 2 
 
 10 = 10 
 
 
 h. J537 . . . 
 
 20 26,8 
 
 105 52 
 
 If 
 
 10 = 10 
 
 
 h. 1395 . . . 
 
 19 19,6 
 
 53 12 
 
 iji 
 
 10 = 10 
 
 
 2. 1795 . . . 
 
 21 17,0 
 
 30 3 
 
 ii 
 
 10 = 10 
 
 
 h. 639 ... 
 
 1 22,4 
 
 94 31 
 
 i* 
 
 10 = 10 
 
 
 2. 609 ... 
 
 4 42,8 
 
 89 4 
 
 if 
 
 10 = 10 
 
 
 2. 1033 . . . 
 
 7 0,9 
 
 37 10 
 
 r 
 
 10 10 
 
 
 2. 1504 . . . 
 
 10 54,3 
 
 85 27 
 
 i 
 
 10 = 10 
 
 
 llth magnitudes. 
 
 h. 1104 . . . 
 
 1 56.2 
 
 22 
 
 5 
 
 11 = 11 
 
 
 h. 1384 . . . 
 
 19 13^0 
 
 34 10 
 
 4 
 
 11 = 11 
 
 
 h. 1850 . . . 
 
 23 0,0 
 
 34 44 
 
 4 
 
 11 = 11 
 
 
 h, 1036 . . . 
 
 25,5 
 
 48 3 
 
 3 
 
 11 = 11 
 
 
 h. 586 ... 
 
 16 27,4 
 
 54 37 
 
 3 
 
 11 = 11 
 
 
 h. 1770 . . . 
 
 22 20,7 
 
 55 19 
 
 3 
 
 11 = 11 
 
 
 h. 1895 . . . 
 
 23 29,0 
 
 34 22 
 
 3 
 
 11 = 11 
 
 
 h. 1145 . . . 
 
 4 17,3 
 
 20 54 
 
 2* 
 
 11 = 11 
 
 
 h. 98 . . . . 
 
 8 28,7 
 
 91 50 
 
 2:: 
 
 11 = 11 
 
 
 h. 1032 . . . 
 
 17 33,5 
 
 65 4 
 
 i|. 
 
 11 = 11 
 
 
 h. 1038 . . . 
 
 26,5 
 
 27 13 
 
 11 
 
 11 = 11 
 
 
 h. 1855 . . . 
 
 23 4,0 
 
 45 21 
 
 i^. 
 
 11 = 11 
 
 
 h. 1838 . . . 
 
 22 52,1 
 
 23 49 
 
 i 
 
 11 = 11 
 
 
 CLASS A. 3rd Division. Minute Stars (below llth magnitude'). 
 
 12th magnitudes. 
 
 h. 399 . . 
 
 6 42,3 
 
 93 4 
 
 3 
 
 12 = 12 
 
 
 //. 545 . 
 
 14 11,5 
 
 50 35 
 
 3 
 
 12 = 12 
 
 
 h. 1392 . . 
 
 19 17,1 
 
 43 53 
 
 3 
 
 12 = 12 
 
 
 h. 791 . . 
 
 8 25,4 
 
 56 51 
 
 a* 
 
 12 = 12 
 
 
 h. 1417 . . 
 
 19 28,1 
 
 106 13 
 
 2 
 
 12 = 12 
 
 
 h. 1300 . . . 
 
 17 27,5 
 
 64 34 
 
 2 
 
 12 = 12 
 
 ( The small star 
 { double. 
 
 13th magnitudes. 
 
 h. 685 . . . 
 
 4 40,6 
 
 90 13 
 
 4 
 
 13 = 13 
 
 
 h. 70 . . . . 
 
 7 45,3 
 
 78 15 
 
 3:: 
 
 13 = 13 
 
 
 h. 1914 . . . 
 
 23 44.3 
 
 35 8 
 
 2 
 
 13 = 13 
 
 
 h. 1704 . . . 
 
 21 48,2 
 
 62 54 
 
 U 
 
 13 = 13 
 
 
124 
 
 LIST OF TEST OBJECTS. 
 
 CLASS A. 3rd Division, continued. Minute Stars (below \Wi mag.') 
 14th magnitudes. 
 
 Object. 
 
 R.A. 1830 + 
 
 N.P.D. 1830 j- 
 
 Dist. 
 
 Magnitudes. 
 
 Remarks. 
 
 
 h m 
 
 1 
 
 n 
 
 
 [Follows a larger 
 
 h. 1150 . . . 
 
 3 27,4 
 
 20 49 
 
 4 
 
 14 = 14 
 
 ' -double star in 
 
 h. 1360 . . . 
 
 18 54,7 
 
 53 35 
 
 3 
 
 14 = 14 
 
 [ same field. 
 
 h. 1265 . . . 
 
 14 52,7 
 
 82 58 
 
 3 
 
 14 , 14 
 
 f The small com- 
 
 /3 2 Equulei . 
 
 20 14,3 
 
 83 54 
 
 2 
 
 14 , 15 
 
 \ panion of /S is 
 
 Below 14th magnitudes 
 
 
 [ double. 
 
 h. 1157 . . . 
 
 5 26,7 
 
 95 30 
 
 5 
 
 .... 
 
 {The small com- 
 
 h. 2948 . . . 
 
 20 11,5 
 
 105 18 
 
 3 
 
 .... 
 
 panidn of *&/$' 
 
 Capricorni is a 
 
 h. 1248 . . . 
 
 14 7,5 
 
 81 52 
 
 2 
 
 ... 
 
 close dble. star. 
 
 h. 709 ... 
 
 5 36,4 
 
 61 5 
 
 2 
 
 .... 
 
 
 h. 649 ... 
 
 2 14,3 
 
 81 10 
 
 *$ 
 
 . . . 
 
 
 h. 836 ... 
 
 10 36,2 
 
 61 4 
 
 ll 
 
 .... 
 
 
 CLASS B. MODERATELY UNEQUAL STARS. 
 
 1st Division : Large Sta?*s. 
 
 I Cephei . 
 
 21 58.5 
 
 26 14 
 
 6 
 
 4-5 , 7 
 
 
 p Cygni . ^ 
 
 21 36^ 
 
 62 1 
 
 5 
 
 5 , 6 
 
 
 / Trianguli 
 
 2 2,4 
 
 60 31 
 
 4 
 
 5 , 8 
 
 Yellow and blue. 
 
 y Leonis . 
 
 10 10,4 
 
 69 16 
 
 3 
 
 2-3 , 4 
 
 
 S Serpentis 
 
 15 26,4 
 
 73 53 
 
 3 
 
 5 , 6 
 
 
 38 Lyncis Fl. 
 
 9 7,8 
 
 52 28 
 
 3 
 
 5 , 8 
 
 
 / Cassiopeiae 
 
 2 15,0 
 
 23 22 
 
 2 
 
 5 , 8 
 
 
 | Cancri . . . 
 
 8 2,1 
 
 71 50 
 
 1* 
 
 6 , 7 
 
 fTiiple. The close 
 1 star. 
 
 A. Ophiuclii . . 
 
 16 22,1 
 
 87 38 
 
 1 
 
 5 , 7 
 
 
 CLASS B. 2nd Division : Small Stars. 
 
 59 Serpentis Fl. 
 
 18 18,3 
 
 89 55 
 
 4 
 
 7 , 9 
 
 
 Ursse 284 B . . 
 
 11 28,9 
 
 24 43 
 
 3 
 
 7 , 9 
 
 
 2. 517. . . . 
 
 4 7,2 
 
 89 59 
 
 3 
 
 8 ,10 
 
 
 2. 2940 . . . 
 
 22 37,0 
 
 18 10 
 
 3 
 
 10 ,12 
 
 
 10 Arietis Fl. . 
 
 1 53,8 
 
 64 55 
 
 2 
 
 7 , 8 
 
 
 Cygni 280 B . 
 
 20 52,9 
 
 40 13 
 
 2 
 
 7 , 8 
 
 
 32 Orionis Fl. . 
 
 5 21,4 
 
 84 12 
 
 H 
 
 8 , 9 
 
 
 2. 1858 . . . 
 
 14 26,6 
 
 53 41 
 
 If 
 
 8 , 9 
 
 
 Canis. Min. 31 B 
 
 7 30,8 
 
 84 22 
 
 I* 
 
 8 , 9 
 
 
 h. 1018 . . . 
 
 11,6 
 
 23 16 
 
 1$ 
 
 10 ,11 
 
 
 2. 1630 . . . 
 
 12 10,5 
 
 32 40 
 
 if 
 
 10 ,11 
 
 
 (f Coronse 
 
 16 7,5 
 
 55 40 
 
 *! 
 
 7-8, 9 
 
 The close star. 
 
 ^Bootis . . 
 
 15 18,0 
 
 52 4 
 
 i 
 
 8 , 9*10 
 
 i The small com- 
 \ paniun of ^. 
 
 2. 770 ... 
 
 5 31,4 
 
 70 52 
 
 i 
 
 9 ,11 
 
 
 h. 2562 . . . 
 
 11 1,2 
 
 57 55 
 
 i 
 
 9 ,12 
 
 
 CLASS C. VERY UNEQUAL STARS. 
 
 1st Division : Small Star conspicuous. 
 
 Cassiopeiae 
 Herculis . . 
 
 38,5 
 17 6,7 
 
 33 7 
 75 24 
 
 12 
 5 
 
 4 , 8 
 3 , 8 
 
 Small star, purple. 
 
 Orionis 
 
 5 32,1 
 
 92 4 
 
 3 
 
 2 , 7 
 
 
 Bob'tis . 
 
 14 37,4 
 
 62 11 
 
 3 
 
 3 , 8 
 
 
 
 
 
 
 
 ("Small f. Not 
 
 E Draconls . . 
 
 19 48,7 
 
 20 11 
 
 3 
 
 4 , 8 
 
 < conspicuous in an 
 
 
 
 
 
 
 unillumined field 
 
LIST OF TEST OBJECTS. 
 
 125 
 
 CLASS C. 2nd Division : Small Star not conspicuous . 
 
 Object. 
 
 R.A. 1830 + 
 
 N.P.D. 1830 + 
 
 Dist. 
 
 Magnitudes. 
 
 Remarks. 
 
 
 h m 
 
 r 
 
 
 
 
 
 ? Sagittae . . 
 
 19 41,2 
 
 71 17 
 
 10 
 
 4 , 9-10 
 
 
 x Pegasi . . . 
 
 21 36,9 
 
 65 8 
 
 9 
 
 4 , 10 
 
 
 d Virginia 
 
 13 0,9 
 
 94 36 
 
 7 
 
 5 , 10 
 
 f Pretfy conspi- 
 < cuous, with il- 
 
 
 
 
 
 
 [ laminated field. 
 
 i Leonis . . 
 
 11 14.8 
 
 77 31 
 
 3 
 
 4 , 9 
 
 
 Hydrae . . 
 
 8 37',6 
 
 82 56 
 
 3 
 
 4 , 10 
 
 
 y Ceti . . . 
 
 2 34,2 
 
 87 31 
 
 3 
 
 3 , 9 
 
 
 h. 3003 . . . 
 
 20 43,0 
 
 114 25 
 
 3 
 
 6 , 11 
 
 
 3 Cygni . . . 
 
 19 39,5 
 
 45 17 
 
 2 
 
 3 , 10 
 
 
 h. 1051 . . . 
 
 35,6 
 
 66 13 
 
 1* 
 
 10 , 14 
 
 
 CLASS D.*~ EXTREMELY UNEQUAL STARS. 
 
 Rigel . . . 
 
 5 6,3 
 
 98 25 
 
 9 
 
 1 , 9 
 
 
 Polaris . . 
 
 59,3 
 
 1 36 
 
 15 
 
 2 , 10 
 
 
 a Lyrae . 
 
 18 31,2 
 
 51 23 
 
 45 
 
 1 , 11 
 
 
 X Geminor . 
 
 7 8,0 
 
 73 9 
 
 15 
 
 4 , 11 
 
 
 t Ursae . . . 
 
 11 9,3 
 
 55 59 
 
 10 
 
 3 , 11 
 
 
 Equulei . . 
 r Orionis . 
 
 21 6,0 
 5 9 ; 3 
 
 80 42 
 97 2 
 
 30 
 18 
 
 4 , 12 
 4 , 12 
 
 Triple. (A. B.) 
 
 1 Pegasi . . . 
 
 22 38,2 
 
 78 42 
 
 15 
 
 5 , 12 
 
 (Triple. The dis- 
 l tant $f 
 
 2. 5 . . . . 
 
 1,1 
 
 79 50 
 
 12 
 
 6 , 12 
 
 
 Persei ... 
 
 3 43,5 
 
 58 38 
 
 10 
 
 3 , 12 
 
 (Triple. The near 
 I star. 
 
 <p Piscium . 
 
 1 4,5 
 
 66 19 
 
 8 
 
 5 , 12 
 
 
 2. 320 . . . 
 
 2 43,1 
 
 11 16 
 
 6 
 
 6 , 12 
 
 
 2. 2587 . . . 
 
 19 43,0 
 
 86 20 
 
 5 
 
 7 , 12 
 
 
 2. 2790 . . . 
 
 21 14,4 
 
 32 6 
 
 3 
 
 7 , 12 
 
 
 /t Coronas 
 
 15 16,1 
 
 59 4 
 
 40 
 
 6 , 13 
 
 (Triple. TheMist. 
 1 star. 
 
 f Coronae 
 
 16 7,5 
 
 55 40 
 
 40 
 
 7 , 13 
 
 f Quadruple. The 
 \ more distant % 
 
 ; Ursae . 
 
 8 47,5 
 
 41 18 
 
 12 
 
 3-4, 13 
 
 
 h, 693 ... 
 
 5 0,7 
 
 82 3 
 
 5 
 
 7 , 13 
 
 
 y Hydrae . . 
 
 11 16,3 
 
 106 44 
 
 3 
 
 4 , 13 
 
 
 r Orionis . 
 h. 2603 . . . 
 
 5 9,3 
 12 5,4 
 
 97 2 
 76 54 
 
 18 
 15 
 
 4 , 14 
 
 7 , 14 
 
 Triple. (A.C.) 
 
 fjt. Sagittarii . 
 
 18 3,6 
 
 111 7 
 
 12 
 
 3-4, 14 
 
 (Quadruple. The 
 1 clo&e ^f 
 
 12 CetiFl. . . 
 
 21,4 
 
 94 54 
 
 8 
 
 7 , 14 
 
 
 x, Geminor . 
 
 7 34,2 
 
 65 12 
 
 5 
 
 4 , 14 
 
 
 <p Virginia . 
 
 14 19,5 
 
 91 23 
 
 4 
 
 5 J 14 
 
 
 /3 Aquarii 
 
 21 22,6 
 
 96 19 
 
 20 
 
 3 , 15 
 
 
 //. 2714 . . . 
 
 14 14.5 
 
 109 1 
 
 15 
 
 7-8, 15 
 
 
 h. 2666 . . . 
 
 13 29,4 
 
 103 58 
 
 8 
 
 9 , 15 
 
 
 32 Leon.Min.R. 
 
 10 23,3 
 
 48 43 
 
 25 
 
 5 , 16 
 
 
 <r Bob'tis . 
 
 1 3 39,0 
 
 71 40 
 
 20 
 
 4 , 16 
 
 
 33 Leonis Fl. . 
 
 10 22,8 
 
 56 45 
 
 20 
 
 6 , 16 
 
 
 31 Cygni Fl. . 
 
 20 8,3 
 
 43 46 
 
 20 
 
 4 J , 16 
 
 
 r Coronas 
 
 16 7,5 
 
 55 40 
 
 20 
 
 7 , 16 
 
 j Quadruple. The 
 [ iatermed ate ^f 
 
126 
 
 LIST OF TEST OBJECTS. 
 
 CLASS D. Extremely unequalled 
 
 Stars, continued. 
 
 Object. 
 
 R.A. 1830 + 
 
 N.P.D. 1830 + 
 
 Dist. 
 
 Magnitudes. 
 
 Remarks. 
 
 
 h m 
 
 f 
 
 tt 
 
 
 
 2. 324 ... 
 
 2 44,9 
 
 43 32 
 
 (12 
 I 8 
 
 8 .{IS::: 
 
 } Triple. 
 
 g Pegasi . . 
 
 22 38,0 
 
 78 43 
 
 11 
 
 5 , 16... 
 
 j Triple. The close 
 i star. 
 
 a 2 Cancri 
 
 8 49,0 
 
 77 28 
 
 10 
 
 4-5 16... 
 
 
 h. 3032 
 
 21 24,0 
 
 85 51 
 
 10 
 
 8 16... 
 
 
 h. 338 
 
 3 44,3 
 
 92 53 
 
 10 
 
 5 16... 
 
 
 h. 2732 
 
 14 26,4 
 
 44 9 
 
 9 
 
 9 16... 
 
 
 h. 2577 
 
 11 25,5 
 
 61 18 
 
 8 
 
 9 16... 
 
 
 a 2 Capricorn! 
 
 20 8,7 
 
 103 4 
 
 8 
 
 3 16... 
 
 
 94 Ceti Fl. . 
 
 3 4 ; 
 
 91 50 
 
 6 
 
 5 16... 
 
 
 30 Pegasi Fl. . 
 
 22 11,8 
 
 85 4 
 
 / 6 
 I 4 
 
 5 ,{}{j;;; 
 
 } Triple. 
 
 h. 333 ... 
 
 3 13,9 
 
 57 4 
 
 3 
 
 6 , 16.:*. 
 
 
 N,B. Among this class D are some very difficult, and some comparatively easy 
 
 objects ; but they require re-examination to arrange them in their proper order. 
 
 CLASS E. RESOLVABLE CLUSTERS OF STARS 
 
 For trying the space -penetrating powers of Telescopes. 
 
 13 Messier 
 
 16 35,7 
 
 53 12 
 
 Between >? and Herculis. 
 
 5 Messier 
 
 15 9,9 
 
 87 16 
 
 
 
 3 Messier 
 
 13 34,3 
 
 60 46 
 
 
 
 2 Messier 
 
 21 24,6 
 
 91 34 
 
 
 
 15 Messier 
 
 21 21,7 
 
 78 34 
 
 
 
 53 Messier 
 
 13 4,6 
 
 70 56 
 
 
 
 28 Messier 
 
 18 14,0 
 
 114 56 
 
 
 
 10 Messier 
 
 16 48,2 
 
 93 50 
 
 
 
 9 Messier 
 
 17 9,1 
 
 108 18 
 
 
 
 19 Messier 
 
 16 52,1 
 
 116 
 
 
 
 22 Messier 
 
 18 26,0 
 
 114 1 
 
 
 
 I. 103 . 
 h. Nova . 
 
 20 26,9 
 15 29,1 
 
 83 10 
 
 83 27 
 
 A faint object. 
 
 I. 70 
 
 Messier 46 
 
 14 20,7 
 7 34,0 
 
 95 12 
 104 25 
 
 f Has a planetary nebula (iv. 39) 
 \ within it. 
 
 CLASS F. REMARKABLE NEBULAE 
 
 Not resolvable into Stars by Telescopes of any ordinary power, but pre- 
 senting very different appearances in Telescopes of different degrees 
 
 of optical capacity. 
 
 
 Nebula in Orion 
 
 5 27.2 
 
 95 32 
 
 
 
 Messier 51 
 
 13 22,6 
 
 41 55 
 
 
 
 Messier 27 
 
 19 52,2 
 
 67 44 
 
 
 
 Messier 17 
 
 18 10.8 
 
 106 15 
 
 
 
 Messier 60 
 
 12 35,1 
 
 77 31 
 
 A double nebula. 
 
 IV. 41 (H) ^ 
 
 17 52,0 
 
 113 1 
 
 
 
 V. 15 . 
 
 20 38,9 
 
 59 53 
 
 Passes through k Cygni. 
 
 V. 19 
 
 2 12,0 
 
 48 25 
 
 A faint object. 
 
 Messier 64 
 
 12 48,4 
 
 67 23 
 
 
 
 Messier 57 
 
 18 48,0 
 
 57 10 
 
 The annular nebula in Lyra. 
 
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