Page:EB1911 - Volume 21.djvu/550

 produced is magnified, it is seen to have a shape like that of a kite. As the exposure is prolonged the small kite-shaped figure gradually increases in size from the point towards the head, and this defect is the more pronounced the farther we depart from the centre of the plate. The result is, speaking generally, that the images near the centre of a plate may be fairly small and circular, but at a certain distance from the centre they become distorted and large. It is a practical problem of great importance to have this distance as great as possible, so that the field of good definition may be large. Estimating in terms of angular distance from the centre of the field, the reflecting telescope has a good field of not more than 40′; a telescope with one compound lens (the ordinary refractor) a field of about 1°, while if two compound lenses are used (as is the case in portrait photography) the field may be very greatly extended, 10° or 15° having been successfully covered. This is naturally a very great advantage of the “doublet” over other forms of telescope, an advantage which has only recently been fully realized. But there is a compensating drawback; to get a large field we must either use a large plate, which is liable to bend or to have a permanent curvature; or if we use a small plate the picture will be on a small scale, so that we lose accuracy in another way.

Star Charts may thus be made by photography with any desired combination of these advantages. The Cape Photographic Durchmusterung is a photographic survey of the southern hemisphere by means of 250 plates each covering 5° × 5° taken at the Royal Observatory, Cape of Good Hope; the plates being afterwards measured at Groningen in Holland by Professor J. C. Kapteyn who recorded the places to 0s.1 and 0′.1. A much higher degree of accuracy is aimed at in the international scheme for a map of the whole sky undertaken jointly by eighteen observatories in 1887. The plates are only 2° × 2°, and each of the eighteen observatories must take about 600 to cover its zone of the sky once, 1200 to cover it twice. Exposures of 6 min., 3 min., and 20 sec. are given, the telescope being pointed in a slightly different direction for each exposure; so that each star to about the 9th magnitude shows 3 images, and stars to the 11th or 12th magnitude show 2; which has the incidental advantage of distinguishing stars from dust-specks. A réseau of lines accurately ruled at distances of 5 mm. apart in two directions at right angles is impressed on the plate by artificial light and developed along with the star images; and by use of these reference lines the places of all stars shown with 3 min. exposure are measured with a probable error which, by a resolution of the executive committee, is not to exceed ±0⋅20″. An additional scheme for a series of charts enlarged from similar plates with much longer exposure has proved too costly, and only a few observatories have attempted it. Meanwhile Professor E. C. Pickering of Harvard, by using doublet lenses which cover a much larger field at once, has photographed the whole sky many times over. The plates have not been measured, and would not in any case yield results of quite the same accuracy as those of the international scheme; but being systematically stored at the Harvard Observatory they form an invaluable reference library, from which the history of remarkable objects can be read backwards when once attention is drawn to them. Thus the history of the asteroid Eros, discovered in 1898, was traced back to 1894 from these plates; new stars have been found on plates taken previous to the time of discovery, and the epoch of their blazing up recovered within narrow limits; and the history of many variable stars greatly extended. The value of this collection of photographs will steadily increase with time and growth.

Spectroscopic Star Charts.—By placing a glass prism in front of the object glass of a telescope the light from each star can be extended into a spectrum: and a chart can thus be obtained showing not only the relative positions, but the character of the light of the stars. This method has been used with great effect at Harvard: and from inspection of the plates many discoveries have been made, notably those of several novae.

The Geometry of the Star Chart.—Let OS in the figure be the object glass with which the photograph is taken, and let its optical centre be C. Let PL be the plate, and draw CN perpendicular to the surface

of the plate. The point N is of fundamental importance in the geometry of the star chart and it is natural to call it the plate centre;

but it must be carefully distinguished from two other points which should theoretically, but may not in practice, coincide with it. The first is the centre of the material plate, as placed in position in the telescope. In the figure NL is purposely drawn larger than PN, and this material centre would be to the right of N. The second point is that where the optical axis of the object glass (CG in the figure) cuts the plate. The object glass is drawn with an exaggerated tilt so that CG falls to the right of CN. To secure adjustment, the object glass should be “squared on” to the tube by a familiar operation, so that the tube is parallel to CG: and then the plate should be set normal to the tube and therefore to CG. This is done by observing reflected images, combined with rotation of the plate in its plane.

The field of the object glass will in general be curved: so that the points of best focus for different stars lie on a surface such as AG (purposely exaggerated). The best practical results for focus will thus be obtained by compromise, placing the plate so that some stars, as A, are focused beyond the plate, and others, as B, nearer the object glass: exact focus only being possible for a particular ring on the plate. The star A will thus be represented y a small patch of light, pq on the plate, which will grow in size as above explained. When we measure the position of its image we select the centre as best we can; and in practice it is important that the point selected should be that where the line Ca drawn from the star to the optical centre cuts the plate. If this can be done, then the chart represents the geometrical projection of the heavens from the point C on to the plane PL. The stars are usually conceived as lying on the celestial sphere, with an arbitrary radius and centre at the observer, which is in this case the object glass: describing such a sphere with C as centre and CN as radius, the lines bCB and aCA project the spherical surface on to a tangent plane at the point N, which we call the plate centre. If we point the telescope to a different part of the sky, we select a different tangent plane on which to project. It is a fundamental property of projections that a straight line projects into a straight line; and in the present instance we may add that every straight line corresponds to a great circle on the celestial sphere. Hence if we measure any rectilinear coordinates (x, y) of a series of stars on one plate, and co-ordinates (X, Y) of the same stars on another plate, and (x, y) are connected by a linear relation, so must (X, Y) be. This property leads at once to the equations

the numerators being any linear functions of (x, y) but the denominators being the same linear function. When x＝0, y＝0, then X=c and Y=f, which are thus the co-ordinates of the origin of (xy) on plate (XY). The co-ordinate of the origin of (XY) on plate (xy) can be shown to be (k, l) if proper units of length be chosen.

As a particular case the co-ordinates

represent the rectangular co-ordinates of a star of RA and declination a and, projected on the tangent plane at the north pole. If the same star be projected on the tangent plane at the point (A, D), then its rectangular co-ordinates will be the axis of  being directed towards the pole. It can readily be verified that can be expressed in terms of (x, y) by relations of the form (1). The co-ordinates have been named “standard co-ordinates” and represent star positions on an ideal plate free from the effects of refraction and aberration. For plates of not too large a field, differential refraction and aberration are so small that their product by squares of the co-ordinates may be neglected, and the actual star positions (x, y) are connected with by linear relations. The linearity of these relations is obviously not disturbed by the choice of origin of axes and of orientation; in which the effects of procession and mutation for any epoch may be included. Hence to obtain the standard co-ordinates of any object on a plate it is only necessary to know the position of the plate centre (the point N in fig. 1) and the six constants in the relations

where (x, y) are rectilinear co-ordinates referred to any axes. The constants can theoretically be determined when there are three stars on the plate for which are known: but in practice it is better to use as many “known” stars as possible. These equations