A L
α D2,

on unit area of the image is therefore I that is I; it is therefore the same as if the lens were a source of light of brightness I. Accordingly, if the image of a lamp flame be thrown upon the pupil of an observer's eye, and be large enough to cover the pupil, he will see the lens filled with light of a brightness equal to that of the flame seen directly.

B

A

Fig. 752.-Field of View.

1041. Field of View in Astronomical Telescope.-Let p m n q (Fig. 752) be the common focal plane of the object-glass and eye-glass. Draw Ba, Ab joining the highest points of both, and the lowest points of both; also A a, Bb joining the highest point of each with the lowest point of the other. Evidently Ba, Ab will be the boundaries of the beam of light transmitted through the telescope, and therefore the points p and q in which these lines intersect the focal plane, will be the extremities of that part of the real image which sends rays to the eye. The angle subtended by pq at the centre of the object-glass will therefore be the angular diameter of the complete field of view. But the outer portions of this field will be less bright than the centre, and the full amount of brightness, as calculated in § 1038 for the case in which the "bright spot" is smaller than the pupil, will belong only to the portion mn bounded by the cross-lines Aa, Bb; for all the rays sent by the object-glass through the part mn traverse the eye-glass, and therefore the bright spot, whereas some of the rays sent by the object-glass to any point between m and p, or between n and q pass wide of the eye-glass and therefore do not reach the bright spot. The complete field of view, as seen by an eye whose pupil includes the bright spot, accordingly consists of a central disc mn of full brightness, surrounded by a ring extending to p and q whose brightness gradually diminishes from full brightness at its junction with the disc to zero at its outer boundary. This ring is called the "ragged edge," and is put out of sight in actual telescopes by an opaque stop of The angular diameter of the field

B

A

Fig. 753.--Calculation of Field.

b

annular form in the focal plane.

of view, excluding the ragged edge, will be equal to the angle which mn subtends at the centre of the object-glass.

To calculate the length of mn, join D, d, the centres of the object-glass and eye-glass (Fig. 753). The joining line will obviously pass through the intersection of Aa, Bb, and also through the middle point of mn. Draw a parallel to this line through m. Then, by comparing the similar triangles of which a m, Am are the hypotenuses, we have

Hence, multiplying extremes and means, and denoting the focal lengths Do, o d by F, f, we have

whence

F (ad-mo) = f(AD+mo),

mo=

F.ad-f.AD
F+f

This is the radius of the real image, excluding the ragged edge; and the angular radius of the field of view will be

a d F+f

The first term is the angle which the radius of the eye-glass subtends at the object-glass. But, it is obvious from Fig. 752 that the line a D would bisect mp. Hence the second term represents half the breadth of the ragged edge, and the whole field of view, including the ragged edge, has an angular radius

1042. Cross-wires of Telescopes.-We have described in § 1010 a mode of marking the place of a real image by means of a cross of threads. When telescopes are employed to assist in the measurement of angles, a contrivance of this kind is almost always introduced. A cross of silkworm threads, in instruments of low power, or of spider threads in instruments of higher power, is stretched across a metallic frame just in front of the eye-piece. The observer must first adjust the eye-piece for distinct vision of this cross, and must then (in the case of theodolites and other surveying instruments) adjust the distance of the object-glass until the object which is to be observed is also seen distinctly in the telescope. The image of the object will then be very nearly in the plane of the cross. If it is not exactly in the plane, parallactic displacement will be observed when the eye is shifted; and this must be cured by slightly

altering the distance of the object-glass. When the adjustment has been completed, the cross always marks one definite point of the object, however the eye be shifted. This coincidence will not be disturbed by pushing in or pulling out the eye-piece; for the frame which carries the cross is attached to the body of the telescope, and the coincidence of the cross with a point of the image is real, so that it could be observed by the naked eye, if the eye-piece were removed. The adjustment of the eye-piece merely serves to give distinct vision, and this will be obtained simultaneously for both the cross and the object.

1043. Line of Collimation.-The employment of cross-wires (as these crossing threads are called) enormously increases our power of making accurate observations of direction, and constitutes one of the greatest advantages of modern over ancient instruments.

The line which is regarded as the line of sight, or as the direction in which the telescope is pointed, is called the line of collimation. If we neglect the curvature of rays due to atmospheric refraction, we may define it as the line joining the cross to the object whose image falls on it. More rigorously, the line of collimation is the line joining the cross to the optical centre of the object-glass. When it is desired to adjust the line of collimation,-for example, to make it truly perpendicular to the horizontal axis on which the telescope is mounted, the adjustment is performed by shifting the frame which carries the wires, slow-motion screws being provided for this purpose. Telescopes for astronomical observation are often furnished with a number of parallel wires, crossed by one or two in the transverse direction; and the line of collimation is then defined by reference to an imaginary cross, which is the centre of mean position of all the actual crosses.

1044. Micrometers.- Astronomical micrometers are of various kinds, some of them serving for measuring the angular distance between two points in the same field of view, and others for measuring their apparent direction from one another. They often consist of spider threads placed in the principal focus of the object-glass, so as to be in the same plane as the images of celestial objects, one or more of the threads being movable by means of slow-motion screws, furnished with graduated circles, on which parts of a turn can be read off.

One of the commonest kinds consists of two parallel threads, which can thus be moved to any distance apart, and can also be turned round in their own plane.

CHAPTER LXXII.

DISPERSION. STUDY OF SPECTRA.

1045. Newtonian Experiment.-In the chapter on refraction, we have postponed the discussion of one important phenomenon by which it is usually accompanied, and which we must now proceed to explain. The following experiment, which is due to Sir Isaac Newton, will furnish a fitting introduction to the subject.

On an extensive background of black, let three bright strips be laid in line, as in the left-hand part of Fig. 754, and looked at through a prism with its refracting edge parallel to the strips. We

shall suppose the edge to be upward, so that the image is raised above the object. The images, as represented in the right-hand part of Fig. 754, will have the same horizontal dimensions as the strips, but will be greatly extended in the vertical direction; and each image, instead of having the uniform colour of the strips from which it is derived, will be tinted with a gradual succession of colours from top to bottom. Such images are called spectra.

If one of the strips (the middle one in the figure) be white, its spectrum will contain the following series of colours, beginning at the top: violet, blue, green, yellow, orange, red.

If one of the strips be blue (the left-hand one in the figure), its image will present bright colours at the upper end; and these will be identical with the colours adjacent to them in the spectrum of white. The colours which form the lower part of the spectrum of white will either be very dim and dark in the spectrum of blue, or will be wanting altogether, being replaced by black.

If the other strip be red, its image will contain bright colours at the lower or red end, and those which belong to the upper end of the spectrum of white will be dim or absent. Every colour that occurs in the spectrum of blue or of red will also be found, and in the same horizontal line, in the spectrum of white.

If we employ other colours instead of blue or red, we shall obtain analogous results; every colour will be found to give a spectrum which is identical with part of the spectrum of white, both as regards colour and position, but not generally as regards brightness.

We may occasionally meet with a body whose spectrum consists only of one colour. The petals of some kinds of convolvulus give a spectrum consisting only of blue, and the petals of nasturtium give only red.

1046. Composite Nature of Ordinary Colours. This experiment shows that the colours presented by the great majority of natural bodies are composite. When a colour is looked at with the naked eye, the sensation experienced is the joint effect of the various elementary colours which compose it. The prism serves to resolve the colour into its components, and exhibit them separately. The experiment also shows that a mixture of all the elementary colours in proper proportions produces white.

1047. Solar Spectrum.-The coloured strips in the foregoing experiment may be illuminated either by daylight or by any of the ordinary sources of artificial light. The former is the best, as gas-light and candle-light are very deficient in blue and violet rays.

Colour, regarded as a property of a coloured (opaque) body, is the power of selecting certain rays and reflecting them either exclusively or in larger proportion than others. The spectrum presented by a body viewed by reflected light, as ordinary bodies are, can thus only consist of the rays, or a selection of the rays, by which the body is illuminated.

A beam of solar light can be directly resolved into its constituents by the following experiment, which is also due to Newton, and was the first demonstration of the composite character of solar light.