prism 2. If a screen were placed to intercept the beam anywhere between prism 1 and prism 2, a short solar spectrum would be seen on it, the violet end lying towards the bases of the prisms; and, assuming the battery of prisms to lie on a horizontal plane, the length of the spectrum—that is, its extension measured from red to violet-would be horizontal. Then this beam

passes to 3; and if a screen were placed between 2 and 3 a somewhat longer spectrum would be seen. Between 3 and 4 the spectrum would be still longer. And, lastly, a screen placed beyond the last prism, as a b, would show the solar spectrum much longer and proportionately fainter than in Newton's experiment. And although no such screen is used by spectroscopists, who receive the emergent rays into a telescope with which they examine the spectrum, it will be convenient for our purpose to refer at present to a spectrum supposed to be received on a screen, as in fig. 25.

Now, on a b I have shown a violet image of the slit v, an indigo one I, and so on, to a red image at R. But there are an infinite number of images ranged from the extreme violet end to the extreme red end. In places, however, no images are formed. The spaces thus left without light are the dark lines.

It is not difficult, then, to see on what conditions the visibility of the dark lines will necessarily depend. If we could have a slit which was a true mathematical line, every dark space would be present in the screen, even though the dispersive power were small. But, as a matter of fact, the slit has a definite breadth, however

narrow we may make it. Now, suppose that A B C (fig. 26) represents a small part of the solar spectrum as shown on the screen in fig. 25, but that the true nature of this part of the solar spectrum is shown in the narrow band a b c, so that in reality sunlight has no rays whose refrangibility corresponds to the band at b. Suppose, further, that the aperture of the slit is equal in width to this band b. Then the light corresponding to the extreme limits of the light in a be, will form the two images of the slit shown at B; these images will meet, and no absolutely black line will be

seen. There will, however, be a dusky band, darkest down the middle, and twice as broad as the true band b. But now consider the effects of an increase of dispersive power. Say we double the length of the spectrum, or rather of the particular part shown in figs. 26 and 27. Then the parts a b c of the real solar spectrum will all be doubled in length, and in the observed solar spectrum the light corresponding to the extreme limits of the band b will produce the two images of the slit

The true nature of the solar spectrum may be regarded as that corresponding to the imaginary case of a slit, which should be a true mathematical line, and of a battery of prisms which should cause no optical faults whatever, insomuch that the image of the slit for rays of any order of refrangibility would also be a mathematical line.

shown at B and B', but these will be no wider than before, and will be separated by a really black band, half as wide as b. This band will be bordered by a penumbral fringe whose boundaries are indicated by the dotted lines, the whole breadth from dotted line to dotted line being half as great again as that of the band b.

The reader will, therefore, at once see the importance of increasing the dispersive power of our battery of prisms; since in this way very fine lines which might otherwise escape detection can be rendered visible. Also, it is obvious that two lines very close together would be shown as one with a certain amount of dispersive power, while with more dispersive power they would be clearly separated. Yet once more, a line in the solar spectrum which seemed to coincide, without being really coincident, with the bright line of some metallic spectrum (brought into comparison with the Sun's in the manner referred to above) might, by increase of dispersive power, be removed appreciably from its supposed counterpart.

So far, then, as the direct examination of the solar spectrum is concerned, we must aim specially at the means of increasing dispersion. It will be seen, also, further on, that in two highly important applications of the analysis-viz. to the examination of the prominences, and to the recognition of motions of approach or recess due to solar cyclones-great dispersion is the chief point to be secured by the spectroscopist.

But fig. 24 shows that certain difficulties have to be encountered in securing great dispersion. Only the

part of the spectrum near G has been formed (in the case illustrated in that figure) by rays which have gone symmetrically through the battery of prisms. The rays forming the part near v have gone through the middle of prism 1, and come out near the base of prism 4; while those forming the part R passing also through the middle of prism 1, come out near the vertex of prism 4. Now, optical considerations render it essential, or at least extremely important as far as the clear definition of the lines is concerned, that each part of the spectrum should be formed by rays which have gone symmetrically round such a battery as is shown in fig. 24.* Furthermore, when the dispersion is very great only a portion of the spectrum will be formed at all (some at either extremity falling outside the last prism-beyond apex and base) when the prisms occupy a fixed position. Then, again, when the light has been bent round a nearly

*The point to be secured is that the rays forming any part of the spectrum under examination should pass into and out of each prism at equal angles (as the light forming the part G of the spectrum in fig. 25 does). It may be shown that in this case those special rays pass with least possible deviation through each prism, so that the condition is generally called that of minimum deviation. But minimum deviation per se has no advantages, and, as a matter of fact, the real condition secured by this arrangement is that the primary and secondary foci of emergent pencils are as nearly as possible coincident; so that, though the image of the slit formed by those special rays is not formed by absolute points of light, it is formed by circles (technically called 'circles of least confusion') having the smallest possible diameter. In a paper in the Monthly Notices of the Astronomical Society, vol. xxx., I have shown that the circle of least confusion has in this case a definite, though exceedingly minute diameter, even in the case of a single prism. The mathematical expression for the radius of this circle is given in that paper, but is somewhat too complex to be repeated with advantage in these pages.

complete circle of prisms, as in fig. 28, the emergent light E E' will be intercepted by the first prism of the battery; and this circumstance limits the dispersion which can be given in this manner.

Let us consider how these difficulties have been or may be encountered.

We owe to Mr. Browning the invention of a most ingenious plan by which, whatever part of the solar spectrum is studied, the battery of prisms will be

properly adjusted. In his automatic spectroscope he attaches to each prism a slotted bar, as shown in fig. 29. All the slots pass over a central pivot, and the prisms are attached at their angles as shown. Hence