will consequently be slightly diminished instead of being increased by the more accurate hypothesis of sphericity. The present investigation is a sufficient reply to Professor Blake's objection that " English writers have hitherto adopted Lord Kelvin's assumption that the earth may be regarded as of infinite radius, and have thus followed him in using linear equations for the conduction of heat. But when later writers go further, and at the same time introduce the radius of the earth, already assumed infinite, into the calculation, they are obviously inconsistent, and it may well be that the whole of the results are derived from this inconsistency itself." Plausible as this criticism at first sight appears, I have now shown that it is altogether unimportant, seeing that the position of the level of no strain is not appreciably altered when the inconsistency complained of is avoided. At the same time, such alteration as its removal introduces tends in the opposite direction to that which Mr. Blake appears to expect, bringing, as it does, the level of no strain nearer to the surface, and therefore making the resulting elevatory corrugations smaller than before. It may be as well to remind the reader that the depth of the level of no strain in a solid globe does not follow the same law as the radial contraction. The former varies as the time, and therefore the rate at which it descends is constant. The latter varies as the square root of the time, so that the rate at which the surface sinks diminishes as the time increases. Professor Blake concludes his critique with a formidable list of difficulties to be overcome before " we can really face the problem of a level of no strain." If it is required to find what its situation would be with accuracy, even within a mile or so, no doubt we are not, and probably even our remote descendants will never be, in a position to do so. But this is obscuring the real issue. The reference to "the positive teachings of geological facts" is beside the question. In this connexion these merely tell us that the superficial strata have again and again been ridged up by lateral pressure. But some minds will not rest satisfied with this " positive teaching" without seeking the cause of this phenomenon. That it is due to the contraction of the globe through cooling is an hypothesis seemingly simple and by prescriptive right orthodox, but not necessarily true; while the arrangement of the axes of elevation in lines following undeviating directions for immense distances, instead of forming a network of polygons, by no means favours it. But the discovery of a level of no strain affords perhaps the strongest argument against this theory, more especially if the earth is assumed to be solid, as in the preceding calculations. And it does not seem probable that a better knowledge of the varying conductivity of rocks, or of their contractibility on cooling, would give such altered values to the constants of the problem as to bring up the calculated amount of elevations so as to approach the actual. Dr. Murray estimates the mean elevation of the land of the globe at 1947 feet above the sea, and the mean depth of the ocean at 12,456 feet*, whereas, according to my estimate, the mean height of the elevations which would be caused by the compression of a solid earth, initially supposed at 7000° F., would be only 6 feet †. If we make the supposition that the crust rests on a liquid substratum, we shall still have a level of no strain ‡, and although the amount of the corrugations formed will in this case be somewhat greater, it will still fall far short of that which the "positive teachings of geology" require us to account for. XII. An Improved Form of Littrow Spectroscope. [Plate VI.] T is rather remarkable that in the development of the prismatic spectroscope there have been no important modifications in the general design of the instrument as first used by Newton, progress having been marked mainly in the mechanical improvements of the various parts. Various modifications have, it is true, been proposed from time to time, but none of them has stood the test of usage, except perhaps the form which was first proposed by Littrow in 1862, and bas since been modified and improved by Young and Lockyer¶, Browning**, Grubbtt, Bracket‡‡, and others. In this form, as is well known, the rays from the slit, after being rendered parallel by a collimating-lens, pass through the prism or train of prisms and fall normally upon a plane * 'Scottish Geographical Magazine,' June 1888, vol. iv. + Physics, &c.,' 2nd ed. p. 103. 'Physics, &c.,' Appendix, chap. xxviii. 8 Communicated by the Author. American Journal of Science, 2nd series, vol. xxxv. ** Ibid. p. 237. ++ Monthly Notices of the Royal Astronomical Society, vol. xxxi. American Journal of Science, 3rd series, vol. xxiv. p. 60. p. 36. reflector, and after reflexion retraverse the train in the opposite direction, and are brought to a focus by the same lens which acts as a collimator. To observe conveniently an image of the spectrum, a small right-angled prism covering one half the field is placed near the slit. In certain respects the advantages of this form over the ordinary one are unquestionably great; for not only does it allow all parts of the instrument, save the prisms and plane reflector, to be fixed in position, but it also involves the use of only one lens, a consideration of some importance in the case of large instruments. Unfortunately in this, its original form, it has two very practical disadvantages:-1st, the general illumination of the field of view by reflexion of a portion of the light from the slit from the surface of the lens; and, 2nd, the close proximity of the observing eyepiece to the slit. Both of these difficulties are avoided in the modified forms already referred to, in which the collimator covers only the lower half of the prism, the plane reflector being replaced by a right-angled prism, which is so placed as to return the ray after two internal reflexions through the upper half of the prism. The observing telescope is consequently entirely above and distinct from the collimator, and can be placed at any angle with the latter (usually it is placed at right angles) by the use of another reflector. This arrangement, while entirely avoiding both of the difficulties mentioned, introduces others of a different character. In the first place the cost is considerably increased; for two objectives are required, one for the collimator, the other for the observing telescope; the prisms for a given aperture of telescope must be twice as large as before; and, finally, two right-angled prisms both of large size, one having the same aperture as the telescope, the other an aperture about 1 times greater, are required. This makes the instrument more expensive even than one of the ordinary form of the same dispersion. Again, the increase in the number of optical surfaces involved diminishes very considerably both the brightness and the distinctness of the spectral image, and increases the number of adjustments required for accurate spectrometric work. For all these reasons it is not surprising that these instruments have failed to displace to any extent the standard form; for the only advantage which they possess over that form is their somewhat greater compactness and rigidity, both telescopes being fixed in position. But the simplicity of design and cheapness of construction, which were distinguishing characteristics of the original Littrow form, have been entirely lost in the attempt to overcome the difficulties already mentioned in regard to the illumination of the field and the inconvenient position of the eyepiece. More recently Prof. Bracket* has, without essentially altering the original design of the instrument, overcome the first and principal difficulty, by making the combined collimator and observing lens with faces of such curvature as to reduce the quantity of light reflected to the observing eyepiece to a minimum. It recently occurred to me, in connexion with an attempt to photograph the spectrum with a spectroscope of this form, that the difficulty could be completely overcome by the use of a concave mirror in place of the lens, and a trial of an instrument so constructed showed that it possessed other advantages also. The following brief description of this form of instrument, which is, I believe, new, may therefore be of interest. Fig. 2 (Pl. VI.) is a plan view, the top plate of the containing box being removed to show the parts clearly, and fig. 1 is a side view. A small right-angled prism a receives the light from the slit 8, and reflects it to a concave mirror b which acts as a collimator. From b the collimated beam is reflected to the prism c, behind which is the plane mirror d, which returns the rays again through the prism to the concave mirror, by which they are finally brought to a focus at the observing eyepiece, which is placed just above the plane of the_slit and near the edge of the prism. A blackened screen L is placed between the prism and the eyepiece to cut off the light reflected from the faces of the former. A second screen, L, is placed between the eye and the slit, or else the beam of light is brought to the latter through a tube or box, as indicated by the dotted lines. Diaphragms m, n are also placed in front of the eyepiece to cut off any general light diffused from the walls of the enclosing box, which are of course carefully blackened. It will be readily seen that with this arrangement of apparatus, the only light which can reach the eyepiece besides that which forms the spectral image is that which is diffused by the reflecting surface of the mirror. If this mirror is properly silvered† the general illumination due to this cause will be insignificant, and the field of view will be quite as *Loc. cit. In order to secure a non-diffusive coat of silver, it is necessary to so manage the silvering bath that the deposited film is bright as it comes from the solution and requires no subsequent polishing; for no matter dark as in the ordinary form of spectroscope. This construction, therefore, overcomes the main objection to the Littrow form, and enables all the advantages of that form to be realized, while it also possesses, as I shall proceed to point out, certain advantages of its own in the way of greater compactness, better definition, and, finally, greater cheapness of construction. As all parts of the instrument save the concave mirror are close together, they may all be placed on a small base, which even for the largest instrument need not be more than 8 or 10 in. in diameter, as there are no heavy rotating or overhanging parts, as in the other forms of spectroscope. The concave mirror itself may then be placed on a separate stand and connected with the rest of the apparatus when the instrument is in use, by means of a paper tube or light wooden frame covered with black cloth. Great focal lengths may thus be easily employed without increasing the cost or bulkiness of the instrument, with a corresponding gain in brightness and in definition. Better definition also results from the fact that the number of optical surfaces concerned is less than in any other form of the same dispersive power. Thus in the ordinary Littrow form (one prism) with an achromatic lens there are 8 optical surfaces, and the ray meets 6 of these twice, making 14 reflexions or refractions between the slit and eyepiece. In the ordinary form of equivalent dispersion (two-prism) spectroscope there are 12 surfaces and 12 refractions, while in the concave-mirror form there are only 5 surfaces and 8 refractions or reflexions. Moreover, there is no change of focus for different parts of the spectrum, an advantage of some moment when photographs are being taken, and although the concave mirror is astigmatic when used as here shown, this astigmatism is no disadvantage when viewing the image of a slit, and may how great care is taken, minute scratches are sure to be made by the polishing pad. To obtain such a coat it is necessary:-- 1st, that great care be taken in cleaning the glass surface; 2nd, that pure chemicals be used for the silvering solution; 3rd, that the temperature of the depositing bath be the same as that of the mirror, and preferably below 70 degrees in order that the deposit may proceed slowly and uniformly. I have obtained good results with both the Rochelle-salts process and the Brashear process; but for this purpose prefer the latter, as it gives a very hard film which may be vigorously rubbed with a pad of absorbent cotton while still wet. The former process, however, is, I think, preferable for "half silvering," i. e. for obtaining a very even semitransparent film. |