arise in the construction of the aplanatic object-glasses of modern telescopes. This step appears to be one of very considerable importance towards facilitating the construction of object-glasses of large dimensions. We may consider, then, that the once difficult question of the removal of spherical aberration in an object-glass as now practically solved, and that too in a manner which requires but little further trouble than the inspection of a set of tables. There does, however, still exist a practical difficulty, where theoretically there was, or even now is, supposed to be none. It is almost universally asserted in treatises upon the subject, that in order to produce an achromatic combination nothing further is required than to make the focal lengths of the two lenses proportional to the dispersive powers of the materials of which they consist. Practically, and even theoretically, this is not the case; but, on the contrary, the proper ratio of the focal lengths of the two lenses is perceptibly influenced by the forms or curvatures of the lenses themselves. It is herein that the eye and the skill of the optician rather than those of the mathematician are required; and (perhaps unexpectedly) it is in this direction that we are to look for one of the weakest and most troublesome elements in the construction of the object-glasses of telescopes. The proper mode to be pursued for obtaining the achromatism required must be reserved for another place of communication. From what has preceded, it will be seen that since the spherical aberration of a lens does not depend solely on the amount of the total deviation which it produces on a marginal ray, but on some function of the relative amounts of the deviation at each of the two surfaces, it follows that there is for every lens a certain proportion in the curvatures of the surfaces which produces a minimum aberration. Hence there must always exist Two forms of a lens of a certain power, which will produce a certain amount of aberration, one on each side of the minimum. Suppose, then, it is required to find the curvatures of the four surfaces of an aplanatic lens. The first thing to be done is to obtain (in a way not here explained) the relative focal lengths of the lenses which will produce an achromatic combination. If the focal length of the combination be known, the focal lengths of the two lenses will then be determined. Suppose now that, for any reason, a certain ratio of the curvatures of the convex or crown lens be assumed. The tables calculated by Mr. Pritchard will at once, by, inspection, give the aberration of that lens for parallel rays. Now, there will be two concave lenses of flint glass of any given optical quality, which will not only achromatise the foregoing crown lens, but also will destroy its spherical aberration. The inspection of a second set of tables will indicate the relative curvatures of the surfaces of this correcting flint lens. Mr. Cooke, in his practice, generally makes the proportion of the radii of his surfaces of the crown lens as 2: 3, because such a proportion leads to no comparatively violent deviations at any of the four surfaces, while it admits at the same time of two concave surfaces for the correcting flint lens, which surfaces, by dint of their concavity, admit of easy examination for the mechanical perfection of figure. Sir John Herschel conducted his investigation of the aberration of a compound lens in such a manner as to give the total aberration in the form B C A+ + when D is the distance of the radiant point flight, and where DD2; A B C are functions of the materials of the two lenses, and of the curvatures of their surfaces. He then, for the convenience of calculation, assigned such a relation between the four curvatures as rendered Bo, assuming at C the same time that D is sufficiently large as to render =0. Finally, the D2 four-curvatures of the lenses are to be made such as also to render A=0. A combination of this sort will be free from aberration for points of light at moderate as well as at practically infinite distances, a result of no real importance. But it will be found that such a combination requires great accuracy in the construction, inasmuch as small errors in the curvatures produce comparatively large amounts of outstanding aberration. The Frauenhofer construction is closely allied to this, if not identical with it. Mr. Dallmeyer modifies Sir John Herschel's form, under the hope, and with the view of reducing the coma attaching to stars viewed obliquely and not near the centre of the field. Thus wide, then, is the choice which exists in the forms of the lenses which will produce an aplanatic combination, and such are some of the reasons which guide the particular forms selected by particular artists. When that great sidereal astronomer, W. Struve, commenced his memorable career at Dorpat, in 1813, he there found the chief instruments constructed by our own countrymen, either Dollond or Troughton. Owing to the baneful influence of the excise laws on the manufacture of glass, it had become impossible in England to obtain a material for the construction of object-glasses of any size beyond four or five inches at the utmost. Hence the art passed away from England and its great artists, to Frauenhofer and Mertz at Munich, where no impediment from the excise intervened. As a necessary consequence, when the new observatory at Pulkowa was furnished in 1839 by imperial munificence with new instruments, not a solitary telescope was procured, or in fact ought to have been procured, from England. Even our own great Faraday was impeded by a meddlesome and mischievous excise in the prosecution of his attempts to improve the manufacture of homogeneous optical glass. At the present time, optical glass of exquisite quality is manufactured by Messrs. Chance in England (though in reality by a foreigner); and no doubt remains that any of our three English artists, Messrs. Cooke, Dallmeyer, and Simms, now more than successfully compete both in quality and price with foreign opticians, in the production of object-glasses of the largest dimensions. COMETARY INTELLIGENCE. COMET I. of 1866. The following elements of this comet are by Prof. J. R. Eastman, of Washington, U.S.: THE EARTH'S ATMOSPHERE. (By G. F. CHAMBERS, F.R.A.S.) THE ancients regarded the atmosphere as one of the four elements, the other three being earth, fire, and water, into which all things in the universe could be resolved; and this opinion remained current for hundreds, nay thousands, of years, until, in fact, the middle of the seventeenth century, when Boyle, Hook, and others first began to doubt the accuracy of the long-received idea; and in the course of another hundred years the non-elementary nature of the atmosphere was finally proved by Cavendish and Lavoisier. In general terms we may say that the air consists of 4 parts of nitrogen and I of oxygen; but it will be well to give the exact numerical results of a recent determination of its various constituents: It will not be inappropriate for me here to speak of these components individually, but briefly, because a systematic consideration of them belongs rather to the province of chemistry.* Oxygen,† symbol, O; equivalent number, 8: combining volume, I; specific gravity, 11057. Oxygen combines with greater or less readiness with all the other known elements, fluorine excepted. Foremost amongst its peculiar properties must be placed that of supporting combustion and animal life. Many substances which in ordinary air, burn calmly, in oxygen burn with great violence and brilliancy; phosphorus, and (if previously kindled) charcoal, and sulphur especially. Its functions in supporting life are all-important; without oxygen no vital being could exist; but the gas must be mixed with other gases, for though a supporter of life in a simple form, yet its stimulating * See especially Dr. W. A. Miller's Elements of Chemistry, by far the best text-book extant. + From otùs, "sour," and yevváw, "I produce." character is such that it cannot be breathed for any length of time without producing over-excitement of the system and fatal consequences. Like air, oxygen is destitute of colour, taste, and smell. It is the most abundant of all elementary substances, and produces the smallest refractive deviation upon rays of light. Many efforts have been made, but chemists have never succeeded in liquefying oxygen either by means of pressure or cold, though a pressure of 58 atmospheres, and a temperature of -145° F. have been attained. Oxygen is feebly but sensibly magnetic; but it loses its magnetic qualities when raised to high temperature, though they are regained when cooling takes place. The former fact was first hinted at by Faraday in 1847*, and proved by him,† and by Becquerel independently, a few years subsequently. It is soluble in water to the extent of 4 per cent. at a temperature of 32°. It is heavier than atmospheric air in the ratio of about 11 to 10. Oxygen was discovered by Priestly in 1774.§ Nitrogen,|| symb. N; eq. no. 14; comb. vol 2; sp. gr. 0.9713. The chemical properties of nitrogen differ most widely from those of oxygen; it supports neither combustion nor animal life, though, as regards the latter, it is not directly poisonous itself. In other respects, however, it resembles oxygen, in having neither colour, taste, nor smell, and in never having been liquefied. Nitrogen is extensively diffused, and occupies an important position in the economy of life. It was discovered by Rutherford in 1772. 2 Carbonic acid, symb. C. O2 eq. no., 22; comb. vol. 2; sp. gr., 1529. Quantitatively carbonic acid is an unimportant constituent of the atmosphere, and it is not necessary for the support of animal life, but without it vegetation would fail; plants requiring a certain feed of it as it were, for their growth and development. Carbonic acid, when pure, is devoid of colour, but possesses a faint odour and taste. It is not inflammable, neither does it support combustion or animal life. When present in the atmosphere to the comparatively small extent of 4 or 5 per cent. it acts as a narcotic poison, and in still less quantities exercises a depressing and, after a time, injurious influence on the system. In the act of respiration, on the part of man and animals, carbonic acid is largely thrown into the surrounding air, and to this circumstance is due the disagreeable effect experienced * Phil. Mag. vol. xxxi. p. 410. 1847. + Phil. Trans. vol. cxli. p. 23. 1851. & Phil. Trans. vol. lxiv. p. 384. 1775. vírpov, "nitre," and yevváw, "I produce;" sometimes called azote, from a, “not,” and wǹ, "life," because it is incapable of supporting life. in large crowded assemblies, in which a free circulation of external air is not provided for. Thus is shown the importance of ventilation. Carbonic acid is largely met with in nature, in union with water, in the form of gaseous springs, more commonly spoken of as "mineral springs." In processes of fermentation it is disengaged in great quantities. Newspaper reports often speak of accidents to persons incautiously entering vats, &c.; these accidents are due to the pressure of a noxious excess of carbonic acid, which should always be carefully guarded against. Carbonic acid is liquefied under a pressure of 36 atmospheres, and at a temperature of 32° F.; liberated in this state the evaporation is so rapid, and the cold resulting so intense (-148° F) that it assumes a solid form, resembling compressed snow, and remains congealed for some little time; even under the ordinary pressure of the atmosphere carbonic acid is half as heavy again as cor mon air, and may readily be poured from one vessel to another like a liquid. It was discovered by Black in 1757. The aqueous vapour existing in the atmosphere will be treated of under the head of hygometry, and the other chemical components are too unimportant to receive special notice here. At one time there existed much difference of opinion as to whether the compounds of the atmosphere were chemically or only mechanically united. Dalton warmly supported the latter theory, when he found by experiment (as he considered he did) that the former was impossible; and it is the one now universally adopted. Dr. Thomson of Edinburgh makes some remarks on the general composition of the air, which I cannot refrain from quoting. He says: "We cannot too much admire the wisdom of the Creator in adjusting the proportions so exactly for the comfort and preservation of His creatures. . . . Two vol. of nitrogen, and half a vol. of oxygen, compose the air we breathe. Two vol. of nitrogen, and one vol. of oxygen, form the nitrous oxide or laughing-gas of Davy-a fluid which, when inhaled for a few minutes, intoxicates, but which would be injurious, if not fatal, if breathed for any length of time. Two vol. of nitrogen, and two vol. of oxygen, form the nitric oxide—a gas which cannot be respired, for, coming in contact with the atmosphere, it is instantly converted into a poisonous acid, the nitrous acid, recognised by its ruddy fumes. Two vol. of nitrogen, and three vol. of oxygen, form the hypo-nitrous acid, which exists only in combination with a base. Two vol. of nitrogen, and four vol. of oxygen, form the nitrous acid already mentioned. Two vol. of nitrogen, and five vol. of oxygen, comprise nitric acid, or aqua-fortis, one of the |
