sets of equally distant and not too thin bars inclined at a small angle. Where the opaque and tranparent parts severally overlap, the obstruction of light is, on the average, less than the double of that due to each set separately*, and consequently these places appear by comparison bright. The interval between the bars is evidently half the long diagonal of the rhombus formed by two pairs of consecutive lines, and is expressed by a cos 0÷sin 0, or approximately a÷0, where a is the interval between the primary lines, and the mutual inclination of the two sets. When parallelism is very closely approached, the bars become irregular, in consequence of the imperfection of the ruling. This phenomenon might perhaps be made useful as a test. If the planes of the films be not quite parallel, bars parallel to the original lines may appear when the line of intersection of the planes is in the same direction. This arises from a foreshortening of one of the sets, making it equivalent to a grating of a somewhat higher degree of fineness. When examined under the microscope, the opaque bar on the copy, which corresponds to the shadow of the groove of the original, is seen to be composite, being not unfrequently traversed along its length by several fine lines of transparency. In one case, where the copy was on common glass, this effect went so far that at certain parts of the grating the periodicity was altered by each line splitting into two, the first spectrum altogether disappearing. In order to make this observation, the eye should be placed at the point where the pure spectra are formed and be focused on the grating. The places in question will then appear as irregular dark bands. The disappearance of the first spectrum is very unusual; but it is common for bands to appear when the eye is placed in the place of the fourth and higher spectra. When the order is high, the bands will not be black, but coloured with light belonging to one of the other spectra. There is no difficulty in understanding how this occurs. In the process of copying, the groove of the original is widened into a bar, whose width depends on the closeness of contact, an element which necessarily varies at different parts of the plate. The dark bands are the locus of points at which the relation of the alternate parts is such as to destroy the spectrum in question. I have not had an opportunity of trying the method of copying on lines closer than 6000 to the inch; but I have no doubt that the limit of fineness was not attained. I should expect to find no difficulty with lines 10,000 or 12,000 to the inch; but beyond that point it is possible that the method would fail, The mathematical reader will easily prove this from the law of absorption. or require special precautions, such as the use of extra-flat glass and greater pressure to ensure close contact in the printing. For preliminary experiments I should be inclined to try mica as a support, whose flexibility would facilitate a close contact. I may mention that I have done copies of the 3000line grating on sheets of mica, which may be obtained very thin and smooth from the photographic dealers. For more convenient manipulation in the preliminary stages of preparation, the mica should be mounted on a sheet of glass of the same size as itself. A small drop of water interposed will ensure a sufficiently close adhesion. I have tried to take copies of copies, but with indifferent success, even when the performance of the first was not perceptibly inferior to that of the original. Gratings may be copied without the aid of photography by simply taking a cast. Following Brewster, I have obtained a fair result by allowing filtered gelatine to dry after being poured on the 3000 Nobert. This method, however, is attended with much more risk to the original, and is besides open to other objections, sufficient, I think, to prevent its competing with photography. [To be continued.] XIII. On Wheatstone's Bridge. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, MR. a Newcastle-on-Tyne, R. BROUGH, in the last Number of this Journal, has called attention to the fact that, in a paper "On the best Arrangement of Wheatstone's Bridge," in the Philosophical Magazine for February 1873, I did not start from the general equation for the strength of the current through the galvanometer irrespective of a balance, but took that form which the expression assumes when at a balance. In fact I assumed (ad-bc) to be indefinitely small. My reason for doing so was, that the question was to find the best arrangement at a balance, the great object of resistance-measuring being to get a balance; besides which, the course I adopted led to much greater simplicity and no less accuracy. To take the special case upon which Mr. Brough dwells, viz. to find the best resistance for the galvanometer. This amounts to finding the resistance external to the galvanometer; and when a balance is obtained, as the galvanometer and battery are conju Si gate resistances, the resistance of the latter does not appear in the expression for the resistance external to the galvanometer, which is not in any way affected by the battery resistance. milarly for the resistance external to the battery, which, at a balance, is independent of the galvanometer resistance. I cannot agree with Mr. Brough that to find the resistance in either case at a balance is a mere mathematical problem destitute of physical meaning; for it is only when at a balance that the problem has any practical importance. As Mr. Brough most truly observes, most Wheatstone's bridges are wrongly arranged. An excellent example of this once came under my notice. A gentleman informed me he was about to make a Wheatstone's bridge, a great improvement, and very economical. Instead of using three separate sets of resistance-coils (a, b, c) he would use only one (c); for he would make a and b equal to 0. Mr. Harris's arrangement appeared to succeed admirably. There was no difficulty whatever in getting a zero; in fact there was always a balance, whether the line under examination was long or short. There was only one drawback; and that was, the improvement afforded no information whatever as to the resistance of the line. I am &c., OLIVER HEAVISIDE. P.S. The condition that the galvanometer should connect the junction of the two greatest with the junction of the two least of the resistances, is necessarily complied with by the equations I have given for the best arrangement with a given galvanometer. and battery; else it would not be the best arrangement. XIV. On Ocean-currents.-Part III. On the Physical Cause of Ocean-currents. By JAMES CROLL, of the Geological Survey of Scotland. [Continued from vol. xlii. p. 280.] Further Examination of the Gravitation Theory of Oceanic Circulation. FEW Introduction. NEW subjects have excited more interest and attention than the cause of ocean circulation; and yet few are in a more imperfect and unsatisfactory condition, nor is there any question regarding which a greater diversity of opinion has prevailed. Our incomplete acquaintance with the facts relating to the currents of the ocean and the modes of circulation actually in operation, is no doubt one reason for this state of things. But doubtless the principal cause of such diversity of opinion lies in the fact that the question is one which properly belongs to the domain of physics and mechanics, while as yet no physicist of note (if we except Dr. Colding, of Copenhagen) has given, as far as I know, any special attention to the subject. It is true that in works of meteorology and physical geography reference is continually made to such eminent physicists as Herschel, Pouillet, Buff, and others; but when we turn to the writings of these authors we find merely a few remarks expressive of their opinions on the subject, and no special discussion or investigation of the matter, nor any thing which could warrant us in concluding that such investigations have ever been made. At present the question cannot be decided by a reference to authorities. The various theories on the subject may be classed under two divisions: the first of these attributes the motion of the water to the impulse of the wind, and the second to the force of gravity resulting from difference of density. The latter may be subdivided into two classes. The first of these (of which Maury may be regarded as the representative) attributes the Gulf-stream and other sensible currents of the ocean to difference of specific gravity. The other class (at present the more popular of the two, and of which Dr. Carpenter may be considered the representative) denies altogether that such currents can be produced by difference of specific gravity*, and affirms that there is a general movement of the upper portion of the ocean from the equator to the poles, and a counter movement of the under portion from the poles to the equator. This movement is attributed to difference of specific gravity between equatorial and polar water, resulting from difference of temperature.. The former theory I examined at some length in a paper in the Philosophical Magazine for October 1870, and the latter theory in a paper in the same journal for October 1871. Since then Dr. Carpenter has done me the honour, in a paper read before the Royal Society†, to discuss at considerable length the various objections advanced by me to his theory. He has also in this memoir stated and explained his views on several points more fully than on former occasions. He further restates at some length the various facts for which his theory is designed to account, facts which he considers I have never attempted to explain. This to a certain extent is true; for as yet I have not reached that part of my paper "On Ocean-currents" in which these points fall to be discussed. One of the objects of the present paper is to endeavour to show that all the facts to which Dr. Carpenter refers can be perfectly well explained without having recourse to any such general movement of the ocean as he * Proceedings of the Royal Society, No. 138, p. 596, foot-note. † See Proc. Roy. Soc. No. 138. assumes to exist. I have also considered more in detail what seem to me to be the radical defects of his theory, and have again reviewed some matters regarding which he appears to have slightly misapprehended the drift of my argument. It was shown on a former occasion that, if the heat received by the ocean in intertropical regions were distributed over the globe, not by currents produced by the wind, but by means of a circulation due to difference of temperature between equatorial and polar waters, then there could be no secular changes of climate resulting from variations in the eccentricity of the earth's orbit-because such a mode of circulation would, as I have shown, tend to neutralize the effects which would otherwise result from an increase of eccentricity. For this reason I have been the more anxious to prove that intertropical heat is conveyed to temperate and polar regions by ocean-currents, and not by means of any general movement of the ocean resulting from difference of gravity. I have therefore on this account entered more fully into that part of the subject than I otherwise would have done. Irrespective of all this, however, the important nature of the whole question, and the very general interest it excites, may be regarded as sufficient excuse for the length of the present communication. Circumstances over which I had no control have delayed its publication for nearly a year. The Facts and their Explanation. "I have thought it desirable," says Dr. Carpenter, "to develope somewhat at length what I regard as the bearings of the results obtained by these inquiries upon the doctrine of a general oceanic circulation sustained by difference of temperature. As no similarly comprehensive examination has been made, so far as I am aware, by any other scientific inquirer, and as the doctrine put forth on the subject by Mr. Croll is likely, if not thus scrutinized, to command the unquestioning assent of those who regard him as a high authority on the subject of oceanic currents and their bearings on geological questions, I venture to hope that the conclusion of its results as an appendix to this Report will not be deemed inappropriate" (p. 538). The Facts to be explained.--He then commences by giving a restatement of the facts for the explanation of which his theory of a general oceanic circulation has been advanced. It is well known that, wherever temperature-observations have been made in the Atlantic, the bottom of that ocean has been found to be occupied by water of an ice-cold temperature. And this holds true not merely of the Atlantic, but also of the ocean in intertropical regions-a fact which has been proved by repeated observations, and more particularly of late by those of Commander Chimmo in the China |