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. Similarly 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 vo 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.

EW 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 inatter, 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

Sea and Indian Ocean, where a temperature as low as 32° Fahr. was found at a depth of 2656 fathoms. In short the North Atlantic, and probably the intertropical seas also, may be regarded, Dr. Carpenter considers, as divided horizontally into two great layers or strata-an upper warm, and a lower cold stratum. All these facts I, of course, freely admit; nor am I aware that their truth has been called in question by any one, no matter what his views may have been as to the mode in which they are to be explained.

The Explanation of the Facts.-We have next the explanation of the facts, which is simply this:-The cold water occupying the bottom of the Atlantic and of intertropical seas is to be accounted for by the supposition that it came from the polar regions. This is obvious, because the cold possessed by the water could not have been derived from the crust of the earth beneath: neither could it have come from the surface; for the temperature of the bottom water is far below the normal temperature of the latitude in which it is found. Consequently "the inference seems irresistible that this depression must be produced and maintained by the convection of cold from the polar towards the equatorial area." Of course, if we suppose a flow of water from the poles towards the equator, we must necessarily infer a counter flow from the equator towards the poles; and while the water flowing from equatorial to polar regions will be warm, that flowing from polar to equatorial regions will be cold. The doctrine of a mutual interchange of equatorial and polar water is therefore a necessary consequence from the admission of the foregoing facts. With this explanation of the facts I need hardly say that I fully agree; nor am I aware that its correctness has ever been disputed. Dr. Carpenter surely cannot charge me with overlooking the fact of a mutual interchange of equatorial and polar water, seeing that my estimate of the thermal power of the Gulf-stream, from which it is proved that the amount of heat conveyed from equatorial to temperate and polar regions is enormously greater than had ever been anticipated, was made a considerable time before he began to write on the subject of oceanic circulation*. And in my paper "On Ocean-currents in relation to the Distribution of Heat over the Globe"+, I have endeavoured to show that, were it not for the raising of the temperature of polar and high temperate regions and the lowering of the temperature of intertropical regions by means of this interchange of water, these portions of the globe would not be habitable by the present existing orders of beings.

*Trans. of Glasgow Geol. Soc. for April 1867. Phil. Mag. for Feb. 1867 and June 1867 (Supplement).

† Phil. Mag. for February 1870.

Phil. Mag. S. 4. Vol. 47. No. 310, Feb. 1874.

The explanation goes further:-"It is along the surface and upper portion of the ocean that the equatorial waters flow towards the poles, and it is along the bottom and under portion of the ocean that polar waters flow towards the equator; or, in other words, the warm water keeps the upper portion of the ocean and the cold water the under portion." With this explanation I to a great extent agree. It is evident that, in reference to the northern hemisphere at least, the most of the water which flows from intertropical to polar regions (as, for example, the Gulf-stream) keeps to the surface and upper portion of the ocean; but, for reasons which I have stated in my last paper*, a very large proportion of this water must return in the form of under currents; or, which is the same thing, the return compensating current, whether it consist of the actual water which originally came from the equator or not, must flow towards the equator as an under current. That the cold water which is found at the bottom of the Atlantic and of intertropical seas must have come as under currents is perfectly obvious, because water which should come along the surface of the ocean from the polar regions would not be cold when it reached intertropical regions.

The explanation hypothetical.-Here the general agreement between us in a great measure terminates; for Dr. Carpenter is not satisfied with the explanation generally adopted by the advocates of the wind theory, viz. that the cold water found in temperate and intertropical areas comes from polar regions as compensating under currents, but advances a hypothetical form of circulation to account for the phenomenon. He assumes that there is a general set or flow of the surface and upper portion of the ocean from the equator to polar regions, and a general set or flow of the bottom and under portion of the ocean from polar regions to the equator. Mr. Ferrel ('Nature,' June 13, 1872) speaks of that "interchanging motion of the water between the equator and the pole discovered by Dr. Carpenter." In this, however, Mr. Ferrel is mistaken; for Dr. Carpenter not only makes no claim to any discovery of the kind, but distinctly admits that none such has yet been made. Although in some of his papers he speaks of a "set of warm surface-water in the southern oceans toward the Antarctic pole" as being well known to navigators, yet he nowhere affirms, as far as I know, that the existence of such a general oceanic circulation as he advocates has ever been directly determined from observations. mode of circulation is simply inferred or assumed in order to account for the facts referred to above. "At present," Dr. Carpenter says, "I claim for it no higher character than that * Phil. Mag. for October 1871, p. 267.

This