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miles per day; the average of the six months of most rapid rate is 60-6 miles per day.

Further, as the maximum rate given by the Meteorological Department is 106 miles per day, and as this rests on only a single observation, it is obvious that the Admiralty maximum of 120 miles per day is a case as exceptional as that of a man who has twenty children by one wife.

The annual mean assumed by Mr. Croll, on the basis of the maximum and minimum rates, thus exceeds the very highest actual monthly average, and is more than double the monthly average of half the year; whilst the annual mean stated by me, on the express authority of the Meteorological Department, is the average of all the observations in its possession.

The foregoing case furnishes a typical example of the arithmetical method on which Mr. Croll relies, in his laboured disproof of the doctrine of a Vertical Oceanic Circulation sustained by Thermal Agency alone, which has received the full sanction, on theoretical grounds, of numerous eminent Physicists (as, for example, of Sir George Airy, in his Presidential Address to the Royal Society in 1872), and which appears to the French Academicians before whom I recently brought it (Comptes Rendus, April 6), to be in entire harmony with the facts of Ocean-temperature as determined by the Challenger' observations.

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But, further, Mr. Croll asserts (p. 99) that "all we really require to account for the cold water which is found to occupy the bed of the ocean in temperate and equatorial regions," is a set of polar under-currents maintained by the winds which impel equatorial water towards the poles; and further (p. 175), that, "so far as the distribution of heat over the globe is concerned, it is a matter of indifference whether there really is or is not such a thing as this general oceanic circulation. The enormous amount of heat conveyed by the Gulf-stream alone puts it beyond all doubt that ocean-currents are the great agents employed in distributing over the globe the excess of heat received by the sea in intertropical regions."

Regarding the facts of the case as better data than Mr. Croll's figures, I would submit whether the following considerations do not furnish a reductio ad absurdum of the foregoing statements:

1. In the Equatorial Atlantic, as is shown by the 'Challenger' sections, the whole mass of water, from 300 fathoms to the bottom at (say) 2500 fathoms, has a temperature descending from 40° to 32°. The isocheimenal of the Equatorial Atlantic (which, as is shown by the temperature-phenomena of the Mediterranean and Red Sea, would be the temperature of all but the superficial stratum throughout the year, if Polar water were excluded) is about 75°. Hence it is clear that the great bulk of this water must have travelled to the Equator from the Polar areas.

That

(1) this enormous mass of glacial water, of which, across the whole breadth of the South Atlantic, the lowest stratum of 500 fathoms has an average temperature below 35°, exerts no cooling influence on the Intertropical area, and that (2) it can have been propelled thither by the agency of the Gulf-stream or of any other superficial wind-currents, seem to me propositions equally opposed to common sense.

2. That Polar water is met with at a much less depth under the Equator than it is in the extratropical zone, seems a clear indication that it is continually rising there from the bottom towards the surface, as would of course be the case on the theory of a Vertical Oceanic Circulation; and this inference is strikingly confirmed by the fact (which is diametrically opposed to another of Mr. Croll's assertions, p. 100), that while the salinity of the bottom-water maintains its low Polar standard as far as the Equator, and while the salinity of extratropical surface-water is considerably higher, the salinity of Equatorial surface-water is as low as that of the Polar bottom-water.

3. Of the Polar-Equatorial flow thus evidenced, a poleward flow of the whole upper stratum is a necessary complement; and the observations made by my colleagues and myself between Lisbon and the Faroe Islands, indicate that the thickness of this north-moving stratum is there not less than 700 fathoms; whilst the course of Dr. Petermann's isothermal lines clearly shows that it extends all across the Atlantic to Newfoundland, where the summer isotherms turn almost due north. That this vast body of water can be propelled by the vis a tergo of the true Gulf-stream (which off Sandy Hook has a breadth of about 60 miles and a depth of 100 fathoms), I have not heard of any one but Professor Wyville Thomson, Mr. Croll, and Dr. Petermann, who would seriously assert. That it exerts no heating influence, not even Mr. Croll would affirm.

4. That the real Gulf-stream, or Florida Current, reaches North-western Europe, is a pure assumption of geographers and meteorologists, to account for the abnormally high temperature brought thither by the sea. On evidence which no one has disproved, it may be affirmed that the real Gulf-stream dies out, i. e. loses all the distinctive characters of a current, in the Mid-Atlantic. On the other hand, a vera causa satisfactory to Physicists has been shown to exist for the poleward movement of the entire upper stratum. And thus Professor Möhn, of Christiania, in sending me his work 'On the Climatology of Norway' (1872), which assigned to the Gulf-stream the mild winter of the Norway coast, informed me that if he had been acquainted with my latest Report he should have expressed himself very differently, being now satisfied that this amelioration is produced, not by the Florida Current, but by the General

Oceanic Circulation,-as is also Dr. Meyer, who has been engaged for some years in the study of the Physics of the Baltic and the North Sea.

If Mr. Croll cannot apprehend a Physical conception which such men as Sir William Thomson and M. Dumas (who have kindly allowed me thus to cite their authority) accept as having a valid scientific basis, I submit that the fault is not mine, but his; and shall not feel called upon to prolong a discussion which will obviously never convince him. My time will be much better employed in working out an experimental investigation by which I have reason to hope that further light will be thrown upon the matter.

A

I remain, Gentlemen,

Your obedient Servant,

WILLIAM B. CARPENTER.

XLVI. A Variation-Barometer. By F. KOHLRAUSCH*. [With a Plate.]

BAROMETER which combines with unbounded sensitiveness the absence of any friction, which requires only a single observation to be made that consumes no time, and possesses so slight a moment of inertia that it follows the variations of the atmospheric pressure in the fraction of a second, will probably excite some interest; wherefore I will describe the simple way in which I have produced such a one (Plate IV. fig. 3).

The air-exhausted metal ring from a Bourdon aneroid† is on one side firmly screwed on a holder; the other, free end pushes with its rounded projection against a small mirror in a metal frame, which is suspended on little steel springs (strips of pendulum-steel). An axis, which I first tried, even the finest, rendered the sensitiveness illusory; I had therefore put aside as useless the apparatus already four years old. The mirror-holder can be shifted a little on the bottom-plate by means of two notches; at the lowest height of the barometer the mirror must rest more securely against the projection. A small wing, soldered to the ring, and dipping deep into the liquid (glycerine) contained in a vessel, serves to rapidly still any vibrations.

The instrument is set up firmly upon a wall-stand, best by means of a screw through the centre of the bottom-plate, after regulating it with the adjusting-screws; and then the observations are effected in the usual manner with telescope and vertical scale ‡. My scale is placed at about 3 metres distance from the mirror. * Translated from a separate impression, communicated by the Author, from Poggendorff's Annalen, vol. cl. p. 423.

† I have obtained such tubes through M. Apel, University Mechanician, Göttingen.

M. Waibler, Mechanician, Darmstadt, supplies the apparatus for 12 thalers.

Thus nearly 25 scale-divisions correspond to 1 millim. of the mercury barometer; so that the variations of pressure which occur with us require a scale a metre in length. Sudden opening or closing the door of the observing-room causes the image to move over 2 or 3 divisions. A further augmentation of the sensitiveness could be obtained without difficulty by increasing the distance of the scale or placing the point of contact higher, but might not answer any purpose.

The instrument is, of course, intended for observations within a brief space of time; nevertheless, in the course of an entire month, mine changed its position relative to a mercury barometer by only about millim. of the latter.

The influence of temperature was uncommonly great, viz. 0.3 millim. for 1°. As a fall of the position corresponds to a rise of temperature, it is evident that the phenomenon arises from too much air being contained in the tube, and that it can be easily obviated. Since we have, as two opposite corrections, the diminution of the elasticity of the metal and the increase of that of the internal air, it must be possible even to reduce to zero the temperature-correction of any aneroid barometer by fixing its content of air at a determinate quantity. From the series of observations which I have made occasionally in the course of the last few months it follows that, as was to be expected, the pressure of the air seldom remains constant, even for a short time. For the most part, very small variations are constantly taking place. It is different, however, at times of high wind. The upper curve, fig. 4, gives for instance the course during three minutes on the 26th of February last, a stormy day. The entire height of the figure corresponds to 1 millim. of mercury; so that the greatest fluctuation denotes millim. In the observing-room a window, turned away from the direction of the wind, was opened. The noting-down took place every three seconds; nevertheless a great number of small variations could not be recorded. The lower curve exhibits the progress during a moderate hail-shower accompanied by a thunder-storm on May 30, likewise in the course of three minutes. The tempest had commenced some minutes previously. The smaller undulations which follow the initial larger wave continue, diminishing, for some time.

The past summer afforded frequent opportunities of observation during violent storms; yet I have never been able to detect any connexion between the oscillations and lightning.

I must remark in conclusion, that M. Röntgen has employed the mirror-reading in another way for measuring the pressure, and also projected an aneroid barometer with mirror and scale*. * Pogg. Ann. vol. cxlviii. p. 624.

XLVII. Notices respecting New Books.

An Elementary Treatise on Quaternions. By P. G. TAIT, M.A., Formerly Fellow of St. Peter's College, Cambridge, Professor of Natural Philosophy in the University of Edinburgh. Clarendon Press Series. Oxford. 1873. (Pp. 296.)

THIS

HIS is the second and enlarged edition of a work first published in the year 1867. It is designed to render the subject of Quaternions "intelligible to any ordinary student;" but it must be understood that the "ordinary student" means one who is already familiar with such subjects as Surfaces of the Second Order, Homogeneous Strain, the Theory of Double Refraction, Electrodynamics, &c. as commonly treated, and so is likely to be interested in seeing the same subjects treated by a new method. It must be a matter of congratulation to all who are interested in Quaternions that a second edition of the present work should be called for after the lapse of only six years; and this fact probably justifies the opinion of the author, that "there seems now at last to be a reasonable hope that Hamilton's grand invention will soon find its way into the working world of science."

Passing to the contents of the volume, we may say that the first five chapters are devoted to an exposition of the principles of the science, viz. to Vectors and their composition, to Products and Quotients of Vectors, to interpretations and transformations of Quaternion expressions, to differentiation of Quaternions, and to the solution of Equations of the first degree. These chapters occupy 103 pp. The remainder of the book is taken up with applications-in the first place to Geometry, in the next to Kinematics and Physics.

Owing to the great variety of subjects treated, it is not easy to give a satisfactory idea of the contents; perhaps our best course will be to state with some minuteness the contents of a single discussion, and leave the reader to draw his own inferences. For this purpose we will take the articles on Homogeneous Strain, a branch of Kinematics which Professor Tait has made his own, having published three distinct accounts of the subject*. The author first shows that the determination of a vector whose direction is unchanged by strain depends on the solution of a cubic equation with real coefficients, and obtains the form which this equation takes when the mass is rigid. He then shows that a mass initially spherical becomes an ellipsoid after strain, and, on the other hand, that a mass spherical after strain was ellipsoidal before strain, the axis of the ellipsoid in either case corresponding to a rectangular set of three diameters of the sphere. After defining a pure strain, he obtains a criterion by which to distinguish it from other strains, and proves that two pure strains successively applied give a strain accompanied by rotation. "The

* Viz. Treatise on Natural Philosophy,' vol. i. pp. 99 &c., 'Elements of Quaternions,' p. 210 &c. (the work noticed in the present article) 'Introduction to Quaternions,' p. 180 &c.

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