sisted of three levers; by pressing them down steel springs moved along a very short, or along longer sheets of conducting material, and formed thus three signs of different lengths. Yet there was a certain time required to work the three keys; to obviate it, and to put the telegraphist entirely at his ease as to the speed attainable for him, and to obtain in such a manner the highest speed possible, I constructed the key in another manner.

A clockwork arrangement moves a small wooden cylinder, whose steel axis is attached to it by a handle, and rotates with great velocity, the rate of velocity being accurately indicated by sounding a small bell as often in a second as the cylinder will revolve in the same time.

The wooden cylinder bears three thin circular disks of brass attached to the steel axis of the cylinder; these disks are differently cut out, in such a manner that the first is a full circle of 360°, the second a sector of nearly 120°, the rest of the circle being covered with an insulating material, viz. wood or india-rubber, to prevent metallic contact.

The third disk is only a segment of 10°, the rest being cut out and covered with the insulating material.

Three levers, put in front of the three disks, bear on their ends platinum wires or plates that touch the disks during one revolution of the cylinder when pressed down.

From the levers a conducting-plate, uniting them, leads to the printing apparatus, and the levers are reduced to their former position by strong steel springs, so that they regain rapidly their positions after the pressure of the finger has ceased. Whatever be the velocity of the paper and the rollers, and the clockwork moving it, the relative length of the sizes and their distances remain unalterably the same.

In the model presented to the General Post Office, the motion endures for 15 minutes, and, being only a model, it is worked by a spring, and it has no rollers for the paper.

In the working apparatus for telegraphic use, the rollers and whole printing apparatus are attached to the key, and the same clockwork moves both the rollers and the rotating cylinder, forming thus only one apparatus together. From that contrivance we obtain :

1. A quite equal distance between the signs, as in printing.

2. By putting the fans of the clockwork in differently inclined positions, the velocity may be carried to as great an extent as a clever clerk can manage it. 3. By using three signs instead of two, the signs for letters, figures, and phrases are reduced about one-third, and as much of time and space is spared.

METEOROLOGY.

On the Importance of the Azores as a Meteorological Station.
By Dr. BUYS BALLOT.

In this paper the author classed his remarks under three heads:-(1) as to the importance of the station; (2) as to the present condition of the question of its establishment'; (3) what remains to be done. He showed that, although we have very copious results of observations made by vessels crossing the various oceans in all directions, there is great deficiency of actual observations at fixed points. After pointing out the very important position occupied by the Azores, as illustrated by the researches of Mr. Buchan and Prof. Mohn with reference to the normal tracks of European storms, and also in their lying so completely in the path of merchant vessels, Dr. Ballot explained that about five years ago he submitted to the British Admiralty a proposal for establishing a chain of barometric stations in the S. and W. of the British Isles, and at the Azores, and obtaining meteorological reports from thence. In April 1866 he applied to the Portuguese Government and to various learned meteorologists; and the Director of the Lisbon Observatory has been to Holland to consult Dr. Ballot on the subject.

A concession has been granted for the laying of a cable to the Azores; a learned 1871.

4

Portuguese has undertaken to provide the instruments and instruct the observer. The only expense involved is the charge for the transmission of the telegraphmessages: it would be most unfair that a country like Portugal should bear all the cost (about £350 per annum for one message daily); and Dr. Ballot thinks that it should be raised jointly and proportionally by the European Maritime States, all of whom would largely benefit by the adoption of the proposal.

Mean Temperature of Arbroath.

Latitude 56° 33′ 35" North, Longitude 2°35′ 30′′ W. of Greenwich. By ALEXANDER BROWN, LL.D.

January

April

May

June

...

1867. 1868. 1869. 1870.

о

O

о

о

330 413 410 364 37.9 37.5 364 36·6-04-15 13 February 421 423 427 367 409 384 370 376-25-39-33 March 378 436 389 408 40°2 399 397 39°7-03-05-05 471 474 477 480 475 480 438 443 +05-37-32 474 526 468 523 497 497 492 49'2 0.0-05-05 55'9 57 546 577 563 559 553 554-04-10-09 540 606 616 610 593 583 582 58.3-10-11-10 58.6 595 578 584 586 576 572 574-10-14-12 September 557 546 554 551 552 543 534 536-09-18-16 October 477 455 481 477 472 473 468 469 +01-04-03 November 425 414 416 400 414 408 404 405-06-10-09 December 38.8 412 352 353 376 388 379 379 +12 +0.3 +03

July
August

Means...... 467 489 476 474 476 470 463 464-06-13-12

The author constructed from his meteorological journals the foregoing Table for the purpose of showing the Mean Annual Temperature at Arbroath, in the county of Forfar, on the east coast of Scotland. In the Table, columns nos. 1, 2, 3, and 4 give the monthly mean temperature, and also the annual mean temperature, of each of the years 1867, 1868, 1869, and 1870. The warmest of these four years was 1868, and the coldest the year immediately preceding, namely 1867. The mean temperature of 1868, as shown by the Table, was 48 9, and that of 1867 4607, the difference between the warmest and coldest year of the four being 2.2. Column 5 is the mean of the monthly and annual temperature of the four years already mentioned; column 6 is the mean of 13 years, from 1857 to 1869 inclusive; eolumn 7 is the mean of 22 years, from 1845 to 1866 inclusive; and column 8 is the mean of 26 years, from 1845 to 1870 inclusive. The annual mean temperature of the 4-year period is 47°6, of the 13-year period 47°0, of the 22-year period 46°3, and of the 26-year period 46°4. It will be observed that the annual means of the two long periods differ by only one tenth of a degree, and are therefore a near approximation to the mean temperature of the locality.

The thermometers used are the Minimum thermometer of Rutherford and the Maximum thermometer of Negretti and Zambra, which have been tested by the Standard instruments of the Scottish Meteorological Society. They are attached to a wooden frame fixed to a window-sill having a northern exposure. Very great care is taken to protect the instruments from the effects of radiation and other causes. The thermometers are placed 11 feet from the ground and 70 feet above the level of the sea, and distant therefrom 783 yards in a direct line.

On the Thermo-Dynamics of the General Oceanic Circulation.
By WILLIAM B. CARPENTER, LL.D., M.D., F.R.S.

The object of this communication was to bring under the consideration of Physicists the fact, ascertained by recent Deep-Sea explorations, of the general prevalence of a temperature not much above 32° F. over the bottom of the great Oceanbeds, at depths greater than 2000 fathoms. As it has been proved by Temperaturesoundings made in the Mediterranean that the temperature of its bottom at like depths is about 54° F., it is obvious that depth, per se, has no relation to the phenomenon. And the explanation of it propounded by the author is, (1) that a body of Polar water flows over the deepest portions of the Oceanic basins which communicate with the Arctic and Antarctic areas; (2) that this flow has its origin in the action of Polar cold on the water subjected to its influence, whereby a descending movement is imparted to the whole mass; besides which, the Polar column, in virtue of its greater density, will have a greater downward pressure than the Equatorial column at the same level; (3) that this bottom outflow will produce an indraught of the more superficial stratum of Ocean water towards the Polar areas; (4) and that a vertical circulation will thus be maintained by difference of Temperature alone, carrying the lower cold stratum of Ocean water from the Polar towards the Equatorial area, and the upper warm stratum from the Equatorial towards the Polar.

A different explanation of the facts, however, has been offered by those who regard the Horizontal Circulation, of which the Trade-winds are the primum mobile, as the sole cause of the amelioration of the temperature of the Arctic basin, by an afflux of warm water; for it has been urged that the driving off of the superficial stratum of Equatorial water in the Gulf-stream must produce a partial void in that area, which will be filled by a deep indraught of Polar water.-This appears to the author extremely improbable, on general physical grounds. A horizontal movement of surface-water in the open Ocean would not draw up water from below, so long as a lateral influx can keep up its level; so that any such horizontal Wind-current must have another horizontal movement to complete the circulation. Such a horizontal complement is obvious in the case of the Gulfstream, of which one portion turns round the Azores to re-enter the Equatorial current, thus completing the shorter circulation; whilst the other portion, which flows onwards in a N.E. direction, has as its complement the various cold surface-currents which are known to set southwards, and of which it is shown by recent observations that one tends towards the coast of Mogador, sending an offset through the Strait of Gibraltar.

Further, it was argued by the author that the temperature-phenomena obtained in recent explorations indicate that a N.E. movement of the upper stratum of Oceanic water extends between the coast of Spain and the Faroe Islands to a depth of 500 or 600 fathoms, and that while this cannot be attributed to any propulsive action derived from the Gulf-stream (the thinned out edge of which is less than 50 fathoms in depth), it is exactly such a flow as would be anticipated on the hypothesis of a vertical circulation sustained by opposition of Temperature.

On the Mathematical Theory of Atmospheric Tides.

By the Rev. Professor CHALLIS, M.A., LL.D., F.R.S.

The purpose of the author in this communication was to point out a process of analytical reasoning by which the solution of the problem of atmospheric tides might be strictly derived from the general equations of hydrodynamics. For the sake of simplicity, the surface on which the atmosphere rests was supposed to be exactly spherical, the earth was conceived to have no motion of rotation, and the tidal motion to be produced by the moon revolving westward in the plane of the earth's equator, at her mean distance (R), and with the mean relative angular velocity (). Also it was assumed that the relation between the pressure (p) and density (p) is at all times and at all points of the atmosphere pap, the effects of variation of temperature not being taken into account.

As tidal motion is oscillatory, and the oscillations are so small that it is un

necessary to proceed beyond the first order of small quantities, the following equations, expressed in the usual notation, were adopted as being sufficiently general and approximate for the purpose :—

P

The proposed method of solving the problem of tides requires, first, that equation (1) should be satisfied by a particular integral of assigned form; and then that the arbitrary quantities contained in this integral, together with that arising from the integration of equation (2), should admit of being determined by the given conditions of the problem. Before giving the details of the method it is necessary to state the meanings of the literal symbols.

The resolved parts of the velocity being u, v, w at the point xyz at the time t, dpudx + vdy + wdz.

The attractions of the earth and moon at the unit of distance being respectively G and m, the impressed forces X, Y, Z are the resolved parts of the forces

-

G
7

' being the distance of the particle at xyz from the moon. The angular distance of the moon westward from the meridian of Greenwich at the time t reckoned from the Greenwich transit is ut. If λ be the north latitude, and 6 the longitude westward, of the point xyz distant by r from the earth's centre,

After transforming by these formula the rectangular coordinates in equation (1) into the polar coordinates r, 0, λ, for certain specified reasons the author assumed that

rof(r) cos sin 2(0-μt),

and then found that equation (1) is satisfied by this value of rp if the form of ƒ be determined by integrating the equation

This integration gave, after omitting the extremely small quantity

lowing value of p, containing two arbitrary constants:

$ = (Cr2 + C'r-3) cosλ sin (20-μt).

The remainder of the reasoning depends altogether on this value of 4, which was considered by the author to be indispensable for the solution of the problem of atmospheric tides, and, as far as he was aware, had not been before employed for that purpose.

For determining the three arbitrary quantities there are three conditions. That introduced by the integration of equation (2) is determined by the condition that at either pole of the earth the density has a constant value, because, as may be inferred from the expression for p, the aerial columns having their bases at the poles are motionless. A second condition is, that at the earth's surface the 26'C

vertical velocity, do, is always zero; so that if b be the earth's radius, C'= dr

3

The third condition necessarily has reference to the circumstances of the fluid at its superior boundary, respecting which the author argues as follows:

That the height of the atmosphere is limited may be inferred from the consideration that, by the continual diminution of the density with the distance from the earth's surface, the upward molecular repulsion must eventually be no greater than the downward acceleration of gravity, in which case there can be no further upward action, and the fluid terminates by an abnormal degradation of the density down

to zero at the extreme limit. The particles within the superficial stratum subjected to this disturbance are maintained in equilibrium by the combined action of molecular repulsion and the earth's attraction, till at a small distance from the extreme limit, where the abnormal variation of density ceases, the density is such as might result from a very small constant pressure applied at all points of a surface bounding a terminal density of finite value. (Views of this kind respecting the condition of the atmosphere at its superior limit were entertained by Poisson.) On these principles it is easy to find a mathematical relation between the terminal density and the height of the atmosphere. The author has, in fact, made the calculation on the supposition that the atmosphere is 60 miles high, and obtains a terminal density equal to six-millionths of that at the earth's surface.

According to the above views a particle at the superior boundary may be supposed to remain at the surface, and to be of the same density, in successive instants.

This condition is expressed by equating the complete differential coefficient (d)

to zero. By means of this additional equation the value of the constant C can be calculated on assuming a certain height for the atmosphere. Supposing the height to be 60 miles, the author obtains C=0·000000830 μ.

The arbitrary quantities being determined, the following results are readily obtained :

Height of tide above the polar column, expressed in feet,

=1084 cosA+1275 cos^ ) cos 2(0– pt).

At the equator, where λ=0, difference between high and low tide =2.55 feet.
Excess of barometer-reading above that at the pole, expressed in inches,

=000117 cosA+0-00139 cos?) cos 2(0 – pt).

At the equator the maximum difference of the barometer-readings=0·00278 in. The data employed in calculating these coefficients were :—

the density of air =0·0013, the density of mercury =13.568.

The above determination of the maximum difference of barometer-readings at the equator admits of comparison with the results of barometric observations made at St. Helena and at Singapore, as given in p. 129 of the Philosophical Transactions for 1852. These results agree with the theory in placing the high tide immediately under the moon; but the maximum difference of readings is 0-00365 in. at St. Helena and 0.00570 in. at Singapore. Both consequently are in excess of the theoretical value 0-00278 in. But it is to be remarked that the latter depends on the assumption that the atmosphere is 60 miles high; if it had been supposed of less height, say 40 miles, there would have been a closer agreement between the observed and theoretical values.

The author's theory accounts in a remarkable manner for the fact that although for the atmosphere high tide occurs under the moon, there is reason to say that for a general ocean of the uniform depth of three or four miles it would be low tide under the moon. The explanation given by the theory is, that there is a certain depth of ocean or height of atmosphere for which the tide becomes infinite, namely, when the rate of propagation of waves, as due to the earth's attraction, is equal to the rate of the moon's relative rotation about the earth. In that case the tide would be accumulative, and might be of unlimited amount. This critical depth, or height, is shown by the theory to be about 8.4 miles for each fluid. It is because the actual mean depth of the ocean is less, and the actual height of the atmosphere greater, than this critical value, that the ocean-tide under the moon is the opposite of the atmospheric tide.

Remarks on Aërial Currents. By Prof, COLDING,