the other, of which our European storms are examples, and which alone are dealt with in this paper, is of very great extent as compared with the height. The modes in which these two distinct kinds of barometric depressions tend to fill up are widely different from each other, owing particularly to the degree in which the element of friction is introduced by the forces set in motion within the storm itself.

Mode in which a Barometrical Depression of a Narrow Diameter fills up. In this case, since the diameter of the depression is small as compared with the vertical height of the storm, it follows that the inflow of the air-currents towards the area of lower pressure will take place over a surface of comparatively small extent, and will consequently meet with but little retardation from friction. Hence the process of inflow toward the centre of the barometrical depression will take place with comparative facility in true tropical cyclones of small extent, and be therefore characterised by steep barometrical gradients.

C

Fig. 1.

Let A B C (fig. 1) represent a vertical section of such a depression, and let the small arrows a, b, c, show the direction in which it will tend to fill up over a surface of comparatively small extent, accompanied by a steepening of the gradients B A and B C.

Mode in which a Barometrical Depression of Wide Diameter fills up and in the process tends to open out.-In European and American storms, the barometer at their centres falls about as low as in tropical cyclones, but the barometric gradients are much less steep, and the disturbances cover a much more extensive region. Redfield has pointed out that their vertical height is often not more than the twohundredth part of their horizontal breadth. It follows from this essential difference between these storms and true cyclones that the mode of inflow of the air-currents towards the central low pressure can neither take place in the same manner nor with a

similar facility, but, on the contrary, much friction must now be called into play, owing to the extensive resisting surface over which the air-currents are drawn. Since friction is much greater near the earth's surface than it is aloft, it follows that such storms are characterised by greatly retarded surface currents, and rapid upper currents. Looking at the mass of the atmosphere on the outskirts and outside the area of the storm as the source whence the incurring air-currents draw their supply, it is obvious that as regards the true cyclone the source of supply is easy and copious, whereas in the case of our widespread European storms, supply is comparatively scarce, and therefore defective. In truth, as the lower and denser air-currents are, owing to the enormous extent of surface they cover, much retarded by friction, the main source of supply for the inflowing currents is chiefly to be found in the rarer, more mobile, and more rapid upper currents which flow comparatively free and unimpeded. This essential difference in the mode of inflow of the aircurrents of these two types of storms is considered to be due to differences in the amount of friction, accompanied also by a great difference in the introduction of the important element of Time. The difference in velocity between the surface and upper currents is often very great. Thus Glaisher has shown from his balloon ascents that the upper currents are sometimes five or six times more rapid than the surface currents, while from observations made at the top and base of Mount Washington, it was shown that on one occasion the wind on the summit was blowing with a velocity of ninety miles an hour at the time that a calm prevailed at the base of the mountain.

The following illustration will show what is meant in this paper by the expression opening out all round. Let a barometric depression be formed several hundred miles in diameter, and let the stratum of air resting on the surface be calm, whilst aloft upper currents flow in upon the centre at the rate of ninety miles an hour. In this case the central inflow will be carried out entirely by the upper currents, and consequently there will result from this mode of inflow an outward extension or an opening outwards of the area of diminished pressure.

In fig. 2, A B C may be supposed to represent the vertical section "Proceedings of R.S. E." vol. viii. p. 613 and p. 614.

of the barometric minimum of a true tropical cyclone as in fig. 1. Let now D B F represent a vertical section of a barometric minimum of a very much larger diameter. When it opens up all round in the way described by means of rapid upper currents, it will be accompanied by a lowering of the surrounding gradients from the upper part of which the main source of supply is derived. The result is

G

D

H

B

Fig. 2.

that the depression originally embracing a circular space whose diameter was D F will widen out, and the diameter extend to G H. The inflow which in this way takes place along the gradients bounded by the circle whose diameter is D F, as shown by the arrows a and ƒ, will now have the effect of lowering the gradients BF and BD to BH and B G. The result of this may be represented by the removal of the air comprised in the spaces G BD and HB F.

When the air moves more rapidly aloft than it does near the surface, it may be conceived as moving onwards, not in vertical, but in inclined columns; and we have endeavoured to show* that this mode of inflow is attended by "lifting," and to some extent by fictitious pressure, by which is meant that although the barometer indicates correctly the elasticity of the air, still it no longer represents its real mass overhead, but a pressure more or less diminished owing to the mechanical movement of the air and to friction. The opening out or extension of the area of barometric minimum, with DF for its diameter, to a wider area, having G H for its diameter, is effected by the upper currents, indicated by a and f of fig. 2. These upper currents, which flow in upon the low central depression from a great distance all round, have their source of supply in the upper still atmosphere around and outside the circular space over which they blow. It is here where outward extension and shallowing out commences, viz., along the curve which

VOL. IX.

*

"Proceedings," vol. ix. p. 412.

4 G

indicates the points where removal of air first begins to exceed restoration. This line is what has been previously designated as "the curve of outward propagation."*

This point, which is considered to be of great importance, may be better understood by an illustration. If a river flowing down an incline does so uniformly, and at an equal rate of speed, removal will equal restoration; but if in the lower part of its course a more rapid removal is inaugurated, while restoration or supply above remains as before, the curve representing the point at which the increased removal begins to travel upwards will represent the forward movement of this curve of outward propagation or extension.† Let ABC (fig. 3) represent the inclined surface of a river, A B the

A

D

B

Fig. 3.

lower part of its course, in which a more rapid flow, and consequently a more rapid removal, has commenced, and D B the curved line which represents increased removal beginning to travel upward. Let us suppose that A is the low centre of a large sheet of water, towards which currents set in all round, and are there carried off. If now the inflow towards this centre there begins to increase in speed, the curve which extends all round will be propagated outwards, or in a direction opposite to that in which the currents flow. A depression may thus practically fill up by shallowing out, extending all round, and thereby lowering the gradients. When a depression fills up rapidly, it is, of course, attended by a correspondingly rapid rise of the barometer; but when it shallows out by a process of lateral extension the barometric rise is much slower. It is only in the case of an imperfect fluid, such as air, flowing over a resisting surface that the more special modes of inflow here insisted on can occur. On a frictionless surface they could not take place. When we consider the differences in the high pressures surrounding the depression on its different sides, and the different qualities of the air, as regards moisture and temperature, in different parts of the * "Proceedings," vol. viii. p. 613. +Ibid. vol. viii. p. 614.

depression, it is evident that the mode of inflow cannot be uniform all round, and that horizontal extension will take place in some one particular direction. This direction will be determined by the curve of outward propagation, which thus marks the direction of the onward course of the depression or storm.

The Mode in which Opening Out takes place, accompanied by a transference of the Depression from West to East.-If a vessel be lowered into the sea a corresponding amount of water will be displaced. Let it then be supposed to move forward to the extent of its own length, an opening out ahead will take place, and a filling up astern. The original displacement will thus be closed up, but a similar displacement will be found in the new position to which the vessel has moved. Owing to its rigidity the vessel moves forward unaltered, but as the surrounding water is mobile, it cannot do so, hence it opens out and fills up. The currents which run aft on each side of the vessel represent its forward movement, while there is no real movement of the surrounding water, except its gradual transference to the rear, in the direction opposite to that in which the vessel moves. When an area of low pressure moves in an easterly direction over the British islands, and to a distance equal to that of its own diameter, it will do so in a somewhat similar manner, viz., by opening out and filling up. There is, however, an important difference to be noted; for while the tranference of the water, which enables the vessel to move forward, takes place on each side in the direction of the stern, the transference of the air, when the depression moves eastwards, takes place on the north segment from the front, where it opens out to the rear where it fills up, as all observation shows. It may be pointed out here that while depressions move forward, the aerial particles, or the mass of air, does not move forward, and viewed in this light the curve of outward propagation may be regarded as being a purely ideal curve.

The severe N.E. storms, which are of so frequent occurrence as to form a marked feature of the climate of the New England States, were long ago pointed out to advance on this region in an opposite direction from that in which they blow. Let the area of the storm be represented by the circle A B C F (fig. 4), then the front part A B C is the curve of outward propagation, which moves toward the N.E. in the direction of the arrow D E, this being the contrary direction to