according as the rate increases or decreases. For instance, suppose, as in Fig. 85, F, that the barometer fell twotenths of an inch between one and two o'clock, and another two-tenths between two and three o'clock, the resulting barographic trace would be a straight descending line, like s; if in the second hour the mercury fell threetenths of an inch instead of only two-tenths, the resulting trace would be a convex, like x; while if it only fell 2 3 Hours In 2 3 FIG. 85.-Illustrating the origin of convex and concave barograms. one-tenth in the second hour, the trace would be concave, as a. If we define the barometric rate as the number of hundredths of an inch which the mercury moves, either up or down, per hour, the above may be put in this form. With a falling barometer, the trace is convex for an increasing rate, concave for a decreasing one. A glance at Fig. 85, R, will show that for a rising barometer the converse is the case; for when the rise is greater the second than the first hour, the trace is concave, as in A; but when less, then convex, as at x; and this result may be stated as follows. With a rising barometer, the trace is convex for a decreasing rate, concave for an increasing one. This is the reverse of what happens with a falling barometer. Now, the simplest and commonest case of barometric change occurs when the centre of a cyclone drifts past a station; the fall of the barometer is then proportional to the steepness of the gradients. When steeper gradients approach, the barogram will become convex; when slighter gradients arrive, the curve will be concave. The converse holds good for a rising barometer: when steeper gradients approach, the curve is concave; when slighter, then convex. Now, as the force of the wind is proportional to the steepness of the gradients, we find that the direction of curvature of a barogram tells us whether a gale is going to get worse or otherwise, because we can tell if the gradients are becoming steeper or otherwise. We must be very careful to remember that, though a rapid rate of fall is in a general way a worse sign of weather than a moderate one, the indications deduced from the curvature of a barographic trace depend on the variation of the rate, and not on the rate itself. For instance, in Fig. 85, the top part of which gives the isobars over Great Britain on November 14, 1875, at 8 a.m., the crossed line denotes the direction of the cyclone, and an unsymmetrical arrangement of the steepest gradients with reference to the centre is very obvious. To get the barographic section of a cyclone, or to find out what curve the propagation of the depression would leave on a recording instrument, we have to draw a line across any portion of the plan, as shown on a synoptic chart, parallel to the path of the cyclone, and then, by measuring the distance in time between any two consecutive isobars, we arrive at the flexures of the trace. For the sake of simplicity, we will suppose, in the first instance, that we are stationed exactly on the line of the path of the cyclone, so that the centre will pass over us. By this we make the line of section of the cyclone coincide with the line of gradients, which is not the case in any other portion of the depression. In the lower part of Fig. 85 we give such a section of the cyclone, sketched in the upper portion, along the line A B. The position of A and B are obverted in the section, so as to read from left to right like an ordinary barogram. Then we see that as the cyclone approached the gradients got steeper, so that the rate of barometric fall increased, and therefore the trace was convex; during this period the gale got worse. After a time, as the ring of steep gradients passed, and the slighter gradients in front of the centre approached, the rate of fall of the mercury decreased and the trace became concave, though still going downwards. The gale moderated somewhat during this time. The passage of the centre marked the turn of the barometer; but as the distance between each consecutive isobar increased regularly after 29.5 inch, the resulting barogram was convex after that level. The actual curve for the day, as given at Stonyhurst, which lay almost in the line of the centre, differs only slightly from this. Thus we see that the normal barographic trace in a cyclone is simply the reflection of the typical shape of isobars in that kind of depression, and that, moreover, to a single observer the direction of curvature-that is, the convexity or concavity of a barogram-enables him to tell whether more or less steep gradients are approaching, and therefore whether a gale is going to get better or worse. There is, however, one limitation which considerably detracts from the value of this deduction. If the line of section of the cyclone which passes over the observer is not square to the isobars, the relative distance between any two consecutive isobars is no longer a measure of the gradients. For instance, if the cyclone in Fig. 84 had passed over an observer anywhere on the line C G, his trace from c to E would have been concave, because C D is a shorter line than D E. But all the time he is getting into a region of steeper gradients, as measured square to the isobars, and therefore the criterion of increased gradients fails. But if a concave need not be an absolute test of decreasing gradients, a convex trace can never fail to indicate steeper gradients with a falling barometer. This may be readily seen by considering the nature of concentric lines. Conversely, with a rising barometer, we see, in Fig. 84, that from E to G the barogram will be concave, though the gradients are decreasing; but under no possible conditions could a convex trace fail to indicate a decreasing gradient. The author's rule is, then, as follows:-Assuming that the force of a gale is proportional to the gradients, a convex barogram is always bad with a falling, and good with a rising barometer; a concave trace is sometimes a good sign with a falling, and not always a bad indication with a rising barometer. This rule, of course, involves the supposition that the motion of the barometer is solely due to the propagation of isobars over the observer, but in practice much more complicated changes sometimes occur. For instance, in a very common class of gale belonging to what we have described as the southerly type of weather, a cyclone, after arriving near the British coasts, remains stationary, but increases, maybe, half an inch in depth. The fall of the barometer which then occurs at any station is no longer of the same kind as that which we have just examined, and the flexure of the trace is determined by other considerations. The direction of curvature would then depend on any variation of the rate of deepening, not on the motion of the cyclone. For instance, suppose a stationary cyclone which began to deepen from increasing intensity-if the rate of deepening was constant, the trace would be a straight descending line; if the rate increased, the curve would be convex; if it decreased, concave. But, as we know that the deepening of a cyclone means increased intensity, we may look on a decrease of that rate as a favourable sign, and therefore the indications of the relation of curvature to weather would remain good. The complications which arise from a deepening or shallowing moving cyclone need not be discussed here, but it is important to notice the two distinct causes of barometric change-the passage of a moving cyclone, and the deepening of a stationary one. APPARENT FAILURES OF THE BAROMETER. So far we have dealt with what may be called the regular movements of the barometer, that is to say, move |