oe _ 
A.—MATHEMATICS AND. PHYSICS. 25 
By means of pilot balloons, cloud heights, and other observations, it is 
possible to follow these surfaces of discontinuities for great distances from 
the place where they meet the ground, rising at a definite slope all the way. 
I have already described how the warm air is pushed up over the cold 
air along these surfaces of discontinuity. As a result of the upward motion 
condensation takes place in the warm air and cloud forms, the cloud layer 
marking out the boundary between the two bodies of air. It now seems 
very probable that all clouds which appear in sheet simply mark surfaces 
of discontinuity separating bodies of air of different origin. This would 
account for the fact that there is nearly always an inversion of temperature 
over a sheet of cloud. 
A great deal of work has recently been done in investigating these 
surfaces of discontinuity, especially by J. Bjerknes, Bergeron, and Stuve. 
By means of the mountain observatories in Switzerland J. Bjerknes has 
been able to follow the temperature and wind changes in a surface of 
discontinuity sloping upwards from ground-level in France to the summit of 
the Sonnblick, 3,000 metres higher, 600 kilometres away (Fig. 4). Stuve 
has investigated a great number of surfaces of discontinuity by means of the 
daily observations of the upper air made at Lindenberg. He finds that the 
slope of the surfaces varies greatly, but the order of magnitude is a rise of 
1 in 100, so that a surface extending in these latitudes from ground-level 
to the stratosphere would be of the order of a thousand kilometres wide. 
Helmholtz first proved that waves can be formed in surfaces of dis- 
continuity in the atmosphere. Recently Goldie has shown that such waves 
can be recognised at the earth’s surface in the squalls and lulls which 
accompany winds, and he has been able to determine the height of the 
surfaces from considerations of changes of pressure and wind at sea-level. 
The ideas which I have described above receive their chief application 
in our knowledge of the cause and structure of the cyclonic storms of 
middle latitudes. The literature on this subject has now become very great, 
and I can do little more here than sketch out as briefly as possible the 
main lines along which progress is being made. The subject is still full of 
difficulty and many problems await solution, but great progress has been 
made and our new ideas are very different from the old. 
The Origin and Structure of Cyclones. 
The old idea of a cyclone was tersely expressed by Sir Oliver Lodge, in 
a letter to The Times last year, as follows: * A cylindrical vortex with its 
axis nearly vertical, rolling along at a rate conjecturally dependent partly 
on the tilt, and with an axial uprush of air to fill up a central depression, 
-which depression, nevertheless, was maintained and might be intensified 
by the whirl, the energy being derived from the condensation of vapour.’ 
If this were the true mechanism of a cyclone we should expect to find 
considerable symmetry around the axis. The air would move in a continu- 
ous stream circulating around the centre but always approaching it ; 
in other words, the stream lines would be continuous spirals, There would 
also be little difference of temperature in the different parts of the cyclone, 
for the same air current would pass successively through all parts. In 
reality the conditions are entirely different. When stream lines are drawn 
by the aid of the wind arrows on synoptic charts it is impossible to connect 
