574 
Proceedings of the Royal Society 
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 
D 
Fig. 3. 
lower part of its course, in which a more rapid flow, and conse- 
quently 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 out- 
wards, 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. t Ibid. vol. viii. p. 614. 
