CAPILLARY RIPPLES. | 51 
are +4 and —4, 1.e., they rise or fall one square for every two squares 
they advance horizontally. This is one of the advantages of logarith- 
mic plotting, any exponential relation is represented by a straight line 
whose tangent of slope is equal to the exponent. The slope indicates 
the law, the exact position gives the numerical relation. Thus the 
chart shews at once that a gravitational wave 100 inches long travels at 
about 80 inches a second, or 10,000 inches long at 800 inches a second. 
Now going down the line of velocities to a wave one inch long we find 
the velocity of travel to be eight inches a second, and of small waves 
qwinch long to be only ;8, of an inch a second. Now if the same law 
of waves which applies to great waves is also true of small waves, then 
a wave ;/, of an inch long should creep along over the surface of the 
water at arate of between two and three inchesa second. Whoever saw 
little ripples on the water creeping along stealthily in that way? Our 
experience tells us at once that there is no such thing, so that when 
waves are small enough the gravitational law appears absolutely to fail. 
Now remember that when the surface of the water is put into the wave 
form itis more extended than itwas when it was flat. Under the influence 
of gravity the higher portions of the water are drawn down because 
they are above the general level, and the lower portions are pushed up 
because they are below the general level, and so the wave advances. 
Again under the influence of capillary force this longer surface tends 
to become as short as possible; it has been stretched in virtue of the 
wave form and so the capillary forces tend to pull the upper parts 
down and to raise the lower parts up, so that under the influence of 
capillary forces the wave also is able to travel. You have exactly the 
same result upon the water (whether you consider gravitational forces 
or capillary forces) except that the law is different. The smaller the 
wave is the greater the capillary effect ; the smaller the wave the lessis 
the gravitational effect. The result is that if you consider gravitational 
effects alone you get a law illustrated by one straight line, which 
applies to all liquids whatever ; if you consider the capillary effects 
alone you find that the line representing the velocity slopes the other 
way, but now a distinction arises between different liquids. Those in 
which the surface tension with respect to the density is great as in the 
case of water andespecially of fluid aluminium have higher velocities than 
liquids where the reverse is the case, as with chloroform for instance. 
In consequence each liquid has its one line representing the velocity of 
capillary ripples, all of which slope down at the same angle that the 
gravitational line slopes up. In reality both forces are acting at the 
same time, and the actual truth is represented by the two straight 
’ branches joined by a curve. This is shown for the case of water, and 
from this it is possible to read by inspection the true velocity of a wave of 
any size whatever, from millions of miles long on the right to a millionth 
of an inch on the left. So long as you have two complete squares on 
each side there is no occasion to carry the diagram longer, because you 
can multiply by ten and by a hundred as often as you like and so 
extend the scope of the diagram indefinitely. It is evident from 
the diagram that gravity has practically no effect in the case of 
ripples of a size of 7y of an inch or less, and so they are called 
