Nov. 2, 1882] 
NATURE 3 
tage of regular canals over natural rivers for hydraulic 
experiments almost disappears when the canal bed is 
scoured out to an irregularity similar to that of a natural 
stream, and the canals are at a disadvantage when arti- 
ficial control at the tail of the reach modifies the condi- 
tions of flow to an extent sensibly felt at the site of the 
experiments. It is, of course, in the lower states of the 
water in the canal in the Roorkee aqueduct reach, that 
the effect of the tail control is most sensible, but then 
experiments made in these conditions are an essential 
part of the data necessary for generalisation. 
Major Cunningham spent a good deal of time in verify- 
ing a supposed theorythat the surface of a stream should be 
convex. The theory is probably a capital instance of the 
frequent mistake of importing the principles of theoretical 
hydrodynamics into practical hydraulics, Ina stream 
flowing from a reservoir, in such a way that the tangential 
forces on the surface of the elementary streams are absent 
or negligible, the energy per pound of fluid is uniformly 
distributed. It follows that in parts where the velocity 
is greater, the pressure is less. A stream may be re- 
garded as a bundle of horizontal filaments coming from a 
common reservoir. If in sucha stream the central fila- 
ments have a greater velocity than those nearer the sides, 
their pressure will be less. Consequently, for equilibrium 
there must be a greater depth of stream towards the 
centre, and the transverse water-line will be convex up- 
wards. Such is the theory which Major Cunningham has 
taken a great deal of trouble to test, and to which he 
attaches weight in spite of his observations. From pre- 
liminary calculations he shows that the known differences 
of velocity would give a difference of level, between the 
centre and sides of the Ganges Canal,,of 3 inches. After 
the most careful measurements, it was found that the dif- 
ference of level varied from +-o'018 foot to —0’095 foot, 
the average difference being almost exactly zero. Ob- 
viously the theory is outrageously wide of the truth, and 
the reason is not far to seek. The differences of velocity 
to which the supposed differences of pressure are due, are 
created by exactly those tangential actions of the fila- 
ments which the theory neglects. ‘There is no reason for 
assuming equal distribution of energy along a filament, 
part of the energy of which is being destroyed by lateral 
frictional actions between the filaments. As to the obser- 
vations in Chapter V., with a guage giving still water- 
level, it is not clear that the small difference of level 
observed was not due to the position of the mouth of the 
tube which communicated with the canal. 
_ The discussion of the vertical velocity parabolas in 
Chapter XI. is extremely interesting, and the method 
ere for finding the most probable curve by the method 
of least squares, is laborious and conscientious. The 
method of weighting the observations seems, it is true, 
rather artificial, especially as the observations at great 
(depth best define the form of the parabola. The general 
conclusion arrived at is, that while all the observations can 
e fairly well expressed by parabolic curves, no formula 
can be found expressing the dependence of the variation 
‘of velocity on the slope, and dimensions of the channel. 
jit would be interesting to see if a parabola with axis on 
he water-line would not agree better with the results, the 
bservations above the line of maximum velocity being 
f course discarded. So far as there is any theory of the 
mutual action of the filaments, it leads to the result that 
the parabolic axis should be at the surface ; and that is 
not inconsistent with one possible explanation of the 
reduction of velocity near the surface. 
In ordinary streams, the velocity is greater towards the 
surface and centre, and less towards the bottom and 
sides. But the greatest velocity is not found at the sur- 
face, but at a variable depth below it, amounting very 
often to one-fourth of the whole depth. The Mississippi 
observers attributed this to the friction of the water 
against the air. In accordance with this they found the 
depression of the line of maximum velocity to depend 
quite directly on the direction of the wind, and they logi- 
cally introduced into their formule of flow, the free surface, 
as forming part of the frictional wetted border. Major 
Cunningham retains the Mississippi observers’ explana- 
tion, while his experiments disagree with theirs on all the 
points which directly support the explanation. He finds, 
for instance, that the depression of the line of maximum 
velocity is entirely independent of the direction and force 
of the wind. Now excepting one suggestion to be 
referred to presently, no kind of retarding action between 
the air and water has been stated which is not of the 
nature of a frictional resistance. The Mississippi ob- 
servers and some others who adopt the explanation of the 
depression of the line of maximum velocity we are now 
criticising, state explicitly that they consider the resist- 
ance between the air and water to be of the same nature 
as the resistance between the water and its solid bed. If 
so, since the line of maximum velocity is ordinarily de- 
pressed to one-fourth the depth at the centre, and gene- 
rally still more towards the sides, the friction between the 
water and air must be something like one fourth as great 
as the friction between the water and solid bed. But is 
it conceivable that the friction between the level water 
surface and mobile air should have anything like one- 
fourth the value of the resistance of the water impinging 
on all the immovable roughnesses of the stream bed? 
Further, any resistance of this kind must depend on the 
relative velocity of the water and air. But the air is 
most commonly in motion, and on the average must as 
often and as long blow down stream as up stream, 
Blowing down stream, it should accelerate the stream to 
the same extent as blowing up stream it retards it. But 
it is known from Boileau’s experiments and others that the 
depression is still persistent with a wind blowing down 
stream at a velocity greater than that of the water. To 
this Major Cunningham’s only answer is that “the time 
required for the penetration of change of velocity of the 
surface current caused by wind to any considerable 
depth appears to be very great. It has been estimated 
that it would take one week for half change of surface 
velocity to penetrate three feet.”” The evidence for this 
is not given, but if it is so, is it not because the friction 
between air and water is extremely small, and it is only 
in those cases where the persistence of the wind action 
fora long time allows an accumulation of effect, that that 
effect is sensible. 
A wind blowing on the surface of a lake is long in pro- 
ducing a current merely because the friction is small, but 
it does produce a current in time, because the action is 
cumulative. On a river it produces no sensible effect at 
all, as Major Cunningham’s experiments show. But if 
