2 
NATURE 
[Wov. 2, 1882 
made by floats, and he has used these simple instruments 
in all their known forms, as surface floats, sub-surface 
floats, twin floats, and rod-floats. Every detail of the 
construction and use of these floats has been studied, 
their form, the length of run, the mode of marking the 
sections and float paths, and the precautions in taking 
the time. The sources of error are weighed, and in some 
degree the limits assigned beyond which the methods 
become unreliable. There will always be cases where 
the methods of float-gauging must be used, and no one 
who has work of this kind to do can afford to neglect 
Major, Cunningham’s directions. A few observations 
were, in fact, made with current meters. But the instru- 
ments used were of a type which must now be regarded 
as antiquated, and as to these Major Cunningham suggests 
no improvement which has not already been tried by the 
German engineers, who have, in fact, converted the 
current meter into a new instrument of precision. 
It is not at all to be regretted that Major Cunningham 
adopted floats in his experiments. Even from the scien- 
tific point of view, if floats are at best a rough means of 
determining velocities, yet they are not liable as more 
complicated instruments are, if used without sufficient | 
care or knowledge, to large and concealed errors. Hence 
float observations may always be used advantageously to 
check observations made in other ways. ‘The progress of 
hydraulics suggests questions, for the solution of which 
float methods are inadequate, and the results obtained 
by Harlacher and Wagner seem to show that floats will 
ke superseded by instrumental means of greater compli- 
cation, but of far greater delicacy. But in truth in 
hydraulics no one method is free from objections and 
researches carried out by all methods, when sufficient 
care is exercised, will prove useful. 
We may now pass to consider briefly the bearing of | 
these experiments on some points of theory. Major 
Cunningham devotes Chapter VI. to a discussion of the 
unsteadiness of the motion of the water in ordinary 
streams. At each point the velocity varies in direction, 
and magnitude from instant to instant. The float-veloci- 
ties taken on 50-feet runs, which are themselves mean | 
velocities for a certain time and distance, vary from 10 
to 30 per cent., so that to obtain the true mean velocity 
over any given float-path, something like fifty float obser- | 
vations are necessary. Recent current-meter observa- 
tions show this variation of velocity still more clearly. 
The essential unsteadiness of the motion of water in 
streams was pointed out with the greatest clearness by 
M. St. Venant (1872), and the still more important fact 
that the motion is periodically unsteady, that is, that the 
variations occur periodically about a constant mean value, 
so that the average velocity for a sufficient but not very 
great length of time is sensibly constant. It is only this 
last fact which has rendered it possible, to apply the 
equations for steady motion to the actual motion of 
streams, and it is a pity that Major Cunningham has not 
adopted St. Venant’s convenient term, mean local velo- 
city, for the sensibly constant average velocity at each 
point of a stream. It is not the “interlacing of the 
stream lines” (p. 07), but the destruction of stream-line 
motion by eddying motions of quite another character, to 
which the unsteadiness seems to be due. 
In Chapter VII. the observations of the surface-slope | large-scale experiments hitherto carried out. 
at different periods of the experiments are discussed, and 
it is here that we think may be discovered the one matter 
in which the conditions of the experiments were unsatis- 
factory, and in which they are markedly inferior to 
Bazin’s small-scale experiments. Taking the Solani 
embankment and Solani aqueduct sites, at which the 
largest amount of work was done, we find that the experi- 
ments were made at about the centre of a ten-mile 
reach, terminated at the upper end by a regulator con- 
trolling the water-supply, and at the lower end by a fall 
where, by artificial means, the water-level was kept up to 
any desired height. The bed of the canal between these 
limits had originally the uniform slope of about a foot 
per mile. This original level is maintained at five points 
by masonry works, but between these the bed is irregu- 
larly scoured out to an extent which must have made 
very sensible variations of velocity within distances of 
a mile. At the tail of the reach is a weir standing 
five feet above the level of the bed, the crest of which 
was further raised by temporary obstructions of a 
height sometimes reaching five feet more. Hence the 
whole height of obstruction was often greater than 
the whole depth of water at the site of the gaugings. 
Under these circumstances the slope of the water surface 
varied, being generally quite different in the part of the 
reach above the site of the experiments from that in the 
part below, where the influence of the tail weir was felt. 
Further, the difference of slope in the parts of the reach 
above and below the site of the experiments differed 
widely in different conditions of the water supply. The 
local surface slope, that is the slope of the water surface 
in the neighbourhood of the gauging site, varied irregu- 
larly with the variation of the slopes above and below, 
being apparently, as might be expected, most affected by 
the obstruction at the tail of the reach, Now as the 
velocity at a given site does not exclusively depend on the 
| surface slope at the site, but to a certain extent on the slope 
above and below, the conditions of the site were initially 
to some extent unfavourable, and that in a degree which, 
although it may be small, is difficult to appreciate. The 
local surface slope itself can only be measured on a con- 
siderable length of stream (1000 to 4000 feet). But in 
that length the surface slope appeared to vary, the slope 
in 2000 feet being as much as 25 per cent. different from 
that in 4ooo feet, and the slope at one bank being 50 per 
cent. different from the slope at the other. It is obvious, 
therefore, that the local surface slope is a quantity which, 
under the conditions of these experiments, was not 
ascertainable with any great accuracy. But the whole 
comparison of the experimental results with formule of 
discharge involves the accurate knowledge of this quantity. 
All inferences from these experiments as to the reliability 
of formulae must be weakened in proportion as the slope 
measurement is doubtful. 
It is not in Major Cunningham’s experiments alone 
that this difficulty in determining the surface slope has 
been found. It is to the uncertainty of this quantity 
mainly, to this fos et ovigo malorum, that the discord- 
ances of large-scale experiments are due. The roughest 
small-scale experiments, those, for instance, discussed by 
Eytelwein and Prony, have furnished coefficients more 
useful in practice and more generally applied than any 
The advan- 
