os 
| He . ° . . . . . . 
_ tered if we take into account the cooling of the air by its rapid dilatation. 
|The experiments above alluded to were made by allowing the air to enter an 
exhausted receiver through a small orifice, and observing simultaneously the 
ON RECENT RESEARCHES IN HYDRODYNAMICS. 13 
_ nation of phenomena depending on motions which are too complicated to 
admit of accurate calculation. It is evident that any arbitrary motion may 
be assigned to a fluid, (with certain restrictions as to the absence of abrupt- 
hess, ) provided we suppose certain forces to act so asto produce them. The 
values of these forces are given by the equations of motion. In some cases 
the forces thus obtained will closely resemble some known forces ; while in 
others it will be possible to form a clear conception of the kind of motion 
which must take place in the absence of such forces. For example, sup- 
posing that there is propagated a series of oscillatory waves of the standard 
kind, except that the height of the waves increases proportionably to their 
distance from a fixed line, remaining constant at the same point as the time 
varies, Mr. Airy finds for the force requisite to maintain such a motion an 
expression which may be assimilated to the force which wind exerts on water. 
This affords a general explanation of the increase in the height of the waves 
in passing from a windward to a lee shore*. Again, by supposing a series 
of waves, as near the standard kind as circumstances will admit, to be pro- 
pagated along a canal whose depth decreases slowly, and examining the force 
requisite to maintain this motion, he finds that a force must be applied to 
hold back the heads of the waves. In the absence, then, of such a force the 
heads of the waves will have a tendency to shoot forwards. This explains 
the tendency of waves to break over a sunken shoal or along a sloping 
beacht. The word tendency is here used, because when a wave comes at all 
near breaking, but little reliance can be placed in any investigation which 
depends upon the supposition of the motion being small. To take one more 
example of the application of this method, by supposing a wave to travel, 
unchanged in form, along a canal, with a velocity different from that of a free 
wave, and examining the force requisite to maintain such a motion, Mr. Airy 
is enabled to give a general explanation of some very curious circumstances 
connected with the motion of canal boats{; which have been observed by 
Mr. Russell, 
IIL. In the 16th volume of the ‘ Journal de l’Ecole Polytechnique §, will be 
found a memoir by MM. Barré de Saint-Venant and Wantzel, containing the 
results of some experiments on the discharge of air through small orifices, 
produced by considerable differences of pressure. The formula for the ve- 
locity of efflux derived from the theory of steady motion, and the supposition 
_ that the mean pressure at the orifice is equal to the pressure at a distance 
from the orifice in the space into which the discharge takes place, leads to 
some strange results of such a nature as to make us doubt its correctness. If 
we call the space from which the discharge takes place the first space, and 
that into which it takes place the second space, and understand by the term 
reduced velocity the velocity of efflux diminished in the ratio of the density 
in the second space to the density in the first, so that the reduced velocity 
- measures the rate of discharge, provided the density in the first space remain 
constant, it follows from the common formula that the reduced velocity va- 
nishes when the density in the second space vanishes, so that a gas cannot be 
_ discharged into a vacuum. Moreover, if the density of the first space is given, 
_ the reduced velocity is a maximum when the density in the second space is 
‘rather more than half that in the first. The results remain the same if we 
take account of the contraction of the vein, and they are not materially al- 
* Art. 265, &c, + Art. 238, &c. 
t Art. 405, &c. § Cahier xxvii. p. 85. 
