14 REPORT—1846. 
pressure and temperature of the air in the receiver, and the time elapsed since 
the opening of the orifice. It was found that when the exhaustion was com- 
plete the reduced velocity had a certain value, depending on the orifice em- 
ployed, and that the velocity did not sensibly change till the pressure of the 
air in the receiver became equal to about 2ths of the atmospheric pressure. 
The reduced velocity then began to decrease, and finally vanished when the 
pressure of the air in the receiver became equal to the atmospheric pressure. 
These experiments show that when the difference of pressure in the first 
and second spaces is considerable, we can by uo means suppose that the mean 
pressure at the orifice is equal to the pressure at a distance in the second 
space, nor even that there exists a contracted vein, at which we may suppose 
the pressure to be the same as at a distance. The authors have given an 
empirical formula, which represents very nearly the reduced velocity, what- 
ever be the pressure of the air in the space into which the discharge takes place. 
The orifices used in these experiments were generally about one millimetre 
in diameter. It was found that widening the mouth of the orifice, so as to 
make it funnel-shaped, produced a much greater proportionate increase of 
velocity when the velocity of efflux was small than when it was large. The 
authurs have since repeated their experiments with air coming from a vessel in 
which the pressure was four atmospheres: they have also tried the effect of 
using larger orifices of four or five millimetres diameter. The general results 
were found to be the same as before*. 
IV. In the 6th volume of the Transactions of the Cambridge -Philoso- 
phical Society, p. 403, will be found a memoir by Mr. Green on the re- 
flection and refraction of sound, which is well-worthy of attention. This 
problem had been previously considered by Poisson in an elaborate memoir. 
Poisson treats the subject with extreme generality, and his analysis is con- 
sequently very complicated. Mr. Green, on the contrary, restricts himself 
to the case of plane waves, a case evidently comprising nearly all the pheeno- 
mena connected with this subject which are of interest in a physical point of 
view, and thus is enabled to obtain his results by a very simple analysis. In- 
deed Mr. Green’s memoirs are very remarkable, both for the elegance and 
rigour of the analysis, and for the ease with which he arrives at most im- 
portant results. This arises in a great measure from his divesting the pro- 
blems he considers of all unnecessary generality: where generality is really 
of importance he does not shrink from it. In the present instance there is 
one important respect in which Mr. Green’s investigation is more general 
than Poisson’s, which is, that Mr. Green has taken the case of any two fluids, 
whereas Poisson considered the case of two elastic fluids, in which equal con- 
densations produce equal increments of pressure. It is curious, that Poisson, 
forgetting this restriction, applied his formulz to the case of air and water. 
Of course his numerical result is altogether erroneous. My. Green easily 
arrives at the ordinary laws of reflection and refraction. He obtains also a 
very simple expression for the intensity of the reflected sound. If A is the 
ratio of the density of the second medium to that of the first, and B the ratio 
of the cotangent of the angle of refraction to the cotangent of the angle of 
incidence, then the intensity of the reflected sound is to the intensity of the 
incident as A—Bto A+B. In this statement the intensity is supposed to 
be measured by the first power of the maximum displacement. When the 
velocity of propagation in the first medium is less than in the second, and the 
angle of incidence exceeds what may be called the critical angle, Mr, Green 
restricts himself to the case of vibrations following the cycloidal law. He 
* Comptes Rendas, tom. xvii. p. 1140. 
+ Mémoires de l’Académie des Sciences, tom. x. p. 317, 
