of which is known for every temperature. The vapour which forms in the second apparatus is collected during ten minutes, before the passing of the current; there is scarcely any; the circuit is then closed, which determines a rapid boiling. The heat supplied is known; the vapour which it has formed without change of temperature is weighed, and the latent heat is deduced.

IV. The two Specific Heats.—A third application of the same principle can be made. In a large bell-glass filled with air a metal wire is stretched; an intense current is passed for a short time through it, which developes a determined quantity of heat; a fraction of this disappears by radiation; the remainder, which is constant, gives heat to the gas, which can be measured in two ways—either by increase of the volume at constant pressure, or by increase of the pressure at constant volume. From these two effects the ratio of the two specific heats can easily be deduced; and the number found is about 1·42, a number indicated by the velocity of sound.

These experiments are now in full operation. I wished by this communication to make my own the general method which will be applicable to all questions of calorimetry. I have associated with me in this work four distinguished pupils of the Laboratoire de Recherches de la Sorbonne, MM. Richard, Amaury, Champagneur, and A. Thenard. We shall presently publish the results of our work. -Comptes Rendus, March 28,-1870.

ON THE FIXED NOTES CHARACTERISTIC OF THE VARIOUS VOWELS. BY M. R. KENIG.

According to the researches of MM. Donders and Helmholtz, the mouth, arranged for the emission of a vowel, has a note of stronger resonance, which is fixed for each vowel, whatever may be the fundamental note on which it is given. A slight change in the pronunciation modifies the vocal notes so sensibly that M. Helmholtz has been able to propose to linguists to define by these notes the vowels belonging to the different idioms and dialects. Hence it is of great interest to know exactly the pitch of these notes for the different vowels. M. Donders sought to arrive at this by observing the rustling or whistling which the current of air produces in the mouth when the different vowels are whispered; the notes which he has found differ considerably from those given by M. Helmholtz. The latter used a set of tuning-forks, which he made to vibrate in front of the mouth when it was arranged to articulate a vowel. Every time the sound was strengthened by the air enclosed in the cavity of the mouth, this mass of air was evidently in unison with the tuning-fork. By this method, which is more correct than the first, M. Helmholtz found that the vowel 'A was characterized by the fixed note (sib),, O by (81b),, E by (sib),; and these results really appear incontestable. As none of the tuning-forks arranged was sufficiently acute for the vowel I, M. Helmholtz tried to determine the characteristic note by the means already employed Phil. Mag. S. 4. Vol. 40. No. 265. Aug. 1870.

L

by M. Donders, and he found it to be re.. If a tuning-fork be tuned for this note, we ascertain, in fact, that it is increased whilst the mouth passes from E to I; at least I have been able to assure myself that the increase occurs before the mouth is exactly arranged for the I. Hence the true characteristic of I must be higher. By constructing tuning-forks more and more acute, I ascertained that this note was approached; it was finally found to be si; with tuningforks still higher, it is immediately felt that the limit has been passed.

For OU M. Donders had given fa,. This note can undoubtedly be strengthened by the mouth, but it is only in departing very little from the position O; and one feels that the note of OU must be much more grave. M. Helmholtz assigns fa, to OU. However, a tuningfork fa, does not resound before the mouth arranged for OU, which M. Helmholtz accounts for by the smallness of the opening of the mouth; but it seemed to me that this smallness of the opening, while rendering a very energetic increase impossible, must still admit an appreciable increase in the intensity of the sound. Having moreover ascertained the simple ratios which exist between the notes of the vowels O, A, E, I, ascending by octaves, I thought that this law would extend to the vowel OU. I verified this hypothesis circumstantially by means of a tuning-fork, the pitch of which could be raised by means of slides; I was thus able to assure myself that the characteristic note of OU (such as I ordinarily pronounce it) was really (sib),; for the maximum of resonance always occurred between 440 and 460 simple vibrations.

For the pronunciation of the Germans of the North (to which the experiments of M. Helmholtz also refer), the vowels are then characterized as follows:

or, in round numbers of simple vibrations, 450, 900, 1800, 3600, 7200.

It seems to me more than probable that we must seek, in the simplicity of these ratios, the physiological cause which makes us find nearly always the same five vowels in the different languages, although the human voice can produce an indefinite number, as the simple ratios between the numbers of vibrations explain the existence of the same musical intervals among most nations.

It is some time since I obtained these results; but I wished to have them verified by several eminent physiologists, whose approba tion has encouraged me to publish them.-Comptes Rendus, April 25, 1870.

COMPRESSIBILITY OF GASES UNDER HIGH PRESSURES.
BY M. L. CAILLETET.

In order to obtain very high pressures applicable to the experiments in which I am engaged, after numerous trials I fixed upon an apparatus which consisted of a hollow steel cylinder firmly

fastened on a cast-iron stand. A piston, also of steel, is moved in this cylinder by a square-threaded screw, which works in a female screw of bronze, wedged in the axis of a fly, also of cast iron. When this fly is turned by means of the pegs on its circumference (as the screw cannot follow it in its rotation, owing to a catch secured by two slide bars), the piston traverses the vacuum of the cylinder in a direction determined by the direction of the motion of the fly. The water which the cylinder contains cannot escape; a leather is fitted so perfectly that, even under pressures of more than 800 atmospheres, scarcely a drop of liquid escapes. To the cylinder in which the compression is effected a steel laboratory-tube can be united by a capillary tube of copper-which, leaving that part of the apparatus quite free, allows the majority of the experiments to be made here. The pressure is estimated by two mutually controlling processes: (1) by a lever which rests on a very moveable valve; (2) by a Desgoffe's modified manometer, which I will briefly describe.

This instrument consists of a cylindrical cast-iron vessel, filled with mercury, upon which rests a metallic disk. A thin membrane of caoutchouc separates the disk from the mercury, which consequently cannot escape. A metal rod penetrates to the centre of the disk, passing through a leather fixed in a bronze cylinder connected with the pressure-machine. When the compressed water acts on the small piston, the pressure is transmitted to the mercury, which rises in a vertical glass tube, communicating with the reservoir.

If the ratio of the surface of the small piston to that of the disk is =1:100, then for a pressure of 100 atmospheres the mercury will only rise in the manometric tube 1 atmosphere, or 0.76 metre.

A grave à priori objection might be made to this apparatus; in fact, it is not known what resistance the leather exercises on the piston. In the apparatus employed by me, the ratio of the surfaces is =1:212, and it is sufficient to lower the piston of a millimetre in order to raise the mercury 4:30 metres, the height of my manometric tube. The path traversed being very small, the resistance will be nearly none. To overcome the inertia, the mercury is caused to oscillate about its position of equilibrium in the glass tube by means of a small lever, which acts on the compressing disk. The manometer thus constructed has been verified up to 80 atmospheres by the help of a very large manometer, in which the compressed air was replaced by hydrogen. The graduation was based on the numbers published by M. Regnault. The apparatus for pressure, such as I have just described it, easily gives pressures from 8 to 900 atmospheres, which can be maintained for a considerable time. Danger from the bursting of any part of the machine, there is almost none: steel tubes filled with liquid have frequently split without any of their parts being projected.

In an experiment, in which I subjected to about 850 atmospheres pressure 60 cubic centimetres of hydrogen, the laboratory-tube was broken, the compressed gas suddenly expanded and exploded with

the sound of a pistol-shot; but the splinters of broken glass were not thrown about, owing to the metal cover.

In order to investigate Mariotte's law under high pressures, I employ a cylindrical glass tube capable of containing 40 to 50 cubic centims. of gas; a capillary glass tube is welded to this reservoir, in which the compressed gases will be measured. The other extremity of the reservoir is open and tapered. This apparatus is filled with the gas to be examined pure and dry, the extremity of the capillary tube is welded, and to the lower point a kind of small inverted gauge filled with mercury is fitted, which admits of the apparatus being placed in the laboratory-tube filled with mercury. At the moment when the pressure is exerted by the machine, the mercury, pressed by the water, will penetrate into the reservoir through the tapered part, will drive back the gases in the capillary tube, and will just stop at a point of its height. In order to determine this point exactly (which cannot be done during the experiment, because the apparatus is enclosed in the steel tube), I had recourse to an artifice which gives extremely correct results.

With this object I slightly gilded the interior of the capillary tube by M. Böttger's process. The mercury, rising in contact with the sides, dissolves the gold; and the height of the bright metal corresponds exactly with the height attained by the mercury. This is noted on a coat of varnish applied to the surface of the glass. It can be understood how a great number of heights, corresponding to the volumes occupied by the gas at pressures determined by the manometer, may thus be found.

The correctness of the determinations which I have obtained depend especially (1) on the marking of the heights attained by the mercury in the capillary tube, (2) on the weights of this mercury, (3) on the correctness of the manometer. I have assured myself by numerous experiments that the volume of the mercury could be obtained very correctly; the weight taken has always been the mean of four operations. I have already discussed the correctness of the manometer; I have moreover compressed at the same time, in the same tube, two different gases. thus proved that the volumes occupied by the two gases under identical pressures corresponded well to the numbers found in my experiments. The numbers obtained have not undergone the correction due to the compressibility of the glass apparatus; I did not know this contraction; I made all my determinations for the different gases under the same pressures, in such a manner that, if a cause of error not recognized should vitiate my results by the same quantity, the experiments, made under identical conditions, will still remain comparable."

As M. Regnault has done in his memorable researches on the compressibility of gases, I have calculated the departures from Mariotte's law by employing the formula the numbers thus obtained were

VP
VIP

taken as lengths of the ordinates for the construction of the curves, which cannot be given here:

The above results were obtained by operating on 43.638 cubic centims. at +15°.

It appears, according to these numbers, that Mariotte's law is not verified for high pressures; each gas in contracting seems to follow a special course. Hydrogen decreases regularly; air, on the contrary, very curiously, reaches a maximum at 80 atmospheres, and afterwards decreases more rapidly than hydrogen.

In presenting these still very incomplete experiments to the Academy, I simply wished to record them, reserving to myself the time necessary for their execution.

I am at present occupied in pursuing my determinations with much higher pressures, and extending them to other gases.Comptes Rendus, May 23, 1870.

NOTE TO MR. MOON'S PAPER ON THE SOLUTION OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER, IN THE PHILOSOPHICAL MAGAZINE FOR JULY.

I desire to point out that when the coefficient U in the equation 0=Rr+Ss+Tt+Pp+Qq+Uz

is finite, the assumptions

c=1,

= &c. C1=C2 =

0

materially cripple the generality of the result; as a glance at the mode in which each of the coefficients A,, A,, &c. is formed from its immediate predecessor will readily show.

July 23, 1870.