phenomenon lasts for an exceedingly short time, so that it is difficult to observe it in all its minute details.

This method, however, may be improved by being arranged so as to give an illumination of the string at very short intervals each time that it returns to the same position. An intermittent series of illuminations is thus obtained, and they succeed each other so rapidly that the illumination appears constant, and causes the string to appear as if fixed in the given position. The point, then, is to discover some means of illuminating the string each time that it reaches one and the same position.

For this purpose use may be made of a disc of cardboard D (fig. 34), which carries a certain number of narrow slits (eight in all) disposed at equal distances round the circumference of a circle. It can be rapidly turned by means of an excellent rotatory apparatus B, set in motion by the weight P, and regulated by the fly V-an apparatus which allows a uniform motion to be given to the disc, and also allows its velocity to be varied at will. This latter result is easily obtained by increasing more or less the weight P, and modifying the form of the fly; after a few trials it is easy to find the required velocity.

The apparatus then operates as follows: The disc being placed before the slit through which the solar rays enter, intercepts them completely; but every time that one of the slits in the disc comes before the slit in the shutter, the rays pass and illuminate the string. If, then, the velocity of the disc be so chosen that in the time that it

takes for the second, third, &c., slit in the disc to come before the slit in the shutter, the string makes a complete movement, and returns to its first position, the string will be illuminated intermittently at equal intervals of time, always when it is in the same position. The string ought to appear fixed, and present the form which it has at the given moment and in the given position. The figures obtained are very clear and complicated, and can easily be drawn, because the phenomenon remains as it were fixed for as long a time as may be wished. But it changes its form according to the way in which the string is made to vibrate. If it be plucked at a third, at a fourth of its length, or at a seventh or eighth, if it be rubbed with a bow at one point or another, sensibly different figures are obtained.

Fig. 35 shows, as an example, the form observed when

f Fig. 35.

the string is plucked at one-seventh of its length. The form is complicated, which is the interesting circumstance. The image is not equally clear and sharp at all its points. At the points a, b, c, d, there is a thin black line; at the intermediate points a', b', c', d', the image is enlarged and fainter. The different portions of the string at these

latter points undergo very rapid vibrations, which the disc, on account of its too slow rate of rotation, does not succeed in analysing. These portions, then, behave as in the ordinary case of a string illuminated by continuous light, which does not show its form, but only the limits between which it vibrates.

4. An apparatus of much use in many acoustic researches, and especially in the present question, is Scott's Phonautograph (fig. 36). A large sounding-board in the form of a paraboloid, open at its large end, and closed at its narrowest part by a very thin animal membrane M, which is stretched more or less by means of three screws v (of which only one is shown in the figure). A piece of elder pith a cut into a right angle is attached to the membrane, and carries at its extremity a very light and flexible point p.

A note produced opposite the paraboloid A is reinforced by it, the membrane M vibrates, the piece a takes part in these vibrations leverwise, and the point p vibrates strongly in a direction perpendicular to its own length. The vibrations are further made visible by means of the graphic method. The point p touches the surface of the revolving cylinder C, and the screw V serves to regulate this contact. The cylinder is covered by a sheet of very smooth paper smoked in a petroleum flame, and a movement of rotation is imparted to the cylinder by means of the handle M, or better still, by means of a clockwork movement arranged to produce uniform rotation, driven by the

weight P. The axis of the cylinder C further has a screw cut on it, so that the traces taken by different turns are not superposed.

The phonautograph is a very useful instrument, which

may be used for many and various researches. The vibrations of a note are traced by it with great regularity. If two organ-pipes differing slightly from each other be taken

and beats be produced, they will be traced with great regularity on the revolving cylinder. Very beautiful curves are thus obtained, similar to those obtained by the optical method [fig. 33].

But this instrument serves not only to demonstrate the vibrations, but may also serve most usefully to make known the form of the special corresponding curve.

In this respect, however, the instrument is not altogether to be relied upon; it may be that it does not register all the partial notes which enter into the formation of the compound note, and it may also be the case that it adds something on its own account.*

But notwithstanding these small defects, it shows admirably that different and very characteristic curves correspond to sounds of different timbre. The modus operandi is the same in every case. All that is necessary

is to produce the sound to be examined before the mouth of the instrument with a sufficient degree of energy, and the instrument then of itself traces the required

curve.

Fig. 37 represents some of the most important cases in this respect. Each horizontal line contains two somewhat different curves, which however belong to the same sound, and which are obtained according to the greater or less

* The effect is more certain, and the curves obtained are more beautiful and clearer, when the pith lever is reversed and only attached by one end to the middle of the membrane, and the rectangular lever provided with a joint so that it can move freely. The curves lately obtained thus are much more beautiful and characteristic than those shown in fig. 37.