While submitting that the different qualities of tone are accounted for by the difference in the number and force of the upper partials in any given compound tone, I must at the same time acknowledge that I can do no more than throw out a few suggestions with respect to the causes that influence the production of such upper partials in this remarkable manner. The partials being in the natural harmonic series, it is evident that if the various proper tones of a vibrating column of air such as is enclosed in a wind instrument are not in exact agreement with this series, the resonance to the partials cannot be at its best. Take for illustration two instruments nominally the same (say two bugles), but with somewhat different qualities of tone. Suppose that a certain compound tone on both should have its first and second partials of equal intensity, but that one instrument has that one of its proper tones that is nearest in pitch to the required second partial a semitone sharper than that partial; the supposed compound tone sounded on that instrument will be deficient in the quality the second partial should give.

As regards instruments of different characters, the chief points influencing the tone are the general form of the instrument (understanding by this the proportions of the column of air, and not the shape into which the instrument may be bent up for the convenience of the player), the extent of the flanging of the bell, and the form of the mouthpiece. As an

illustration of the first of these conditions the trombone may be compared with the euphonion; the tubing of the trombone is cylindrical for about two thirds of its length from the mouthpiece, but the euphonion opens with gradually increasing curvature from the mouthpiece to the rim of the bell. The high upper partials being more powerful on the former than on the latter instrument, it would appear that the cylindrical tubing has the power of maintaining the intensity of the short waves to a greater extent than the tapering tubing has. The bellflange may be increased in size to a considerable degree without altering the pitch of an instrument; but such increase has a marked effect on the quality of tone, greatly subduing the force of the upper partials. I find by experiment that the pitch is not altered by the extension of the flange curvature beyond a point at which its tangent would make an angle of about 40° with the axis of the instrument, although the quality of tone is decidedly altered by such extension. This may be illustrated by changing the bell-end of a bugle for a bell with much wider flange, more like that of a French horn: comparing the two, it will be noticed that the change in quality of tone is very marked.

The form of the cup of the mouthpiece varies for different instruments, from that of a long deep conical funnel to that of a comparatively shallow well-rounded cup-the first form representing the French-horn mouthpiece, and the second the mouthpiece for instruments of brilliant tone, as the trumpet and trombone; those for cornets, bugles, and saxhorns are of an intermediate character. Although it is manifest that a shallow cupped mouthpiece favours the production of high upper partials, I have not as yet succeeded in arranging any experiments which would illustrate the cause of this. One fact, however, noticed by many observers, appears to me to be suggestive, and worth bearing in mind in connexion with this subject. It is this:-If a vibrating tuning-fork be placed on a sounding-board, the quality of tone it gives varies with the pressure applied: touching the board very lightly with the fork the prime tone is well heard; but on pressing the fork down to the board the tone appears to jump up an octave; at least the second partial (octave of the prime) is heard with great distinctness. This experiment appears to prove that if an elastic resonant body (in this case the resonant board) is in a state of initial pressure at the point of origin of vibrations, a vibration that would otherwise be simply pendular becomes a vibration compounded of two or more simple pendular vibrations. Applying this consideration to wind instruments, and bearing in mind the initial pressure caused by the escape

of air from the lips, it would appear probable that mouthpieces of different forms so modify this initial pressure as to cause a variety in the number and intensity of the upper partial tones.

XVII. On the Nebular Hypothesis.-IX. Radiation and Rotation. By PLINY EARLE CHASE, LL.D., S.P.A.S., Professor of Philosophy in Haverford College*.

[Continued from vol. v. p. 367.]

AMONG the most interesting of the unsolved astronomical

problems are the questions as to the origin of solar radiation and of cosmical rotation. These two problems, as I have already shown, are intimately connected, at the centre of our system, by the ultimate equality which exists between the velocity of light, the limiting centrifugal velocity of solar rotation, and the velocity of complete solar dissociation.

It has been commonly assumed that physical forces tend to ultimate equilibrium and consequent complete stagnation. The imperfections of any plan which looks to such a final result have led some writers to suppose that there may be some compensating provisions, hitherto undiscovered, for a renewal of activity. In the search for such provisions, the equality of action and reaction, and the possibility that the compensation is continually furnished by Him who is ever "upholding all things by the word of his power," seem to have been wholly overlooked.

If we assume the existence of a luminiferous æther, whether as a reality, or as a convenient representative of coordinated central forces, its undulations, when obstructed by inert centres, would necessarily lead to such phenomena as those of gravitation, light, heat, electricity, magnetism, &c. Confining ourselves for the present to the action of gravitation, it is well known that the limiting velocity of possible gravitating action and consequent centrifugal reaction at any given point is √2gr, the velocity varying as If, according to the hypothesis of Mossotti, each particle is provided with a definite æthereal atmosphere, the density of that atmosphere in a condensing

1

nucleus should vary as But, according to Graham's law,

* Communicated by the Author, having been read before the American Philosophical Society, June 21, 1878.

να

Therefore, in order to satisfy the conditions of gravity, the æthereal elasticity, within any nucleus which is either wholly or almost wholly gaseous,

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Since such is the supposed character of the solar nucleus, it seems not unlikely that, the centrifugal radiations of any heavenly body being at all times equivalent to the centripetal radiations which it intercepts, solar and stellar light and heat are only the reactionary consequences of such perpetual internal oscillations as the æther has first transmitted to the luminous orbs and then resumed. The fact that the reaction which is shown in the centrifugal force of solar rotation, and the action which is shown in parabolic orbital velocities, find a common limit in the velocity of light, may perhaps be regarded as a crucial test of this hypothesis, which is further strengthened by the following considerations.

In the huge comet-like nebulosity which is indicated by the solar-stellar paraboloid, the interesting relation which has been pointed out by Stockwell* between the perihelia of Jupiter and Uranus, and the many indications of normal "subsidence which I have shown in previous papers, suggest the probability of an early ellipsoidal nucleus with subordinate nucleoli-the major axis of the nucleus being bounded by 24 (60-939) and 235 (41-358), and the Sun being in the focus. The vis viva of condensation would give velocities of incipient orbital separation at (30-470) and &5 (20-679); and 41 would then be in the centre of the entire system (30-470-20-679÷2=4.885; 414-886), even as 3 is nearly in the centre of the secondary system (+12=1.017).

3

If we apply Gummere's criterion (n=11.656854), we find that three prominent centres of "subsidence" were determined by this early ellipsoidal nucleus. For 2¥¿÷n=5·228, 43 being 5.203; 2-n=3548, which is near the outer limit of the asteroidal belt, (107), being 3·560; (¥1—1)÷n=1·022, the centre of the secondary system being, as above stated, 1.017. The Earth is still in the centre of a "subsidence" ellipsoid, of which the Sun is in one focus, while the outer asteroidal region (3-2028) and 43 (5-2028) are at opposite apsidal extremities. of the major axis. Moreover 3-2035 is the extremity of an atmospherical radius which would move with the velocity of light, provided the sun's surface were moving with orbital velocity, or the velocity of incipient dissociation (√gr).

Smithsonian Contributions, xlv. p. 232.

Phil. Mag. S. 5. Vol. 6. No. 35. Aug. 1878.

K

It seems probable that, in consequence of subsidence, Jupiter, which, as we have already seen, was the centre of nucleal volume, may have also been the centre of nucleal mass at the time of its complete orbital separation, and that it was therefore the primitive Sun of the extra-asteroidal planets before it became our Sun's "companion star." For with the present mass of the system, and with a mean radius vector = 41+41 (34-4845), the orbital period of Neptune would be 73,966 days. Two successive subsidences (34-4845÷n') would bring the solar nucleal surface to about of 3, or 54:53 solar radii. The angular acceleration of rotation, due to subsequent nucleal contraction, would a Therefore, when the Sun had contracted to its present limits, its rotation-period would be 73966-54-53224.88 days*.

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If this were the only coincidence of its kind, we might perhaps have some good grounds for looking upon it as merely curious and accidental; but the bond of connexion which we have already found between rotation and revolution, in the limiting formative undulations which are propagated with the velocity of light, may prepare us for accepting evidences of a similar bond in the phenomena of nebular subsidence.

There are three other known systems of cosmical rotation which may help us to judge as to the rightfulness of such an acceptance, viz. :-that of the extra-asteroidal planets, with an estimated average period of about 10 hours; that of the intraasteroidal planets, with an estimated period of about 24 hours; and that of the moon, with a synodic period of 29.5306 days. If these periods are dependent upon the same subsidence which led to the early belt-formations, we may reasonably look for evidence of that dependence of a character similar to that which we have found in the case of the sun.

We have seen that the first subsidences from 2 and 34 account for the orbital ruptures of Jupiter and Earth; secondary subsidences from points within the orbital belts account

*These relations may have an important bearing on Croll's hypothesis of the origin of solar radiation. In the stellar-solar paraboloid, of which traces still exist between Sun and a Centauri, there must have been frequent collisions. Some of Croll's critics have shown strange misapprehensions as to the possible velocity of collision. The limit of possible relative velocity, from the simple gravitation of two equal meeting masses, is 22gr. This would be equivalent, taking the values of g and rat Sun's apparent surface, to 01774r, or more than 750 miles per second. If projection were added to gravitation, or if the two masses had small solid nuclei of great density, while the greater part of their volume was gaseous, or if there were a large number of equal masses, the limit of possible velocity might be largely increased.