have suspended three balls, at equal intervals, by strings of equal length. I set the middle one swinging, and you see how it gradually imparts its motion to the two lateral balls, and comes to rest itself. Now the side balls are losing their motion, and the middle one takes it up again, until it swings almost as far as at first, and its companions hang motionless. These alternations continue until the resistance of the air overcomes the motion, and the balls are all quiet, as at the beginning. The motion, however, has not ceased; it has merely been imparted to the air, and by the air to the æther, so that we do not see it, and we are unable to follow it through all its changes.

When the regularly recurring vibrations of an elastic medium are transmitted to the ear through a suitable medium, they produce the sensation of sound; if the interval between the successive vibrations is short enough, the sound is musical. We may distinguish between the music in the sounding body and the music which we hear. A bell may ring when swung by the wind, but it will give no sensation of sound unless its vibrations reach the drum of the ear with energy enough to make it vibrate. I strike this tuning fork, but you hear nothing except a single ring. I bring it near the opening of this wooden box and the oscillations of the fork are imparted, first to the air, then to the wood, and the note of the fork is sounded, loud, clear and musical.

It is not necessary that the unison should be exact, or, in other words, that the fork and the resonator should make the same number of pendulum swings in the same time. If the vibrations coincide at intervals which are so short that the ear cannot distinguish between them, one body, for example, making three vibrations and another two in the hundredth part of a second, both sounds are said to be harmonious. Whenever any elastic medium is vibrating, its waves tend to produce harmonic vibrations in all bodies which they strike.

If the elastic force of the æther is more than a million million times as great as that of the air, its musical rhythm, if our ears were sensitive enough to hear it, should be of a far higher order than that of any earthly choir. Chemical atoms and molecules, the particles of heated or electrified bodies, satellites, planets, suns, stars and nebulæ, all intercept the luminous waves. Hence there should be a continual tendency to relative positions which would make all the motions harmonic, or rhythmical. Such a tendency is shown in atomic weights, spectral lines, mechanical equivalents of heat, the various phenomena

of electro-dynamics, the relative positions of satellites, asteroids and planets, and the bonds of union between our own system and the nearest of the fixed stars. The truth of the radio-dynamic hypothesis has been further confirmed by the indication or prediction of harmonic nodes beyond Neptune, as well as between Mercury and the Sun, fourteen of which have been subsequently corroborated by the calculations of various European and American astronomers.

If you throw a ball, or fire a projectile upwards into the air, it will continue to rise until the resistance of the air and the attraction of gravitation have overcome the velocity of projection. If there were no air, and no resistance to the upward flight except gravitation, the relation of projectile velocity to gravitation and height of projection would be represented by the equation

The relation of velocity to time of rise, or to the equal time of fall would be represented by

In solar rotation each particle is alternately projected from and drawn towards the universal centre of gravity. Substituting the equatorial values of g and t in equation (2), we find that v is the velocity of light.

The circular-orbital velocity of a particle at Sun's surface, v, is connected with the velocity of rotation, r,, and the velocity of light, CA, by the equation

(3)

The velocity of a particle, at any distance whatever from any attracting centre, can be deduced from equation (3), by means of the eleventh fundamental law, that centripetal accelerations vary directly as the mass and inversely as the square of the distance. Hence we see that all gravitating velocities are dependent on the velocity of light.

The distribution and motions of the principal planetary masses are also dependent upon the same velocity. The largest planet is Jupiter, which is more than twice as large as all the other planets. The mean centre of gravity of the solar system is therefore the same as the mean centre of gravity of Sun and Jupiter. The next planet in point of magnitude is Saturn, which is more than two and three-fourths times. as large as all the remaining planets, and which is placed at the nebular centre of planetary inertia. When the primitive planetary belt was successively divided into inter-asteroidal and extra-asteroidal belts, WHOLE NO. VOL. CXII.-(THIRD SERIES, Vol. lxxxii.)

9

two-planet belts and single-planet belts, the amount of inertia remained unchanged. But in these divisions the rectilinear propagation of luminous waves has been changed into the synchronous oscillations of conical pendulums, introducing the length-ratio of 4 to 1; the synchronous oscillations have been changed into orbital oscillations, in which the time varies as the power of the distance; nebular radii have given place to radii of subsidence-collision, which are only as great; and centripetal tendencies vary as the fourth power of orbital tendencies. If we designate Saturn's mass by me, and the mean velocity of rotation of the centre of gravity of the solar system by, these changes and their dependence on the velocity of light are shown by the proportion

4 M : (3) mơ và

Bessel's estimate of the comparative masses of Sun and Saturn was M35016 m. Substituting this value in the above proportion, we find

l'λ = 141815

The most accurate estimate that we are able to make of v is 1.31405 miles per second. This velocity, which is so readily deduced from the velocity of light, is also the wave-velocity which represents the conversion of water into vapor.

Let 0 represent the latent heat of steam, then well-known laws of thermo-dynamics give us the equations

Among the various experimental values which have been obtained for 0, the following are generally regarded as the most trustworthy:

According to the kinetic theory of gases the internal movements of the particles of steam are rectilinear. When the steam is condensed, in the form of water or ice, the internal energies tend to maintain a spherical figure. The synchronous oscillations of the two conditions may be represented, according to Fourier's theorem, by linear and conical pendulums. The height to which the vapor would be projected above the water level being represented by 750,098 feet, or 142-064 miles, the length of the conical pendulum is as great, or 47355 miles, and the length of the linear pendulum is as great, or 189 419 miles. The heat of sphericity should be, therefore, of the latent heat of steam, or 179-93°. Deducting 100° for the expansion of water from the freezing to the boiling point, we have 79-93° for the "latent heat" of ice, or more properly speaking, for the heat which is required to overcome the crystallizing energies of water. The following values have been obtained experimentally :

The combined influence of photo-dynamic vis viva and the nebular "subsidence" which was pointed out by Herschel, is shown in the proportion

1.015552 (3) ms: m

The radius of incipient subsidence for Neptune's orbit (Law 10, p. 61) is 101555; is the ratio of the ris vira of wave propagation to the mean vis viva of oscillating particles (Law 22, p. 62). If we substitute Bessel's estimate for me in the above proportion we find

=

1050 ms.

1

3501.6

If we take Stockwell's estimate of Neptune's radius of incipient subsidence, 10145, we get M Bessel's estimate was 1017-879; Leverrier's, 1050. The difference between the two estimates is only of one per cent. Bessel's is the one which is adopted by the British and American Nautical Almanacs, but the reputation of Stockwell and Leverrier seems to render it probable that the true values may be intermediate between the two which are here given. The photo-dynamic relations of mass and distance become still more striking when we find that the incipient subsidence at the nebular centre, Jupiter, is at a mean proportionate distance between the centre

of condensation, Earth, and the incipient subsidence of the primitive planetary belt, Neptune. This is shown by the proportion

1: 5.52 :: 5:52: 30:47

If we represent Earth's semi-axis major by 1, Jupiter's secular aphelion is 5.52, and Neptune's secular aphelion is 30:47.

These comparisons might be extended almost without end. We have now surveyed the whole field of physical science, and have found, in every direction, that all possible physical energies can be expressed in terms of the greatest and most pervasive energy, through the mass of the Sun and the velocity of light. Simple gravitation, solar rota tion, nebular subsidence, orbital revolution and all other gravitating motions, cosmical aggregation, the distribution of planetary masses, the establishment of centres of inertia, condensation and nucleation, evaporation, crystallization, heat, mechanical work, barometric pressure, atomic energy, chemical combination, electricity and magnetism, are all so simply connected by the universal laws of action and reaction in elastic media, that they all furnish ready methods for estimating the mass and distance of the Sun and the velocity of light.

THE PROPERTIES OF AIR RELATING TO VENTILATION AND HEATING.

By ROBERT BRIGGS, C.E.

Reprinted from the Sanitary Engineer, with additions by the author.

The surface of the earth is covered by a gaseous body, some forty or fifty miles in depth, which is called the atmosphere. Chemistry has discovered and isolated various gases, some of which, so far as further separation is concerned, may be deemed elementary, while some are chemical compounds of definite proportions of other elementary gases and bodies. In some cases bodies which in their elementary form, at temperatures subsisting in nature, are solid, become portions of chemical combinations as gases at similar temperatures.

The atmosphere is composed mainly of a mixture of two elementary gases, together with small but appreciable quantities of two other gaseous bodies, products of combustion; beside other gaseous bodies of various kinds, in nearly inappreciable quantities, the latter varying somewhat in character in inhabited localities. Its substance, as a