its true position as much as 20°. The cause of this phenomenon I take to be, that the dark heat from the face of the observer warms mainly that part of the flask directly opposite him; this causes a feeble ascending current of air in that region, and this again a horizontal current toward the heated wall, the latter current acting on the disc precisely as the wind does on a weather-cock. The deflection from this cause was pretty constant, and did not prevent qualitative observations from being made, though in the more important cases I avoided it altogether by quickly taking the reading with the aid of a screen, and then retiring for some minutes to the other side of the room before taking a second reading.

Experiment with gas flame and a solution of alum.-The light of a luminous gas flame at a distance of a foot, after passing through a saturated solution of alum 41 mm. thick, was allowed to act on the blackened side of the disc, and forty readings were taken at intervals of about twenty seconds. A repulsion from the light was produced; below is given the deviation indicated by the mean of each successive set of ten readings.

The alum solution was now removed, when the disc began to move rapidly toward the light, and after twenty readings, had reached a final deviation of 28°7 toward the light. Here it remained stationary with small fluctuations. Being convinced that the deviation of 28°7 was due solely to the heating of the glass by the naked gas-flame, causing thus a current to set toward it, and drawing the disc in that direction after the manner of a weather-cock, I moistened the side of the glass next to the gas flame with water at the temperature of the room, by the aid of a small camels' hair brush. For a second or two, no effect was produced; then a large repulsion ensued rather forcibly, the disc being driven away from the light, a deflection of as much as 180° being obtained, which tended of course to confirm the idea I entertained.

While making the observations just mentioned, I was seated near the apparatus: they were now repeated, at intervals of two minutes, the alum solution being employed, and the observer removing each time to a considerable distance from the apparaBelow are the results of three experiments, consisting each of only two determinations of the zero point, and two of the deflection: 16°, 15°4, 15°8 away from light.

tus.

These and other equally constant results established beyond a doubt the fact that repulsion takes places when the radiations are such as not sensibly to heat the walls of the flask, and it is seen that with these conditions, the disc under the full atmospheric pressure imitates the behavior of one suspended in a vacuum.

I conceive the cause of these phenomena to be as follows: the radiations falling on the blackened disc heat it, and generate thus an ascending current of air, which sweeps upward along the surface of the disc, gathering volume as it travels from the lower to the upper edge, and tending thus to drive the dise away from the light. The cross section of the ascending current of heated air would then, roughly speaking, assume a shape like a V. To test this idea, I arranged the disc so that its upper edge should be bent away from the light, like an A, so as to give room to the ascending current of air; now, instead of hanging with its walls vertical, they were deflected as much. as 15°. This deflection was so small as not materially to diminish the projection of the surface exposed to the light, but it was found practically to destroy the repulsion. Four experiments were made, each consisting of four readings of the zero point, and as many of the position of the disc after exposure, the observer removing each time to a distance from the apparatus; the results are given below.

Toward the light.
0°.2

Away from light.
24, 0°1, 11.

This gives as the mean result a repulsion of 0°.8, and shows that the phenomenon differs essentially from that involved in a Crookes' radiometer.

With this same apparatus, the disc being still bent out of its vertical position, I now repeated the fundamental experiment of exposing the apparatus to the action of a naked gas flame under atmospheric pressure; the results of these trials are given below.

(1.) The disc remained stationary a moment, and then moved toward the light.

(2.) Same result.

(3.) Moved a few degrees away from the light, afterward 40° or 50° toward it.

(4.) 8° away from light, then a large number of degrees toward it.

(5.) Small deviation toward light, small deviation away from it, large deviation toward it.

(6.) Disc stationary, 5° away, 50° or 60° toward light.

(7.) 5° or 6° toward light, stationary, large deviation toward light.

The blackened disc was now arranged so as to hang vertically, and the experiment repeated, all the other conditions remaining unaltered.

(1.) Repelled 20°; then began to move slowly toward flame; on extinguishing the latter, a large sudden motion in same direction.

(2.) Repulsion of 40° or 50°; return to zero point; remained nearly stationary at zero point; sudden and large deflection toward flame, when it was extinguished.

(3.) Same as last.

(4.) Repulsion of about 5°, attraction 60°.

These experiments show that, as a general thing, the first effect is repulsion, the second attraction. They are, I think, sufficiently explained by assuming the existence of a vertical current, on the heated surface of the disc, and a horizontal current directed toward the heated side of the flask; these act antagonistically, and when the disc is vertical, often balance each other more or less perfectly for quite an interval. On extinguishing the flame, the vertical current is greatly weakened, while the horizontal one is not much affected, hence the violent deflection toward the heated side of the flask.

New York, June 27th, 1876.

ART. XLIV.-Experiments on the Sympathetic Resonance of Tuning Forks; by ROBERT SPICE.

IT is well known that a pair of forks having a vibration number of 256, (Koenig's Ut3 forks) show the phenomenon of sympathetic resonance at distances apart varying from three to six feet. Beyond six feet, special and delicate means have to be employed to exhibit their resonance.

It is also well known that a pair of forks having a vibration number of 512, (Ut forks) exhibit the phenomenon with similar intensity at far greater distances. The accepted solution of this difference of deportment is, that as in the latter case double the number of impulses are delivered in a second, consequently double the energy is conveyed to the distant fork.

If this explanation be sufficient, the following result should follow Forces radiating from a center obey the law of inverse squares; hence, if the amount of motion (or force?) received by an Ut fork at a distance of six feet from its excited fellow be represented by n; then (assuming an Ut fork to have double the energy of an Ut3 fork,) clearly, the amount of motion. received by an Ut fork at a distance of twelve feet from its

n

excited fellow, should be represented by. But so far is this

from being the case, that the intensity instead of being one-half (as calculated) is more than double. In fact, at twenty feet the

intensity of resonance of Ut forks is undoubtedly greater than the intensity of Ut3 forks at six feet.

A pair of forks were cast in a kind of bell-metal, and tuned to Ut3. On Koenig's boxes the resonance was quite obvious at twenty feet, and at forty feet the responding fork drove a cork ball 8mm diameter a distance of 10mm! This result was greater than that obtained with the steel Ut' forks of Koenig. In view of these facts, it seemed to me that a different explanation was required to clear up the difficulty: and, after a careful experimental examination of the question, I offer the following hypothesis:

The intensity of sympathetic resonance of forks on their cases increases with the angular deviation or motion of the prongs.

The question of number of vibrations per second has its proper value, but this value is small compared with the element above stated.

I proceed to explain this bypothesis. Suppose that we wish to set a pendulum in motion, but are required to fulfill the two following conditions: First. We are obliged to hold the cord of the pendulum (point of suspension) in our hand, and this hand is also to be the motive power, to start and keep the pendulum in motion. Second. We are only to be allowed a lateral movement of the hand of one inch each way, making in all two inches.

Now the amount of motion or amplitude of a pendulum is estimated by the angle the cord or rod makes with the vertical; and clearly, if the point of suspension moves laterally, it thereby creates an angle. If, further, the point of suspension has a reciprocal motion in accord with the possible time of the pendulum, then, by the principle of the summation of impulses, the motion of the entire pendulum will be gradually augmented up to a limit determined by well-known mechanical theorems. But if amplitude is expressed by angular magnitude, then, if the initial angle be increased, the total motion must be acquired in less time and be greater. From which it follows that, retaining the conditions above stated, if we operated on a pendulum ten inches long, we should set it in its maximum motion in less time and with less expenditure of force than if we operated on a pendulum fifty inches long. Experience confirms this.

A fork vibrates after the manner of a pendulum, and may be looked upon as an inverted pendulum; but whereas, the length of a pendulum determines its vibrating period, the length and thickness together determine the period of a fork. Again: the period of a fork varies directly as the thickness, but inversely as the square of the length; hence a small alteration of length will make a large difference in its period; or, conversely, a

large alteration of period does not imply a large difference in length.

From measurements made with an electro-chemical registering apparatus, which I designed for this and similar investigations, I find that when a fork of the usual dimensions (between Ut3 and Ut) is in vibration, its stem or handle alternately rises and falls in accord with the period of the fork, through a dis tance of about inch. When a fork on its case is influenced by a distant fork, the case gives the stem this up and down motion, which is conveyed to the prongs and sets them in vibration after the manner of the hand starting a pendulum as specified above.

This motion of inch may be looked upon as a constant, and corresponds to the two-inch motion of the hand in the illustration. If we decrease the length of the fork without altering the constant, we thereby allow of a greater initial angle; the result of which we have already noted-it is the same as shortening the pendulum cord. This much understood, we are in a position to explain the deportment of the bell-metal forks cited. The velocity of sound in bell-metal is much less than in steel, hence, retaining similar thicknesses in both cases, an Ut3 fork in bell-metal would be shorter than an Ut3 fork in steel; the ratio of the length of the steel to that of the bell-metal ranging as 90 75. Therefore, though we retain the vibrationnumber, we gain advantage from the shortness of the fork, and hence from the increase of angular motion of the prongs.

It was suggested to me that possibly bell-metal had the property of accepting motion more readily than steel. To test this point I made a pair of Ut steel forks, shorter than Koenig's, and of course thinner, in order to retain the vibration-number. These forks behaved just like the bell-metal forks. Further, I made a pair of Ut forks as long as Koenig's Ut3 forks, and of course thicker. These behaved like Koenig's Ut3 forks. Finally, taking a Koenig Ut fork on its case, and one of the short Ut forks also on its case; on placing them twenty feet apart, it was found that, on exciting Koenig's fork, my short fork responded well, whereas on exciting the short fork Koenig's did not respond at all.

230 Bridge st., Brooklyn, July, 1876.