two or three turns, unwind with a nearly constant velocity, so that, if there is to be much variation in the exposures, (for example, a ratio greater than 1 to 3 or 1 to 4,) we must resort to complicated gearing. For those who are satisfied with these small ratios and comparatively long exposures, as those who are engaged in photographing yachts exclusively, a coiled spring leaves little to be desired, as it is compact and readily carried. On the other hand, if one wishes to vary the exposure through a large range, such as 1 to 100, or to get an exposure of less than of a second, the drop-shutter arrangement offers peculiar advantages.

sec.

Such a shutter has been constructed in which the drop is four inches and the diameter of the aperture seven eighths of an inch; but by attaching two two-inch brass spiral springs beneath it, and doubling the velocity by means of a pulley, the speed has been increased from to sec. The tension of the springs may be adjusted, and any intermediate exposure given. A string which is attached to the top of the shutter passes over a pulley, and has a twenty-gram weight fastened to its other end. This exactly balances the shutter when the springs are released, permitting it to remain motionless in any position. This is desirable for focusing, and also for hand exposures. By thus counterbalancing the weight of the shutter, removing the brass springs and pulley, and attaching small weights in their place, the length of the exposure may be increased from sec. to sec. A shutter constructed on these principles has been in use by me now for some months, and works admirably. The exposures under similar circumstances can always he relied on, and never vary among themselves more than ten per cent. Its total weight does not exceed a pound, and it can instantly be adjusted to give any exposure from second, or to give hand exposures.

to

INVESTIGATIONS ON LIGHT AND HEAT, MADE AND PUBLISHED WHOLLY OR IN PART WITH
APPROPRIATION FROM THE RUMFORD FUND.

XXVI.

CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF HARVARD UNIVERSITY.

ON A NEW METHOD FOR DETERMINING THE MECHANICAL EQUIVALENT OF HEAT.

By A. G. WEBSTER.

Communicated by Professor Trowbridge, May 26, 1885.

IN 1867 Joule published the results of his experiments for determining the mechanical equivalent of heat, by means of observations on the thermal effect of an electric current. In his experiments a calorimeter was used holding over a gallon of water, the temperature of which was taken by a thermometer. The method about to be described differs from Joule's in that the temperature is measured by the change of resistance of a wire, which is heated by a current, and no water is employed. The idea of the method was suggested by Professor John Trowbridge. Accuracy is not claimed for the results which follow, as the experiments were undertaken only with the view of ascertaining the practicability of the method.

The method of conducting the experiments was as follows. A thin ribbon of steel about 45 cm. in length and 1 mm. in breadth, and weighing .23 gr., was included in one side of a Wheatstone's bridge, by which its resistance was measured. It was then thrown into another circuit, and a transient current from twelve large Bunsen cells was passed through it. The quantity of electricity transmitted was measured by a ballistic galvanometer, and the difference of potential of the ends of the steel strip was compared with the electromotive force of a Daniell's cell by means of a quadrant electrometer. The rise in temperature of the steel was found by immediately measuring its resistance again. It had been previously found, by a series of experiments made between the temperatures of 90° and 10° C., that the resistance of the steel used was represented by the equation

being the temperature.

Ra (1.00503 ),

If then R be the initial resistance of the strip, and R1 the resistance after the passage of the current,

If w be the weight of the strip, and s its specific heat, the quantity of heat imparted to it by the current, is

h=ws (01- 0%)

=

ws (R1-R)
αβ

(1.)

But if Q is the quantity of electricity transmitted, and E the difference of potential between the ends of the strip,

Jh=QE,

where Jis the mechanical equivalent of heat. We have

where a is the first swing of the needle of the ballistic galvanometer, G the galvanometer constant, T the period of a single vibration of the needle, and H the horizontal component of the earth's magnetic force. G was determined by comparison of the deflections on the scale of the ballistic galvanometer with the readings of a tangent galvanometer whose constant was calculated, included in the same circuit. In the experiments, 2 sin was considered as proportional to 8, the deflection on the scale, and the value of G for 81 cm. was found to be 769.4. A shunt was used with the galvanometer, so that the value of r being the resistance of

a

2

Q above given is to be multiplied by "+

the galvanometer, and S that of the shunt.

The arrangement of the apparatus was as follows:

R. The steel strip enclosed in a glass tube to protect it from draughts

K. Key for battery B, and galvanometer G.

K. Key for passing current from B, through strip.

K. Key in auxiliary circuit with commutator C, and a second coil of galvanometer G2, for bringing the needle quickly to rest without heating strip R.

The two galvanometers were arranged to throw their spots of light on the same scale. The key K, was first depressed, R being then in the bridge circuit, and the spot of G, was brought to zero by adjusting the resistance c. a was always 1,000 ohms, and 6 one ohm. On K

being raised, a sufficient extra resistance was inserted in c, so that when K, was momentarily depressed, and K, was immediately afterwards again depressed, the spot G did not move. The hand soon became accustomed to pressing K, just long enough to accomplish this result. In the experiments, c had to be increased from 1,167 ohms by the amount of 50 ohms, and the temperature of the strip accordingly rose about ten degrees. As the resistance was measured almost simultaneously with the passage of the current, the rise in temperature could be very exactly known, and the effect of radiation could be very easily determined.

Combining equations (1) and (2), we have

E, as measured by the electrometer, was about one volt, =108 C. G. S. units. H was .171; r, the resistance of the ballistic galvanometer, was 3,296 ohms; S1, the shunt, was 1,025 ohms; T, the time of a single vibration of the needle, was 12.6 sec.; a, the resistance of the strip at 0°, was 1.072 ohms; B was .00503, the weight of the strip was .230 gr.; its specific heat, .114; the gain in resistance of the strip was .05 ohm, and 8, from twenty experiments, was 26.8 cm. G was 769.4 for 81.

108 X .171 X 12.6 × 26.8 X 4.321 x 1.072 X .00503
769.4 π.05 × 1.025 × .230 × .114

= 4.14 X 10 ergs per gram-degree.

In Joule's experiments, the process of heating was continued for nearly an hour, whereas here it lasts for less than a second. In the former method, it was necessary that the current should remain sensibly constant throughout the experiment, and the calorimeter was radiating heat throughout that time. In the short time required by the latter method, the radiation must be very small, and the error from the inconstancy of the current is avoided. I intend to undertake a further course of experiments in order to obtain an accurate determination, the purpose of the present paper being merely to show the method.

JEFFERSON PHYSICAL LABORATORY.