It will be noted that the exposures Nos. 1, 2, 3, 9, 10, and 11, as shown by the diagrams, last each for two units of time, and may therefore be readily compared with one another. No. 3 lets through the greatest amount of light for any single slot (.58), and No. 11 for a double slot (.79). These are therefore the best forms to use, and if their lengths can be increased in proportion to their breadths so much the better. No. 11 is the better of the two, but presents more mechanical difficulties of construction when high speeds are desired. With No. 8 the exposure is only one half that of No. 11, but its coefficient is somewhat less (.57). This is only a modified form of No. 11, and with No. 7 gives the shortest exposure of any aperture that uncovers the full size of the lens. The ideal practical shutter will then have an aperture of the form No. 3, 8, or 11, as the case may be, and as much lengthened as possible.

(4.) Motive Power. Now as to the driving force to be employed. It has been found that, with a very sensitive plate (Allen and Rowell extra-quick, or the Stanley) and a rapid rectilinear lens, an exposure of sec. was sufficient to make a fair printing negative. The ideal shutter should then give a minimum exposure of not more than o of a second and a maximum of perhaps a second. Let us suppose that the aperture between the lenses is one inch in diameter. The slot, if single, must then be capable of moving with a maximum velocity of two inches in of a second. Theoretically this could be obtained by the force of gravity alone only by a fall of sixteen feet. But a shutter of these proportions is evidently out of the question; therefore, for rapid exposures one must resort to springs. These are of three kinds, -india-rubber, metallic coiled, and metallic spiral. The former are convenient and cheap, but cannot be relied upon to give uniform results. Coiled springs, after they are wound up

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 0 to second, or to give hand exposures.

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 0),

If then Ro 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

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

Jh=QE,

where is 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 Q above given is to be multiplied by r being the resistance of " S the galvanometer, and S that of the shunt.

a

r+s

The arrangement of the apparatus was as follows:

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

K1. Key for battery B, and galvanometer G1.

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

K. Key in auxiliary circuit with commutator C, and a second coil of galvanometer G, 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 b one ohm. On K