convolutions of the strip being kept from touching one another by being screwed to a light framework composed of two horizontal strips of vulcanised fibre, F, F, joined by three thin vertical rods of ebonite, E, E, E. The two ends of the strip are soldered to two stiff vertical copper wires, c, c, about 0.128 inch thick and 6 inches long, the soldered

joints being covered over with varnish to prevent galvanic action taking place at the joint (see § 132, page 428), and the strip м м, and the upper wires c, c are also varnished to prevent electrolysis being produced by the current leaking through the water. The whole is immersed in about 122 cubic inches or 2 litres of water contained in a thin glass beaker, GG (Figs. 152, 153), which is just wide enough to take the framework of manganin strip, and, to diminish the risk of this beaker being broken, a piece of felt N is placed between it and the base board o o.

L

Electric connection is made with the stiff wires c, c by means of two insulated very flexible leads, L L, each composed of a strand of about 210 thin copper wires, the copper wires being each about 0.011 inch thick. The current is measured with an accurately-calibrated ammeter, A, and the P.D. set up between the upper ends of the stiff copper wires by means of an accuratelycalibrated voltmeter, v (Fig. 153).

The object of using a flat conducting strip and forming it into the box shape seen in the figures is to enable the conductor itself to act as an efficient stirrer when it is moved up and down in the water, the flexible leads L, L, which are fastened to a wooden rod P P fixed to the base board o o, as shown in Fig. 153, serving as a handle to hold the box м м by. The heat generated in the strip is, therefore, given off fairly uniformly to the water, and the mean temperature can be read with considerable accuracy on a single stationary thermometer, t.

When the apparatus is constructed as described, a current of 30 amperes requires a P.D. to be maintained between the binding screws B, B of about 8.8 volts, corresponding with the energy given to the apparatus at the rate of about 264 joules per second. This is about the rate that theory shows leads to most accurate results when the amount of water used is 2,000 cubic centimetres, and this rate of expending electric energy causes a rise of the temperature of the water of about 7.5°C. in four minutes. The thickness of the copper wires C, C has been chosen so that a current of 30 amperes passing through them raises their temperature also by about 7.5°C., this rise of temperature being, however, a constant, and not increasing with time, except during the first few seconds after applying the current. The cross

section of the strand of copper wires in each of the covered leads L, L is chosen as being a little larger than that of each of the stiff copper wires c, c, the former being about 0.0192 square inch and the latter about 0.0141 square inch. Hence the rise of temperature in

the covered flexible leads is also about 7°C., and by this device any considerable transference of heat by conduction into, or out of, the manganin strip is automatically prevented when a current of about 30 amperes is passing for four minutes.

It is partly for the reason just given that the apparatus illustrated in Figs. 152 and 153, when constructed with the dimensions described, enables results to be obtained with currents of about 30 amperes which differ from the truth by less than 1 per cent. ; a sample of a set of results actually obtained by students at the Central Technical College being given in the following table. But the error is not much greater when currents of 20 or 40 amperes are used corresponding with rates of production of heat respectively about half as great and twice as great as when a current of 30 amperes is employed.

Average deviation from the mean = 0·001 per cent.

= 0·42

Now we saw in § 107 that the true number of calories per joule was about 0.2388, hence no one of the preceding results obtained by the students differs by more

than 1 per cent. from the truth, while the mean of the nine observations gives a result which has an error of only about one half per cent. Consequently the result aimed at in designing this apparatus has been achieved.

In carrying out the investigation we may vary either— (1) The time during which the current is allowed to flow; (2) The current made to flow through the strip; (3) The resistance of the conductor by using similar stirrers made of somewhat thicker or thinner

manganin strip;

and when a series of experiments is made varying each of these three conditions, one at a time, it is found that the rise of temperature of the water, and therefore the amount of heat produced, is proportional to the time, proportional to the square of the current, and proportional to the ratio of V to A—that is, to the resistance of the arrangement. Further, if we take as the calorie the heat required to raise the temperature of 1 gramme of water by 1°C. when the water is at a temperature of about 15°, we find that the relationship between the number of calories, the current in amperes, the resistance in ohms, and the time is practically that given in the last section.

Example 64.-A current of 30 amperes is passed through a coil of wire immersed in water for five minutes, a voltmeter reading 10·3 volts at its terminals. The volume of water is 2,000 cubic centimetres, and the temperature rises from 15.7° to 26.66°C. What result does the experiment give for the heat equivalent of one joule in calories?

Answer. -0.2364, a result about one per cent. too low, no corrections having been made for cooling during the experiment.

Example 65.-A temporary resistance is made by putting a coil of wire of 4 ohms' resistance into a wooden bucket containing 37 pounds of water. If a current of 40 amperes be sent through the coil, what about will be the rise of temperature of the water in the first three minutes? Answer.-16°C.

109. Power.-"Power" is the name given to the rate of doing work-that is, the rate of transformation of one form of energy into another—and it must be carefully distinguished from the amount of work done, there being the same sort of difference between power and work that there is between a velocity and a distance. The word power was, however, used in the older books on dynamics to stand for the applied force, and that is the meaning of the word power in such expressions as "the mechanical advantage of a machine is the ratio of the weight to the power." Again, the word power is sometimes wrongly used for energy, as in the expression the "storage of power." Beginners must, therefore, be on their guard against being misled by such loose expressions, and they should never employ the name power, or "activity," as suggested by Lord Kelvin, in any other meaning than the rate of doing work. In that sense, of course, power cannot be stored, for while a certain quantity of water in a reservoir at the top of a hill represents a certain store of energy, the power that this water can exert at time when flowing out of the reservoir will depend on the rate at which it is allowed to flow.

any

When work is being done at a constant rate the power is constant, and it is measured by dividing the number which expresses the work done in any time by the number expressing the time. If, however, the rate of doing work at one moment is greater than at another -for example, when a person runs upstairs quickly at first and then more slowly-we do not mean by the power expended at any moment, the actual work done in a minute or even in a second, for the rate of doing work may be changing very rapidly. In such a case the power at any time is the limiting value of a ratio obtained thus:-Measure the work done in a very short time, a portion of which precedes, and the remainder of which follows, the instant at which we wish to measure the power; divide the work done in the very short time by that time, then this ratio more and more nearly represents