56 ELECTRICITY [HEATING EFFECTS. jars, each of capacity C, if q be the whole charge, we get immediately, from (48) of Mathematical Theory (p. 34), and 2Cn (3). Hence, if we keep the thermometer and inserted wires the same, the thermometer indications will be proportional to , or, in words the heat evolved in the whole or in any n given part of the circuit is proportional to the square of the battery charge directly, and to the number of jars (i.e., to the battery surface) inversely. If the thermometer wire remain the same, while the length, section, and material of the inserted wire is varied, then, r being the specific resistance, I the length, and p the diameter of that wire, R = 2 . Then, according to (3), the heat developed in the thermometer is given by H= "^ where A and B are constants. If, again, we use two wires of the same material of lengths I and I and diameters p and p, and make two ob servations with these for inserted and thermometer wires respectively and vice versa, then, if H^ and H 2 be the heat evolved in the two cases, H (5), since R + S is the same in the two cases. When the discharge is not complete, we have only to substitute for Q in (3) the appropriate expression for the exhaustion of the electric potential energy. Similarly we may find the heating effect caused by the discharge of a battery of jars arranged in series and charged by cascade in^Franklin s manner (p. 35). If we discharge through a multiple arc, we may assume that the discharge divides itself between the branches in the ratio of the conduc tivities, so that the conductivity of the whole arc is the sum of the conductivities of its parallel branches. On these principles it is easy to calculate the heat generated in the whole circuit or in any branch of the arc. All the cases we have alluded to were treated experiment ally by Riess, and satisfactory agreement with formula (2) established in every case. Compari- By means of formula (4) he compared the specific con- son of ductivities of a variety of metals. A and B were determined, cpnd.uc- and a standard wire of platinum of given length kept iu the thermometer ; the wires to be compared with it were inserted in the outside circuit, and the heating in the thermometer observed. From the .result the specific con ductivity (in terms of platinum) of the wires could be cal culated, their dimensions being known. The results agree very well with those got by other means. 1 Heating Heating by Constant Current. The heating effect of the constant current f urn ised by a voltaic battery was recognized as current. a distinct and often very remarkable phenomenon for a considerable time before any definite quantitative law was established regarding it. Davy 2 experimented on wires of the same dimensions but of different materials, and found that the metals could be arranged in the following order : silver, copper, lead, gold, zinc, tin, platinum, palladium, iron, those standing nearer the beginning of the list being less heated by a given current than those nearer the end. Joule 3 was the first, however, to establish a definite law Joule s connecting the amount of heat evolved per second with the ^w. current strength and the resistance of the wire. He wound the wire in which the heat generated was to be measured round a glass tube which was immersed in a calorimeter. The resistance of the water is so great that we may assume without sensible error that the whole of the current passes through the wire. The temperature of the water was de termined by means of a mercury thermometer immersed in the calorimeter. The amount of heat developed in the wire per second could then be found by the usual calori- metric methods. The strength of the current was mea sured by means of a galvanometer inserted in the battery circuit along with the wire. By experiments of this kind Joule established that the amount of Jieat generated in a given time varies directly as the product of the resistance oj the wire into the square of the strength of the current. So that, if we choose our units properly, we may write H-BI S < (6), 1 See Wiedemann s Galvanismu^, Bd. i. 194. 8 Phil. Trans., 1821 where R is the resistance of the wire, I the strength of the current, and H the quantity of heat generated in time t. The experiments of Joule were repeated with increased precau tions against error by Becquerel, 4 Leiiz, 5 and Botto. Becquerel allowed the wire to disengage beat till the calorimeter readied such a temperature that the loss of beat by radiation and convection, &c., was just equal to the gain from the wire, so that the tempera ture became stationary. The current was then stopped, and the loss of beat per second found by observing the fall of temperature in the calorimeter. Botto used an ice calorimeter. Lenz b made a series of very careful experiments with a calorimeter, in which the liquid used was alcohol, which is a much worse conductor than water. He first cooled his apparatus a few degrees below the temperature of the surrounding air, and then allowed the current to generate heat in the wire till the temperature of the whole calorimeter (which was kept uniform by agitation) had risen to an equal number of degrees above the temperature of the air. The current was then stopped, and the time t which it had flowed noted. According to Joule s law, <RI 2 ought to be constant, and it was found to be so very nearly. A very convenient instrument for demonstrating and measuring the heat generated by the electric current in a wire is the galavano- thermometer of PoggendoriF, which consists simply of an alcohol thermometer with a large bulb, into which is let a spiral of fine wire. The heat generated is deduced from the expansion of the alcohol, which is measured by means of a scale fastened to the stem of the thermometer. The value of the graduations is found by com parison with an ordinary thermometer. The thermoelectrometer of Riess might also be used in a similar way. Heating in Electrolytes. Joule s law applies also to Electn electrolytes. The phenomenon, however, is not so simple b tes - as it generally is in the case of metallic conductors. Dis turbances arise, owing to the heat evolved and absorbed in the secondary actions that take place at the electrode ; and superadded to this we have in all probability an ab sorption or evolution of heat corresponding to the Peltier effect between different metals, of which we shall have to speak directly. Joule eliminated these disturbing influ ences by using a solution of copper sulphate with copper electrodes. In this case copper is dissolved from one elec trode and deposited on the other, so that if we except the slight difference in the states of aggregation of the dis solved and deposited copper, the secondary processes are exactly equivalent, and must compensate each other. Joule 7 found that in a certain solution of CuS0 4 5 50 units of heat were generated in a certain time, while in a wire of equal resistance 5 88 units were generated by an equal cur rent in the same time. In a similar manner E. Becquerel 8 found that a current, which would produce a cubic centi meter per minute of explosive gas, generated _in certain solutions of CuSO 4 and ZuS0 4 213 and 365 units of 3 Phil. Mag., 1841- * Ann. de Chim. et de Phys., 1843. 5 Pnrjg. Ann., Ixi., 1844. 6 Wiedemann s Galvanismus, Bd. i. 670.
7 Phil. May., 1841. 8 Ann. de Chim. et de Phys., 1843.