194
CONEY
distribution of temperature in a bar or wire heated by an electric current. The advantage is that the quantities of heat are measured directly in absolute measure, in terms of the current, and that the results are independent of a knowledge of the specific heat. Incidentally it is possible to regulate the heat supply more perfectly than in other methods. (a) In the practice of the resistance method, both ends of a short bar are kept at a steady temperature by means of solid copper blocks provided with a water circulation, and the whole is surrounded by a jacket at the same temperature, which is taken as the zero of reference. The bar is heated by a steady electric current, which may be adjusted so that the external loss of heat from the surface of the bar is compensated by the increase of resistance of the bar with rise of temperature. In this case the curve representing the distribution of temperature is a parabola, and the conductivity k is deduced from the mean rise of temperature {E - E~‘)/aE'‘ by observing the increase of resistance E~E° of the bar, and the current 0. It is also necessary to measure the cross-section q, the length l, and the temperature-coefficient a for the range of the experiment. In the general case, the distribution of temperature is observed by means of a number of potential leads. The differential equation for the distribution of temperature in this case includes the majority of the methods already considered, and may be stated as follows. The heat generated by the current (7 at a point x where the temperature-excess is 6 is equal per unit length and time (t) to that lost by conduction -d(qkd0/dx)/dx, and by radiation hpO (emissivity h, perimeter p), together with that employed in raising the temperature qedd/dt, and absorbed by the Thomson effect sCdd/dx. We thus obtain the equation— + aO)ll = - d(qkdeidx)ldx+hpd + qcddjdt + sCdejdx. (8) If (7=0, this is the equation of Angstrom’s method. If h also is zero, it becomes the equation of variable flow in the soil. If dd/dt-0, the equation represents the corresponding cases of steady flow. In the electrical method, observations of the variable flow are useful for finding the value of c for the specimen, but are not otherwise required. The last term, representing the Thomson effect, is eliminated in the case of a bar cooled at both ends, since it is opposite in the two halves, but may be determined by observing the resistance of each half separately. If the current C is chosen so that C2Rca=hpl) the external heat-loss is compensated by the variation of resistance with temperature. In this case the solution of the equation reduces to the form— 6—x{l-x)C2Ej2lqk. (9) By a property of the parabola, the mean temperature is 2/3rds of the maximum temperature, we have therefore— (R — Ra)laR0 — lC2RJqk, (10) which gives the conductivity directly in terms of the quantities actually observed. If the dimensions of the bar are suitably chosen, the distribution of temperature is always very nearly parabolic, so that it is not necessary to determine the value of the critical current C2 = hpl/aRo very accurately, as the correction for external loss is a small percentage in any case. The chief difficulty is that of measuring the small change of resistance accurately, and of avoiding errors from accidental thermo-electric effects. In addition to the simple measurements of the conductivity (M ‘Gill College, 1895-96), some very elaborate experiments were made by King (Proc. Amer. Acad., June 1898) on the temperature distribution in the case of long bars with a view to measuring the Thomson effect. Duncan College Reports, 1899), using the simple method under King’s supervision, found the conductivity of very pure copper to be TOO? for a temperature of 33° C. (b) The method of Kohlrausch, as carried out by Jaeger and Dieselhorst [Berlin Acad., July 1899), consists in observing the difference of temperature between the centre and the ends of the bar by means of insulated thermo-couples. Neglecting the external heat-loss, and the variation of the thermal and electric conductivities k and k', we obtain, as before, for the difference of temperature between the centre and ends, the equation— Qmax ~K= VRllZqk = EClfiq = Wk'fik, (11) where E is the difference of electric potential between the ends. Lorentz, assuming that the ratio kjk' — ad, had previously given ^-O^Ha, (i2) which is practically identical with the preceding for small differences of temperature. The last expression in terms of kjk' is very simple, but the first is more useful in practice, as the quantities actually measured are E, C, l, q, and the difference of temperature.
ISLAND The current C was measured in the usual way by the difference of potential on a standard resistance. The external heat-loss was estimated by varying the temperature of the jacket surrounding the bar, and applying a suitable correction to the observed difference of temperature. But the method (a) previously described appears to be preferable in this respect, since it is better to keep the jacket at the same temperature as the end-blocks. Moreover, the variation of thermal conductivity with temperature is smali and uncertain, whereas the variation of electrical conductivity is large and can be accurately determined, and may therefore be legitimately utilized for eliminating the external heat-loss. From a comparison of this work with that of Lorentz, it is evident that the values of the conductivity vary widely with the purity of the material, and cannot be safely applied to other specimens than those for which they were found. 19. Conduction in Gases and Liquids.—The theory of conduction of heat by diffusion in gases has a particular interest, since it is possible to predict the value on certain assumptions, if the viscosity is known. Some account of this will be found in the article on Diffusion of Gases, or in Meyer’s Theory of Gases. The experimental investigation presents difficulties on account of the necessity of eliminating the effects of radiation and convection, and the results of different observers often differ considerably from theory and from each other. The values found for the conductivity of air at 0° C. range from -000048 to •000057, and the temperature-coefficient from -0015 to •0028. The result should be independent of the pressure within wide limits if molar convection is eliminated, and should be proportional to the product of the viscosity and the specific heat at constant volume; but the numerical factor is probably different for different gases according to the complexity of the molecule. The conductivity of liquids has been investigated by similar methods, generally variations of the thin plate or Guard-Ring method. A critical account of the subject is contained in a paper by Chree (Phil. Mag., July 1887). Many of the experiments were made by comparative methods, taking a standard liquid such as water for reference. A recent determination of the conductivity of water by Milner and Chattock, employing an electrical method, deserves mention on account of the careful elimination of various errors (Phil. Mag., July 1899). Their final result was &='001433 at 20° C., which may be compared with the results of other observers, Lundquist (1869), ‘OOISS at 40° C.; Winkelmann (1874), '00104 at 15° C.; Weber (corrected by Lorberg), ‘00138 at 4° C., and -00152 at 23-6° C.; Lees (Phil. Trans., 1898), -00136 at 25° C., and -00120 at 47° C. j Chree, -00124 at 18° C., and "00136 at 19-5° C. The variations of these results illustrate the experimental difficulties. It appears probable that the conductivity of a liquid increases considerably with rise of temperature, although the contrary would appear from the work of Lees. A large mass of material has been collected, but the relations are obscured by experimental errors. (h. l. c.) Coney Islcincl, a sand bar at the west end of the south shore of Long Island, New York, U.S.A., within the corporate limits of Greater New York City. It is five miles long east and west, and about a mile in average breadth, and is separated from the mainland by a narrow creek and a stretch of marsh. It is about ten miles distant from the centre of Brooklyn, with which it is connected by several lines of railway, while with New York in summer it is connected by several lines of steamboats. It is a popular resort for the metropolis. On a fine sandy beach five miles in length, which gently shelves to the Atlantic and has little undertow, several seaside places—Manhattan Beach, Brighton Beach, West Brighton, and West End—face the sea. The first two have immense hotels, with ample pleasure-grounds and bath-houses. West Brighton is, in the season, the most crowded and most popular. All the
