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ture-coefficient), about 4 inch wide, 0.03 inch thick, and about 5 feet long, was bent into a series of zigzags (fig. 1) so as to
form a kind of circular gridiron, M M, in which the successive portions of strip lie all in one plane, the whole being held rigid by a strip of vulcanized fibre É crossing the gridiron and to which each portion of strip was screwed. Another precisely similar gridiron was placed 3 inches below the first, and they were held together by three thin ebonite pillars E screwed to the strips of vulcanized fibre, the whole forming the top and bottom of a sort of cylindrical box, 5 inches diameter and 3 inches high. The two grids were joined in series, and the ends of the strip of manganin were soldered to two copper wires CC, about 0:128 inch thick and 6 inches long, which were insulated from one another by vulcanized fibre separators, and constituted a kind of handle by means of which the open box could be moved up and down in the containing vessel.
The whole surface exposed to the water received a thin coat of varnish to prevent any electrolysis due to the difference of potential between the different parts of the strip. At two points in the same vertical line the zigzags forming the two grids are bent so as to leave a space for the passage of a thermometer t, the bulb of which is midway between the grids when the lower one is resting on the bottom of the vessel. The whole heating surface exposed to the water is about 60 square inches, or 400 square centimetres, The vessel used to hold the liquid is a thin glass beaker of just sufficient diameter to take the framework of manganin strip.
Electric connexion with the two stiff wires which form the handle is made by means of two well-insulated very flexible leads L L, each composed of a strand of about 210 copper wires •011 inch diameter. The size of the stout copper wires and of the flexible lead was chosen with the intention that there should neither be heat received nor heat lost on account of these connexions. The sectional area of the insulated flexible lead is rather greater than that of the stout copper wires, and the ultimate rise of temperature of both with a current of 30 amperes is about 7° C.; the rise of temperature during the short time that the current is passed being thus about equal to that of the water, and automatically preventing gain or loss of heat. The number of watts taken by the copper wires and flexible leads at 30 amperes is about 1.9.
It may here be pointed out that it is far better, from the point of view of getting a good mechanical design, to use a large current at a low pressure than to take the same power from a small current at a considerable pressure. Thus it is easy to design a strong stirrer of the shape described above which will have a resistance of } of an ohm, carrying 30 amperes at 10 volts pressure; but it would be by no means so easy to make an equally efficient and substantial stirrer of 33.3 ohms resistance to take 3 amperes only at 100 volts.
It was thought worth while to ascertain to what extent conduction through these leads influenced the rate of cooling of the vessel when no current was passing, and cooling curves were therefore taken with the manganin framework in the vessel and attached to the leads. The average rate of cooling was found to be 0.000242 calorie per square centimetre area of surface per 1° C. excess temperature; which is only about 4
per cent. greater than in the previously mentioned experiments, in which a light wooden stirrer only was used, the value then obtained being 0:000232.
III. Use of the Apparatus. In the following table are given the results of several successive experiments made with the apparatus described above by Messrs. Solomon and Grogan, students at the Central Technical College, under our supervision. The amperes and volts are expressed in the international units adopted at the Chicago Congress. The ammeter and voltmeter used were the well-known Weston-d'Arsonval type instruments. The current was known within about of one per cent., and the average potential-difference within about } of one per cent., the instruments having recently been tested against our standards at the Central Technical College. 2000 cub. centim. of water were used in all the experiments, and were measured with a graduated glass jar, fresh water being used in each experiment. The weight of the glass vessel up to the waterlevel was determined as 184 grammes, and the specific heat being about 0·2, the water-equivalent is 37 grammes. The weight of the manganin strip is 114 grammes, and the specific heat being about 0·09, the water-equivalent is 10; the equivalent mass of water used being therefore 2047 grammes.
Mean 0.2375 Average deviation from the mean=·001=0:42 per cent. With this apparatus, then, we get in about 10 minutes, including the experiment and subsequent calculation, a result for the heat-equivalent of the watt-second ; and these results have an average deviation from the mean, if several experiments are made, of less than ļ of one per cent. This result, as we have seen above, should not differ from the true value by as much as one per cert. It may here be pointed out that as the water taken from the ordinary water-supply is sure to be at least two or three degrees below the atmospheric temperature at the time, it is exceedingly easy to arrange that its mean temperature during the experiment shall be exactly equal to the temperature of the air, for no artificial method of cooling is required, as would be the case if a greater range of temperature were used. This, however, was not done except in one or two of the above experiments, and is not necessary to ensure the accuracy that was required.
The mean temperature of the water in the above experimenis was 15 degrees Centigrade; and our final result is that at that temperature 0.2375 gramme of water are raised 1° C. in temperature by the energy of one watt-second,
Now we know with considerable accuracy the equivalent in ergs of one watt-second, which certainly does not differ from 10% by more than one tenth of one per cent.; that is to say, the international volt and ampere do not differ from 108 and 10-1 C.G.S. units of electromotive force and current by more than that amount (see section on the recent history of the electrical units). Hence the result we have obtained, the error in which is less than one per cent., gives us at once a value for the mechanical equivalent of heat with the same accuracy.
Since we find the equivalent of the watt-second in grammedegrees at 15° C. to be 0.2375, we have at once, taking 107 ergs equal to one watt-second, the mechanical equivalent of heat in ergs per gramme-degree at 15° C. equals 4.211 x 107.
Reducing this to foot-lbs. at Greenwich per lb.-degree C. at 15° C., it becomes 1408, or in foot-Ibs. per lb.-degree F. at 59° F. it is 782.
A series of four experiments made subsequently by some students at the Central Technical College, in which the cooling error was eliminated by making the mean temperature of the water equal to that of the air, gave as their mean 0·2384 calorie per watt-second, or 4:195 10' ergs per grammedegree at about ° C. Reducing this value to foot-lbs. at Greenwich per lb.-degrees C. and F. respectively, we get 1403 and 779 foot-lbs.
IV. Previous Determinations of the Mechanical Equivalent
It is of interest to compare these figures with some of the more recent results obtained for the mechanical equivalent.
Rowland's value for the mechanical equivalent in ergs per gramme-degree at 15° C. is 4:189 x 107, which reduced to foot-lbs. at Greenwich per lb.-degree C. is 1401, and in footlbs. per lb.-degree F. at 59° F. is 778.3. Rowland used the method of direct friction of water, and was the first to discover that the specific heat of water was a minimum at 30° C. and varied one per cent. between 50 and 30° C. (Proc. American Acad. 1879–80).
Dieterici (1889) gives as the result of a determination by the electrical method in which Bunsen's ice-calorimeter was used, the number 4.244 x 10?. Correcting from the “legal” ohm employed by him to the international unit, we get the numbers 4-232 x 10', 1415, and 786 (Annalen der Physik, vol. xxxiii. p. 417).
Miculescu's careful determination by the direct method in
1892 gives 4:186 x 107 on the mercury scale of hard glass, or 4.187 on the hydrogen scale, at about 12° C. The latter number expressed in foot-lbs. at Greenwich per lb. degree C. is 1400, and in foot-lbs. per lb. degree F. is 778. A platinum non-thermal junction was used in these experiments, and was calibrated against a Gonnelot standard mercury thermometer.
Griffiths, using the electrical method, gives as his final result (Proceedings Royal Society, vol. iv. p. 26), 4.198 X 10', the corresponding numbers in the other units being 1404 and 780.
The recent determination of Schuster and Gannon, also by the electrical method, gives 4:180 x 107 on the mercury scale of hard French glass, or 4.192 on the hydrogen scale, at a temperature of 19°1 C. The latter value expressed in foot
: lbs. at Greenwich gives 1402 and 779.
Joule's values obtained by friction of water in 1878 gave the numbers 4:159 x 10", 1390:5, and 772-5 respectively (mercury scale); while his values obtained by the electrical method in 1867, when corrected for the error in the B.A. ohm, give 4.155 x 107, 1389, and 772, the average temperature of the water being 19° C. The following table gives the results obtained by various methods since 1867, the numbers having been recalculated from those given in a table at the end of M. Miculescu's paper (Ann. de Chimie, vol. xxvii. p. 202) :
Ergs per Foot-lbs grammedegree C. degree F.
776 772 770 778
1867. Joule, Electrical.
4.155 x 107 1870. Violle. Heating of a disk between the 4.269 X 107
poles of a magnet. 1875. Puluj. Friction of metals.
4:179 x 107 1878. Joule. Friction of water.
4:159 x 107 1878. Weber. Electrical.
4.145 x 107 1879. Rowland. Friction of water 15°.
4.189 x 107
dp 1888. Perot. By the relation L=r(0, -v1) āt
4:167 x 107 1889. Dieterici. Electrical.
4.232x107 1891. D'Arsonval Heating of a cylinder in a mag- 4:161 x 107
netic field. 1892. Miculescu. Friction of water.
4:186x107 1893. Griffiths. Electrical.
4.198 X 107 Schuster 1894. and Electrical,
4.192 x 107 Gannon.
774 786 773
The results obtained since 1879 by stirring water and by electrical methods may be tabulated thus :