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temperature required is the excess of temperature of the rod over the air, this was done by merely subtracting the temperature of the air at the given moment from that of the rod at the same moment.
Experiment showed that it was possible to move the iron wire on the rod, and replace it, and obtain the same reading as previously; thus showing that the resistance of the joint did not appreciably alter. As the galvanometer was made somewhat sensitive, its sensitiveness was tested during the experiments by a Daniell cell passing through a large resistance (about 13,000 ohms), the E.M.F. of the Daniell being compared with that of a Clark cell. Zero readings were also taken between each deflexion. The readings of the galvanometer were afterwards standardized, a known difference of temperature being produced between the two junctions, and the deflexions observed. The following table gives an example of a standardization :
See fig. 2, which is plotted for these values.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Deflexion in centimetres of scale.
When the temperature of the rod has settled down to its regular cyclic state, the excess of temperature u of any particular point at any instant t may be expressed by
u = a + b1 sin (2π + B1) + b2 sin (4π +B2)
where T is the time-period of the alternations.
The constants a, b1, B1, &c. are determined by the method of least squares from the observations made.
If a, b, B1, &c. and a', b', B', &c. are the constants for the two points A and B respectively, and a the distance between them, then
b = b'eg and B-B'=qx
(see Ann. Chim. Phys. lxvii., 1863).
Hence g and q can be determined, and
where n=1, 2, 3, &c., according as you use the constants of the 1st, 2nd, 3rd, &c. sine term ;
c-specific heat of the rod;
8=density of the rod.
Hence k and h can be determined from each sine term. In the experiments as carried out only the first, and perhaps the third, sine terms are available for these determinations, as the others are very small, the even terms being especially so. Besides these, there is the "a" term of the above formula (the constant term of the Fourier series), which is large, and represents the mean excess of temperature of the rod. From this term we get
If we use the previously determined value of k, we can get from this equation a secon 1 value of h. This will be referred
to later on.
The rods experimented upon were three brass rods (commercial specimens) of roughly 1, 1, and in. diameter; their 8 lengths were about 3, 5, and 6 ft. respectively. They were cleaned, but not polished. The time-period of the alternations, and the positions of A and B, were chosen so that the cycle of changes gone through should be as nearly as possible the same in the three cases.
The specific heat was determined by heating a portion of each rod to 100° in a Regnault's apparatus in the usual way. The following are the results obtained:
The mean result 0945 was assumed for all the rods. No correction was made for change of specific heat with temperature.
The following readings are given to show how far they agree for different cycles on the same day :
The above readings are deflexions in centimetres : 1 cm. of scale corresponds to a rotation of the magnet through 11', or 1 cm. corresponds to a difference of temperature between the two junctions of 14 degrees Cent.
The following expressions show the series required to fit the temperatures obtained; they are the expressions for Set I. of Rod II., but the constants are of approximately the same magnitude with all the rods :
Temp. A=13.95+12·67 sin (2π +2∙1412) +·42 sin (4π +3·91)
+2·18 sin (6+1·13) +·18 sin (8π+3·33)
+*80 sin (10π+·56)+.
+56)+...+31 sin (14π
Temp. B= 6·16+3′92 sin (27+1.3806) + 10 sin (4π+241)
+38 sin (677 -40)+04 sin (87 +1.14)
+ '07 sin (10′′ — −1·70) + . . . +03 sin (147 −2·68).