Measurement of Resistance by the Wheatstone Bridge.—The principle of this method is shown in [fig. 31], where a and b are two fixed resistances of known value; d is an adjustable resistance; x the resistance to be measured; B a battery; and G a sensitive galvanometer. If, in this circuit, d be adjusted until no deflection is shown on the galvanometer, then a⁄b = x⁄d; or x = (a × d)⁄b. Hence, if a = b, then x will be equal to d.
It is not difficult to construct a portable apparatus, suitable for workshop use, by means of which the value of x may be determined to 0·01 ohm; and in the laboratory, with a very delicate galvanometer, 0·001 ohm may readily be detected. The Wheatstone bridge method is the best for the accurate measurement of resistance; but in resistance pyrometers it is sometimes advisable to sacrifice extreme accuracy in order to gain advantages in other directions, as will be shown subsequently.
Relation between the Resistance of Platinum and Temperature.—As platinum is the only feasible metal to use in the construction of resistance pyrometers, it is essential that the effect of temperature on the resistance of this metal should be known. Difficulties were experienced, in the early days of resistance pyrometers, from the fact that different samples of platinum wire, of varying degrees of purity, gave widely differing results in this connection; and no certainty was attained until 1886, when Professor Callendar thoroughly investigated the subject, and evolved a formula from which the temperature of a given kind of platinum could be deduced with great accuracy from the resistance. In order to understand this formula and its application, it will be necessary to consider the underlying principles upon which it is founded.
If the resistance of a platinum wire be measured at a number of standard gas-scale temperatures, and the results depicted graphically by plotting resistances against corresponding temperatures, the curve obtained is part of a parabola, exhibiting a decrease in the rate at which the resistance increases at the higher temperatures. A second platinum wire, of different origin and purity, and of the same initial resistance as the foregoing, would furnish a curve which, although parabolic, would not overlap that obtained with the first wire. The advance made by Callendar was to deduce a formula from which the temperature of any kind of platinum wire could be deduced from its resistance, after three measurements at known gas-scale temperatures had been determined. The calibration of a resistance pyrometer was thereby reduced to three exact observations, instead of a large number distributed over the scale; and, moreover, the formula in question was found to give results of great accuracy over a wide range of temperature for any kind of platinum wire.
Before dealing with Callendar’s formula, the term “degrees on the platinum scale” will be explained. Such degrees are obtained by assuming that the increase of resistance of platinum is uniform at all temperatures; that is, that the temperature-resistance curve is a straight line, and not a parabola. For example, a piece of platinum wire of 2·6 ohms resistance at 0° C. will show an increase to 3·6 ohms at 100° C.—an addition of 1 ohm for 100°. We now assume that a further augmentation of 1 ohm, bringing the total to 4·6 ohms, will represent an increase of 100°, or a temperature of 200°. Similarly, a total resistance of 5·6 ohms would indicate 300°, and 12·6 ohms 1000°. The temperature scale obtained by this process of extrapolation is called the “platinum scale,” and differs considerably from the true or gas scale, the difference becoming greater as the temperature rises. This is indicated in [fig. 32], in which A represents the true parabolic relation between resistance and temperature, and B the assumed straight-line relation. Reading from curve A, the temperature corresponding to 8 ohms resistance is 600° C.; but from B the same resistance is seen to represent only 545° C., which is the “temperature on the platinum scale” to which this resistance refers. An inspection of [fig. 32] shows that at all temperatures, except between 0° and 100°, the platinum-scale readings for given resistances are less than those indicated on the gas scale.
Callendar’s formula is expressed in terms of the difference between the gas-scale and platinum-scale readings, and takes the form
t - p = δ { (t⁄100)2 - (t⁄100) }
where t = temperature on the gas scale,
p = temperature on the platinum scale.
δ = a constant, depending upon the purity of the wire.
Fig. 32.—Connection between Resistance of Platinum and Temperature:
A, on Gas Scale; B, on Platinum Scale.