From Example I it is evident that at any distance exceeding 20 feet the position of the image will only be a minute and negligible fraction over 3 inches; hence v may be taken as 3.
Applying values in the formula d⁄d1 = u⁄v; and taking d1 as equal to the diameter of the junction, = 0·1 inch,
12⁄0·1 = u⁄3, and u = 360 inches, or 30 feet.
Beyond this distance the image would be less than the junction. The conclusions to be drawn from the foregoing examples are: (1) that the amount of energy received by the junction does not vary, provided the image overlaps it; and (2) that the limiting distance at which a correct reading can be secured is that at which the size of the image is equal to that of the junction. Thus, taking distances of 10 and 20 feet, as in Example II; at the former distance the energy striking the mirror is four times as great as with the latter; but, on the other hand, the area of the image at 10 feet distance is four times as great as that obtained at 20 feet. Hence, at the greater distance, the proportion of the image impinging on the junction is four times as great, and the fact that only ¼ the amount of energy strikes the mirror is thus counterbalanced. All the reflected rays which fail to strike the junction are ineffective, and pass out through the entrance of the tube.
Fig. 46.—Féry’s Spiral.
The two-scale form of instrument described above is extremely useful for general purposes, but when all the temperatures to be controlled fall within the limit of one of the scales, it is simpler and cheaper to dispense with the diaphragm, and to use an indicator furnished with one scale only. The single-scale mirror pyrometer is for this reason more generally employed for industrial purposes; and the Cambridge and Paul Instrument Company now make a pivoted indicator for use with full aperture, which is less liable to damage than one which possesses a suspended coil.
