Pyrometry: A Practical Treatise on the Measurement of High Temperatures

by Charles R. Darling

Fig. 45.—Féry’s Mirror Pyrometer. End View.

The wires pass to terminals b and b´ on the outside of the tube, from which leads are taken to the indicator. In order to discover when the junction is in the focus of the mirror, an eye-piece, O, is fitted in the end of the tube, which enables the junction to be seen, magnified, through a hole in the centre of M. By means of an optical device placed near the junction, the image of the sighted object, produced by M, is reflected in two portions to the eye-piece O. When the junction is exactly in the focus of M, a circular image is seen round the junction; when out of focus, the appearance presented is that of two semi-circles not coinciding laterally. The adjustment consists in moving the mirror until the separate semi-circles produce a continuous circle; a method at once simple and definite. The front end of the pyrometer is shown in [fig. 45], in which it will be seen that the entrance may be partially closed by a diaphragm, or left entirely open, as required. The diaphragm is used to cut off a definite proportion of the radiations, and is used for very high temperatures, at which, with full aperture, the indicator needle would be urged beyond the limits of the scale. On the indicator two separate temperature scales are provided, one referring to full, and the other to partial aperture. The same end might be achieved by inserting a suitable resistance in series with the indicator: but in this case the junction might be unduly heated, and possibly damaged thereby. The proportions of the pyrometer are such that at the highest temperatures measured the heat incident on the junction never raises it above 110° C. Although the intensity of radiations diminishes as the square of the distance, the quantity impinging on the junction is, within limits, independent of the distance: This arises from the property of concave mirrors with respect to the relation between the size of an image and the distance of the object producing it. If r = the radius of the mirror, u the distance of the object, and v the distance of the image, both measured from the centre of the mirror, the relation ¹⁄_u + ¹⁄_v = ²⁄_r holds for a concave mirror, and when two of these are known the third may be calculated. Further, if d be the linear dimension of an object, and d₁ that of its image, the relation ^d⁄_d1 = ^u⁄_v also holds, and from these two expressions all the points arising in connection with the Féry pyrometer may be determined, as will best be made clear by examples.

Example I.—To find the position of the image of an object formed by a mirror of 6 inches radius, with object at distance (a) 10 feet, (b) 20 feet.

Reducing to inches, and applying in the formula

¹⁄_u + ¹⁄_v = ²⁄_r,  ¹⁄₁₂₀ + ¹⁄_v = ¹⁄₃

and

¹⁄₂₄₀ + ¹⁄_v = ¹⁄₃

from which the values of v are 3-¹⁄₁₃ inches and 3-¹⁄₂₆ inches respectively, a difference of only ¹⁄₂₆ of an inch.

If u were 6 inches, v would also be 6 inches; if u were infinity, v would be 3 inches. The movement of the image, when an object is brought towards it from a great distance, would in the mirror under notice be from 3 inches away to 6 inches away, and at distances of 10 feet and upwards would only differ in position by small fractions of an inch.