As an application of this result, let us investigate what amount of temperature disturbance in the tube of a telescope may be expected to impair definition. According to J. B. Biot and F. J. D. Arago, the index μ for air at t° C. and at atmospheric pressure is given by
| μ − 1 = | .00029 | . |
| 1 + .0037 t |
If we take 0° C. as standard temperature,
δμ = -1.1 × 10-6.
Thus, on the supposition that the irregularity of temperature t extends through a length l, and produces an acceleration of a quarter of a wave-length,
¼λ = 1.1 lt × 10-6;
or, if we take λ = 5.3 × 10-5,
lt = 12,
the unit of length being the centimetre.
We may infer that, in the case of a telescope tube 12 cm. long, a stratum of air heated 1° C. lying along the top of the tube, and occupying a moderate fraction of the whole volume, would produce a not insensible effect. If the change of temperature progressed uniformly from one side to the other, the result would be a lateral displacement of the image without loss of definition; but in general both effects would be observable. In longer tubes a similar disturbance would be caused by a proportionally less difference of temperature. S. P. Langley has proposed to obviate such ill-effects by stirring the air included within a telescope tube. It has long been known that the definition of a carbon bisulphide prism may be much improved by a vigorous shaking.