-1 10 Lord Rayleigh's Investigations in Optics. 



temperature t° C. and at atmospheric pressure is given by 



•00029 

 ^-1 = 



1 + -0037* 

 If we take the freezing-point as standard temperature, 



o>=-l\Uxl(T 6 (11) 



Thus, supposing that the irregularity of temperature t extends 

 through a length Z, and produces a retardation of a quarter of 

 a wave-length, 



\\=VlltxlO- 



■5 



or, if we take \=5'3 X 10" 



Z*=12, (12) 



the unit of length being the centimetre. 



We may infer that, in the case of a telescope-tube 12 centi- 

 metres long, a stratum of air heated one degree Cent., 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 of the tube to the other, the result would be a lateral dis- 

 placement of the image without loss of definition; but in 

 general both effects would be obseiwable. In longer tubes a 

 similar disturbance would be caused by a proportionally less 

 difference of temperature. 



In the ordinary investigations of the aberration of optical 

 instruments attention is usually given to a quantity called the 

 longitudinal aberration, which is the distance between the geo- 

 metrical focus and the point at which the extreme ray meets 

 the axis. In order to adapt these calculations to our purpose, 

 it is necessary to establish the connexion between longitudinal 

 aberration and the deviation of the actual surface of the con- 

 verging waves from a truly spherical surface having its centre 

 at the geometrical focus. 



If the axis of symmetry be taken as that of z, and the tan- 

 gent plane to the wave-surface as plane of ay, we have as the 

 equation of the ideal wave-surface, 



f being the distance of the focus from the origin ; or if we 

 limit our attention to the plane y = 0, 



e=/-.v7*=7»i£ + i£ . . . (13) 



The actual wave-surface, having at the origin the same cur- 

 vature, is represented by 



* = ij+*p, (14) 



where "k is a constant depending upon the amount of aber- 



