260 Mr Mayall, On ■the Diffraction Pattern [Feb. 22, 



by the equations 



U 



If - is not nearly equal to unity, i. e. for points which are not 



far from the centre of the image compared with its radius, the 

 series Vj and V are rapidly convergent and may be calculated 

 with ease from the tabulated values of the Bessel functions. They 

 were in fact calculated by Lommel for values of y equal to ir, 27r, 



...107T, and for values of z from 1 to 12. But if - is nearly equal 



to unity and at the same time y and z are fairly large, the cal- 

 culation would become extremely laborious, for the function J n 

 does not become negligible in comparison with J 1} J 2 ... when z is 

 large until n is also large, so that a great number of terms of the 

 series would have to be taken in order to get even a moderate 

 aj3proximation to their true value. Now in the present case y 

 may be much greater than 107T, even when the screen is very close 



r 

 to the focus, thus if ^ = == the screen would have to be placed at 



a distance of only about a millimetre from the focus in order that 

 the value of y should be so small as 107r. And at the same time, 



experiment shows that it is just when — is nearly equal to unity 



that it becomes most important to determine theoretically what 

 the intensity of illumination ought to be. 



A very interesting series of star-photographs has been obtained 

 by Mr Newall on plates exposed to the light of a star near the 

 focus of the large refractor at the Observatory. It appears from 

 these that when the light has been rendered as nearly as possible 

 monochromatic the image takes the shape of a bright ring sur- 

 rounding a darker space more or less uniformly illuminated. The 

 position of this ring is just about the boundary of the geometrical 

 image, and within it can be seen traces of one or two other rings 

 but much inferior to the first in brightness. A great portion of 

 the light in the image is thus confined to the immediate neigh- 

 bourhood of the geometrical boundary, and as there is no reason to 

 suspect any excessive concentration of light there due to spherical 

 aberration, it is important to know whether the phenomenon is a 

 direct result of the undulatory theory of light or not. 



An examination of the curves traced by Lommel. to represent 

 the variation in intensity of the light at different points of the 



