[X FOCAL PLANE OP TELESCOPE. 



329 



y=Jà 2 (x) + Jî 2 (x) in the simplest manner. It shows that (he curve is to 

 the first approximation a. rectangular hyperbola. 



xy=-j^> (D) 



if x be not very small. To the second approximation, we shall have 



to introduce the term — -5—, which gives the curve an undulating 



appearance ; the effect of the third and fourth terms is still smaller, 

 so that for practical purposes, it is sufficient to assume the mean 

 curve to be a hyperbola, as it is almost useless to push the cal- 

 culation to the fourth decimal place. To show the difference in y„ 

 calculated from (13) and from (D), I give the following table : 



calculated from (B) 



3.832 

 7.016 

 x s = 10.173 

 a: 4 = 13.324 



//!=(). 1622 

 # 3 = 0.0901 

 ?/, = 0.0624 

 t/ 4 = 0.0477 



calculated from (D) 



^=0.1661 



#, = 0.0907 

 y s = 0.0626 

 2/ 4 =0.0478 



Thus the coincidence becomes closer with increasing values of x. 



§ 4. Intensity at the centre of a circular disc. 



Equation (II„) § 1. shows that the intensity of light at the centre 

 of a luminous disc as observed through a telescope is given by 



1= \-JJ{r)-j;\r).= l-y 



If the luminous disc be divided by a series of concentric circles 

 of radius x n into a number of zones whose breadth is equal to the 

 difference between the successive roots of J l (x)=0, we find that the 

 illumination at the centre due to each of these zones is given by the 

 height of the corresponding step in the curve j/=J^ x ) + Ji\x). The di- 

 minution in the height of these steps with increasing x shows that the 



