23 2 
MR. AIRY ON THE THEORETICAL EXPLANATION OF 
This expression is exactly similar to that obtained for the case when the luminous 
point is too distant for distinct vision, in the following particulars, which we shall 
find to be very important. First, the general form is the same. Secondly, the argument 
of the functions Cand S has the quantity b with the positive sign in both expressions; 
and therefore, in both expressions, the argument increases as b increases. We shall 
also find the following remark to be not without importance ; that, in the arguments 
of the functions in the two expressions, the quantity g enters with different signs. 
Our expressions now depend entirely upon the three functions, 
1 + 2 (c GO) 2 + 2 (S (*))*, 
1 - 2 (C (,))* - 2 (S(*))*, 
2 C 0) - 2 SO), 
which we shall call AO), DO), and E(s). Adopting Fresnel’s values of C’O) and SO), 
I have computed the following values of AO), DO), and E(.s). 
s. 
A(<). 
D («). 
E (•). 
s. 
A(s). 
D («)• 
EM- 
0-0 
+ 1-000 
+ 
1-000 
0-000 
2-9 
+ 1-969 
+ 0-031 
+ 0-306 
0-1 
+ 1-020 
+ 
0-980 
+ 0-199 
3-0 
+ 2-227 
-0-227 
+ 0-220 
0-2 
+ 1-080 
+ 
0-920 
+ 0-391 
3-1 
+ 2-308 
— 0-308 
— 0-039 
0-3 
+ 1-180 
+ 
0-820 
+ 0-571 
3-2 
+ 2-139 
-0-139 
-0-253 
0-4 
+ 1-318 
+ 
0-682 
+ 0-728 
3-3 
+ 1-869 
+ 0-131 
— 0-226 
0-5 
+ 1-493 
+ 
0-507 
+ 0-856 
3-4 
+ 1-754 
+ 0-246 
+ 0-019 
0-6 
+ 1-700 
+ 
0-300 
+ 0-942 
3-5 
+ 1-912 
+ 0-088 
+ 0-236 
0-7 
+ 1-929 
+ 
0-071 
+ 0-976 
3-6 
+ 2-176 
— 0-176 
+ 0-193 
0-8 
+ 2-169 
— 
0-169 
+ 0-949 
3-7 
+ 2-249 
-0-249 
— 0-064 
0-9 
+ 2-401 
— 
0-401 
+ 0-852 
3-8 
+ 2-042 
— 0-042 
-0-234 
1-0 
+ 2-601 
— 
0-601 
+ 0-685 
3-9 
+ 1-809 
+ 0-192 
— 0-105 
1*1 
+ 2-743 
— 
0-743 
+ 0-457 
4-0 
+ 1-850 
+ 0-150 
+ 0-157 
1-2 
+ 2-802 
— 
0-802 
+ 0-186 
4-1 
+ 2-111 
-0-111 
+ 0-197 
1*3 
+ 2-758 
— 
0-758 
— 0-093 
4-2 
+ 2-221 
— 0-221 
-0-042 
1*4 
+ 2-609 
— 
0-609 
-0-339 
4-3 
+ 2-018 
-0-018 
-0-208 
1-5 
+ 2-371 
— 
0-371 
— 0-502 
4-4 
+ 1-812 
+ 0-189 
-0-047 
1-6 
+ 2-084 
— 
0-084 
-0-545 
4-5 
+ 1-930 
+ 0-070 
+ 0-184 
1-7 
+ 1-814 
+ 
0-186 
— 0-449 
4-6 
+ 2-176 
-0-176 
+ 0-103 
1-8 
+ 1-630 
+ 
0-370 
— 0-233 
4-7 
+ 2-126 
-0-126 
— 0-150 
1-9 
+ 1-591 
+ 
0-409 
+ 0-043 
4-8 
+ 1-870 
+ 0-130 
-0-125 
2-0 
+ 1-713 
+ 
0-287 
+ 0-291 
4-9 
+ 1-879 
+ 0-122 
+ 0 131 
2-1 
+ 1-957 
+ 
0-043 
+ 0-416 
5-0 
+ 2-133 
-0-133 
+ 0-130 
2*2 
+ 2-225 
— 
0-225 
+ 0-363 
5-1 
+ 2-132 
— 0-132 
-0-124 
2-3 
+ 2-398 
— 
0-398 
+ 0-149 
5-2 
+ 1-879 
+ 0-121 
— 0-115 
2-4 
+ 2-385 
— 
0-385 
— 0-128 
5-3 
+ 1-903 
+ 0-097 
+ 0-135 
2-5 
+ 2-186 
— 
0-186 
— 0-322 
1 5-4 
+ 2-149 
— 0-149 
+ 0-087 
2*6 
+ 1-908 
+ 
0-092 
-0-321 
5-5 
+ 2-070 
-0-070 
-0-150 
2-7 
+ 1-719 
+ 
0-281 
— 0-120 
2-8 
+ 1-744 
+ 
0-256 
+ 0-153 
00 
+ 2-000 
0-000 
0-000 
For negative values of s, the numerical values of A(s), D(s), and 
E(s) are the same as for the equal positive values of s : the signs of 
A (s) and D(s) are the same for the positive and negative values of s, 
hut the signs of E (s) are different. 
