AN APPARENT NEW POLARITY IN LIGHT. 
233 
The first remark which presents itself, in looking at this table, is, that the numbers 
D ( s ) and E (s) increase and diminish, and then change signs and increase and 
diminish, with increasing values of s; that the maximum of one always coincides 
nearly with the vanishing point of the other ; and that the maximum values are nearly 
equal in both series (regard being had to the general diminution of the numbers as 
s increases) ; in fact, that these numbers may be represented as the cosine and sine 
of the same arc, the radius being slowly variable. To prove this, let us make D (s) 
= G (s) . cos <p (s), E (s) = G (s) sin <z> (s), and investigate the values of G (6') and 
p (s) for every value of s in the Table. They are easily found by the formulae 
GW = \/{l r W 12 + EWl ! }, tan . <p (s) = 
In this manner the following Table is formed ; in which, for more distinct apprecia- 
tion of the progress of <p (s), the differences of p ( s ) are set down. 
o-o 
o-i 
0-2 
0-3 
0-4 
0-5 
0 6 
0-7 
0-8 
0- 9 
1 - 0 
M 
1-2 
1-3 
1-4 
1-5 
1-6 
1-7 
1-8 
1- 9 
2 - 0 
2-1 
2-2 
2-3 
2-4 
2-5 
2-6 
2-7 
2-8 
G (*). 
(*)• 
1-000 
1-000 
1-000 
0-999 
•997 
•993 
•988 
•979 
•963 
•943 
•909 
•869 
•822 
•762 
•696 
•622 
•532 
•490 
•441 
•413 
•424 
•419 
•428 
•424 
•404 
•372 
•335 
•309 
0-300 
360° + 
720 ° + 
0 
11 
23 
0 
28 
5 
34 52 
46 52 
59 21 
72 15 
85 51 
100 8 
115 15 
131 15 
148 26 
166 53 
187 2 
209 7 
233 31 
26 1 12 
292 31 
327 45 
6 3 
45 15 
4 
47 
84 
121 
159 30 
198 23 
239 57 
285 59 
336 53 
30 52 
Difference. 
11 28 
11 37 
11 47 
12 0 
12 29 
12 54 
13 36 
14 17 
15 
16 
17 11 
18 27 
20 
22 
24 24 
27 41 
31 
35 
19 
14 
38 18 
39 12 
38 49 
37 43 
37 43 
38 53 
41 34 
46 2 
50 54 
53 59 
53 22 
s. 
G («). 
<t> (*)• 
2-9 
0-307 
720°+ 8i 14 
3-0 
•316 
135 43 
3-1 
•311 
187 10 
3-2 
•288 
241 11 
3-3 
•263 
300 7 
3-4 
•249 
1080°+ 4 22 
3-5 
•252 
69 30 
3-6 
•261 
132 30 
3-7 
•256 
194 31 
3-8 
•235 
259 52 
3-9 
•218 
331 16 
I 4-0 
•217 
1440° f 46 16 
4-1 
•226 
119 15 
4-2 
•225 
190 39 
4-3 
•209 
265 8 
4-4 
•195 
345 59 
4*5 
•198 
1800°+ 69 14 
4-6 
•204 
149 37 
4-7 
*195 
230 0 
4-8 
•180 
316 15 
4-9 
•180 
2160°+ 47 13 
5-0 
•186 
135 38 
5-3 
•180 
223 17 
5-2 
•169 
316 32 
5-3 
•169 
2520°+ 54 25 
5°4 
•173 
149 33 
5-5 
•1 66 
244 55 
00 
•000 
Difference. 
51 29 
51 27 
54 1 
58 56 
64 15 
65 
63 
62 
65 21 
71 24 
75 0 
72 59 
71 24 
74 29 
80 51 
83 15 
80 23 
80 23 
86 15 
90 58 
88 25 
87 39 
93 15 
97 53 
95 8 
95 22 
For negative values of s, the numerical values of G ( s ) and <j> (s) are the same as for 
equal positive values of s ; the sign of G ($) is always positive, but the sign of <j> (s) is 
the same as that of s. 
9 
H 
IVIDCCCXL. 
