51G 
PROFESSOR A. SCHUSTER ON THE DIURNAL 
For moderate values of 8 we may use the form 
where 
K 
B 
71 
iS 
2n + 1.2n + 3 
-^n — \ "f" —1 
1 _^_ 
2.4.2% + 3.2% + 5 ^ 2. 4.6.8, 2% + 3.2?i + 5.2% + 7.2% + 9 
g __ _ 
2.2% + 3 2.4.6.2% + 3.2% + 5.2% + 7 “ ’ ' ' ' 
The following Table gives the values of A^, Bj, Ag, Bg, Ag, Bg, for various values of 8. 
It may possibly be of service in other investigations. 
Table XXIX. 
A,. 
B,. 
^ 3 - 
B3. 
A5. 
B5. 
1 
+ 0-996429 
+ 0-099934 
+ 0-998738 
+ 0-055539 
+ 0-999359 
+ -038456 
2 
+ 0-985726 
+ 0-199471 
+ 0-994952 
+ 0-110982 
3 
+ 0-967918 
+ 0-298216 
+ 0-988647 
+ 0-116230 
4 
-|- 0*943050 
+ 0-395773 
+ 0-979832 
+ 0-221187 
1 
5 
+ 0-911184 
+ 0-491751 
+ 0-968518 
+ 0-275757 
6 
0*872401 
+ 0-585759 
+ 0-954720 
+ 0-329843 
7 
+ 0-826800 
+ 0-677412 
+ 0-938455 
+ 0-.383350 
8 
+ 0-774498 
+ 0-766327 
+ 0-919714 
+ 0-436182 
9 
+ 0-715628 
+ 0-852126 
+ 0-898610 
+ 0-488246 
10 
+ 0-650341 
+ 0-934439 
+ 0-875083 
-h 0-539448 
+ 8-936309 
+ -3784 
20 
- 0-310366 
+ 1-489206 
+ 0-516311 
+ 0-984135 
30 
- 1-628644 
+ 1-351846 
- 0-029614 
+ 1-248628 
40 
- 2-912855 
+ 0-337304 
- 0-688914 
+ 1-265555 
50 
- 3-716054 
- 1-563371 
- 1-366602 
+ 0-993199 
100 
+ 12-514840 
- 10-691120 
- 1-308236 
- 3-811231 
- 1-9434 
- -6646 
If we write 
the above fraction becomes 
A,j + i B„ — 
+ 1 ;(<l> — <J> + j-iri 
. —«+i «-i ^ / 
2% + 1.2% + 3 S„_i 
If we prefix the minus sign this gives the ratio {k') of the vertical forces. To get 
the ratio (k) of the horizontal forces we must multiply by n/{7i +1). 
For large values of 8 we may make use of the second form of y,,.. Thus 
r cosh ^ sinh H 
xi = 3 |-^ 
Xs = 3.5.7 + j|)cosh ^ - (^ + sinh j|, 
