A useful form of this relation is found by solving for functions of 
@. Thus: 
Ry %o 
—— (ee ee Inicot—= 
cot $ =e 1) Lae eae [14] 
and applying trigonometric identities gives 
cot S =P tan$ R b 
CONG aren naa cosh] Gees fescg,) + In cot | [15] 
2 a 2 
g g 
cot — tan 9 
GO 3 SSeS 
[16] 
sinh| 24 (4 + fesed,) + Incot So 
0 2 
We may now easily obtain formulas for T, s, and x in terms of y and 
the end conditions Ty) and ¢) at the origin O. From Equations [7] and [15] 
T,(1 + feosh| 24(a + feseg) + In cot $2) “aan 
Pl ene SON Pe ae ee Oe tenons es Sa ae 
I + f esc'g 
—— 
From Equations [9] and [16] 
T Nee + fesed,) + In cot So = | 
=) 0. 
R 
[18] 
1 + fescdy 
and from Equations [11] and [15] 
Ry sal = 
ee it, cosh { (1 + fesego) + Incot 9 esc by [19] 
IR, 1+ fesc@, 
We may also express T, x, and y in terms of s and the end condi- 
tions, by solving Equation [9] for functions of ¢. These relations are: 
Rs 1} 
T 2 aS 
ea sft os fl oe a + fesego) T, + cot ¢y| 
[20] 
1 + f csc dy 
AL 
45 la + Peseey qr cota] — ese by 
To i (20) 
R a CSCIOn 
