radiumque 
licienda est 
s tentando 
abbreviari 
ae pretium 
fortasse se 
s casus qui 
ere licebit, 
[per II. vel 
et r simul 
lubet, in 
65,41236: 
RELATIONES AD LOCUM SIMPLICEM IN ORBITA SPECTANTES. 
33 
invenitur per F 
Hinc aequationi N = XetangF — logtang (45° —(— 4 F) satisfieri ii 
= 25° 24 27 66, unde bt per formulam 111. 
logtangF .... 9,3530120 
log tangit .... 9,53 181 79, 
lofftanff^-^ .... 9,82 I 1941 adeoque U’—33 3 L 29"89 atquex>=67°2'5 9"78. 
,01342266 
n O * 
,12650930 
Hinc porro habetur 
,11308664 
O. log cos £ (v -j- 4») . 
0,2137476 
4759575 
0. log cos I (v—^). 
0,0145197 
3324914 
9,9725868 
143466 L 
logr 
0,2008541 
9 J 445 
0,1992279 
0,1992280 
27. 
8i aequatio IV. ita differentiatur, ut u, v, simul ut variabiles tractentur, 
P 1 ' 
>dit 
d u sin 'I; d v -f- sin v d <b . r siit v ^ . 
u 2 cos -.V (v — -i) cos I {v + 'b) p ' P cos ’b 1 
Difterentiando perinde aequationem XI., inter variationes differentiales 
quantitatum m, N emergit relatio 
( / I 1 \ i I (u u— I) sili 'P I 1 
\e\ L4-— idw + ^-r '-r^-d^, sive 
1 \ I uu) U1 1 2iiCOS'l/ 1 7 
V sin V 
d N 
X 
d jV 
T i 
, = —du 
X bu 
b cos 'f 
d'h 
Hinc eliminando du adiumento aequationis praecedentis obtinemus 
d N 
X 
rr 
h h tang <b 
1 I / . I \ /• Sin V 1 , • ^ 
-d-y-4- 1-4- r r ddn sive 
1- <h I \ 1 P I b COS 't ' J 
bbtmg'b j \r ¡b i b \ sin p tang ( |. 
dv = u -°^y-dN—r + • 
X r r \ r p 
= <>}psi <i .v-li + 'M 
X r r \ 1 r / sin <b 1 
28. 
Hifferentiando aequationem X., omnibus r, />, c, u pro variabilibus liabitis, 
o. TH. M.