Lda 
substituted for + 6”.41 and — 6".00 respectively. The numerical 
coefficients in the next line of formulas then become 
8".62, — 45".4 and — 8”.07. 
Then, discarding the assumption regarding “/j,: /p, and intro- 
ducing J’ and A’, the formulas (2) are easily derived. 
Comparing (1) and (2) we find 
1 i (TELE) mae. 
J' = 0.000435 0.000410 0.000422 zE 0.000055 | 
K' =0,000009 0.000057 0.000033) & 0.000082 | - 
3. The ratios 
C'—B' C'—A' B—A' 
Ce AN re tS 
(3) 
GN 
are. in the case of the moon, so small that we may neglect the 
difference of the numerators, and take B= a + y. 
These ratios appear in the theory of the libration of the moon"), 
C—A 
where they are analogous to H = aie in the theory of precession 
5 B a . 
and nutation. Generally 3 and ots are introduced as unknown 
( 
quantities to be determined from the observations. The constant @ is 
derived with great accuracy from the mean inclination of the moon’s 
equator on the ecliptic. The equation determining this mean inclina- 
tion U, as a function of 3 is given by TissERAND, Vol lly p42; 
and also, more exactly, by Hayy, Selenographische Koördinaten, I”), 
p. 900, with a further addition on p. 909. The values of 9, derived 
by different investigators are: 
Franz, from observations by Scuniter 7, = 1°31'22"1 + 7.3 
STRATTON, 5, Ms a ss Oot: a 
ait cs ANR RAe eed BETE Ae er 1.597 6 22005 
1 adopt 
6, = 1931/40" + 20". 
Introducing this into Hayy’s equation, I find 
B(1 +. 0.0047 f) = 0.0006286 + .0900022. 
For f=0 this gives @ = 0.0006286, 
pnd, tok fa NEN 8 = 0.0006257. 
Now we have from (3) 
J' 4 4 K' = 0.000439 + .000066 
1) See e.g. TISSERAND, Mécanique céleste, Tome II, Chapter XXVIII. 
2) Abh. der K. Sächs. Ges. der Wiss. Band XXVII, Nr. IX, 1902. 
