12] EFFECT OF THE LONG INEQUALITY OF JUPITER AND SATURN. 225 



wrong, viz.: 0,000264 cos (x + 48, 27), which is taken from t. iv. p. 341, 

 line 8 from bottom, and represents the term oft. in. p. 138, last line but one, 



- (1 + /LI V ) . 0,0003042733 cos (5n*t - 2ri v t + 5e v - 2e iv - 13,4966), 



modified by the change in the mass of Saturn introduced in t. iv. p. 337 ; 

 the correctly modified coefficient is 0,000290, and it is curious to notice 

 that the same mistake occurs again in t. iv. p. 341, line 16, where the 

 coefficient of cos ((f -2q* -2,88 + t . 58",0) should be -0,000290 in place 

 of 0,000264, the two terms from which this is derived (t. in. p. 128, 

 lines 4, 5) uniting to give a coefficient 0,00030503 which modifies into 

 0,000290; finally the term above upon which all depends 



- ( 1 + /t v ) . 0,0003042733 cos (5n v t - 2ri v t + 5e v - 2e iv - 13,4966) 



is got by taking with wrong sign the term (t. in. p. 138, line 7 from bottom) 



- a^H cos (5n"'t - 2ri*t + 5e v - 2e iv - sr iv + A). 

 To correct these errors, read in t. in. p. 138, last line but one, 



- (1 + //') 0,0002465 cos (5n r t - 2n"t + 5e v - 2e iv + 32,4l), 

 using centesimal degrees ; 



in t. iv. p. 341, line 16, -0,000290 for -0,000264; 



25, -0,0002343 cos (5 ? v -2 ( / v + 32,4l); 

 t. V. p. 462, line 6, -0,0002343 cos (x + 94, 18) ; 

 and for the coefficients of the inequalities of the satellites 



I II III IV 



-0",618 -8",788 -12",872 -30",404 



each being multiplied into sin (x+ 48,09) or sin (5q v -2q" 13, 68) ; or if 

 we employ Laplace's values of the ratios which deduce I, II, III from IV 

 (values which are only approximate), we get 



I II III IV 



-0",682 -8",810 -12",874 -30",404 

 in place of the values of the Mecanique Celeste : 



-0",994 -12",847 -18",774 -44",334. 



The degrees and seconds are centesimal. [Oct. 1881. 



If we take the formula of M. Souillart* 



SA \ 



-- + Jbd-ti , 



-j --- -- - , 



at n \ A j 



and use Le Verrier's formulae (Mem. Ob. Paris, t. xn. pp. 14, 23), we have 



* Theorie . . .des Satellites de Jupiter, Mem. B. A. S. XLV. p. 89. 

 A. II. 29 



