(31 ) 



Equations of the contacts 



I LR-^ Lr^ 0.903 Zi«(_o — 0.405 Lö^-q = + 3".78 

 ri LR — Lr — 0.9668 Zi«( -^ — 0.2007 A(f(_o + 



+ 0.0004 Z-'«(_c — O.OO3I) LaL(f -f 0.0091 AM(_c = — 6".52 ^) 

 /// LR — Lr^ 0.3085 A«(_o - 0.9489 Arf(_o + 



+ 0.0104 ^''«(-G + 0.0068 LaLó + 0.0012 Z.M(_o = + 4".02 

 /F LR-^ Lr — 0.889 A«(-q + 0.435 LÖ(-q = — 11".18. 



A mere glance at the equations derived from the distances of the 

 chords shows the impossibility to derive from them all the unknown 

 quantities. On account of tlie proportionality of the coefficients 

 we may use one single equation instead of the first 25 equations 

 after the 1^* contact; the same for the 35 others. In order to diminish 

 the weight of the observations immediately after the first and before 

 the last contact — when the chord is less sharply defined and varies 

 rapidly — I have formed the two normal equations not according 

 to the method of least squares but simply by addition. 



We obtain the following equations : 



68.1(Ai2+Ar)-f 56.2Zia-25.2Ad= + 489".46 - 0.2>o{LR-Lr) - 12. 9A^ 

 — 81.6(A72+Ar)-f65.1A«-31.6Ad=+397".87 + 0.24(A7?-A/-)-fl2.8A.T 

 whence : 



LR + A?- = + 1".05 — 0.015 Ad — 0.003 [LR — Lr) — 0.16 A.t. 

 A«= 4- 7".428 + 0.465 Ad — 0.001 (LR — Lr) - 0.02 Arr. 



Neglecting the last terms, we find for the result from the equations 

 derived from the length of the chords: 



Ai? + Ar = 4- 1".05 — 0.015 Ad(_o 

 A«(_Q znz -{- 7".428 + 0.465 Ad(_o. 

 From the equations of the 2^^ and 3"^ contact we derive: 

 A«(_0 = + 7".793 + 0.464 Ad(_0. 

 A«(_o = + 7".13 + 0.667 (LR — Lr) 

 Ad(_o = — r'.43 + 1.437 [LR — Li-). 

 And lastly the equations of the 1^^ and 4^^ contact yield : 

 A«(_o = -f 8".35 + 0".468 Ad(-o 

 [LR -f Ar = — 3".781 

 The latter result for LR -\- Ar, w^hich differs entirely from that 

 found above is little reliable. We can entirely account for it bj' 

 assuming that the first contact has been observed too late and the 

 last contact too earlv. It can hardlv be doubted that the 1*' contact 



1) It is not allowed (as it is generally done) to neglect the quadratic terms 

 in the equations of the 2°'^ and 3"^^ contact, because the corrections A^and ^}, as 

 compared with the distance between the centre of the sun and that of the moon, 

 (in this case 40') are too large. 



4* 



