146 



there that a constant error in the latitude must lead to a term in 

 R.A. of just the form that he finds, as with fairly close approximation 



(let = — 0.40 cos hli^ 



while the new term is pretty nearly 



— 0".66 cos X. 



The special form of the deviations of the limb, which would 

 account for the result now found, would be such that the centre of 

 figure would lie 1".65 more to the north than according to our 

 ephemerides. 



If we assume, disregarding the inclination of the lunar orbit and 

 the influence of tlie librations, that the moon's equator always 

 coincides with the ecliptic, then in the transit-observations parts of 

 the limb are used, which varj with the longitude of the moon over 

 arcs lying between points 23°5 on each side of the moon's equator. 

 These arcs would then belong to a centre with a latitude,!". 65 

 larger than according to the ephemerides, therefore, as these include 

 Hansen's constant term — 1".0 a latitude 0".65 larger than that 

 according to pure theory. As further, in the course of one year, each 

 value of the moon's longitude successively co-incides with each 

 value of the elongation B and therefore the same number of times 

 with observations of Limb I and Limb [I, tiie two symmetrically 

 lying parts of the limb must each time co-operate. 



Last 'year, I deduced from an investigation of the declinations of 

 the moon observed at Greenwich during the period 1883 — 1909, 

 that these, after they had been freed from systematic errors as far 

 as possible, and reduced to the fundamental system of Newcomb, 

 point to a centre 0".8 to the south of the centre of gravity, that 

 is nearly to Hansen's centre, while the uncorrected declinations 

 would place the centre of figure even more to the south. I found 

 further that the observations of the declination of Mösting A lead to 

 precisely the same results as those of the limbs, or that, when re- 

 duced to the centre of the moon with the existing data, they placed 

 it also 0".8 to the south. De Vos's results now show that the 

 southerly centre, which satisfies arcs of 47° lying symmetrically with 

 respect to the north and south pole, certainly does not satisfy the 

 easterly and westerly arcs which are used in the observations of 

 the rightascensions. 



' A centre of figure coinciding with the centre of gravity certainly 

 brings about a better agreement. This would correspond with a 

 correction-term — 0".40 cos /, and the question therefore arises 

 whether this smaller co-efficient sufficiently satisfies the observations. 



