312 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [42 



generally chosen to be the coefficient of the principal inequality in the 

 obliquity of the ecliptic. The accurate determination of this constant is 

 important, not only from its being required for the reduction of star 

 observations, but also from its affording one of the best means we have 

 of determining the mass of the Moon. 



In precession we see the effect of the joint action of the Sun and 

 Moon, but by means of the observed quantity of nutation, we can ascertain 

 what part of this is due to the Moon's action, and having thus obtained 

 the ratio between the actions of the Sun and Moon, the Moon's mass 

 easily follows. 



The most trustworthy determinations of the constant of nutation, 

 previous to this of M. Peters, are those of MM. Von Lindenau, Brinkley, 

 Robinson, and Busch ; and M. Peters begins his memoir with a critical 

 examination of their labours. 



The results of the three latter astronomers present an admirable 

 agreement, while that of Von Lindenau differs from them by about a 

 quarter of a second. Von Lindenau employed about 800 observations of 

 right ascension of Polaris, made at different observatories, and therefore 

 his result is liable to be vitiated by the different personal equations of 

 the several observers. We shall find in the sequel that this remark is 

 important. 



Brinkley deduced his value of the constant from 1618 observations 

 of ten stars, made about the times of two opposite maxima of nutation 

 in declination with the Dublin meridian circle, the proper motions of the 

 stars being determined by the comparison of his own declinations with 

 those in the Fundamenta. As these observations embrace only half a 

 period of the Moon's nodes, the result is liable to be affected by errors in 

 the supposed proper motions. 



Dr Robinson's investigation is contained in the eleventh volume of the 

 Memoirs of the Royal Astronomical Society. He employs the declinations 

 of the polar star, and of fourteen others observed at Greenwich between 

 the years 1812 and 1835 with Troughton's mural circle. There can be no 

 doubt of the high value of this investigation, but M. Peters thinks that, 

 in consequence of the way in which the error of collimation is determined, 

 errors of observation may exist with a yearly period, and that these may 

 slightly affect the resulting value of nutation. Baily's coefficient of aber- 

 ration is employed, the annual parallaxes of the stars are neglected, and 

 the equations of condition are not treated by the method of least squares. 



