314 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [42 



While M. Peters was employed in these investigations, M. Lundahl 

 was likewise engaged in discussing the observations of declination of the 

 same star, made also at Dorpat within the same space of time. The value 

 of the constant of nutation which he deduces agrees admirably with those 

 found by MM. Peters and Busch. 



Finally, M. Peters takes the mean of the three results, giving the 

 proper relative weights to the several determinations, and he finds the 

 most probable value of the constant to be 9"'2231, with the probable error 

 0"'0154. This value differs very little from Brinkley's, which has generally 

 been employed by English astronomers, but M. Peters' determination un- 

 doubtedly possesses much greater weight. 



M. Peters next enters upon a theoretical investigation of nutation, far 

 more complete than any that had before appeared. Starting from the 

 equations of Poisson's theory, he develops them, taking into account the 

 ellipticities of the orbits of the Earth and Moon, and also the principal 

 lunar inequalities. He thus obtains a great number of small terms which 

 had previously been neglected. Most of these may be safely omitted ; but 

 there are two terms which should be taken into account in delicate 

 investigations, as they have an annual period, and are therefore mixed up 

 with the eifect of aberration and parallax. M. Peters takes care to apply 

 the requisite corrections to the coefficients of aberration, and to the parallax 

 of Polaris given by his investigations. Although most of the new terms 

 found by M. Peters are very small, yet these researches are not the less 

 valuable, since it is always satisfactory to know what we really neglect. 



M. Peters takes into account the effect of a possible difference between 

 the ellipticities of the two hemispheres, which he determines by means of 

 the pendulum experiments collected by Mr Baily in his "Report on the 

 Experiments made by Foster," in the seventh volume of the Memoirs of 

 the Royal Astronomical Society. It fortunately happens that this effect is 

 insensible, as this difference of the two hemispheres is extremely doubtful. 



The last part of M. Peters' paper contains researches on the obliquity 

 of the ecliptic and the precession of the equinoxes, so that he treats of 

 all the elements which relate to the apparent changes in the places of 

 the stars, due to the motion of the pole of the Earth. He deduces 

 the secular diminution of the obliquity of the ecliptic by comparing the 

 obliquity for 1757, given by Bradley 's observations, with that for 1825 

 given by the observations at Dorpat, both being reduced to the mean by 



