1869.] Astronomy, 421 



Let a cone, Laving its vertex at P, circumscribe the interior 

 ellipsoid. All the mass of the shell outside this cone may be 

 neglected when the shell is suj^posed indefinitely thin. Of the part 

 within, it will be obvious, on consideration, that the two portions 

 separated by the circle in which the cone and the inner ellipsoid 

 touch each other, attract P equally. The portion nearer to P may 

 bo di^dded into two, by a plane touching the inner ellipsoid, when 

 the normal through P meets it, and of these parts only the one next 

 to P need be considered, the attraction of the other vanishing in 

 respect to that of this part. Thus, finally, we get the attraction 

 on P equal to twice that of a cone having P as vertex, and in- 

 scribed within the shell, so that its base touches the inner ellijjsoid. 

 In the limit, the vertical angle of this cone becomes equal to two 

 right angles, and the attraction of the cone becomes that of an 

 mfinite plane, whose thickness is equal to the normal thickness of 

 the shell at P. 



The same eminent mathematician gives a remarkably simple 

 explanation of Gauss's solution of the problem of determining a 

 planet's orbit, from three observations. We must refer those of 

 our readers who are interested in this problem (selected by the 

 Cambridge University as the subject of the Adams' Prize Essay), 

 to the paper itself, as it would be wholly impossible either to 

 abbreviate Professor Cayley's treatment of the question or to give 

 the whole of it in these pages. 



Mr. Dunkin gives another of those interesting papers on per- 

 sonality in observation, which have recently been founded by the 

 Greenwich observers on the immense amount of valuable material 

 avaUabJe to them for the purpose. The object of the present 

 paper is a personahty in observing transits of the moon's limb. It 

 has been described by the Astronomer Eoyal as, strictly speaking, 

 a difterence between the personal equation for the moon and that 

 for the stars ; the duration of the impression on the nerves of the 

 eye not being the same when the moon is observed as when a star 

 is. The efi'ect of the personality is visible more in the tabidar 

 errors in the first half of the lunation than in the second, but the 

 differences of each observer's mean from the mean of aU are too 

 small to enable one to trace the personahty to any particular 

 source. An important result of the investigation is the evidence 

 it afibrds of the necessity of intermixing observers, when absolute 

 places have to be determined. 



Mr. Kincaid describes a driving-clock founded on hydraulic 

 principles. The contrivance would need trial, we should imagine, 

 before its actual quahties can be pronounced upon. Theoretically 

 it is exceUent. 



