TBANSACTIONS OF SECTION A. G17 



additional unknown quantities to be determined by the simultaneous linear equa- 

 tions. The solution has to proceed by continued approximation, and is exceedingly 

 laborious. In an admirable paper in the current number of the American Journal, 

 Prof. E. W. Brown has shown how the new part of the motion of the perigee and 

 node can in all cases be evolved from the terms previously calculated. This con- 

 sideration not only shortens very considerably the labour of the continued approxi- 

 mations, but it enables us to regard one of the simultaneous equations as an equation 

 of verification. Professor Brown's paper — undoubtedly the most valuable of all 

 the papers that are based upon Dr. Hill's researches — concludes with some exten- 

 sions of Adams's theorems connecting the mean value of the parallax with the 

 motions of the node and perigee. These extensions possess an analytical interest, 

 but as applied to the development of a solution of the problem of three bodies in 

 series, they only provide some equations of verification of a value far inferior to 

 those investigated in the earlier part of his paper. 



The following advances have been made towards a complete development of 

 the problem of three bodies. Dr. Hill calculated the variation terms ; Professor 

 Brown the terms depending on the ratio of the parallaxes, the terms depending on 

 the first, and subsequently the second and third powers of the moon's eccentricity ; 

 also the terms depending on the first power of the sun's eccentricity, and also the 

 product terms containing the first powers of both the eccentricities. These latter 

 are the only product terms hitherto calculated by Dr. Hill's methods. The con- 

 vergence of the series Delaunay obtains in his literal development is exceedingly 

 slow, and the arithmetical values show a residue in some of Delaunay's series of 

 over one second. I have calculated terms depending on the fiist three powers of 

 the inclination. Besides this, Dr. Hill has obtained the principal part of the motioi* 

 of the perigee, and Adams the principal part of the motion of the node. Professor 

 Brown has calculated the correction to the motion of the perigee depending on the 

 square of the eccentricity, and I have calculated the correction to the motion of th& 

 node depending on the square of the inclination. 



At the beginning of his last paper, referred to above. Professor Brown has 

 collected the bibliography of the subject. 



10. The Relation between the Morphological Syimnetry and the Optical 

 Symmetry of Crystals. By William Barlow. 



Starting from the well-known facts of the influence of the presence of 

 molecular matter generally on the velocity of light, and of the directional optical 

 properties of crystals, the author reaches the conclusion that ether-movements 

 which take place in the same crystal in different directions experience different 

 degrees of resistance and retardation, so that a state of things prevails roughly 

 comparable to what would happen if a space occupied by a crowd of people were 

 studded with posts arranged on parallel lines and evenly distributed ; the move- 

 ments of the crowd as it surged to and fro would be less impeded in some direc- 

 tions than in others, especially if the posts were not round, but of similar sectioa 

 sameways orientated. In the case of both the ether and the crowd what are 

 compared are the collective resistances in each direction, differences in the retarda- 

 tion experienced by diflferent particles or persons moving side by side in the same 

 direction not being discriminated. 



Even if the crystal emploj-ed belongs to the cubic system, and is therefore 

 isotropic, the ether-movements must, as in the case of less symmetrical crystals, 

 experience diff'erent retardation in diff'ereut directions ; and the necessary deduc- 

 tion from this is that if tbe influence of a homogeneous molecular structure on 

 light depends on t/ie arrangement of the molecular matter, it is an average, effect, 

 the velocity of a ray in any given direction depending, not merely on the resistance 

 to ether-movement experienced in some single direction definitely related to the 

 direction of polarisation of the ray, hut on that experienced in a number of different 

 directions inclined to one another. The writer cites in support of this conclusion 

 the fact that in crystals belonging to the less symmetrical crystal systems, irk 



