22 BEPORT— 1870. 



and the consequence is that the entire question remains involved in doubt. Duiing 

 the last seventeen months as many as 1227 observations of the spots on Plato alone 

 have been made ; and although the vaiying state of the earth's atmosphere affects 

 in no slight degree the visibility of such delicate objects, phenomena are presenting 

 themselves which call for a much more rigorous treatment than has yet been 

 accorded to them. The affirmation of change on, or quiescence of, the moon's sur- 

 face must depend, not upon the accumulation of desultory and undiscussed obser- 

 A^ations, but upon such as are undertaken on a weU-an-anged system and discussed 

 with reference to every known agency capable of affecting them. The present 

 state of the question is therefore one of doubt, one that calls for observation of the 

 most vigorous character and discussion of the most rigorous nature to settle it. 

 Observation of late has been tending towards a registration of minute detail detected 

 on the moon's smface, but discussion in various ways is behind the requirements 

 of selenography, and until it can keep pace with observation the doubt alluded to 

 above must remain. 



On the Distribution of Cometic Perihelia. By A. S. Davis, B.A. 



The hypothesis that those comets whose orbits are undistinguishable from para- 

 bolas are moving in hyperbolic, non-periodic orbits, leads to the following theore- 

 tical law for the distribution of their perihelia. The number of comets within any 

 distance from the sun is proportional to that distance. This follows from an inves- 

 tigation contained in a paper on cometary orbits published in the Philosophical 

 Magazine for September 1870. The first object of the present paper was to show 

 that the actual distribution of the perihelia of parabolic and hyperbolic comets is 

 probably in accordance with this law. For this puii^ose the numbers of comets 

 having perihelion distances lying respectively between 0-0 and 0-1, between 0-1 

 and 0'2, and so on, were ascertained. It was found that, instead of these numbers 

 being nearly equal, they were respectively 11, 10, 14, 17, 11, 33, 18, 23, 21, 24, 15, 

 10, 8, 4, 5, 1, 1. It was then shown that this want of agreement with the theore- 

 tical law of distribution might arise from the fact that the probability that a comet 

 wiU be observed depends upon the magnitude of its perihelion distance, those 

 comets being most likely to be observed which have perihelion distances rather less 

 than the radius of the earth's orbit. That this cause does produce a considerable 

 effect upon the apparent manner of distribution of perihelia was shown thus : — The 

 known comets were arranged in three groups containing respectively those which 

 appeared before 1750, between 1750 and 1800, and between 1800 and 1865. The 

 nmubers representing the distribution of perihelia for these three groups were re- 

 spectively 



1, 3, 2, 8, 3, 16, 4, 7, 3, 6, 2, &c., 



4, 2, 6, 3, 7, 7, 7, 10, 6, 7, 5, 2, 1, &c., 



6, 6, 6, 6, 1, 10, 7, 6, 12, 11, 8, 8, 7, 4, &c., 



showing that the distribution of the perihelia of a later gi-oup are much more nearly 

 in accordance with the theoretical law than that of an earlier group, owing doubt- 

 less to the fact that the probability that a comet would be detected was formerly 

 more dependent upon the magnitude of its perihelion distance than it now is. It 

 seems probable that if all the comets which visit the sun were obseiTed, the distri- 

 bution of their perihelia would be nearly in accordance with the above-stated theo- 

 retical law. Such an accordance the author thought would be an argiunent in 

 favour of the theory that the parabolic comets are non-periodic. 



In the second part of the paper the author showed that a statement made by 

 Prof Kirkwood regarding the distribution of cometic perihelia was incorrect. Prof. 

 Kirkwood, on finding that the longitudes of the perihelia of a large proportion of 

 those comets with \evy small perihelion distances do not differ greatly from the 

 longitude of the solar apex, concluded that this fact was due to a crowding of the 

 perihelia about the solar apex, produced, he thought, by the sim's motion in space. 

 Prof. Kii'kwood had not shown that the latitudes of the perihelia were nearly the 

 same as the latitude of the solar apex. The author found, by marking upon a celes- 

 tial globe the positions of the perihelia of all parabolic and hyperbolic comets with 



