13 REPORT— 1876. 



of lier rotational velocity, or, as a timekeeper, is going slower by 11^ seconds per 

 annum now than tlien. According to this rate of retardation, if uniform, tlie 

 earth at the end of a century would, as a timekeeper, he found 22 seconds behind 

 a_ perfect clock, rated and set to agree with her at the beginning of the century. 

 Newcomb's subsequent investigations in the lunar theory have on the whole tended 

 to confirm this result ; but they have also brought to light some remarkable ap- 

 parent irregularities in the moon's motion, wliich, if real, refuse to be accounted 

 for by the gTavitational theory without the influence of some unseen body or bodies 

 passing near enough to the moon to influence her mean motion. This hypothesis 

 Newcomb considers not so probable as that the apparent irregidarities of the moon 

 are not real, ajid are to be accounted for by irregularities in the earth's rotational 

 \elocity. If this is the true explanation, it seems that the earth was going slow 

 from 1850 to 1862, so much as to have got behind by seven seconds in these twelve 

 years, and then to have begun going fester again so as to gain eight seconds from 

 1802 to 1872. So great an irregularity as this woxdd require somewhat greater 

 changes of sea-level, but not many times greater than the British Association 

 Committee's reductions of tidal observations for several places in dift'erent parts of 

 the world allow us to admit to have possibly talcen place. The assumption of a 

 fluid interior, wliich Newcomb suggests, and the flow of a large mass of the fluid 

 ''from equatorial regions to a position nearer tlie axis," is not, from what I liave 

 said to j'ou, admissible as a probable explanation of tlie remarkable acceleration of 

 rotational velocity which seems to have taken place about 1862 ; but happily it is 

 not necessary. A settlement of 14 centimetres in the equatorial regions, with cor- 

 responding rise of 28 centimetres at the poles (which is so slight as to be absolutely 

 imdiscoverable in astronomical observatories, and which woidd involve no change 

 of sea-level absolutely disproved by reductions of tidal observations hitherto made), 

 vrould sufiice. Such settlements must occur from time to time ; and a settlement 

 of the amount suggested might residt from the diminution of centrifugal force due 

 to LOO or 200 centuries' tidal retardation of the earth's rotational speed. 



Mathematics. 



/S'((!' les Mouvements apcriodiquea des Si/stemes de Points Mutarieh. 

 By IT. Yalestino Ceeeuti. 



A .short communication referring to a system of points subject to their mutual 

 action and to that of fixed exterior points. 



Sur les Si/siemes de Sjyhh-es ct les St/stemes de Droites, 

 Bij Professor Luioi Cre!\io>'A. 



C'utte communication avait pour objet d'exposer une methode pour transformer 

 les conc/rimtces (systemes donblement infiniaj de droites, conteuues dans uii com- 

 plexe lin(5aire donne, de nianiere qua chaque droite de la congruence corresponde 

 un point d'une surface, et vice-versa. La methode resulte de la combinaisou 

 des transformations de I'espace a trois dimensions, exposi?es par I'auteur dans 

 les ' Annali di Matematica' (serie 2'", tome 5*), avec la transformation, donnt'e par 

 -MM. Noetlier et Lie, d'un complexe lini5aire en I'espace ordinaire (point-espace). 

 Suivant cette transformation, les plans de I'e.space correspondent aux congruences 

 lineaires du complexe donne qui contiennent une droite fixe ; et aux autres congru- 

 ences liut'aires du meme complexe correspondent les spheres de I'espace ordinaire. 

 La methode expos(5e dans la communication donne toutes les transformations d'un 

 complexe linijaire en I'espace ordinaire, telles qu'aux congruences lineaires con- 

 tenant une droite flxe correspondent des surfaces d'un ordre donne. En particulier, 

 on obtient toutes les congruences (non-lineaires, ccmtenues dans le complexe donne) 

 qui sont susceptibles d'etre representees sur uu plan, de maniere que chaque droite 

 de la congruence ait pour image un point determine du plan et que, \ ice-versa, 



