ON THE THEORY OF POINT-aROUPS. 77 



two independent variables only, is foreign to Cayley's purpose, as it was 

 to Pliicker's and Jacobi's ; the only application of the results in which 

 the additive combination of three functions is considered is to the 

 equations of surfaces which involve three independent variables. 



For our present purpose it will be sufficient to note very briefly the 

 results of this paper so far as they apply to the case of two independent 

 variables. A formula is, in the first place, found for the number of 

 arbitrary constants in 9, when any number of variables are involved, 

 which is an extension of that found in the former paper for two indepen- 

 dent variables, and the fact is pointed out, once again, that, for curves, 

 when r<ni + n — 3, ((7' — in — n)) more arbitrary constants exist than 

 would exist if B had passed through m7i perfectly arbitrary points. The 

 following general question is then attacked : To find the number of 

 relations widch exist between K(^-|-l) variables, forming K systems, each of 

 which satisfies simultaneously equations of the orders m, n, p, . . . respec- 

 tively ; the number of these equations being anything less than <p ; or (p 

 being equal to 6, jirovided at the same time K^mnp . . . This question, 

 as Cayley points out, is that solved by Jacobi for the particular case in 

 which K=7n?i, (^=2, 0=2, the 'relations' being equivalent to Jacobi's 

 ' equations of condition.' Cayley's general formula verifies Jacobi's 

 result. 



Seismological Investigations. — Eighth Report of the Committee, con- 

 sisting of Professor J. W. Judd {Chairman), Mr. J. Milne 

 (Secretary), Lord Kelvin, Professor T. G. Bonney, Mr. C. V. 

 Boys, Professor G. H. Darwin, Mr. Horace Darwin, Major L. 

 Darwin, Professor J, A. Ewing, Dr. R. T. Glazebkook, Professor 

 C. Gr. Knott, Professor R.Meldola, Mr. R. D. Oldham, Professor 

 J. Perry, Mr. W. E. Plummer, Professor J. H. Poynting, Mr. 

 Clement Reid, Mr. Nelson Richardson, and Professor H. H. 

 Turner. (Drawn itp by the Secretary.) 



[Plate I.] 

 Contents. 



TAGE 



I. General Notes on Stations and Registers 77 



II. The Oriffin of lai-ffe JSarthquakes recorded ifi 1902 and since 1S99 . . 78 



III. Large Earthquakes and small Changes in Latitude 78 



IV. Covvparison of Records from three Milne Pendulums at Shide . . .81 

 V. Comparison of Records from Shide, Keif, Bidston, and Edinburgh . . 81 



VI. Earthqualie Commencements as recorded at Strassburg and in Britain . . 82 

 VII. The Speed of Earthquahe Motion and Inferenoes based thereon relating to 



the Interior of the World 8-1 



I. General Notes on Stations and Registers. 



DuKlNa the past year the registers issued are Circulars Nos. 6 and 7. 

 These refer to Shide, Kew, Bidston, Edinburgh, Paisley, Toronto, Vic- 

 toria (B.C.), San Fernando, Cairo, Cape of Good Hope, Calcutta, Bombay, 

 Kodaikanal, Batavia, Baltimore, Mauritius, Trinidad, Irkutsk, Perth, 

 Wellington, Christchurch, Cordova (Argentina), Honolulu, and Tokio. 

 Mr. F. A. Chaves, Director of the Meteorological Service in the Azores, 



