5°o 



NA TURE 



[March 26, 190^ 



place of one which was originally granted by the Highland 

 Society. Teachers of agricultural science have alleged that 

 the regulations in connection with the national diploma are 

 unsatisfactory, but notwithstanding the attempts of the 

 Agricultural Education Association to secure their improve- 

 ment, the joint board seems unwilling to alter the conditions 

 of awarding diplomas. Prof. Wallace, of Edinburgh Uni- 

 versity, enumerates some of the disadvantages attached to 

 the present state of affairs in a recent pamphlet, and among 

 them he mentions that Scottish students have to travel 

 twice to Leeds to be examined by a board from which 

 teachers of agriculture are practically excluded, that the pre- 

 sent scheme encourages cramming, and that it is national 

 only in name. Prof. Wallace has obtained the opinion of the 

 Solicitor-General of Scotland as to the position of the High- 

 land Society in relation to its Charter on Education, 1856. 

 This Charter empowers and requires the council of the 

 Highland Society to appoint a board of examiners and to 

 grant diplomas, and the opinion of counsel is that by its 

 action in 1899 in agreeing to the joint board, the council 

 of the Society is not acting in conformity with the pro- 

 visions of its Charter. Prof. Wallace is, it appears, en- 

 titled to take steps to compel the council to proceed in 

 accordance with the Charter. 



The following announcements of gifts to higher education 

 in the United States have appeared in Science since the 

 beginning of December, 1902 : — Mr. James Stillman, 20,000/. 

 to Harvard University for the endowment of a professorship 

 in comparative anatomy. Mr. Peabody has offered to the 

 University of Georgia a 10,000/. building, provided the 

 Legislature will appropriate to the University for mainten- 

 ance the sum of 2000/. a year for two years, and make im- 

 provements costing 240!. A bequest of 16,000/. was made 

 to Yale University by the will of Mr. Benjamin Barge. Mr. 

 .Morris Jesup, 2000/. to Princeton University. Mr. John D. 

 Rockefeller, 200,000/. to the University of Chicago, to be 

 added to the endowment, and other sums amounting to 

 105,200/. have been given to the same university. Tulane 

 University has been made the residuary legatee of the late 

 Mr. A. C. Hutchinson, and it is expected that it will receive 

 200,000/. The University of Rochester has received 2000/. 

 from Mrs. Steele. Yale University will ultimately receive 

 10,000/. for the aid of poor students bv the will of the late 

 Mrs. Courrier. Dr. D. K. Pearsons has given to Illinois 

 College, Jacksonville, 10,000/.; to Fargo College, Fargo, 

 X. D., 10,000/. ; to West Virginia Conference Seminary, 

 Buchanan, 10,000/.; to Pomona College, at Claremont, 

 10,000/. ; and to Fairmount College, Wichita, Kas., 5000/. 

 This makes the total of Mr. Pearsons's contributions to 

 colleges 800,000/. Mr. Henry Phipps, 60,000/. for the 

 establishment in Philadelphia of " The Henry Phipps Insti- 

 tute for the Study, Treatment and Prevention of Tuber- 

 culosis." Cornell College, Iowa, has added 14,300/. to its 

 endowment funds. A friend whose name is not yet made 

 public gave 10,000/. Mr. Fred W. Brown has given 2000/. 

 Harvard University received 10,000/. by the will of Rebecca 

 C. Ames, the income to be used for the support of poor 

 students. The University of Pennsylvania received gifts 

 during the year to the value of 187,370/. Mr. Robert E. 

 Woodward, 10,000/. to the Brooklyn Institute of Arts and 

 Sciences. The Duke de Loubat, 20,000/. to Columbia 

 University for the establishment of a chair of American 

 archaeology. Oberlin College has received an anonymous 

 gift of 10,000/. from the same donor who recently gave 

 10,000/. By the will of the late Prof. Waterhouse, Washing- 

 tun University received 5000/., and Harvard University and 

 Dartmouth College each 1000/. Mr. S. M. Inman, 5000/. 

 toward the proposed Presbyterian university to be erected in 

 Atlanta, Ga. Cornell University has received an anonymous 

 gift of 30,000/. for the establishment of a pension fund. Mr. 

 James B. Colgate, 20,000/. to Colgate University, Hamil- 

 ton, N.Y., to which he had already given more than 

 200,000/. Mr. Andrew Carnegie, 20,000/. to Western Re- 

 serve University for the establishment of a school for the 

 training of librarians. Columbia University received 2000/. 

 for the establishment of a scholarship by the will of Mrs. 

 Banker. It thus appears that in three months universities 

 and colleges of the United States have, owing to the liber- 

 ality of American citizens, benefited to the extent of more 

 than one and a quarter millions sterling. 

 NO, 1743, VOL. 67] 



SCIENTIFIC SERIAL. 

 Journal of Botany, March. — Under Limonium Mr. E. S- 

 Salmon discusses the varieties and synonyms which Hooker, 

 in his " Student's Flora," places together under Statice 

 auriculaefolia. — The fresh-water algae reviewed by Messrs. 

 W. West and G. S. West are mostly small Chlorophyceae, 

 and include five new species and a new genus, Polychajto- 

 phora. — The notes on Myricacea? contributed by Dr. Rendle 

 were prompted by a rearrangement of the British Museum 

 plants consequent upon Chevalier's recent revision of the 

 group, whereby certain forms are separated from Myrica 

 to form the new genera Gale and Comptonia. — The diag- 

 noses presented by Mr. Spencer Moore refer to new sym- 

 petalous plants collected in the Coolgardie district of W. 

 Australia. — The following short articles occur; — " Rubi of 

 the Neighbourhood of London," by Rev. W. M. Rogers; 

 " Lepidium Smithii," var., by Mr. F. Townsend ; " Possible 

 Use of Essential Oils in Plant Life," by Dr. G. Henderson. 



SOCIETIES AND ACADEMIES. 



London. 



Royal Society, March 5. — "The Differential Invariants of 

 a Surface, and their Geometric Significance." By Prof. 

 Forsyth, F.R.S. 



The present memoir is devoted to xhe consideration of 

 the differential invariants of a surface ; and these are de- 

 fined as the functions of the fundamental magnitudes of 

 the surface and of quantities connected with curves upon 

 the surface which remain unchanged in value through al! 

 changes of the variables of position on it. They belong 

 to the general class of Lie's differential invariants ; and 

 some sections of them were obtained about ten years ago 

 by Prof. Zorawski, who, for this purpose, developed a 

 method originally outlined by Lie. Earlier, they had 

 formed the subject of investigations by a number of 

 geometers, among whom Beltrami and Darboux should be 

 mentioned. 



Prof. Zorawski 's method is used in this memoir. Ire 

 applying it, a considerable simplification proves to be 

 possible ; for it appears that at a certain stage in the solu- 

 tion of the partial differential equations characteristic of the 

 invariance, the equations which then remain unsolved can 

 be transformed so that they become the partial differentiaS 

 equations of the system of concomitants of a set of simul- 

 taneous binary forms. The known results of the latter 

 theory can then be used to complete the solution. 



The memoir consists of two parts. In the first part, the 

 algebraic expressions of the invariants up to a certain order 

 are explicitly obtained ; in the second, their geometric- 

 significance is investigated. 



An invariant, which involves the fundamental quantities 

 of a surface E, F, G, L, M, N (these determine the surface 

 save as to position and orientation in space) and their 

 derivatives up to order n, as well as the derivatives of 

 functions ip, ip, of position on the surface up to order »+i, 

 may itself be said to be of order 11. The invariants up to 

 the second order inclusive are obtained. It appears that, if 

 two functions <p and i|* occur, all the invariants that occur 

 up to the second order can be expressed algebraically in 

 terms of 29 algebraically independent invariants ; while, if 

 only a single function <p occurs, all the invariants that occur 

 up to the second order can be expressed in terms of 20 

 algebraically independent invariants. 



The significance of these respective aggregates of 29 andi 

 of 20 invariants is obtained in connection with curves 



<p = o, 1^ = 0, 



drawn upon the surface. The investigation reveals new 

 relations among the intrinsic geometric properties of a curve 

 upon a surface. In particular, up to the second order, four 

 such relations exist for a single curve, and their explicit 

 expressions have been constructed. 



March 12. — " On the Histology of Vredo dispcrsa, 

 Erikss., and the ' Mycoplasm ' Hypothesis." Bv Prof. H. 

 Marshall Ward, F.R.S. 



The paper deals with a detailed study of the histological 



