August 8, 1895] 



NA TURE 



545 



puff had its characteristic black colour, due to the quantity 

 <ii accessory sand and dust. 



At 22 o'clock, the up|)crcrateret gave out a little vapour 

 and a little lava, but again became quiet. At 23 o'clock, 

 the lower crateret showed new cracks around about it, 

 with the escape of vapour. ' 



During the night, between the 4th and 5th, the lava 

 -again increased, so that it is reported the next morning 

 to be advancing at the rate of 25 m. per hour. It had 

 turned to the west, and flowed down on the south side of 

 the Lion's Paw, or the Observatory ridge, and had divided 

 into two main streams, which subsequently subdivided 

 into minor ones that radiated in different directions. 



On July 5, the explosions at the central crater were 

 powerful, so as to form from time to time pine-shaped 

 vapour plumes over the volcano. .\t others, the vapour 

 was bent over the .\trio by the sirocco wind, so as to 

 spread a shower of dust and sand right across that 

 •depression. One of these is well indicated in Fig. 4. 



.So far no damage has been done except to a private 

 ■carriage road that crosses the Piano di Ginista to 

 the lower railway station. Xo cultivated land has 

 been reached. The lava is, however, on a steep slope, 

 and is flowing^ in the direction of the valley called 

 the Cupa Pallarino, over the edge of which a magnificent 

 -cascade of incandescent rock was formed in 1872. 



The eruption is quite identical in all its details 

 with the usual antecedent ones, resulting from the for- 

 mation and extension outwards of radial dykes. Many of 

 such eruptions 1 have described in these pages and else- 

 where, and fully explained their mechanism, production, 

 jjrowth and closure. 



Three results may happen : (l) The radial sheet of 

 rock may cool and seal the rift so that the volcano will 

 soon return to the cone-forming stage, as seems to be 

 indicated by the appearance of pasty lava cakes amongst 

 the cjecta on July 5. (2) The fissure may enlarge and 

 extend downward with the outflow of lava, as in 1872, 

 with the formation of a much larger central crater. (3) It 

 may follow the more usual course, as its immediate prt- 

 •decessor, and gi\e issue to a small but almost continuous 

 outflow of la\a during months or years. 



H. J. J0HNSTON-L.4VI.S. 



/'. L. CHERYSHEV iTCHEBICHEFF). 



T^ H E death of Prof. Chebyshev has hardly been noticed 

 -•■ in the English papers ; and even in Russia, except 

 for a short sketch in the University Bulletin, and in a 

 speech of Prof .Markoffs with reference to him, which 

 is reported in the Bulletin de r Academie imperinlc des 

 Sciences dc St. Pelersiourt;, no biographical notice has 

 ;ippearcd of this celebrated mathematician. 



I'aphnyty Levovitch Chebyshev was born on May 14, 

 182 I, al .\katovo, in the g^overnment of Kaluga ; and after 

 being educated privately, entered .Moscow I'niversity : he 

 completed the usual courses, and took his Bachelor de- 

 gree. In 1846 he received his Master's degree at the same 

 university for his " Essay on the elementary analysis of 

 the thcor)' of probability," and in the following year 

 commenced a series of lectures as assistant lecturer in 

 Petersburg University. He received the Doctor's degree 

 in 1849 '"r h'* well-known "Theory of Comparison," 

 which contained a model exposition of the forma- 

 tion of the theory of numbers, and clearly proved the 

 strength of his mathematical genius. In 1852 Chebyshev 

 was promoted to an extra professorship, and in i860 to 

 a regular professorship. During 1853-59 he was elected 

 successively assistant, extra, and ordinary tutor in the 

 Academy of Sciences. He remained a professor, doing 

 active work of the most valuable kind, thirty-five years, 

 •during the course of which, at various times, he lectured 

 on every branch of pure mathematics, and during one 

 period- in 1849- 5'— on practical mechanics. 



NO. 1345, VOL. 52] 



In his numerous writings Chebyshev left a veiy great 

 deal to the reader's imagination, often giving deductions 

 simply without proofs, but in his lectures he never left 

 a point without the fullest explanation ; and his lectures 

 are distinguished not only for elegance and accuracy, 

 but for their extraordinary simplencss ; the already- 

 mentioned " Theor)' of Comparison " may serve as a 

 good example, as well as his proof of Bernoulli's theorem, 

 which is now given in all works on the theorv- of 

 probability. 



The professorial services of Chebyshev had a great 

 significance to the Petersburg University. He placed 

 the teaching of mathematics on a firm basis, and formed 

 an independent school of thought. .\11 the present staff 

 of mathematical teachers m the Petersburg University, 

 except a very few of quite the youngest, are his pupils 

 and follow in his footsteps. His moral influence did not, 

 therefore, cease when he resigned his professorship in 

 1882. The Council of the University elected him an 

 honorary member, and his pupils kept up the habit of 

 going to him on certain days to have lively discussions 

 on various scientific subjects, in which his indomitable 

 energy acted on his hearers in the most animating 

 manner. He was always to be found engaged either on 

 some complicated calculation or on models of mechanism 

 he had invented. 



Everything Chebyshev did bore the impress of genius ; 

 he invented new methods for the solution of difficult 

 problems, which had appeared and had remained un- 

 solved ; he suggested himself a series of most important 

 problems, and worked at them till the end of his life. 

 His very first writings on the theory of numbers, devoted 

 to the problem of the inter-dependence of the prime 

 numbers, and on limits, gave him a European reputation, 

 and his succeeding investigations on irrational differ- 

 entials, and maximal and minimal quantities, assured his 

 position as the most original mathematician of the 

 nineteenth century. 



He died November 26, 1894 ; his works will shortly 

 be republished by the Petcr-^burg University. 



NOTES. 



As already briefly announced in these columns, the Institule 

 of France will celebrate its centenary next October. The pro- 

 gramme of the fetes which have been organised in connection 

 with that event has just been sent to the Members and Cor- 

 respondants of the Institute, the intention being that the cen- 

 tenary shall be marked by a reunion of all the men of light and 

 leading who belong to the Institute. f)n the afternoon of 

 October 23, there will be a reception in the Palais de I'lnstitul 

 of the Foreign .Vssociates and Correspondants and of French 

 Correspondants, and in the evening the Minister of Public 

 Instruction will hold a reception. On October 24, a meeting 

 will be held in the Great Hall -of the Sorbonne, at which the 

 President of the Republic will attend. Discourses will he 

 delivered by the President of the Institute, the Minister of 

 Public Instruction, and M. Jules Simon. .-V banquet, to which 

 all the .\ssociales and Correspondants are invited, «ill take place 

 on the evening of the .same day. On October 25, there will be a 

 special performance at the Comedie Fran^aise, and a reception 

 will he held by the French President. The celebration will ba 

 concluded on October 26, by a visit to the Chateau de Chantilly. 

 Ii will be seen from this that the hundredth anniversary of the 

 foun<lation of the Institute of France will be celebrated in a 

 manner worthy of the high position which the Institute holds 

 among the world's societies of science, art, and literature. 



Thk seventh session of the .•\ustralasian .\ssociation for the 

 .\dvancement of Science will he held in .Sydney, from January 

 3 to 10, 1897. under the presidency of Prof. .\. Liversidge, 

 F.R.S. The Presidents and Secretaries of the Sections are 



