2l8 



NATURE 



[December 27, 1900 



(Lummer and Pringsheim, Paschen, &c. ), of the form of this 

 function f is perhaps the most fundamental and interesting 

 problem now outstanding in the general theory of the relation 

 of radiation to temperature. The theoretical relations on which 

 this expression is founded have been shown to be in agreement 

 with fact ; and it appears that the form c^e'cd^"^ fairly repre- 

 sentsy(AT) over a wide range of temperature.^ These relations 

 have been derived, as usual, from a dynamical discussion of the 

 aggregate intensity of radiation belonging to the temperature ; 

 it may be shown that the same results, but nothing in addition, 

 will be gained by applying the same principles to each con- 

 stituent of range 5a by itself, assigning to each its own 

 temperature. 



SCIENTIFIC SERIALS. 



American Journal of Mathematics, vol. xxii., No. 4. — Asym- 

 ptotic evaluation of certain totient sums, by D. N. Lehmer, is 

 an attempt to account for what seems to be a remarkable law, 

 first observed in particular cases in 1895. I' is thus stated : 

 •Consider any set s oi k linear forms, an-\-bi{i=\ . . . . k), all 

 of which have the same modulus a, and where [a, (5j]=i, 

 '{a, b] stands for the G.C. divisor of a and b. Consider, further, 

 a function e,(jf) such that e,(jr) = i or o, according as each of the 

 prime divisors of x belongs to one of the forms of the set s or 

 >not. If, then, v{x) denotes the number of distinct primes in x, 

 we have 



2 



Lim -^=t 



N=:00 



N^-Wg/-) 



N 



= constant 



The author's aim here is to prove this law where s is the set of 

 linear forms belonging to a binary quadratic form. He also 

 determines the constant in this case (pp. 293-335). Dr. 

 E. H. Moore's paper concerning Klein's group of («+i)! 



-ary coUineations is a modification of a communication made to 

 the American Mathematical Society, December 30, 1898. 

 This short note is related to several papers by the author, 

 amongst others with one communicated to the London Mathe- 

 matical Society (December 1896, see vol. xxviii. , p. 357). The 

 closing paper (pp. 343-380), is one by H. E. Slaught, 

 entitled " The Cross-ratio Group of 120 Quadratic Cremona 

 Transformations of the Plane. Parti., Geometric representation." 

 The group specially studied is a particular case, n = 5 of the 

 general cross-ratio group of order n\ Its consideration was 

 undertaken as a dissertation at the University of Chicago at the 

 suggestion and under the direction of Dr. Moore, and so is 

 closely connected with the two papers referred to above. A few 

 plates of figures are given at the end of the number, and also an 



-obituary notice of Prof. T. Craig by Prof. S. Newcomb. 



)kiSymons''s Monthly Meteorological Magazine, December. — 

 "Climatological table for the British Empire for the year 1899. 

 'This interesting summary of the climatological tables which 

 liave been published for a number of selected stations for the 

 last quarter of a century shows that, generally speaking, the 

 extreme values fall much to the same stations as usual. 

 Adelaide records the maximum shade temperature, 11 3° '6 (in 

 February). This temperature has only once been exceeded in 

 these tables --viz. by II4°'2 in 1876. It had also the maximum 

 temperature in the sun, I75°7; this value is also unusual, the 

 only higher reading being 180°, in 1882. It is also the driest 

 station, the mean humidity being 59. The dampest station 

 was Colombo, mean humidity 79 ; this station also records the 

 highest mean temperature, 8l°*9, and the greatest rainfall, 

 73 "5 inches. The lowest temperature in the shade was -46° "5 

 at Winnipeg (in February) ; this station had also the greatest 

 range in the year, I35°*9, the greatest mean daily range, 22°*3, 

 and the lowest mean temperature, 34° '2. Mauritius was the 

 most cloudy station — viz. 57; this extreme has several times 

 been recorded at London, but in 1899 the cloud value was 5 '6, 

 only three out of the preceding forty years having been less 

 cloudy. 



1 This might, however, be multiplied by (TA)*, and the experiments 

 would hardly discriminate between the values zero (Wien), unity (Rayleigh), 

 and one-half (Thiesen) for k ; the latter value, which is entirely empirical, 

 seems to fit best. 



NO. 1626, VOL. 63] 



SOCIETIES AND ACADEMIES. 

 London 



Royal Society, December 6.— "On the Bacterial Disease 

 of the Turnip [Brassica napus)." By M. C. Potter, M.A. , 

 F.L.S., Professor of Botany in the University of Durham 

 College of Science, Newcastle-upon-Tyne. Communicated by 

 Sir M. Foster, Sec.R.S. 



This paper gives the results of an investigation into the cause 

 of a special disease of the turnip crop. The disease was dis- 

 cernible in plants still growing in the fields, some roots being 

 found which were quite rotten, the decaying portion being white 

 with a highly offensive and peculiar smell. The most careful 

 microscopic search failed to detect any trace of hyphje of the 

 higher fungi in the decaying mass, but only a swarming mass of 

 bacteria. The tissues were completely disorganised, the cells 

 separating from each other along the middle lamella ; the cell- 

 walls were soft, swollen and faintly striated ; the protoplasm, 

 too, had lost its natural colour and become slightly brown and 

 contracted. The disease could be readily communicated to 

 sound, growing roots by merely making a slight incision and 

 inoculating the root at the injured surface. 



After a long series of cultures a bacterium was isolated, and 

 pure cultures obtained grown from a single individual, which 

 produced all the symptoms of " white rot" when sown upon 

 sterile blocks of living turnip. This bacterium rapidly liquefies 

 gelatine, it is a short, motile rod with a single polar flagellum, 

 and, adopting Migula's classification, has been described under 

 the name of Psendomonas destructaus. When growing in a 

 living plant tissue or in nutrient solutions, a cytase is secreted ; 

 this was isolated by the well-known method of precipitation by 

 alcohol, and has been shown to cause the dissolution of the cells 

 and the softening and swelling of the cell-walls of the host. 



The appearance of the diseased tissue could not be entirely 

 explained by the action of the cytase. It was found that the 

 boiled, filtered juice of a turnip, which had become rotten 

 through the influence of a pure culture of P. destructaus, had a 

 powerful toxic effect upon the living plant cell. This toxin 

 proved to be oxalic acid. A reaction probably takes place 

 between the calcium pectate of the middle lamella and the oxalic 

 acid produced by the bacteria, the calcium pectate neutralising 

 the oxalic acid and thus permitting the continued growth of the 

 bacteria. 



The action of this bacterium upon living plant tissues is similar 

 to that of some of the parasitic fungi ; in both cases the invading 

 organism produces oxalic acid, which acts as a toxin to the 

 protoplasm and, decomposing the calcium pectate, furthers the 

 dissolution of the cells ; and also there is the secretion of a 

 cytase, which has a destructive action upon the cell-wall and 

 intercellular substance. The question of the parasitism of the 

 bacteria thus stands in these respects on the same platform as 

 that of the fungi, and a complete homology is established 

 between them. 



From numerous observations in the fields it would appear 

 that P. destructaus is always introduced at a wounded surface, 

 and through the agency of slugs and larvae. 



"On the Tempering of Iron Hardened by Overstrain." By 

 James Muir, B.Sc, B.A., Trinity College, Cambridge, 185 1 

 Exhibition Research Scholar, Glasgow University. Communi- 

 cated by Prof, Ewing, F.R.S. 



It is well known that iron hardened by overstrain — for ex- 

 ample, by permanent stretching — may have its original proper- 

 ties restored again by annealing — that is, by heating it above a 

 definite high temperature and allowing it to cool slowly. Ex- 

 periments described in the paper, of which this is an abstract, 

 show, however, that if iron hardened by overstrain be raised to 

 any temperature above 300° C, it may be partially softened in 

 a manner analogous to the ordinary tempering or "letting 

 down " of steel which has been hardened by quenching from 

 a red heat. This tempering from a condition of hardness in- 

 duced by overstrain, unlike ordinary tempering, is applicable 

 not only to steel, but also to wrought iron, and possibly to 

 other materials which can be hardened by overstrain and softened 

 by annealing. 



The experiments described in the paper were all carried out 

 on rods of iron and steel about fths of an inch in diameter and 

 II inches long, the elastic condition of the material being in all 

 cases determined by means of tension tests, in which the hard- 

 ness of the material was indicated by the po.sition of the yield- 

 point. 



