December 12, 1912] 



NATURE 



425 



method, though certain groups are obtained. Just 

 the same applies to the Zeeman effect. 



After the discussion, Dr. Duffield also showed 

 photographs of the arc spectrum of nickel under pres- 

 sure. The effects resemble those obtained with the 

 iron arc. 



Dr. T. M. Lowr}- explained how he had calibrated 

 a wave-length spectroscope in the infra-red region by 

 aid of the fringes from a lightly-silvered etalon, using 

 a thermopile and galvanometer instead of an eyepiece. 

 Between A8000 and ai-,ooo the error was not more 

 than 20 to 50 A.U. ; thence up to ^20,000 the error 

 may have amounted to 100 A.U. Prof. McLennan 

 stated that one of his assistants had made measure- 

 ments to A2 1,000. Prof. McLennan gave a brief 

 account of some measurements in his laboratory of the 

 series lines in the arc-spectrum of mercury and on 

 their resolution by an echelon grating. In these ex- 

 periments he found that the best spectrograms were 

 obtained with an ordinary commercial glass Cooper 

 Hewitt mercury lamp provided with a side tube 

 carrying a window made from a plate of crystalHne 

 quartz. 



Radio-activity and Electronics. 



Mr. James Robinson described his experiments on 

 the photoelectric properties of thin metal films show- 

 ing a discontinuity in the behaviour when the film 

 attains a particular thickness. Prof. Rutherford 

 asked whether this break in the curve implied that 

 the total energy emitted was discontinuous. Prof. 

 McLennan suspected the possibility of a coherer action 

 when the thickness attained a definite limit. In reply 

 to a query by Prof. Millikan, Mr. Robinson stated that 

 the 6-volt electrons obtained corresponded to about the 

 limit capable of producing ionisation. He did not 

 think Prof. McLennan's suggestion fitted in with the 

 facts. 



Prof. Millikan summarised his already published 

 experiments on the discharge of ultra-violet light of 

 high-speed electrons, in which far higher velocities 

 were found when a spark is employed from those for 

 a mercury arc. Prof. Strutt suggested that what was 

 required was to bridge over the gap between the arc 

 and spark experiments, and indicated that it might 

 be done by gradually altering the pressure of the gas 

 in which the spark took place. Prof. Millikan replied 

 that he had altered the conditions gradationally. He 

 pointed out that only i in about 100,000 electrons have 

 the high velocity. He also read a paper on the law 

 of the fall of a drop through air at reduced pressures 

 and a redetermination of e. 



A law of fall of the form — • 



9 1^ I n) 



is found to hold so long as ;/a<o'4, but beyond that 

 limit an extra term must be added inside the curly 

 brackets, viz. B. exp. (—call), in which .\, B, and c 

 are all positive constants. If I is obtained from the 

 Boltzmann formula, ," = o'3502i?;)ic/, then A = 0.874, 

 13 = o'35, and c=i'7. The accurate evaluation of the 

 constant A makes possible a redetermination of e 

 which has a probable error of no more than i/io per 

 cent. This value is 6 = 4775 x 10-'° E.S. units. 



Prof. J. C. McLennan, on the intensity of the earth's 

 penetrating radiation over land and large bodies of 

 water, claimed inter alia to prove that the earth's 

 penetrating radiation has practically the same intensity 

 within a brick structure at Cambridge and a stone 

 building in Scotland as within a brick or a stone struc- 

 ture at Toronto; and further to disprove the exist- 

 ence of a diurnal variation of this radiation at Cam- 

 bridge. Prof. Strutt could not help thinking that it 

 existed. 



NO. 



2250, VOL. go] 



Prof. E. Rutherford and Mr. H. Robinson con- 

 tributed a paper on the heating effect of radium 

 emanation and its products. They raised the ques- 

 tion as to whether the energy of the alpha particle is 

 a measure of the heating effect produced, and came 

 to the conclusion that there is a distinct difference 

 between these quantities, and thence that there must 

 be a small rearrangement of the original atom. The 

 paper will shortly be published by the Vienna Academy 

 of Science. 



In a second paper, Prof. Rutherford discussed the 

 origin of the beta and gamma rays from radio-active 

 substances. The evidence used was afforded by the 

 relations between the energies of the numerous groups 

 of beta rays which are obtained. The simplest way 

 of regarding these relations is to suppose that the 

 same total energy is emitted during the disintegration 

 of each atom, but the energy is divided between beta 

 and gamma rays in varying proportions for different 

 atoms. For some atoms most, if not all, of the energy 

 is emitted in the form of a high-speed beta part, in 

 others the energy of the beta particle is reduced by 

 definite but different amounts (as it might be if, in 

 escaping, it had to pass through successive rings of 

 electrons) bv the conversion of part of its energy into 

 that of gamma rays. 



Prof. F. Soddy exhibited the apparatus (as shown 

 in his Royal Institution lecture) for drawing the curves 

 of radio-active changes. 



Mathematics. 



M. G^rardin, of Nancy, described a mechanism for 

 factorising large numbers. By means of this instru- 

 ment, which is of the nature of a slide rule, factorisa- 

 tion is exceedingly expeditious, e.g. the decomposition 

 of Mersenne's number M^. required only four 

 minutes. Lieut. -Col. .\. Cunningham congratulated 

 the author. With such a machine one would be quite 

 able to investigate the remaining Mersenne's numbers, 

 but he was afraid that it would require to be very 

 large. 



Lieut.-Col. Cunningham himself read a paper on 

 Mersenne's numbers, .^n additional prime factor has 

 been found for M.j, viz. 212885833 (due to Mr. Rame- 

 sam, of Mylapore) ; E. Fauquembergue has con- 

 firmed that Ms, is prime ; the author has shown that 

 M,-, = 0(mod. '730753). Thereby three mistakes have 

 now been proved in Mersenne's classification, viz. : — 

 M„ proved composite. M„ and M,, proved prime. 



Lieut. -Col. Cunningham, in a second paper, dis- 

 cussed the arithmetical factors of the Pellian terms. 



Prof. E. H. Moore dealt with the theory of the 

 composition of positive quadratic forms. The n-ary 

 quadratic form — 



A= 2 (7, .-.r.-.r,- (r? ,•,• = «;,), 



with real coefficients a,j, is positive if, for real values 

 of the n variables, .t,. it takes on only positive or 

 zero values. From two such forms, A and B, we 

 obtain bv multiplication of corresponding coefficients a 

 third form, C, their inner composite. For this inner 

 composition the property of positiveness is invariant, 

 i.e. the inner composition is likewise positive; other- 

 wise expressed, the class of positive «-ary quadratic 

 forms is closed under the process of the inner com- 

 position of forms. The theorem in its generality 

 is readilv proved by consideration of the fact that a 

 form is positive if, and only if, it is expressible as 

 the sum of squares of a finite number of linear forms 

 with real coefficients. Mr. Hilton suggested that the 

 theorem might be proved by using the fact that the 

 zeros of the characteristic drterminants were real and 



