August 29, 1907J 



NA TURE 



461 



experiments made wilh radium inside an explosion 

 chamber, proving that a sudden rise of temperature does 

 not affect the rate of disintegration, but that subsequent 

 effects are due to a change as if of B and C together. 



In the discussion on tlie latter Mr. Makower stated that 

 the experiments afforded a confirmation of his own ex- 

 periments and those made by him in conjunction with 

 Mr. Russ. The only point in which the experiments do 

 not agree with the view that it is radium C which is 

 affected by temperature is that after the diminution of 

 activitv succeeding the explosion the rate of recovery is 

 too .slow. This might be accounted for by assuming a 

 sudden change in the activity of radium C accompanied 

 by a change in its period instead of assuming a change 

 of activity in both B and C. 



Mr. H. Stansfield read a note on the echelon spectro- 

 scope and the resolution of the green mercury line, in 

 which the detection of several faint new components is 

 described ; and a paper by Mr. L. F. Richardson, on a 

 freehand potential method, had to be taken as read owing 

 to lack of time. 



The proceedings on Tuesday, August b, opened with 

 a discussion on modern methods of treating observations. 

 This was initiated by a paper by Mr. W. Palin Elderton 

 expository of the methods developed by Prof. Karl 

 Pearson. After defining the principal quantities involved 

 in the new methods, the paper dealt with correlation and 

 its calculation. Examples were given examining possible 

 correlation between rainfall in different districts, rainfall 

 and typhoid in Surrey districts, and other meteorological 

 questions. In the case of rainfall and typhoid, the 

 statistics made use of indicated so little correlation that 

 " it is impossible to assert definitely that there is any 

 relation " between them. In the discussion Dr. W. N. 

 Shaw emphasised the present need of a consideration of 

 ** departures from the mean." He directed attention to 

 other methods of treating observations besides that of 

 Prof. Pearson; for example. Prof. Schuster's periodogram 

 method and the " method of residuation " adopted by 

 Prof. Chrystal in discussing the component periods of 

 oscillation of the seiches of Scottish lochs. He showed 

 diagrams, prepared in the Meteorological Office, which 

 illustrated the relation of the mean to the frequency of 

 occurrence of the various values. Mr. G. Udny Yule 

 explained that to be content with the arithmetic mean 

 was to neglect all the other characters in which two 

 frequency distributions might differ. The standard 

 deviation was the most convenient measure of " scatter," 

 but the difference between the two values, which were 

 just exceeded by one-quarter and three-quarters of all the 

 observations respectively, was the most readilv calculated. 

 The correlation coefficient was a measure of the approach 

 towards a simple linear relation between two variables, 

 and could be extended to cover more complex cases. 



Mr. A. R. Hinks, who was somewhat sceptical as to 

 the general applicability of the new methods, inquired 

 what meaning could be attached to the value 0-3 of the 

 correlation coefficient in such cases as y = log.v. He also 

 gave an example in which questionable conclusions had 

 been arrived at by the method, the reason being that 

 certain groups of stars had been studied for special pur- 

 poses, while others had been neglected. The choice of 

 observations introduced a fictitious law of distribution. 

 The discussion was continued by Mr. Hooker, Prof. 

 Turner, and Prof. Edgeworth. 



Prof. Hicks then read a paper on the use of calcite 

 in spectroscopy. In order to be able to make use in 

 spectroscopy of the large dispersion in the ultra-violet 

 produced by calcite. Prof. Hicks first polarises the light 

 in order to do away with the duplication of the spectral 

 lines. When a quartz lens is employed in the collimator 

 it is made a compound lens of right- and left-hand quartz ; 

 the polariser for very short wave-lengths (down to \ 2300) 

 was a small Foucault fixed like a comparison prism. The 

 Hon. R. J. Strutt pointed out the great advantages that 

 fused quartz would have. 



A series of papers on astronomy and cosmical physics 

 were now taken. Dr. O. Backlund detailed the work 

 done in determining the variation of latitude. Dr. W. N. 

 Shaw read a paper on some recent developments of the 

 method of forecasting by means of synoptic charts. 



NO. 1974 VOL. 76] 



These are the methods of M. D. (ir^ville, of Paris, and 

 M. Guilbert, of the Meteorological Society of Calvados, 

 for obtaining an approach to a second approximation in 

 forecasting weather. Mr. C. Michie Smith gave an 

 account of the Kodaikanal Observatory in South India. 

 The Rev. A. L. Cortie, S.J., read a paper entitled " The 

 \'ariability in Light of .Mira Ceti and the Temperature of 

 Sun-spots," the purport of which was to indicate the 

 relatively low temperature of sun-spots from the behaviour 

 of the bands of titanium oxide in o Ceti, when the star 

 is at two different temperature levels represented by a 

 whole magnitude in luminous power. Concomitant 

 evidence of the variation of temperature of the star was 

 furnished by the character of the hydrogen lines. 



Prof. H. H. Turner read a paper descriptive of a 

 method which is being tried at Oxford for improving the 

 constants of the plates for the Astrographic Catalogue. 

 He also read one on the determination of periodicity from 

 a broken series of maxima. I-'or example, observations of 

 the light curve of a variable such as U Geminoruni are 

 generally absent altogether near a minimum, and cannot 

 be supplied ; moreover, the maxima are often lost from 

 cloudy weather, &:c. The paper suggests a method of 

 examining these for the detection of periodicity. Let 

 E,, E„, E, be the epochs of maxima. Kind the differences 

 between these and the nearest theoretical maxima E„, 

 E„-(-2», E„-l-4ij, &c., where an is a period to be tried. 

 Find (a) the algebraic mean of these differences, (b) the 

 sum of their squares. In certain circumstances (6) shou'd 

 be a minimum when we have hit on a real periodicity. 

 If (a) comes out sensibly different from zero, we must 

 alter E„ until (a) is small enough. When there is no 

 periodicity near 2(1, (b) will approximate to mn'fj, m 

 being the number of maxima treated. Miss M. White, 

 T. V. Pring, and J. E. Petavel communicated a note on 

 an analytical study of the meteorological observations 

 made at the Glossop Moor kite station during the session 

 1906-7, and a preliminary note by W. A. Harwood and 

 J. E. Petavel was read on the recent international balloon 

 ascents (Manchester station). A paper by T. J. J. See, on 

 results of recent researches on the physics of the earth, 

 was taken as read. 



Meanwhile, the mathematical department had been 

 meeting separately, continuing the group of papers on the 

 elements of analysis with one by Dr. W. H. Young on 

 the introduction of the mathematical idea of infinity. 

 Dr. Young stated that, of the three types of mathe- 

 matics, viz. the logical, formal, and practical, his sympa- 

 thies were w'ith the first and third rather than with the 

 second. He pointed out a number of instances in which 

 learners were brought into contact with the notion of 

 infinity, and advocated the policy of boldly facing the 

 difficulty instead of trying to avoid it. A paper by Mr. 

 C. O. Tuckey on the teaching of the elements of analysis 

 unfortunately had to be cut short owing to lack of time. 



Mrs. Booie-Stott exhibited a series of beautifully con- 

 structed models of three-dimensional sections of regular 

 hyper-solids in four dimensions, and models illustrating 

 the rotation of a four-dimensional body about a plane. 

 Prof. Schoute showed some lantern slides in connection 

 with this subject. He also exhibited three models of 

 developable surfaces the tangent planes of which are given 

 by the equations 



«3+ 3/r-i-l- 3«/ +: = 

 II* + 6n".v+ A"J' + = = 

 !i''-l$!i* +lS!i-.x+6!iji + : = o 



and indicated certain results when the parameter u in the 

 equation of the plane occurs to a higher degree. Prof. 

 A. M. Worthington showed a series of slides, directing 

 attention to the fact that the impact of a drop excavates 

 a perfectly spherical hollow which reaches its greatest 

 depth at apparently the same time that the water thrown 

 up attains its maximum height. The volume of this pit 

 is enormously greater than that of the drop. The object 

 of the paper was to obtain suggestions from mathe- 

 maticians explanatory of this phenomenon, but none were 

 forthcoming. Prof. Hilton gave an account of a new 

 property of Abelian groups, and Lieut. -Colonel A. Cunning- 

 ham read a paper on the factorisation of the terms Tn, fn, 

 of the Pe'lian equation t„--Dj'„-=i. 



