January 6, 1910] 



NATURE 



279 



An Example of Spurious Correlation. 



If 1 am not mistaken, the first method of forecasting 

 the summer season proposed by -Mr. A. B. MacDowall 

 in Nature of September i6, 1909 (vol. l.xx.xi., p. 335), is 

 based upon a spurious correlation. If we talce a series of 

 departures from normal of a meteorological element and 

 tabulate the sums of consecutive groups of thirty, there 

 xviU always be a relationship between these sums, although 

 l\^^ original departures may be entirely independent, and 

 hence the relationship between the sums cannot be utilised 

 for forecasting an individual term of the original series. 

 That such sums of independent departures are not in- 

 dependent may be seen in the following way. If we 



denote the original independent departures by d,, d^ 



and the sum of thirty quantities beginning with rf, by Sp, the 

 correlation coefficient between such quanlities as Sj, and .f;,+i, 

 as given by statistical methods, will be the mean value ot a 

 long series of products Sp j,,+, divided by the product of the 

 square roots of the mean values of s'p and of S'p^^ Now as 

 dp, d,, are independent the mean value of the product dp d,, 

 will hi zero ; and it is easily seen that the correlation coeffi- 

 cient in question is the mean value of (</-p+i + rf"-p+2 + +fl'>+29) 

 divided by the product of the square roots of the mean values 

 of ((/>+ . . . +n-p+j9) and of (f/-',,+, + +d-pj^^^ ; if we denote 

 the mean value •! U'-., by w'-, this becomes 2.<)i)i lyini-, or 29/30. 

 Thus the thirty-year sums of independent annual departures will 

 tend to vary closely together, and the dots in a diagram 

 like that of p. 335 would tend to lie on a straight line. 



The relationship actually found by Mr. MacDowall 

 between the sums does not appear, therefore, to afford a 

 satisfactory basis for a forecast. Gilbert T. Walker. 



India Meteorological Department, Simla, 

 December 16, 1909. 



On Fluorescence Absorption. 



It is desirable to direct attention to Prof. R. W. Wood's 

 most important paper in the Philosophical Magazine for 

 December, 1908, on a method of showing fluorescent 

 absorption directly if it exists ; but it seems certain that 

 he has, at the end, drawn a conclusion from his experi- 

 ments the very opposite, as I venture to think, to that 

 to which they really lead. He compares the light appar- 

 ently transmitted by a fluorescent body when fluorescence 

 ii; and is not, taking place, and finds that there is no 

 difference in the resultant effect. This, I think, is as it 

 should be; but the inference he draws is that there is no 

 difference in the absorption. For my part I must admit 

 that it only confirms my results published in the Philo- 

 sophical Transactions, vol. cxci., A, 1898, that there is 

 such an absorption ; for if there were none such the light 

 apparently transmitted would be less when the body is not 

 fluorescing, owing to the fact that the fluorescent light 

 would increase the apparent transmission, and a flickering 

 should ensue; but Wood's experiment demonstrates that 

 this is not so. The inference I should draw, then, is that 

 during fluorescence there is an increased absorption of the 

 light transmitted. 



Prof. Wood appears to assume, moreover, that the 

 resultant effect on the retina of two successive flashes is 

 equal to the sum of the two acting simultaneously, which 

 is not the case, since the successive flashes act merely as 

 an intermittent single flash would do. 



Nichols and Merritt, who have fully confirmed my 

 results spectroscopically, have shown that the absorption 

 effect diminishes as the intensity of the transmitted light 

 increases, so that when the intensity of the transmitted 

 light is large in comparison with that of the fluorescent 

 light there is no effect at all. owing to the fact that this 

 transmitted light itself is sufficiently intense to excite 

 fluorescence, and there is therefore no change of state in 

 the two cases. 



If uranium glass is used for the absorption — it was with 

 uranium glass that I observed the effect — the source of the 

 transmitted light should also be uranium glass. I may add 

 that the best results were obtained by using the light from 

 the spark between cadmium electrodes for exciting fluores- 

 cence. With a suitable Leyden jar in the circuit, the 

 illumination is sufficiently steady, and any errors in this 

 respect can be detected by the null method I have 

 described. J. Butler Burke. 



December 18, 1909. 



NO. 2097, VOL. 82] 



Adsorption. 



" The above effects, however, become of consequence 

 in those frequent cases in which a muddy liquid is only 

 partially filtered through a dry filter in order that some 

 analytical estimation may be made in a given volume of 

 the filtrate. Tlte first drops of the filtrate must therefore 

 be discarded." The above quotation is from Ostwald's 

 " Foundations of Analytical Chemistry " (English transla- 

 tion), the italics being in the text. Ostwald makes this 

 a purely theoretical deduction, but the practice of discard- 

 ing first drops does not, I think, originate vifith him. 

 Doubtless many analysts neglect the precaution, but many 

 use it. 



Some experimental work on adsorption which I am at 

 present carrying on seems to point to the practice being 

 quite uncalled for in at least the majority of cases. I am 

 not yet ready to speak definitely, but it seems to be as 

 unnecessary as it would be to reduce weighings to a 

 vacuum standard in everyday analytical work. Ostwald's 

 extreme positiveness, however, makes me wonder whether 

 I have overlooked some serious fault in my experimental 

 methods, and I should be much indebted to anyone who 

 would point out to me any references in the literature 

 which give an experimental justification of the practice. 

 The absence of any library facilities in this place makes a 

 systematic search of the literature impossible to me. 



Alfred Tingle. 



Imperial Chinese Pei Yang Mint, Tientsin, 

 December 8, 1909. 



The Terminal Velocity of Fall of Small Spheres in Air. 



.^T the Winnipeg meeting of the British .Association 

 Prof. Zeleny and Mr. McKeehan read a paper on the 

 terminal velocities which they had found when Lyco- 

 podium and other small spores fall through air. The 

 measured terminal velocities were only about half those 

 calculated by Stokes's formula. The fall was steady, no 

 Brownian motion or rotation being visible. The authors 

 of the paper have since succeeded (see Nature, December 

 0, 1909, p. 158) in making minute spheres of wax and 

 mercury which do obey the theoretical law, but add that 

 the reason for the deviations in the former cases is not 

 clear. 



May not the reason for these deviations be the rough- 

 ness of the spore? The drops, through surface tension, 

 are smooth and practically perfect spheres, whereas a 

 spore of Lycopodium is very rough relative to its size. 

 (Using a microscope objective with large aperture, and 

 oblique illumination, Lycopodium spores of about 14 /i 

 radius were seen to be coated with hair-like projections.) 

 The spore would, from its roughness, leave a tail of small 

 eddies behind it. The increased energy of this turbulence 

 represents the increased resistance which the spore experi- 

 ences on account of its roughness, as compared with that 

 experienced by the smooth drop considered in the theo- 

 retical law, much as the speed of a ship is lessened when 

 its bottom is foul. 



As a suggested experimental test, an increase in the 

 pressure of the air will not affect the viscosity, but will 

 alter the energy in this tail of small eddies. So also 

 would a moderate decrease in the pressure, while yet it 

 would probably not bring the relative size of the spore 

 and of the gaseous molecular free path too close for the 

 theory to be applicable. Should this be the case, how- 

 ever, it would be shown by the appearance of Brownian 

 motion. Edith A. Stoney. 



Positions of Birds' Nests in Hedges. 



Lieut. -Colonel Tull Walsh's observations as to the 

 positions of nests (Nature, December 16) are interesting, 

 as they tally with the aspect of arboreal cryptogams, as 

 already noted by me. South-west winds depositing 

 sulphurous and nitrous products to leeward of towns cause 

 lichens and mosses to flourish best on the eastern side of 

 trees and hedges ; and, moreover, this is general, for winds 

 bearing spores from the south-west continually play on 

 the trunks and blow away spores as they settle. If it 

 were not for a kind of capillary attraction or rotary motion 

 drawing the spores round the trunk to leeward, or east 

 O'- north-east, they would never germinate. So the eastern 

 side is the most productive, though often the western 



