August 9, 1900] 



NA TURE 



359 



daylight, more by an electric arc-light, most by bright sunlight. 

 It is abolished by boiling the leaf, and by the action of an 

 aniesthetic, carbon dioxide. 



The first experiments, made at the end of March, were upon 

 iris leaves taken from plants about 6 inches high, and the response 

 to light was then between oooi and o 002 volt in value. Experi- 

 ments upon similar leaves were resumed early in May, when it 

 appeared that the external condition by which the state of the 

 leaf IS most obviously governed is temperatttre. On warm days 

 the response ranged from 0-005 to 0-02 volt ; on cold days it 

 did not rise above above 0-005, and was sometimes nil. Some 

 tests upon leaves in a warmed box gave satisfactory results, 

 which ^may be thus summed up :— The normal response at 

 15 -20 C. is diminished or abolished at low temperature (io°), 

 augmented at high temperature (30°), diminished at higher 

 temperature (50°), and abolished by boiling. 



As the month of May advanced, the iris leaves, even in the 

 warm box, became more and more inert, and by the 23rd inst., 

 when the plants were mostly full grown and in flower, no satis- 

 factory leaf could be found. Leaves of iris appear to give 

 more marked response at or about mid-day, than at or about 

 6 p.m. Tested by Sach's method the leaves gave no evidence of 

 starch activity during insolation. 



On the failure of the iris leaves to react, other leaves were 

 sought for which should give evident differences of reaction in 

 correlation with evident differences of state. Leaves of tropje- 

 olum and of mathiola gave a response to light contrary in the 

 main to the ordinary iris response, viz. "positive" during 

 illumination, and subsequently " negative. "^ In these two 

 cases leaves empty of starch acted better than leaves laden with 

 starch. Leaves of begonia gave a variety of responses strongly 

 suggestive of the simultaneous action of two opposed forces 

 effecting a resultant deflection in a + or direction. Leaves 

 of ordinary garden shrubs and trees, &c., e.g. lilac, pear, 

 almond, mulberry, vine, ivy, gave no distinct response ; this is 

 possibly due to a lower average metabolism in such leaves as 

 compared with the activity of leaves of small young plants in 

 which leaf- functions are presumably concentrated within a 

 smaller area. The petals of flowers gaVe no distinct response, 

 which indicates that chloroplasts are essential to the reaction. 



The effect of carbon dioxide upon the iris leaf was abolition 

 of response during and after passage of the gas, with subsequent 

 augmentation. Upon mathiola and tropreolum, augmentation 

 of response followed on applying air containing i to 3 per 100 

 of carbon dioxide, and prompt abolition resulted from a full 

 stream run through the leaf-chamber. On the air supply being 

 kept clear of carbon dioxide there was gradual abolition of 

 response, followed by gradual recovery on the re-admission of 

 a small amount of carbon dioxide. 



" Fatigue " effects may be produced if the successive illumina- 

 ations (of 5 minutes duration) are repeated at short intervals 

 (10 minutes). At intervals of i hour, successive illuminations 

 of 5 minutes produce approximately equal effects. With the 

 leaf of mathiola, periods of illumination of 2 minutes at intervals 

 of 15 minutes were used without provoking any obvious sign of 

 fatigue. ^ 



June 21.— "Note on Inquiries as to the Escape of Gases 

 D S ■^J^'^^P^^''^^-" ^y ^' Johnstone Stoney, M.A., Hon. 



Three investigations have been published which profess to 

 supply information about the escape of gases from atmospheres. 

 Two of them, those of Messrs. Cook -' and Bryan,=* while differ- 

 ing in other respects, agree in reasoning forwards by the help of 

 the kinetic theory of gas from the supposed causes ; the third * 

 pursues a method regarded as trustworthy by the present writer, 

 and reasons backwards by the help of the same theory from the 

 observed effects. 



VVhere,as in the present instance, the a/nV/and a posteriori 

 methods have led to inconsistent numerical results, it is incum- 

 bent upon us to search for the mistake or mistakes which must 

 somewhere have been made. If these can be found and cor- 

 rected, an important advantage is gained ; and the present is an 

 attempt to trace some of them by inquiring whether there are 

 conditions or agencies in nature which facilitate the escape of 



ne«iiv/n^}w' '^•l^'' 'f ■" '* employed >n physiological literature, i.t. 

 negative pole of positive element ("zincative") 



^ /Utrophysical Journal for January 1900. 



1 ■?"•>'■ ^''<^- Proc., April 5, 1900, p. 335. 

 AstfZZi'^';'^r""^',T' "{*'" ^"^"^ Dublin Society, vol. vi. Part 13 ; or 

 helium r^'"'7"'^ ^l' January 1898. And for further evidence that 

 helium IS escaping from the earth, see Nature of May 24, 1900, p. 78. 



NO, 1606, VOL. 62] 



gaseous molecules from the earth, and which are omitted, or 

 which have not been sufficiently taken into account, in Mr. 

 Cook's and Prof. Bryan's investigations. 



Let aV be a volume containing at a given epoch a large 

 number « of molecules of the atmosphere, and let A/ be a dura- 

 tion commencing at that instant. Also, let n' be the number of 

 encounters which each of these molecules on the average meets 

 with in the times A/. Then will 



N = nn' 



be the total number of their free paths in that time ; and the 

 actual number of the.se free paths, in which the initial speed 

 after an encounter lies at the time t between v and v + dv, must 

 be precisely 



dN = 'iHv + S)dv, (I) 



where w is the probability function (that employed by Mr. Cook, 

 or that employed by Prof. Bryan, or some other), and 8 (the 

 deviation function) represents whatever is the real divergence of 

 the actual number from that computed by the formula used by 

 them, viz. : 



efS = tindv; (2) 



in other words, computed on the supposition that 5/ir is of 

 negligible amount. 



Now TT is one fully-determined function in Mr. Cook's investi- 

 gation, and another fully-determined function in Prof. Bryan's ; 

 but little is known of what 5 is in either case, except that it is in 

 both an excessively comf)lex function of N, v, t, with several 

 other variables, some of which it is difficult even to indicate ; 

 and that by its amount for any given value of I and at any given 

 position in the atmosphere it must supply in equation (i) the 

 actual effect, at that time and place, of all natural agencies which 

 had not been taken into account in calculating the expression ir. 



If due care has been taken in framing the probability law tt, 

 it will in many cases be legitimate to assume that S/w is suffici- 

 ently small to warrant our using equation (2) when computing 

 the approximate distribution among the free paths of those 

 speeds which assign /arge values to n, while at the same time it 

 may need proof and may not be a legitimate assumption in 

 reference to those values of v which make ir sinall^ Now it is 

 in this latter case that the assumption has to be made by Mr. 

 Cook and Prof. Bryan. 



The conditions under which the assumption is likely not to be 

 true are the following : — 



A. Where the events, the law of whose distribution purports 

 to be represented by the w function, are of such a kind that a vast 

 number of the events need to be passed under review in order to 

 secure an approximate conformity to any fixed law. Now 

 experiment shows that in ordinary air trillions of the free paths, 

 probably many trillions, must be grouped together in order to 

 make manifest any law in the distribution of the speeds. In all 

 such cases we are not entitled to ignore the S function, except in 

 estimating the frequency of such speeds as can be shown to 

 assign a sufficient preponderance to the ir function. Accordingly 

 it is not legitimate to ignore the S function when treating of the 

 frequency of speeds which make w excessively small, such as are 

 the speeds which carry molecules away from the earth. 



B. But a more important omission occurs where the function ir 

 has been arrived at without taking into account agencies in 

 nature which affect the distribution of speeds. Where this has 

 been done the 8 function must include the whole effect of these 

 agencies, and this again forbids our relying upon equation (2) in 

 computing the frequency of any speed which makes the value of 

 T small. 



B I. Thus in Mr. Cook's computation no notice is taken of 

 the anisotropic character of the outer strata of the earth's 

 atmosphere, which facilitates the escape of molecules. In 

 Prof. Bryan's this is partly taken into account by treating the 

 molecules as moving in a constant field of force. This may 

 possibly be sufficient, though it ignores the reactions which are 

 also necessarily present. To include them it would be necessary 

 to extend the partition of energy beyond the molecules of the 

 atmosphere to all the other molecules of the earth which attract 

 them. 



B 2. Then, again, both computations ignore the incessant 

 turbulence of the atmosphere which, in its lower strata, 

 produces all the phenomena of weather, and in its upper regions 

 phenomena which are swifter and on a larger scale. This 

 turmoil, with all its dynamical, thermal and electrical effects, is 



