August 29, 1907] 



NA TURE 



459 



equation of the first kind, /(j)= / (t(-f,/) <^{t]dl, in which 



the forms of k and / arc known and is to be deter- 

 mined, he showed that the solution of this equation was 

 unique if no solution could be found of the so-called 

 " homogeneous " allied equation 



0= I K{s,t) <p\t)dl 



if 



■b h 



is essentially positive whatever the form of the (con- 

 tinuous) function <v(t). Types of such functions K{s,t) are 

 given in the paper, and also a simple proof of a theorem 

 of Hilbert. 



Major MacMahon read a paper on operational in- 

 variants, in which he obtained several interesting and 

 elegant results in this abstruse department of analysis. 



Prof. Love read the first of a group of papers on the 

 best methods of introducing certain fundamental results in 

 analysis. In this he detailed a method of proving the 

 fundamental properties of the exponential function. Start- 

 ing from the attempt to differentiate o-'. he introduced the 

 number e as the limit of (i-|-i;'n)" when n is infinite, 

 and by applying the theorem of the mean value to the 

 expression 



fi6-.r)V (*-j-)"-V (*-,<-)"„ 



\1 



\{»-l) 



/)•' 



where R is the difference between e' and the first n terms 

 of the series for e'; he obtained readily the exponential 

 theorem. In the interesting discussion which followed 

 this paper Dr. Young suggested that the concept of an 

 infinite series was really simpler than that of a limit, 

 since the former involved only a countably infinite number 

 of steps, which was not necessarily true of the second. 

 Dr. Hobson emphasised the value of Prof. Love's method 

 as making the student familiar with a type of proof of 

 great generality and power, but Mr. C. S. Jackson de- 

 precated the too early introduction to beginners of difficult 

 mathematical concepts. 



In the department of general physics, which proceeded 

 simultaneously with the above, Mr. Sidney Russ read a 

 paper on the transmission of the active deposit from 

 radium emanation to the anode. He showed that, whereas 

 the .imount of active deposit obtained on the negative 

 electrode diminishes as the pressure of the air is 

 diminished, as has already been found by Makower, it 

 is found that the amount obtained on a positive electrode 

 simultaneouslv increases. E.xperiments have also been 

 made in various gases on the amount of active deposit 

 on the two electrodes, and it is shown that between the 

 pressures of o-i mm. and i mm. hydrogen behaves 

 differently from air. 



Miss L Homfray detailed a series of experiments on 

 the absorption of argon by charcoal. Miss Homfray finds 

 that a formula of the same type as Bertrand employed 

 for vapour pressures holds for the equilibrium pressures 

 of the absorbed gas at various temperatures and constant 

 concentration. The constants in the equation change with 

 the concentration, and moderately simple equations are 

 obtained expressing the mode of dependence. The result- 

 ing equation is much more satisfactory than the experi- 

 mental formula usually taken. 



Sir Oliver Lodge then read a paper on the density of 

 the ether, in which he summarised the arguments for a 

 very high density of the ether which had been given by 

 him in Nature, March 28, p. 510. His conclusion is that 

 every cubic millimetre of the universal ether of space 

 must possess the equivalent of a thousand tons, and every 

 p.-u't of it must be squirming internally with the velocity 

 of light. The latter part of this statement is based on 

 the fact that the existence of transverse waves in the 

 interior of a fluid can be explained only on gyrostatic 

 principles, and the internal circulatory speed of the in- 

 trinsic motion of such a fluid must be comparable with 

 the velocit\' with which such waves are transmitted. 



NO. T974, VOL. 76] 



Prof. Trouton showed an electrical experiment illus- 

 trating the two modes of condensation of water vapour 

 upon surfaces. If a bell jar be placed over a Bunsen and 

 then placed over a charged gold-leaf electroscope, this 

 often leaks as though the air were ionised. The action 

 is, however, somewhat uncertain. If the insulating 

 shellac of the electroscope is gently dried with a flame, 

 the experiment if made fails, but if the shellac be now 

 moistened and wiped so dry with a cloth as not to con- 

 duct, the experiment if made will be successful. The 

 action is therefore due to the moisture, but in the former 

 case it is deposited with difficulty for the same reason 

 that well-dried phosphorus pentoxide absorbs moisture with 

 dilliculty. 



.An important paper was read by Mr. A. O. Rankine on 

 a theoretical method of attempting to detect relative 

 motion between the ether and the earth. If a dumb-bell 

 shaped body shortens in accordance with the Lorentz hypo- 

 thesis in the direction of the ether drift, its moment of 

 inertia will depend upon its azimuth unless Its effective 

 mass changes in a compensating manner. The change in 

 its mass necessary for compensation turns out to be of 

 opposite sign to that which would be indicated by the 

 ratio between longitudinal and transverse mass, as given 

 by any of the current theories. Thus there is either some- 

 thing very wrong in these theories or a real effect arising 

 from motion relative to the ether is theoretically detect- 

 able in opposition to the view held by Larmor, Einstein, 

 and others. Unfortunately, it has to be recognised that 

 the effect is too small to be actually detected by experi- 

 ment. In the discussion Sir Oliver Lodge advised caution 

 amongst the many pitfalls in this difficult subject, and 

 appeared to be in favour of the view that when allowance 

 is made in accordance with a complete theory which holds 

 good for large as well as small velocities, the supposed 

 effect will be found to vanish. Prof. Trouton mentioned 

 another experiment which he was making in collaboration 

 with Mr. Rankine. If a wire changes in dimension with 

 its azimuth, it might be expected that its electrical resist- 

 ance will simultaneously change. Four coils are con- 

 nected to form the arms of a Wheatstone's bridge, 

 adjacent arms having their axes at right angles to one 

 another. Balance is obtained, and then the framework 

 on which the coils are mounted is rotated through a 

 right angle. When the temporary disturbance has sub- 

 sided, the arrangement is again tested for balance. The 

 experiments are in progress, and so far a small positive 

 effect has been obtained, but it requires confirmation 

 before so minute though important an effect can be con- 

 sidered certain. 



The afternoon meeting began with a challenging paper 

 by Prof. H. E. Armstrong on the nature of ionisation. 

 This attracted the physical chemists in particular, who 

 appeared with the object of combating Prof. .'Armstrong's 

 views. These may be summarised as follows : — 



We do not " need to imply more by the term ionisation 

 than that the medium is in a state in which it will con- 

 duct electricity." "The doctrine of electrolytic dissoci- 

 ation is destitute of common sense." Ohm's law is con- 

 sistent with a modified Grotthus hypothesis. " The 

 assumption that any electromotive force, however small, 

 will condition sensible electrolysis " is a fact which can- 

 not be regarded as established, as it is impossible to avoid 

 some polarisation. Electrolytic conductivity and chemical 

 activity se conjonde (Arrhenius). Chemical interactions 

 are dependent on " mutual attractive relations of the 

 particles." In effecting hydrolysis in the case of sugars, 

 " enzyines act selectively; therefore their action cannot 

 be attributed to dissociated hydrogen ions." "The mis- 

 take has been made that liquids are comparable with 

 gases — a preposterous contention." "'Ionised' molecules 

 are complex, reversible systems formed of solvent and 

 solute under the influence of the force of residual affinity." 

 " As such systems break down under the influence of the 

 current new ones to take their place must arise spon- 

 taneously in the solution : the molecules, therefore, would 

 draw one another apart at a rate proportional to th- 

 polarisation," and hence Ohm's law would be satisfied. 

 In the discussion Sir O. Lodge emphasised the distinc- 

 tion between the terms "electrolyse" and "ionise." 

 Electrolyse signifies decomposition, ionise means making 



