February 26, 1920] 



NATURE 



713 



Raman and B. Banerji : Kaufmann's theory of the 

 impact of the pianoforte hammer. — Comdr. T. Y. 

 Baker and Prof. L. N. G. Filon : A theory of the 

 second order longitudinal spherical aberration for a 

 symmetrical optical system. The authors obtain a 

 formula for the lonfjitudinal spherical aberration in 

 a symmetrical optical system of the type 



A^ = (.At' + Ef')/(i + B«=), 



where Ax is the longitudinal spherical aberration on 

 the axis, t is the slope to the axis of the emergent 

 ray calculated by Gauss's method, and A, B, E are 

 polynomials in the magnification of degrees 4, 3, and 

 6 respectively. It is shown (i) that a formula of this 

 kind is, on the average, superior in numerical 

 accuracy -to the first two terms of tha usual series of 

 aberrations of successive order ; and (2) that it re- 

 moves a number of difficulties connected with con- 

 vergency which occur in the methods at present in 

 use. In particular, developments in powers of trigono- 

 metrical functions of the true inclination of the 

 emergent rav are shown to be unsatisfactory. Certain 

 invariant relations are obtained, connecting A, B, and 

 E in general, and facilitating their computation. 

 Formulas are found enabling the functions .\, B, and 

 E to te calculated for a combination of lenses when 

 the corresponding functions for the individual lenses 

 are given, and a method is indicated whereby the con- 

 tribution of each lens to the final image defects can be 

 rapidly traced.— Prof. J. W. Nicholson : The lateral 

 vibrations of sharply pointed bars. The paper is a 

 sequel to one alreadv published, which arose from a 

 suggestion as to the formation of siliceous deposits 

 on sponge-spicules of a certain type. The present 

 paper deals with an exceptional case, for which the 

 necessarv analvsis presents unusual features. It is 

 that of a double rod each half of which is generated 

 bv rotation of the parabola y = .Ax- about the axis 

 of X. The influence of sharpness on the frequencies 

 and nodal positions of the notes is traced numerically 

 after the general analysis. It is shown that a limiting 

 frequencv and nodal position exist, so that the fre- 

 quencv is a lower limit to those producible under 

 anv conditions of support. .\s the rod becomes 

 sharper all its frequencies tend to this value, while 

 of the nodes one for each frequency tends to a definite 

 position, and all the others to the e.xtreme ends of 

 the rod. The same conclusions applv to a single rod. 

 — R. E. Slade and F. C. Toy : '.V new method of 

 soectrophotometrv in the visible and ultra-violet and 

 the absorntion of light by silver bromide. .^ new 

 method of measuring the absorption of light bv a 

 substance has been devised. This method is inde- 

 pendent of the relation between density and exposure 

 of the photographic plate. The following values of 

 the extinction coefficient of silver bromide at various 

 wave-lengths have been determined : 



A fe A fe 



^ifi fkfx ... 270 400 /i// ... 2000 



440 ,, ... 410 3qo ,, ... 27qo 



430 ,, ... 600 I 380 ,, ... 3800 



420 ,, ... Cfio 370 ,, ... 5100 



410 ,, ... 1380 ' 360 ,, ... 6700 



This extinction coefficient is defined by the formula 



where T, and L are the intensities of the light at 

 points d centimetres apart in the absorbing medium. 

 It is estimated that the average error of anv of these 

 values is less than 3 per cent. — Dr. S. Chapman : A 

 note on Dr. Chree's discussion of two magnetic 

 storms. — Dr. C. Chree : An explanation of the 

 criticisms on Dr. Chapman's recent paper, " .^n Out- 

 line of a Theory of Magnetic Storms." 



NO. 2626, VOL. 104] 



Linnean Society, February 5. — Dr. A. Smith Wood- 

 ward, president, in the chair. — Dr. R. Ruggles Gates : 

 The existence of two fundamentally different types of 

 characters in organisms. The experimentalist point 

 of view regarding evolution, resulting from the work 

 in mutation and Mendelism, is frankly antagonistic 

 to the views of paleontologists, anatomists, and others 

 who deal with orthogenesis and the inheritance of 

 acquired characters. While these two factors bear 

 entirely different relations to evolutionary changes, 

 both are necessarv to account for evolution as it has 

 taken place. The conclusion is reached that higher 

 organisms exhibit two contrasted types of characters, 

 which differ fundamentally (i) in their manner of 

 origin, (2) in their relation to the structure of the 

 organism, (3) in their relation to such phenomena as 

 recapitulation, adaptation, and inheritance, and (4) in 

 their relation to geographic distribution. To the first 

 category belong cell-characters, which arise as muta- 

 tions, are represented in every cell of the individual, 

 and are usually inherited as distinct entities. To the 

 second category belong organismal characters, which 

 arise graduallv through impact of the environment or 

 through orthogenetic changes, may modify only 

 localised portions of the life-cycle, and may not be 

 incorporated in the germ-plasm from the first. 



Zoological Society, February 10. — Prof. E. W. 

 MacBride, vice-president, in the chair. — H. R. Hogg : 

 Some Australian Opiliones. The genera and species 

 described belonged to the sub-orders Palpatores and 

 Laniatores, the Palpatores being represented by the 

 genera Pantopsalis and Macropsalis of the family Phalan- 

 giidae, and the Laniatores bv genera of Tria^nobunidae 

 and Trianonvchidae. In the case of the Phalangiidae 

 the author had been able to establish that long 

 mandibles were a male and short mandibles a female 

 character. — Dr. C. F. Sonntag : Larynx and ceso- 

 phagus of a common macaque, exhibiting several un- 

 usual features.— R. E. Turner and J. Waterston : A 

 revision of the Ichneumonid genera Labium and 

 Poecilocryptus. 



Physical Society, Februarv 13. — Prof. C". H. Lees, 

 president, in the chair.— Prof. C. H. Lees: Presi- 

 dential address : The temperature of the earth's 

 interior. In an average cubic centimetre of matter 

 within the earth's substance the energy generated by 

 radio-active matter is equivalent to the sum of the 

 following quantities : (i) Heat utilised in rise of 

 temperature, (2) loss of heat by conduction, etc., 

 (3) change in gravitational energy, and (4) thermal 

 stress. The onlv factor known with certainty is the 

 loss bv conduction, which works out to an average 

 of 10' ergs per annum per c.c. The approximate 

 water equivalent of the material of the earth is o-8; 

 therefore a rise of temperature of 1° C. requires 

 33,000,000 ergs. Hence, if there was nothing to take 

 into account but the conduction loss, the temperature 

 would fall bv 1° in 3-3 million years. The discovery 

 of radio-activitv. however, showed that near the 

 earth's surface the average amount of energy radio- 

 activelv generated is 1000 ergs per c.c. The quantity 

 falls off rapidlv as deeper rocks are reached. The 

 present Lord Ravleigh suggests that the average may 

 be about 10 ergs— just sufficient to balance the heat 

 lost from the surface. If we accept this theory, we 

 have to deal with a steadv state, in which the tem- 

 perature neither rises nor falls, and the calculation 

 of the temperature at points inside the mass is sirnple. 

 The equilibrium theory has been much criticised, 

 however, and it is necessary to consider other alterna- 

 tives. There are two pos.sibilities r Either the tem- 

 perature mav be rising^ due to the radio-energv ex- 

 ceeding the surface loss, or it may be falling if the 

 balance is the other wav. The geological evidence 



