April 24, 19 19] 



NATURE 



145 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of. rejected, manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



lonisation and hadiation. 



When X-rays pass through a gas, only a very 

 small fraction of the molecules — in favourable circum'- 

 stances, one in a billion— is ionised bv them, and the 

 extent of this ionisation is unaffectedby temperature. 

 Writers on radiation seem to have difficulty m recon- 

 ciling this with the wave theory of light. I venture 

 to suggest that the difficulty arises from an imperfect 

 comprehension of what the wave theory requires. 



The inverse square law of intensity ought not to 

 hold for very small spaces and very sniall times. The 

 uniform spherical wave spreading out from a point 

 source is a mathematical fiction. What we really 

 have is a very great number of spherical wavelets, each 

 diverging from a different electron, criss-crossing in 

 various directions, and consequently interfering with 

 one another. For example, suppose that there are n 

 electrons in the source, all close together, and that 

 the intensity of radiation is required at a point P at 

 a distance r. great in comparison with the linear 

 dimensions of the source, and so sensibly the same 

 for all the electrons. Let the intensity at P due to a 

 single electron be I/r^. Then the resultant intensity 

 max he anything from o to n*I/r^, according to the 

 number of wavelets coincident in phase at P, the lower 

 values predominating. If the phases of all the dif- 

 ferent waves are absolutely at random, the problem 

 reduces to a celebrated one solved by Lord Rayleigh, 

 and the chance of a particular intensity J is 



moon's reflected light is yellowish, that of the sky is 

 blue, due to scattering, and is considerably polarised 

 90° from the sun. Between us and the moon there is 

 sky,^ The whiteness of the daylight moon is, in my 

 opinion, an example of case (2)'above, and at the first 

 quarter I find that she behaves to a Nicol in the way 

 already described. I have not previously met with 

 any account of this grand natural example of the fact 

 that a mixture of blue and yellow lights produces 

 white. C. T. Whitmell. 



Invermay, Hyde Park, Leeds, April 15. 



Jr^/l 



In 



VJ. 



It follows simply from the laws of chance that the 

 intensity must be exceptionally great at some points ; 

 the very existence of an average value implies this. 

 If one in a billion molecules is ionised, the ionising 

 intensity works out at 276 times the average intensitv 

 at P. If there is any regularity of structure in the 

 ^aurce. Lord Rayleigh's expression may not do justice 

 ro the higher intensities. 



Thus it is not necessary to assume that X-rays con- 

 sist of neutral atoms, or that the ether has a fibrous 

 structure, or to take refuge in the nebulous phraseo- 

 logy of the quantum theory; the explanation follows 

 Tiaturallv from the principle of interference as ex- 

 pounded bv Fresnel. R. A. Houstoun. 



University, Glasgow, .April 11. 



The Whiteness of the Daylight Moon. 



Water holding in suspension fine particles of 

 mastic scatters a blue light. Place behind the con- 

 taining vessel a yellow surface, (i) If this is bright, 

 its light, transmitted through the vessel, prevails, and 

 we see the yellow. (2) Subdue the illumination of 

 the yellow surface sufficiently, and the water appears 

 white, the yellow and the blue just compensating each 

 other. (3) Subdue the yellow still more, and the scat- 

 tered blue again becomes evident. If in case (2) we 

 use a Nicol, then, for minimum transmission, the 

 white changes to yellow; but, for maximum trans- 

 mission, to blue, because the scattered blue light is 

 lar^elv polarised. 



Now .Nature supplies us on a large scaile with an 

 admirable example of similar phenomena. Suppose 

 the moon to be at her first quarter in daylight. The 



NO. 2582, VOL. 103] 



REFRA CTO METERS. 



A MONGST the physical properties which are 

 •^*- characteristic of a substance, the refractive 

 index is one of the most important. From a 

 theoretical point of view, the fact that refractivity 

 is mainly an additive quantity — the molecular re- 

 fractivity being approximately the sum of the 

 atomic refractivities — is highly sig-nificant. From 

 a practical point of view, the ease and accuracy 

 with which refractive indices can be determined 

 by modern methods are of great service, both to 

 the, physicist and to the chemist, in the examina- 

 tion of the materials with which they have to deal. 

 Whether for purely scientific or for technical 

 purposes, such a determination affords a rapid 

 method of finding the concentration of solutions 

 and the purity of oils, fats, waxes, and foodstuffs. 

 New applications are continually arising in a 

 v^ariety of industries dealing with drugs, sugars, 

 paints, varnishes, glue, gelatine, and other col- 

 loids. The physicist finds the method of service 

 in the identification of optical glasses or in the 

 study of singly or doubly refracting crystals. 



A ray of light passing from an optically dense 

 to a rarer medium is bent away from the normal 

 to the surface, and when the angle of incidence 

 assumes a certain definite value the emergent ray 

 just grazes the common surface. For angles of 

 incidence greater than this critical angle, the light 

 is no longer refracted, but undergoes total in- 

 ternal reflection. The refractive Index, in passing 

 fiom the rare to the dense medium, is the reci- 

 procal of the sine of the critical angle. It is inte- 

 resting to learn that the first to apply this property 

 as a practical method for finding the refractive 

 index was AVollaston, who constructed and de- 

 scribed in the Philosophical Transactions in 1802 

 a critical-angle refractometer, using a right-angled 

 prism as adopted later by Pulfrich. 



In 1874 E. Abbe, of Jena, described the refracto- 

 meter which, as constructed by the firm of Zeiss, 

 has been familiar for the past forty years. 'In 

 this instrument the substance to be examined is 

 placed on the hypotenuse face of a right-angled 

 prism, having one of its angles accurately 60°. 

 When the substance is a solid, optical contact with 

 the prism is made by means of a liquid of higher 

 refractive index than the solid; when a liquid is 

 to be examined, one or two drops are enclosed 

 as a film between two similar prisms. It has been 

 pointed out previously in these columns that both 

 these prisms should' be made of glass otf high 

 refractive index, in order to secure sufl5cient illu- 



