4o6 



NATURE 



[April i, 1922 



Worthington, whose name, however, is nowhere 

 mentioned. " These kinetic examples of the action 

 of heat must not be expected to simpHfy the theory, 

 except in so far as they give the mind something 

 definite to grasp ; what they do is to substitute some- 

 thing we can see for what we can barely conceive." 



The Mass Formula of Cathode-ray 

 Corpuscles. 



Verification experimentale de la formule de Lorentz- 

 Einstein. Par Prof. Ch.-Eug. Guye, en col- 

 laboration successive avec S. Ratnowsky et Ch. 

 Lavanchy. (Memoires de la Societe de Physique et 

 d'Histoire naturelle de Geneve, vol. 39, fasc. 6.)' Pp. 

 273-364 + plates 4-6. (Geneve: Museum d'Histoire 

 naturelle, 1921.) 20 francs. 



THIS memoir gives a detailed account of ex- 

 periments made by MM. Guye and Ratnowsky 

 in 1907-9, and by MM. Guye and Lavanchy in 1911-13, 

 with the object of testing the mass-formulae of Abraham 

 and of Lorentz for the cathode-ray corpuscles. Pre- 

 liminary notices of these researches have appeared 

 from time to time, but now they are published in their 

 final form, preceded by a theoretical and historical 

 introduction of twenty pages, whilst twenty pages are 

 devoted to the experiments of Guye and Ratnowsky, 

 and forty pages to those of Guye and Lavanchy ; the 

 whole concludes with a small collection of tables and 

 plates. There are records of twenty - seven experi- 

 ments by Guye and Ratnowsky for the range from 

 /3 = o-2i to /:? = o-59, and of 151 experiments by Guye 

 and Lavanchy from /J = 0-25 to ^ = 0-49. The first 

 series of experiments gives for the excess of the 

 observed mass of the electron above the Lorentz mass 

 a mean value of five thousandths, and for that above the 

 Abraham mass a mean value of nineteen thousandths, 

 with a probable error of about three thousandths ; 

 the second gives for the same quantities two ten - 

 thousandths, eleven thousandths, and one two- 

 thousandth respectively. Thus the evidence of these 

 investigations is strongly in favour of the Lorentz 

 mass formula, in complete agreement with previous 

 researches of similar rank, such as those of Bucherer, 

 Wolz, and Neumann on ^-rays, and of Hupka on 

 accelerated photo-electrons. 



Like Hupka, Guye and his associates used a relative 

 method ; the electric or magnetic force, as the case 

 happened to be, which was required in order to produce 

 a prescribed deflection of a given fast cathode-ray 

 pencil, was compared with that needed to produce 

 an equal deflection of a slow cathode-ray pencil selected 

 as a standard. But whilst Hupka used only the 

 magnetic deflection and relied for the determination 

 NO. 2735, VOL. 109] 



of the speed of his photo-electrons on the measurement 

 of the vacuum tube potential employed in accelerating 

 them, Guye and his associates used both the electro- 

 static and magnetic deflections, not simultaneously, 

 as had been the usual previous practice, but separately 

 and alternately. Thus they eliminated errors due to 

 variations in the state of the vacuum tube, rejecting 

 ab initio all experiments in which sudden changes in 

 its condition were suspected. They avoided the 

 large errors which are almost inseparable from the 

 measurement of very high potentials (of the order of 

 80,000 volts), which completely vitiated Hupka's 

 results, at any rate according to Heil's criticism of his 

 experiments. 



The relative method, or method of " identical 

 trajectories," as Guye and his associates call it, has 

 the advantage of not requiring an exact knowledge of 

 the distribution of the electric and magnetic forces, 

 which, especially for the electric field, is very difficult 

 to determine with sufficient accuracy. Since the speed 

 of an electron is not altered by a magnetic field, we can 

 for two cathode-ray pencils of different speeds make the 

 terminal deflections equal by a proper choice of the J 

 ratio of the magnetic forces at corresponding points, I 

 and so ensure that the trajectories are identical 

 throughout ; then the electro-magnetic momenta 

 (transverse mass x speed) will be in the ratio of 

 the magnetic forces — i.e. of the electric currents 

 generating the field. But for the electric field the 

 equality of the terminal deflections of two cathode-ray 

 pencils of widely different speeds does not guarantee 

 the identity of their trajectories, if only because the 

 electric field generally alters the speed. In the experi- 

 ments of Guye and his associates the changes of speed 

 produced amounted to only a few thousandths of 

 the whole, so that the trajectories were very nearly 

 identical, and the error arising from this cause was 

 negligible. Consequently for two cathode-ray pencils 

 of widely different speeds undergoing equal electro- 

 static deflections the products of their transverse 

 masses into the squares of their speeds could be taken 

 to be in the ratio of the deflecting electric forces — i.e. 

 of the differences of the potential between the plates 

 of the condenser used to produce the deflection. Thus 

 the ratios of the speeds and of the transverse masses 

 of the two cathode-ray pencils could be expressed in 

 terms of the measured ratios of the currents in the 

 magnetising coils and the potential differences of the 

 condenser. In this way the speeds and masses of a 

 number of cathode-ray pencils of various high speeds 

 were compared with those of a pencil of a standard 

 low speed, without the need of finding the distribution 

 of the electric or magnetic fields or the discharge 

 potentials for the high-speed pencils. 



