168 BELL SYSTEM TECILXIC.IL JOURXAL 



forming tlic atom consists mainl\- of data about their energy-values. 

 We have a key to the arrangements themselves, and this is pro- 

 vided by the deflections of electrons as they pass throiigii the 

 atoms. .An electron shot directly at an atom will be deflected by the 

 combined actions of the nucleus and the atom-electrons; and by 

 postulating a particular arrangejnent of the electrons \vc could, in 

 principle at least, calculate the deflection. This may be likened 

 to the performance of an astronomer who, observing a comet ad\ancing 

 into the solar systein from outer space, calculates the path which 

 it will follow through the system under the influence of the sim and 

 the major planets, and the direction along which it will depart. The 

 astronomer has the advantages of knowing exactly where the mem- 

 bers of the solar system are, and of being able to follow indi\idual 

 comets. We do not know where the members of the elcctron-s\stcm 

 are, and cannot shoot a single electron at an atom and discern its path. 

 The latter disadvantage is not as serious as it may seem. By 

 projecting an enormous number of electrons in parallel directions 

 against an atom or a la>er of atoms, and measuring the fraction which 

 are de\iated through a given angle or range of angles, it is possible 

 to test a particular atom-model. Assume that the atom po.ssesses 

 spherical symmetry; tlu-ii Uic deflection suffered by an oncoming 

 electron will dejiend onU on a single \-ariable, the minimum distance 

 p from the centre of the atom to the line (extended) along which 

 the electron approaches at first (before the deviation begins). Des- 

 ignating by </) the angle between the initial and final directions of 

 motion of the electron (i.e., the amount of the tleflection), we ha\e 



<A=/(» />=/-' (0) (1) 



liic lunclion / (k'|)cndiiig on the particular aloni-niodcl. Su|)|)(ise an 

 enormous number N of electrons directed normalK- against a thin 

 layer of metal atoms, in which Q atoms lie side by side. The number 

 of electrons which will approach the la>-er along lines passing some 

 atom-centre — any atom-centrt> — at distances greater than a gi\'cn 

 value /> and less liian a slighth' greater gi\cn \alue /)-f-r//>, is 



<IX = XQ-2wl>-,lp (2) 



This is likewise tiie number of electrons which will i)e deflected through 

 angles lying between <t>=fip} and <)>+d4> =f(p+dp) =f{p) + (dj/<l p)dp; 

 which thcrefori' nia\' lie written as 



(IN = NQ • 2Trp{(lp, 'dj)(lf = I'\<i,)d<t>. (4) 



