SOME coNrEMi'OK.iRy .-iDr.ixcns IX rnysics-ii w) 



riu' expressions for p and dp'df arc to 1k> taki-n from equation (1). 

 The I'inirtion 



F(4>) = .\Q-'^^f>i<lp /''<>) (5) 



represt-nts the (iistribiitioH-in-ani'lc of the dcflecteil electrons. If it is 

 ialrulate<l for any particular atoin-nuxlel and then determined by 

 ex(XTiment, the comparison l)ct\veen calculation and data afTf)rds a 

 test of the atom-model. .An instructive comparison can be made 

 e\en if the value of XQ is unknown, since the form of the F-vcrsiis-(i> 

 curve, as well as the absolute height of its ordinatcs, (le[iend?- iii)(in 

 the atom-model. 



Tor electrons or other charged particles of charge e and mass m, 

 streaming with uniform spceil f^ against a group of much more massive 

 nuclei each l>earing a charge E, the functions / and F assume the 

 forms 



/(/>) = 2 • arc cot ( w U"-p V£) (6) 



Fi4>) = NQir{eE/m L-)- cot il<f>) coscc=(^<^). (7) 



This case, insignificant as it may appear, suddenly assumed the 

 greatest importance when, in 1913, Rutherford, Geiger and Marsden 

 established that the distribution-in-angle of alpha-particles (particles 

 of twice the charge and alx)ut 7,500 times the mass of an electron) 

 deflected by metal atoms is of precisely the form (7). This means 

 that around each atom-nucleus there is an empty space so wide that 

 full-speed alpha-particles passing close enough to a nucleus to be 

 dertectetl through 5° or more, undergo almost their entire deflection 

 within it; hence, most or all of the electrons surrounding the nucleus 

 must lie beyonil this vacant central region. From the data of these 

 classiciil experiments, Rutherford and his collaborators deduced that 

 the radius of the empty region encircling the gold nucleus is at least 

 3tiXlO '- cm. After the war, the problem was again taken up in 

 Rutherford's laboratory- in Cambridge. J. Chadwick gave 14X10"'* 

 cm. as .1 minimum value for the radius of the vacant space around 

 the platinum nucleus. Last year P. M. S. Blackett made a statistical 

 study of the deflections of comparatively slow alpha-particles, using 

 the C. T. R. Wilson expansion-method, which was described in the 

 last issue of this Journal. Paths of some of these deflected particles 

 are shown in Fig. 9. By using these slow-moving particles, which 

 begin to turn in their Cf)urscs while still much farther away from the 

 nucleus than the minimum distance at which fast alpha-particles 

 begin to respond to its repulsion, Blackett was able to search farther 



