44 BELL SYSTFAI TECHNICAL JOURNAL 



With the introduction of the molecular theory and the theory 

 of quanta, it has been necessary to modify some of our older con- 

 ceptions. Thus, more and more we are led to consider the problem 

 of measuring any physical quantity as that of establishing its most 

 probable value. We are led to concei\e of tlu' physico-chemical 

 laws as a statistical determinism to which "ihc law of great num- 

 bers" ' imparts the appearance of infinite precision. In order lo 

 obtain a more comprehensive understanding of the laws of nature 

 it is becoming more necessary to consider not only the average value 

 but also the variations of the separate observations therefrom, .^s 

 a result, the application of the theory of probabilities is receiving 

 renewed impetus in the fields of physics and physical chemistry. 



Statistical Nature of Certain Physical Problettis. .As typical of the 

 newer type of physical problem, we may refer to certain data given h\- 

 Prof. Rutherford and H. Geiger.'- In this experiment the number of 

 alpha particles striking, within a gi\en interval, a screen sulxending a 

 fixed solid angle was counted. Two thousand six hundred and eight 

 obser\ations of this number were made. The first column of Table I 

 records the number of alpha particles striking this screen within a 

 given interval. The second column gi\es the fre(iuenc\- of occurrenci- 

 corresponding to the difti-renl numbers in the first cdliimn. 



No. of .■Xlplia ()l)served Frequency 



Particles of Occurrence 



"i 



1 20.5 



2 .58.? 



3 52.S 



4 .x52 



5 4(),S 



6 27.5 



7 1.5'> 



8 4.S 



9 27 



10 10 



11 4 



12 



13 1 



14 1 



ll is (ili\i(iusK impossible from tiie nature of the exi)eriinent to at- 

 tril)iilc tile xariatidus in tlie c>l)scr\ed numbers to errors of obserxa- 

 licin. liistr.id, the xariations are inherent in the statistical nature 

 of the jjlienomenon under observation. 



' Each cl.iss of event eventually occurs in an ai)i)arcntly dctinitc iiroportiun 

 of cases. The constancy of this proportion increases as the numlier of cases 

 increases. 



" I'liilosofhUal Magacinr, Octol.er, 1910. 



