.tfi'i.ic.iiiox (II- si.iiisrn .11. mhiiioiks w 



has .ilriM(l\- lu'on iiidicilnl in I'.ililr III. To iMiiph.isizi- tliis point, 

 howi'vcr, li-t us considi-r oiuv mori> liu- distrihution of alpha particles 

 given in 'ral)li' I. Tlu-so data tD^ji'ther with \arioiis thi-oreticaM* 

 distributions are given in Table \'ll. 



Let us consider the ilata gi\en in Table I b\ following tin- pro- 

 cwlure of analysis outlined in the previous section. The factors k 

 and /3; when Cfunpared with their errors should indicate whether or 

 not the distribution is normal. .\s shown in Table \'I!, k and /ij 

 tlifTer from and '•] respect i\ely, by more than '.i times their respective 

 standard deviations. As has already been pointed out, this is suffi- 

 cient evidence to indicate that the distribution is not normal. In 

 order to show, however, that if we follow the next step and calculate 

 theoretical distributions based upon the assumption of the different 

 laws; that is, in this case, normal, second approximation, and the 

 law of small numbers, wc arc naturalK' led to the choice of the best 

 distribution. This choice is materi.dK' influenced by the measure 

 of the probabilit\' of ht as recorded in the table. The law of small 

 numbers is obviousK- a \er\- close a|>pro,\imatiiin to tiie obsi-rxed 

 frequencies. 



One of the ob\ious things to do in this problem, but one that has 

 not been done pre%iously, is to calculate the N'alues of />, q and «, and 

 from them the terms of the binomial expansion 2()08(/)+7)". The 

 prf)bability of fit between the terms of this expansion and the obser\'efl 

 fre<|ucncies is the highest gixx-n in the table. This increases the 

 e\idence that the distribution is random. It also does nore. It 

 serves to establish the facts that the probability p that an alpha 

 particle will strike the screen is .046, and that the maximum number 

 of alpha particles which may e\-er be expected to strike the screen 

 is of the order of magnitude of 84. (irantcd then that we can always 

 find the most probable theoretical frequency distribution, let us 

 consider next the influence that the result may have in our determina- 

 tion of the most probable \'alue, the number of obscr\'ations betw'een 

 any two limits and the casual relationships go\-erning the distribution. 



Let us consider first the dependence of the most prf)bable value upon 

 the type of rlistribution. In our present work in the study of carbon 

 the resultant distributions have been in most instances either random 

 or such that through a proper transformation they could be reduced 

 to such. F(jr any distribution consistent with the second approxima- 



"Thc source ot all distrihutions previously calculated are indicated. The 

 I'oisson-Charlier series is similar to the tiram-C"harlicr series, except that the 

 law ol small iiumhers is the generating I'luution. It serves as an admiraMe 

 method i>l graduating certain classes of skew distrilmtion as illustrated liy this 

 example and by that given in Table III. 



