.//■/'/./( .///(».v or sr.iiisTii .11. mi. limits 51 



Wiiv Do W'v. Ni:i:i) to Know tiik I.wv ok Dkviation ok tiik. 

 nii-i-i:Ri:Nr ()hsi:k\ Aiios-i Anon So\ii; Mi;.\n \ai.i i:' 



In all of tlio alH)vi' pri>l)K'ins as in mery physical and enninocrin^ 

 oiu'. certain t>pical ciucstions arise which can he answered only if we 

 know the law of distrilnition v=/(.v) of the ol)ser\'ations where v 

 refiresents the fre<|uency of occurrence of the deviations .v front some 

 mean value. At least three of these queslions are the same for both 

 fields of investigation.* 



Let us consider the physical problem. From a group of n observa- 

 tions of the magnitude of a physical quantity, wc obtain in general n 

 distinct values which can be represented by A'l, A's, . . . A'„. From 

 a study f)f these we must answer the following questions : 



1. W hat is the most probable value? 



2. What is the frequency of occurrence of values within any two 

 limits? 



3. Is the set of observations consistent with the assumption of a 

 random system of causes? 



The answers to these questions are necessar\- for the interpretation 

 of Prof. Rutherford's data referred to above: They are recjuircd in 

 order to interpret the data presented in Fig. 1 which are typical of 

 physical and chemical problems arising in carbon stud\'; these same 

 answers are fundamentally required in the analysis of all physical data. 

 These queslions can be answered from a study of the frequency dis- 

 tribution. If this be true, it is obvious that the statistical methods 

 of finding the best distribution are of interest to the physicist. 



Let us next consider the engineering problem where we shall see 

 that the same questions recur. Assuming that manufacturing 

 methods are established to produce a definite number of instruments 

 within a fixed period, one or more of the characteristics of these 

 instruments must be controlled. We may represent any one of 

 these characteristics by the symbol A'. The total number of instru- 

 ments that will be manufactured is usually very indefinite. It is, 

 however, always finite. Even with extreme care some variations 

 in the methods of manufacture may be expected which will |)r(i(!u(r 



' In (irdcr to caliliratc the machine referred to in a prccciling paiaKrapli 

 and also to determine the relationships lictwccn the physico-chemical and micro- 

 phonic properties of carl'on, it was necessary f) study the correlation between 

 two or more varialiles, luit in each case it was necessary to determine first the 

 law of distriliution for each varialilc in order to interpret the physical siKniti- 

 cance of the measures of correlation liccause this depends upon the laws of 

 distribution. The reason for this is not discussed in the i)resent paper, for 

 attention is here confined to the method of establishing the best theoretical 

 frequency distribution derived from a study of the observations. 



