ECONOMIC QUALITY CONTROL OF PRODUCT 371 



by saying that a particle moves at a given instant in a given direction, 

 say AB, because the resultant force of the molecules hitting it in a plane 

 perpendicular to this direction from the side away from B is greater 

 than that on the side toward B ; but at any given instant of time there 

 is no way of telling what molecules are engaged in giving it such mo- 

 tion. We do not even know how many molecules are taking part. 

 Do what we will, so long as the temperature is kept constant, we can- 

 not change this motion in a given system. It cannot be said, for ex- 

 ample, when the particle is at the point B that during the next interval 

 of time it will move to C. We can do nothing to control the motion 

 in the matter of displacement or in the matter of the direction of this 

 displacement. 



Let us consider either the x or y components of the segments of the 

 paths. Within recent years we find abundant evidence indicating that 

 these displacements appear to be distributed about zero in accord with 

 what is called the normal law. That is to say, if x represents the 

 deviation from the mean displacement, zero in this case, the probability 

 dy of X lying within the range x to x -\- dx is given by 



dy = ^^e-^^'l^'^'Hx, a) 



where a is the root mean square deviation. 



Such evidence as that provided by the law of mortality and the law 

 of distribution of molecular displacements leads us to assume that there 

 exist in nature phenomena controlled by systems of chance causes such 

 that the probability dy of the magnitude X of a characteristic of some 

 such phenomenon falling within the interval X to X + dX is express- 

 able as a function / of the quantity X and certain parameters repre- 

 sented symbolically in the equation 



dy=f(X,K\,, ■■■,\J,dX, (2) 



where the X's denote the parameters. Such a system of causes we 

 shall term constant because the probability dy is independent of time. 

 W^e shall take as our second postulate: 



Postulate Z — Constant systems of chance causes do exist in 

 nature. 



To say that such systems of causes exist in nature, however, is one 

 thing; to say that such systems of causes exist in a production process 

 is quite another thing. Less than ten years ago it seemed reasonable 

 to assume that such systems of causes existed in the production of 

 telephone equipment. Today we have abundant evidence of their 



