Nipher — Friclional Effect of Railway Trains upon the Air. 223 



These equations were tested by making observations on 

 fast passenger trains which made long runs at fairly 

 uniform speed. The b;ir carrying the pressure collector 

 was continually varied in position through the limit from 

 to 30 inches as is shown in the following table. In this 

 table the values of the pressure corresponding to the various 

 positions d, are each the means of 87 separate determina- 

 tions. The number of measurements represented in this 

 table is therefore 11 X 87 = 957. 



The values of P, and <V in equation (1) were computed by 

 the method of least squares, since the form of the equation did 

 not easily lend itself to graphical solution. The equation may 

 be put in the form 



pd = a + Pel — d'p 

 where a = Pd' — c. 



The normal equations for a, P and d! are respectively, 



2 pd - 



Zpd 2 



Zp*d 



va — Zd.P + Zp.d' = 0. 

 -Zd.a—Z'i* P + Zpd.d'=0. 

 .2p.a — 2.pd.P + Zp 2 .d' = 0. 



From these equations d' and P were found by elimination. 

 The value of c was then computed from the observations by 

 substituting these values in equation (1). 



