250 UNIVERSITY OF VIRGINIA PUBLICATIONS 



velocity increases the value of m diminishes becoming more nearly con- 

 stant as in the case of short pipes, the resistance head becomes more and 

 more nearly proportional to the square of the velocity with increase of 

 velocity. 



We write in view of careful consideration and with the effort to use 

 a rational form 



^4= -^ (11) 



l + hV+t'- ^'• + '« 



r 



6. The complete form of the coefficient of resistance M we assume to 

 be of the type 





Vr-\-q 



+ !;> (12) 



1 _i_ ^^ \ Q^^ L 



V yr +B 

 r 



all letters being constants except V, r and L. 



In the previous paper referred to at the beginning of this article the 

 writer proposed for the form of m the expression 



'"^l+aF + ar (13) 



This has a wider range than Darcy's form and may be considered a 

 next approximation. The form (12) has a much wider range than (13) 

 and it is believed that the sequel will show that it is more precise and 

 comprehensive than any form hitherto proposed. 



7. The determination of the constants and the forms of the functions 

 of V and r which occur in m must be carried on hand in hand. The in- 

 vestigator meets with much discouragement over the discrepancies in 

 the reported results of experiments. It is only when large numbers of 

 experiments are massed and tabulated that law and order appears beyond 

 the first crude approximations. There are not as yet available any series 

 of experiments through continuously graduated sizes and velocities for 

 a single particular pipe construction to justify conclusions drawn from 

 this particular style of pipe alone. One has to consider the mass of evi- 



