KINEALY — PRESSURE OF THE WIND ON ROOFS, ETC. 339 



Letting the right-hand member of the equation be represented 



by y, we have sin / = e-^, where e is the base of the Naperian 

 system of logarithms. 



Expanding this expression, we have 



Sin/=I J^y-\-^-^^-{-8LC. 



Throwing away all of the terms but the first and second of the 



right-hand member and reducing, we have as an approximate 



result — 



cos I 



1.842 



sm t =z ^, 



I — cos- 2 



Solving this equation by trial, we find that IV will have its 

 maximum value when t is about 6S°. 



These results given by the formula are incompatible with good 

 theory, for the impulse of either a limited or an unlimited stream 

 upon a plane inclined to its direction. The impulse of wind on 

 a roof may be considered as that of an unlimited stream upon a 

 plane surface of the same area and inclination as the roof. 



According to Weisbach, if A is the area of a surface impinged 

 upon by an unlimited current whose density is d and velocity v, 

 the impulse on the surface when it is perpendicular to the direc- 

 tion of the current is 



_ K v^ Ad, 



where A' is a constant to be determined by experiment, and g" is 

 the acceleration due to the force of gravity. 



According to Duchemin, when the surface is inclined at an 

 acute angle / to the current, the impulse in the direction of the 

 current is 



Tj ICv^Ads'xn'^t 



■^ ; i '• 9 rr (See Weisbach's Mech.) 



^(i +sm- i) 

 Dividing this expression by the former, we obtain 

 2 T'sin^ i P 



R = 



I -j-sm^ / I -j- cot^ i 



2 

 7? in this formnla represents the horizontal compone7it of the 



