,33^ TRANS. ST LOUIS ACAD. OF SCIENCE. 



direction of motion, and R the lesistanee when the plane is in- 

 clined at an angle i to the direction of motion. 



If then R^ /'(sin i) ' "^ is the expression for the 



horizontal component for the pressure of the air on the plane, the 

 normal pressure, JV, on the plane is 



__ R r^w . .X 1.S42 cos / — I. 



sm z ^ ^ 



This is the formula given by Unwin, and used by him to cal- 

 culate the table of wind pressure on roofs published in his book 

 on "Iron Bridges and Roofs." 



This formula JV=z P (sin i) ''^^^ cos z— i ^.^^^ ^j^^^ ^^^^^ 

 to be some very peculiar results. 



It is evident that N is equal to P when 



, . .. 1.843 cos i — I, 



(sm I) ^ — I5 



, , . .. 1.S42 cos z — I, , .,, 



and (sin t) ^ — i^ when eitlier 



sin / =: I , or when i .843 cos i — • i zir o, 



sin / =^ I when i = 90° ; and 1.842 cos / — 1^0, when 



'^^^ '= 1784^ °^' ' = 57° lo'- 



In other words, the formula says, the normal pressure on a 

 surface inclined at an angle of 57° 10' to the direction of the wind, 

 is the same as it would be if the surface were perpendicular to the 

 direction of the wind. 



If the surface is inclined at any angle between 57° 10', and 90° 

 A'' will be greater than P. Since for all such angles 1.843 cos i 



— lis less than zero, and sin /, in the formula, has a negative ex- 

 ponent ; and as sin i for any value of i less than 90° is less than 

 unity, A^ becomes equal to P divided by a fraction. 



From what has been said, it is evident that TV has its maxi- 

 mum value for some value of i between 57° 10' and 90°. 



Differentiating the expression for A" with respect to z, and put- 

 ting the differential co-efficient equal to zero, we obtain the equa- 

 tion 



— 1.843 (sin i) ^' ^^ ^'^^ ^ log sin i -\- (1.842 cos i — i ) cos i 



, . .. 1.842 cos / 3 



(sm I) ^ =0, 



, . . 1 .842 cos^ i — cos t 



whence log sm z = — 5 -, ^^t~ 



^ 1.842 (I — cos- t) 



