258 Mr. W. G. Adams on the Application of the 



To find the accurate values of the integrals of these functions, 

 suppose a is one of the angles for which the value is known, 

 then we must integrate for the variable angle 6 between the 

 limits -f2J° and — 2J° on each side of a, and then add the 

 results of the integrations. 



Let 6 = cx + a i 



where c is the circular measure of 5°, so that the limits for x 

 are +.\ and —J. 



If/ ; (0) and/ i; (0) be the mean of the first differences and the 

 second difference corresponding to one of the values of «, then 



/W=/(0)+^(0)+|/,X0); 



therefore 



J. 



/(«)<fc=*/(0) + |//0) + ^/„(0), 



/(*).c.«fe = c{/(0)+A/ ll (0)}. 



The sum of the second differences (which is the same as the 

 last of the first differences) divided by 24, 



= — '002666 for the resistance, and 

 = — '001366 for the moment. 

 Hence the correction for the resistance 



= - -002666. c, 

 and the correction for the moment 



= -•001366. c; 

 therefore the resistance becomes 



£ftfi>V . c{5'884150--002666} 

 =ip i o) 2 r 4 xc(5-881484) 

 = i/o i ®V x '513256 = i/3a) 2 (rad) 4 x -101384, 

 and the moment becomes 



JftwVc {6-577423 -'001366} 

 = J^ft>V. ex (6-57605 7) 

 ssJpjoV x •573869 = ip / t» 2 (rad) 5 x '075572,— 



the resistance and moment being expressed in powers of the 

 radius of the wheel for the sake of comparison with the resist- 

 ance and moment on a flat float. 



Now considering the resistance and moment on a flat float 

 where the radius of the wheel and the length and breadth of 

 the float are in the ratio of 10 : 6 : 3 respectively. In this 

 case the resistance on one float 



