68 



Mr. C. Chree on the Theory of 



magnitude and direction of the relative velocity of the wind 

 to the plank at its central line. 



V-* 



& 



X' 



V^ 



The figure represents the horizontal plane in which moves 

 a given point in the plank's central line. is the centre of 

 rotation ; x x' the direction the wind blows in. The rotation 

 is from x to y. A, B, C, D represent four positions of the plank. 

 U is the velocity of the wind relative to the plank at its central 

 line. 6 and ^ denote the inclinations of the directions of V* 

 and U to the normal to the plank drawn always in the direction 

 in which the plank moves. The relations 



TJ 2 =Y 2 +v 2 -2Yvcos6, 



v 

 cot yjr = cot 6—^j cosec 6, 



(4) 



hold obviously throughout the motion. 



If the breadth b be very small compared to the distance I 

 of the plank's central line from the axis of rotation, the 

 velocities v and U may practically be supposed to apply over 

 the whole plank. But even then there is one obvious objection 



3C 



