850 Dr. C. Y. Burton : An Experiment indicating 



accelerations may be omitted from the right-hand side of (1). 

 The forces experienced by m and m' are then seen to be equal 

 and opposite; taken together they form a couple, whose 

 moment about the ^-axis in the sense ^-axis to y-axis is 



= 3^W [ ^ (IJ2 _ V2)+(7?2 _ f)UV + fW(?v _ 7;W)]j(2) 



in virtue of (1). 



17. If we are dealing with a body of uniform density cr, 

 mm' must be replaced by a 2 dx dy dz dx' dy' 'dz', and the 

 component turning moment about the z-axis due to the 

 velocity (U, Y, W) of the body through the sether has to be 

 found by integration. If the body has the form of a 

 rectangular plate whose edges are parallel to the axes of 

 reference, only those terms of (2) will survive the integration 

 which do not change sign with f, or with 77, or with f ; so 

 that the expression for the turning-moment reduces to 



V*t 'W 



uyggg!j|)[|j (y-y') , -( a - a ')' < to ( fy < fe < to'dy' ( fe'. ( 3) 



Let the edges of the plate be a, b, c, and let b : c be small, 

 but a : c not necessarily small : then the approximate value of 

 (3) is found to be 



UY.FV.^^-Tr + ^tan-^ + ^log^-^ + l)-^- 1 ^^ 2 -!)^, (4) 



where M = abco- (the mass of the body) and k = b/a. When 

 b/c is vanishingly small, this expression becomes exact. 



18. The turning-moment about the ^-axis exerted upon a 

 rectangular plate such as that now considered takes the 

 form 



UY.F^.M<7.H, (5) 



where H is a numerical coefficient depending on the ratios 

 a ib : c. When b : c is very small, we find from (4) 



b/a O'l 0-2 1 



H 1 -7575 -6126 



The values assumed by H when b : c and a : c are both finite 

 could of course be found, though not necessarily in finite terms. 

 In the actual apparatus b : c was successively about 1 : 13 

 and 1:17, and the table just given provides values abundantly 

 accurate for the purpose in view. It will be noticed that, 

 when the proportions are fixed, the turning-moment due to 



