MR. Ct. T. walker on BOOMERANGS. 
27 
ratio 1:5 or 1:6 as deduced from experiment, then the couples XU®. cf and 
should be the same. This would give a value of k varying from point to point. We 
therefore, for convenience, treat k as constant, and give it the magnitude corre¬ 
sponding to the mean value of c. 
.It must be realised at the outset tliat the following analysis does not claim to be. 
more than a first approximation, in which the quantities neglected may be of a 
tenth of the magnitude of those retained. Our knowledge of the laws of the resistance 
of the air is not at present great enough for accurate results to be attainable, and I 
have accordingly not hesitated to neglect small terms in order to eflFect a material 
simplication in the mathematical analysis. 
It may appear that such processes reduce the method to little more than a 
qualitative one, but though much may be done by qualitative methods applied to 
this subject, and all the chief terms may be traced to their .source without the use of 
algebraical symbols, yet, as will soon become clear, the effects of the forces in action 
are conflicting. It is therefore necessary, in order to obtain results which are 
qualitatively right, to adopt methods which, although not accurate, have at any rate 
some approach to quantitative correctness. 
We now take axes fixed in the body, 1 and 2 being along and perpendicular to the 
axis of symmetry in the primary plane. 
Fig. 4. 
If the velocity at any point xyz have components v, iv, and the direction cosines 
of the normal on the convex side there be /, m, n, then the normal pressure in the 
direction — — m, — n will be 
{lu -j- mv -f mv), 
where I, m, iv are small quantities and cf = + n- fi- 
The couple per unit area will have moment 
{I u -{- '>xiv -{- nw) 
about an axis whose direction cosines are 
E 2 
