Minimum Wave Resistance for Dipole Distributions 119 
of the sectional area curve. This rearrangement of the series then resulted in an alteration 
in the sectional area curve from a rebuilding of the series. In two or three cases where this 
was tried there was some improvement in performance, but there were some failures as well. 
In one particular example where a drastic change was made in the sines with the inten- 
tion of completely removing a large hump in the resistance curve, a reversal of the analysis 
gave a sectional area curve with a large hollow in it at or about midships. From the prac- 
tical point of view this was laughable. Yet some work by Prof. Weinblum and others have 
produced such sectional area curves. 
An intriguing thought pertaining to this hollow is provided by the fact that the sectional 
area curve for the model in motion, taking the wave profile into account, can show such 
peculiar hollows. 
I throw these thoughts to the mathematicians in the hope that they may be able to adapt 
their powerful mathematical methods to the daily needs of the less expert practitioners. It 
might be better if these experts could recognize the needs of their humbler brethren — said 
in all sincerity. On the other hand it would be as helpful if we more practical people paid 
greater attention to the more general but more fundamental work of the mathematicians. 
