494 Dr. T. H. Havelock. 
one due to the bow and stern systems. This follows on general grounds, and 
might be represented analytically as in §4, but it is worth while examining 
other distributions with this character. 
In the first place consider one which does not give the desired interference 
effect, namely, 
pecs 
E+ a? ‘ 
The graph has been drawn for certain numerical values of the constants 
and is curve A in fig. 1. 
P (16) 
1) tee 
We have x= | goat = tmAe~*. 
Hence, from (7) and (8), 
¢=0; sp = wAc*; 
gpR = x? Ate 2, (17) 
We have here the same form for R as a function of vas in(11) for the single 
hump of positive pressure; we do not get the interference effect which might 
have been expected. This may be explained by remarking that the pressure 
falls away from the maximum only slowly; in other words, the hump and 
hollow are not sufficiently pronounced for their individuality to show 
directly in the final formula. In the previous section, where the distribu- 
tion is 1/(£#+ «*) instead of &/(E?+), the maximum and minimum are more 
pronounced and we get a typical oscillating term in the final result. This 
view may be confirmed by another example. 
6. Consider 
AE 
p = Fda (18) 
This distribution is graphed in curve B of fig. 1, arranged so as to have the 
same minimum and maximum as for (16); the curves A and B illustrate 
99 
