194 T. A. Hirst on Ripples, 
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Of these results the first five or six are less trustworthy than 
the rest,—and this for several reasons, amongst which the follow- 
ing may be cited :—The rapidity of the rotation renders the de- 
termination of the position of the cusp more difficult ; the proxi- 
mity of the immersed axis interferes with the clear definition of 
the cusp ; and lastly, the consequences of a small error in esti- 
mating the distance of this cusp from the axis increase as this 
distance diminishes, since the cusp approaches the axis asympto- 
tically (art. 21). On the other hand, the rapid diminution of X 
shown in the Table, can in some measure be accounted for by 
the fact that, in order to avoid disturbing too much the surface 
of the water in the bath, it was found necessary, with rapid rota- 
tions, to use only one jet, and it of course issued at a small angle 
towards the horizon, so that the impact between the jet and the 
water in the bath was necessarily a very oblique one. But, as 
already mentioned in art. 20, the tendency of this obliquity is to 
diminish the velocity }. There can be no doubt that the rapid 
diminution of » in the Table is to be ascribed chiefly to these 
causes ; though it is also worth mentioning that the property of 
the wave insisted upon by Weber, 2. e. that its velocity diminishes 
as its radius increases (see art. 2), would also tend to produce 
the effect observed. 
In the last twelve observations recorded in the Table, two jets 
(or a jet and a cylinder) were used, and the ripple of the vertical 
one was chiefly examined. As a consequence, the values of A 
vary far less, and 7°5 inches per second may be taken as a mean 
value of the velocity with which waves thus produced are pro- 
pagated. 
