ON VORTEX MOTION. 
277 ' 
we should not otherwise have found out, and of which we may 
some day find the application. But as regards the direct object 
in view, the revelation of the actual motion of fluids, the re- 
search has completely failed. And now that generations of 
mathematicians have passed away, now that the mysteries of the 
motions of the heavenly bodies, of the earth itself, and almost 
of every piece of solid matter on the earth have been explained 
by mathematicians, the simplest problems of fluid motion are 
yet unsolved. 
If we draw a disc flatwise through the water, we know by a 
process of unconscious geometrical reasoning that the water 
must move round the disc ; but by no known mathematical 
process could the motion be ascertained from the laws of motion. 
If we draw the plate obliquely through the water we experience 
a greater pressure on the one side than on the other. Now this 
case, representing as it does the principle of action of the screw- 
propeller, is of the very highest importance to us ; and yet,, 
great as has been the research, it has revealed no law by which 
we may in a given case calculate the resistance to be obtained, 
or indeed tell from elementary principles in what way the water 
moves to let the plate pass. Again, the determination of the 
resistance which solid bodies, such as ships, encounter is of such 
exceeding economic importance, that theory, as shipbuilders 
call it, having failed to inform them what to expect, efforts have 
been, and are still being, made to ascertain the laws by direct 
experiment. Instances might be multiplied, but one other must 
suffice. If we send a puff of fluid into other fluid we know that 
it will travel to a considerable distance, but the manner in which 
it will travel and the motion it will cause in the surrounding 
fluid, mathematics have not revealed to us. 
Now the reasons why mathematicians have been thus baffled 
by the internal motions of fluids appear to be very simple. Of 
the internal motions of water or air we can see nothing. On 
drawing the disc through the water there is no evidence of the 
water being in motion at all, so that those who have tried to- 
explain these results have had no clue ; they have had not only 
to determine the degree and direction of the motion, but also- 
its character. 
But although the want of a clue to the character of the 
motion may explain why so little has been done, it is not so 
easy to understand how it is that no attempts were made to 
obtain such a clue. It would seem that a certain pride in 
mathematics has prevented those engaged in these investigations 
from availing themselves of methods which might reflect on the 
infallibility of reason. 
Suggestions as to the means have been plentiful. In other 
cases where it has been necessary to trace a particular portion. 
