276 
ON VORTEX MOTION. 
By Professor OSBORNE REYNOLDS, 
Owens College, Manchester.* 
I N commencing this discourse the author said, Whatever in- 
terest or significance the facts of vortex motion may have, 
is in no small degree owing to their having, as it were, eluded 
the close mathematical search which has been made for them, 
and to their having in the end been discovered in a simple, not to 
say commonplace, manner. In the Royal Institution it is the 
custom to set forth the latest triumphs of mind over matter, 
the secrets last wrested from nature by gigantic efforts of reason, 
imagination, and the most skilful manipulation. For once, 
however, it would seem that the case is reversed, and that the 
triumph rests with nature, in having for so long concealed what 
has been so eagerly sought, and what is at last found to have 
been so thinly covered. 
The various motions which may be caused in a homogeneous 
fluid like water, present one of the most tempting fields for 
mathematical research. For not only are the conditions of the 
■simplest, but the student or philosopher has on all hands the 
object of his research, which, whether in the form of the Atlantic 
waves or of the eddies in his teacup, constantly claims his atten- 
tion. And, besides this, the exigencies of our existence render 
a knowledge of these motions of the greatest value to us in 
overcoming the limitations to which our actions are otherwise 
subject. 
Accordingly we find that the study of fluid motion formed 
one of the very earliest branches of philosophy, and has ever 
since held its place, no subject having occupied the attention of 
mathematicians more closely. The results have been, in one 
sense, very successful; most important methods of reasoning 
have been developed — mathematical methods, which have helped 
to reveal numberless truths in other departments of science, and 
have taught us many things about fluids which most certainly 
* A lecture delivered at the Royal Institution, February 2, 1877, and 
printed here by permission of the author. 
