British Association for the Advancement of Science. 283 
cent., the difference between the two years being, on the total ship- 
ments £5,996,301, and on the shipments to America £1,857,150. 
Without admitting or denying that these figures give evidence of 
over-trading, he called attention to the circumstances of the two 
people—namely, that the means of obtaining the comforts of life are 
enjoyed by a larger proportion of them than is the case with any 
other people; that the habits and predilections of the citizens of the 
United States lead them to give a preference to British goods; that 
ours is the cheapest market in which they can procure many arti- 
cles necessary to them ; and that we are, out of all proportion, their 
best customers for the raw produce of their soil; and he asked 
whether, if the trade of the two countries were put upon a prop 
footing, and conducted upon enlightened principles, that amount of 
traflic could be considered excessive which gives annually to every 
citizen of the United States articles of British growth and manufac- 
ture to the value of sixteen shillings and ninepence three farthings ! 
On the Mechanism of Waves in reference to Steam Naviga- 
tion.—Mr. Russell had, at previous meetings of the British Associa- 
tion, given an account of his investigations on the resistance of fluids 
to the motion of vessels, and ascertained the law of interference of 
the wave in modifying the nature and amount of that resistance. 
Since the last meeting of the Association he had extended his obser- 
vations to a variety of subjects of practical importance, and amongst 
others to the improvement of the navigation of such rivers as the 
Thames and the Clyde, in which steam navigation was extensively 
employed. In these rivers it was found that steam navigation was 
conducted under very great disadvantages when compared with the 
open sea. Mr. Russell had discovered that in shallow water one 
great impediment to high velocities was the generation of, what he 
termed, the great wave of translation of the displaced fluid,—not 
undulation of fluid, but translation of one part of the fluid, reaching 
to the whole depth with equal velocity. When the vessel is pro- 
pelled, the water heaped on its side generates this great anterior 
wave of translation, which increases as the velocity increases ; the 
section of displacement of water is increased in the ratio of the sine 
of inclination. In one instance, where the depth was five feet, the 
anterior wave was three feet above the level of the water, so that 
‘the bow was buried in it, and when the vessel stopped the wave 
moved at eight miles an hour, and though the vessel drew but 
twenty inches water, her helm was knocked off. This anterior wave 
