514 
ON THE TRACTION OF BOATS IN CANALS. 
went over the arguments which had 
been used, and pointed out some of 
their practical relations, — mistaking, 
however, as it appears to us, a remark 
which had been made, that the effect, 
of the friction of the train, as distin- 
guished from the engine, would on the 
whole, be the same, whatever be the 
inclination of the plane ; this assertion 
(made by Professor Moseley) he ques- 
tioned ; not, it appears to us, having 
paid attention to the Professor’s ex- 
planation, that this friction, varying 
in amount, as the co-sine of the incli- 
nation, and its whole effect being esti- 
mated by its amount, multiplied by the 
distance through which it operates, 
that product must, both in the ascent 
and the descent, vary as the product 
of the length of the plane by the co-sine 
of the inclination ; that is, it must vary 
as the horizontal base of the plane, and 
be the same as though the carriage 
were worked along that base instead 
of up the plane. 
The discussion here terminated, and 
Mr. Russell, of Edinburgh was called 
upon to lay before the Section the 
result of certain experiments, made by 
him, on the traction of boats in canals 
at different velocities. The researches 
of Mr. Russell on this subject had al- 
ready occupied the attention of the 
Association, and are published among 
the reports of its last Meeting ; and it 
is one of many instances that may be 
produced of the advantages which have 
been already conferred by it on the 
cause of Practical Science, that the ap- 
probation which was so largely and so 
justly given to Mr. Russell’s communi- 
cation of last year, has encouraged him 
to make these further investigations, of 
which this communication is the result. 
On the general principle, of the resis- 
tance of fluids to bodies moving in them, 
was grounded the conclusion, that it 
would be an impracticable thing to 
move the cumbrous boats upon canals 
at any but very low velocities, except 
by an expenditure of power so great 
that the ordinary methods of conveyance 
by roads would be cheaper. It was 
believed, that the resistance would in- 
crease with the velocity, by a law so 
rapid in its variation, that for two miles 
an hour speed, there would be four times 
the resistance of one mile ; for three 
miles, nine times that of one mile ; for 
four, sixteen times ; and so on, as the 
squares of the velocities. Here, there 
was an obstacle to rapid communica- 
tion by canals, which appeared insu- 
perable. Mr. Russell has shown that 
there is practically a circumstance which 
so completely modifies the application 
of this principle, that when over a cer- 
tain point of speed is attained, the re- 
sistance, instead of increasing when the 
speed is yet further increased, in point 
of fact diminishes. In one of his ex- 
periments, he found, for instance, that 
the resistance to the traction of a canal 
boat, estimated by a dynamometer, 
increased with the velocity of its mo- 
tion nearly according to the law of the 
squares, up to 7| miles per hour, being 
then 330lb ; the speed being then in- 
creased to 8^ miles per hour, instead of 
further increasing the resistance, fell 
to 2101b. The speed was yet further 
increased, and it increased again the 
resistance to 2361b ; yet, less, be it ob- 
served, than at 7| miles ; 12 miles an 
hour brought it to 3521b. Scarcely more 
than the resistance of 7§ mes. These 
results, confirmed by a number of others, 
had manifestly a practical application, 
and they have been applied to the work- 
ing of fast canal boats in Scotland. Mr. 
Russell has devoted himself to the ex- 
planation of them. He states, that 
where the water of a canal is disturbed 
by any cause, as, for instance, the ad- 
mission of a rush of water momentarily 
into one extremity of it, or the impeding 
of a body moving in it, there is genera- 
ted a certain wave, whose motion along 
the canal is altogether independent of 
the nature or velocity of the impulse 
given to it, and dependent only upon 
the depth of the canal ; its velocity being 
precisely that which a stone would ac- 
quire in falling down one half the depth 
of the canal. With this velocity, the 
wave moves uniformly and steadily to 
the very end of its motion, moving 
slower, (if the depth of the canal remain 
unchanged,) but only diminishes its di- 
mensions, until it disappears, and this 
not for a very considerable space. He 
stated, that he had himself followed 
waves a mile and a half, and that they 
had been traced unbrokenforthree miles 
from the spot where they originated. 
The velocity of the wave depending 
on the depth of the canal, it is manifest, 
that each canal, differing in depth from 
another, will have a different velocity 
of wave, and that each part of the canal 
