The Liverpool Standard and General Commercial Advertiser.
Liverpool, Merseyside, England, 1842-09-20 00:00:00

LIVERPOOL POLYTECHNIC SOCIETY.

The general monthly meeting of this society took place on
Tuesday evening last, at the Royal Institution—John Gran-
tham, Esq., the President, in the chair. The attendance
was pretty numerous, and the business of the evening of an
interesting character.

The CH AIRMAN, in a brief address, expressed the pleasure
he felt, after the vacation, to resume the office he had the
honour to fill; and while he lamented the commercial de-
pression that had existed, and still continued to a considerable
extent, and which tended to throw a damp upon scientific
pursuits, he congratulated the meeting on the improvement
that had taken place, and which he trusted would call forth
new exertions on the part of the members to further the
objects of the society. During the recess, the corn mittee had
determined to award prizes, at the close of the present ses-
sions, for communications, &c., of adequate merit. on several
subjects; and in doing so, it was thought advisable, in order
to greater encouragement, to receive communications trom
parties at a distance, as well as from those resident in the
town. He requested the secretary to read the advertise-
ment (published in the beginning of July), which some of
the members might possibly not have seen.
The Secretary read the advertisement, which appeared in
this paper on the Ist of July.
The President then called on Mr. James ,Steel for his
promised communication
" ON THE RESISTANCE OP WATER TO BODIES MOVING
THROUGH IT."
Mr. STEEL then came forward and said, it is impossible to
obtain correct ideas respecting the resistance of water to
bodies moving through it without possessing a clear under-
standing of the laws affecting the generation and destruction
of motion ; to promote which object I shall direct your atten-
tion to the " via inertice" of bodies, by which is understood
the disposition that all matter has to remain in any state in
which it may be placed, whether of motion or rest, in con-
formity to which principle it is held that there is no essential
difference between the action of a body in motion and the
resistance of a body at rest. In case of impact between them,
they both resist ; or as Gravesande expresses it, " A body
in motion resists not while its motion continues, but while 1
it loses motion,—a body at rest resists not while it continues
at rest, but while it is acquiring motion." From this princi-
ple of inertia it is obvious in case a moving body meets with
any obstacle to its motion. The obstacle (of whatever kind)
will give a resistance proportionate to the force of the blow
with which it is struck ; that is to say, if the body in motion
has a velocity of ten feet per second, and impinges on another
body at rest, there will be a given resistance, which resistance
will be doubled provided the velocity of the moving body be
increased to twenty feet per second.
In addition to inertia, there is likewise the cohesiveness
between the particles of bodies which may and does occasion
resistance, both in solids and fluids. Thus, in the case of a
log of wood lying loosely on the ground, and a projectile
being sent against it ; the resistance to the projectile will
depend on the cohesiveness and inertia combined ; for sup-
posing the force of the blow does not separate the particles or
fibres of the wood, the projectile will meet a resistance equal
to the whole momentum of the log of wood ; because as one
particle cannot move without the others, unless separation
take place, and as by the supposition the force of the blow
is not able to effect the separation of the particles, the inertia
of the entire mass will be the resistance to the moving body :
or suppose, again, that the log of wood be fixed in the ground
endways, and a projectile be sent against it, although the
blow would be quite strong enough to overcome the inertia
of the wood, yet, as it is fixed in the ground it will not per-
haps move, and in such case the resistance will be composed
of the inertia of the wood, the inertia of the soil in which it
is fixed, and the cohesiveness between the particles of wood :
and unless the latter resistance of itself were greater than what
the force of the blow could overcome, it is obvious the
motion of the projectile could not be entirely destroyed, as
the wood would break.
Having stated the laws of resistance from inertia, the next
inquiry is—in what manner are we to estimate the compara-
tive resistances of bodies ? and how are we to measure the
forces of various powers?
It is clear that to measure 'any force we must do so by its
effects, and the Newtonian mode of comparing the effects of
different powers is to compare their contemporary effects—
that is, their effects in any given time. (Mr. Steel here
quoted from several authors, expressly pointing out the ab-
solute necessity of estimating time in all comparisons of
powers).
By applying the principles laid down, the resistance of
water to bodies moving through it, becomes a matter easily
understood—because, as the cohesion between the particles
of water is almost, if not altogether, inappreciable, the re-
sistance of water will consist entirely of inertia, the laws of
which are simple, but, from not attending to them, great
difficulties have been supposed to exist in the calculations of
the resistances of fluids, the general principles of which, as
stated by writers on mechanics, is, that the resistances of
fluids to bodies moving through them vary as the squares of
the velocities—because, at double velocities the particles of
water give double resistance,—and further, in the same time
the moving body has to meet with and remove twice the
number of particles ; but it is to be observed that this state-
ment of the law of fluid resistance always supposes that in
the comparison of the resistance at different velocities the
same time is occupied in the experiments, for the Newtonian
theory is expressly based on that supposition, which is fully
stated in Parkinson's Hydrostatics, to the effect that the re-
sistance of fluids (like the resistance of solids) is to be mea-
sured by the quantity of motion acquired by the fluid, or by
the quantity of motion lost by the, moving body in a given
time—and, as the latter is the more easily measured, the re-
sistance of fluids is generally measured in that manner.
It is important to observe, then, that the philosophic theory
is that to produce a double velocity in a moving body. There
must be exerted a power of double intensity which has to be
supplied twice asfast, which is the rationale of the quadruple
theory of the books,* but which theory practical engineers,
and philosophists too, have strangely misunderstood to mean.
That, to produce a double velocity, it is requisite to exert a
power of quadruple intensity having to be supplied twice as
fast, thereby occasioning an absolute expenditure of power in
the same time as 8 to 1, when the velocities are as 2 to 1.
To illustrate this point, Mr. Steel quoted from Mr. Booth's
pamphlet on " the theory and practice of propelling through
water," and from " Gordon, on Elemental Locomotion,"
containing the statement made by Mr. Palmer, before the
committee of the House of Commons in 1825, on the Man-
chester Railroad Bill, and also from the evidence of Mr.
Rastrick, the engineer, as given before the same committee.
This error of the engineers has arisen from the manner of
making experiments, in which weights have been the motive
power—for the engineers' theory has rested on the fact, that
when the same arrangement of machine was used in the ex-
periments at different velocities, there was always required a
quadruple weight to impart a double velocity. Thus, in
Colonel Beaufoys experiments made for the Society of Naval
Architecture, it appeared that when he doubled the velocity
of his boats moving through water, he had to quadruple Lis
weight, and when the velocity of his boat was increased three
times, he had to increase his weight nine times. Mr. Booth
was the first to make experiments in Which at a different ve-

locity of the boat, he altered his machine, and it was matter
of surprise to find a great difference between the results of
his experiments when thus made, and of experiments made
in the ordinary method, and he justly attributed the differ-
ence to the peculiarities of the laws of gravitation, as affect-
ing bodies falling at different velocities, but he had not a just
idea of the quadruple theory, and consequently did not
arrive at a sound conclusion on the matter.
Mr. Booth's experiments were made on a small boat, in a
large trough of water. lie affixed a string to the boat, which
string passed over a pulley at the end of the trough, so as to
keep it always in an horizontal position; and then the string
was carried upwards and passed round a pulley fixed on a
shaft of light wood, upon which were pullies of various sizes.
His first experiment was made by hanging a 21b. weight on a
pulley of the same size as that to which the string from the
boat was attached. The result was—the 21b. weight descended
7ft. Gin. in 6 seconds, dragging the boat the same distance in
the same time.

Everything remaining the same, he substituted an 81b.
weight for the 21b., and then the result was—the 81b. weight
descended ift. 6in. in 3 seconds, dragging the boat the same
distance in the same time.

These two experiments were in conformity with the com-
mon theory—namely, a quadruple weight or power, expended
twice as fast when a double velocity was given to the boat.
How is this to be explained ? Facts never contradict each
other. How, then, is this to be reconciled with the theory
before stated?

It is a fact, that all bodies, if unimpeded, would fall at the
same velocity ; thus, a feather and a guinea, in a vacuum,
fall at the same speed ; but, in the atmosphere, the feather
would fall slowly and the guinea quickly, the difference
being attributed to the resistance of the air. It is obvious, if
the resistance of the air bore the same ratio to the weight of
the guinea as it did to the weight of the feather, that they
would fall at the same rate. From this it is manifest that a
difference of velocity in falling bodies can only take place
when there is a difference of relation between the resistances
and weights. By applying this principle to Mr. Booth's
experiments, the difficulty is cleared up. We find the 21b.
weight gave a certain velocity to the boat, which, by the law
of inertia, would occasion a corresponding resistance, per-
mitting the weight to fall at a definite speed. By increasing
the weight to 81bs. it gave a double velocity to the boat,
thereby occasioning a double resistance in the water ; but
before the boat could attain a double velocity, the weight
would have to fall twice as fast as in the first experiment,
which could not happen unless the relation between the
weight and the resistance were doubled. That is to say, as
the boat, at a double velocity, has to overcome a double
resistance, it will require double power; and as the ratio
between the weight and resistance has also to be doubled
before the weight can fall twice as fast, there will be required
double power for that also, making a quadruple weight (not
power) requisite to produce a double velocity, and to over-
come its concomitant double resistance.

Mr. Booth's third and sixth experiments were made by
causing the string of the boat to pass over a pully twice the
size of that to which the weight was attached ; consequently,
the boat was dragged at twice the speed of that at which the
weight fell. The result was, as between experiments 3 and
6, the same ratio of resistance maintained as between 1 and
2, but when No. 3 or 6 was compared with No. 2, there was
a wonderful difference. In No. 2, it required 81bs. falling
7 ft. 6 in. in 3 seconds to drag the boat 7 ft. 6 in. in 3 se-
conds; in No. 3, it only required slbs. falling 7 ft. 6 in. in
6 seconds to drag the boat 15 feet in 6 seconds, the motion
of the boat being at the same rate as in No. 2; but observe
the weight only fell at half the rate as in No 2, and conse-
quently the relation between weights and resistance were
different, and taking into account that the friction of the
shaft was also different, we have a full explanation of the
whole matter; for, according to the theory now advocated,
a quadruple weight falling the same distance, and dragging
a boat at double leverage, will produce exactly the requisite
conditions of the quadruple theory—that is, a double power
moving at double speed ; but in Mr. Booth's third ex peri-
ment there was only 51bs., not 81bs. To what is the differ-
ence attributable ? Some persons may doubt of the friction
being sufficient to account for the difference as between Bibs.
and 51bs. ; but it is easily shewn to be so. The axle of Mr.
Booth's shaft consisted of half-inch iron, working in a hole
in a prop made of .good ; and there does not appear to have
been any means taken to obviate the enormous friction con-
sequent upon such an arrangement, as, on Mr. Booth being
applied to on the subject, his answer does not mention that
such means had been taken, and as the shaft was made of
light wood, it is reasonable to suppose the prop was of the
same material. It is to be observed that friction is a thing
but imperfectly known ; but there is sufficient known to
assure us that increase of weight upon an axle makes a dif-
ference in the friction, and also that an increase of speed
makes a difference ; and as in No. 2 the weight was Bibs.,
and in No. 3 only slbs., and as in No. 2 the axle turned
round twice as fast as in No. 3, it is evident there must have '
been much more friction in experiment No. 2 than in No. 3.
I am aware engineers have a theory that friction is the
same at all velocities, but it can easily be shown that such is
absurd.

Mr. Steel here quoted from Mr. Booth's pamphlet, Gor-
don, and others, stating this principle, more especially as
referable to railroads, upon which subject he then proceeded.
It is surprising to find men of eminent ability, in the face
of their own every-day experience, adopting such a theory ;
thus it appears admitted on all hands, that supposing the
load to remain the same in a railroad train, it will require an
engine of double power to drag it at a double speed, and as
in the same time the engine will travel twice as far; it is ob-
vious that there will be consumed a quadruple quantity of
steam, because, as the area of the piston will he double, each
stroke will consume a double quantity of steam, and to go
double distance the engine will have to make twice the num-
ber of strokes. It is true, that if you merely estimate the
consumption of steam, while travelling a given distance, that
then the quantity of steam consumed will only be double ;
but that would be to set at nought one of the fundamental
laws of Newtonian philosophy, which is, to estimate various
powers and resistances by their cotemporary effects, that is
to say, by their effects in a given time, in which case railroad
travelling has no advantage over water conveyance, in which
the law is undoubted. " That the resistances at different
velocities is as the squares of the volocities."
But it may be objected to me, if you maintain that it does
not require an octaple expenditure of steam power in a given
time to propel a boat through water at a double speed; how
do you reconcile your theory to practice? for instance, Mr.
Seaward read, to the society of engineers, a table of the
practical results of steam navigation, which approximated
very closely to the octable theory—to this I answer, that a
mere table of results is not of much authority without the
data from which it was calculated; for men of the greatest
eminence occasionally make great errors in calculating the
results of their own experiments; thus, in Mr. Wood's
work on railroads, he gives the table of the power of loco-
motive engines, stating, that taking an engine of given power
it will be able to drag different loads at different velocities,
namely

At 20 miles an hour...
15
PP %I
10
which is exactly the octable theory, because, at 20 miles an
hour, the engine will use twice the quantity of steam it uses
at 10 miles an hour, supposing it to be at work fur an hour
in both cases, and we may therefore take the table as show-
ing that the same quantity of steam at double speed will only
drag one-eighth the weight that it can drag at single speed.
The most surprisir, part of this table is, that it contradicts
the experiments made by Mr. Wood himself, and is in oppo-
sition to every other authority ; for instance, Mr. Rastrick's
table in the British Encyclopaedia, article railroads.
On examining the report of the evidence before the Com-
mittee of the Houie of Commons of 1825, 1 find that both
the promoters and opponents of the Liverpool and Man-
chester Railroad Bill were quite satisfied that on a railroad,
if you applied a given power to a given load, you always pro-
duced the same effect, no matter at what velocity you
dragged the land ; whereas on a canal, if you doubled the
velocity you had to increase the power eight times; and to
prove this position Mr. Palmer calculated a table, which was
handed to the committee. stating the comparative effect in
dragging a load as between a canal and railway. By the
table it appears the canal effect was much greater than the
railroad effect at all velocities less than 4i miles per hour,
but at higher velocities the railway effect was infinitely
greater than the canal effect. Thus the effect of 11b. at 4
miles per hour per canal was 200, per railway 180 ; 11b. at 2
miles per hour per canal was 1,600, per railway 180.
In conclusion, Mr. Steel stated that the great difference
between steam-vessels and locomotive carriages was, that the
fulcrum of the steamer was moveable, but the fulerum of the
locomotive was fixed, there was also a difference in the in-
crease of resistance at high speed from the wave the steamer
created at her bow, and also from the water not closing in
upon her stern as she passed through it, which two kinds of
resistance were denominated by Col. Beaufoy as plus and
minus pressures. On the subject of waves, Mr. Steel read
some extracts from the report made by Mr. J. S. Russell to
the British Association in 183 t and 1835, but as they had no
immediate reference to the laws of inertia, we do not deem it
necessary to quote them.
Mr. Steel was heard with much attention, and was cheered
at the close of his address.
The CHAIRMAN then invited any remarks which gentlemen
present might think fit to make, and a short discussion en-
sued, in which Sir. Booth, Mr. Lord, Mr. Steel, the Chair-
man, and a few others took part, but we have not space to
enter into detail. Mr. Booth supported the accuracy of his
experiments, and Mr. Lord also questioned some of the
positions of Mr. Steel, who explained, and urged with equal
confidence the data on which he had proceeded and the de-
ductions he had drawn from them. The Chairman remarked
(arid this appeared to be admitted by them all) that in the
power required to propel a vessel through the water, much
depended upon the form or model of the vessel's bottom.

20 tons.

vote of thanks was then passed to Mr. Steel for his
communication.

The minutes of the council were then read, and sonic
explanations were given relative to the communications, &c.,
for the close of the year, for which it had been announced
that prizes should be awarded.
The business of the meeting then concluded, and a number
of the members retired to the Committee-room, and partook
of tea and coffee before they took their departure.

* In support of this view Mr. Steel read an extract from
Gravesand's Natural Philosophy, relating his experiments on
the pressure upon bodies at rest, occasioned by water flow-
ing against them at different velocities.
Note.--In Mr. Seward's table, as quoted in Mr. Booth's
pamphlet, he says, that to propel a vessel of 1,200 tons at
four miles per hour, require 30-horse power engine ; at 8
miles per hour, requires 112-horse-power engine ; at 10
miles per hour, requires 250-horse-power engine.
This is either a misprint, or it is a palpable instance of the
fallaciousness of tables—as at 12 miles an hour the engine
ought only to be of 270-horse-power--being 9 times the
power for a treble velocity ; or if we look upon 8 miles as
the initial velocity, then at 16 miles an hour, the engine
ought to be 448-horse-power, whereas at 10 miles an hour it
is put down as of 250-horse-power, which is greatly in excess
of the octuple theory, taking the initial velocity either at
4 miles or 8 miles per hour.

MEETING OF OPERATIVE BAKERS.—Last night a meet-
ing of the journeyman bakers of this town was held at the
Reform News Room in Paradise-street, to take into consi-
deration the propriety of uniting with the Union of the trade
in Ireland and Scotland, as the best means of ameliorating
their condition. Mr. Wilkie was called to the chair, and
after opening the business, introduced to the meeting Mr.
Christopher Whalan, from Dublin, who entered into an
explanation of the movement in the trade in Ireland. He
stated that the operative bakers in Dublin, and the several
larger cities in that country had, after finding that the
monopoly which they had each before adhered to for years
was not beneficial, formed a union for mutual support and
the removal of the evils under which they laboured—and par-
ticularly night-work—and that they had been joined by the
principal towns in Scotland. He drew a distressing picture
of the sufferings of the trade, arising chiefly from the order
of nature being in their case inverted as to the time of labour,
&c.—and as a delegate called upon those present to join with
his countrymen and the Scotch to form a strong national
union, in order to their enjoying the privileges and the
name of tradesmen, which they bad not yet attained in com-
mon with their fellow-tradesmen of other denominations. A
good deal of discussion took place, and resolutions were passed,
to the effect thatit was exnedient the operatives here should join
the Irish and Scotch of the trade, as a branch of the national
union, and pledging themselves to do so. No unfriendly
feeling whatever was evinced towards the master bakers,
and though there was some difference of opinion as to
primary proceedings, the meeting was unanimous on the
main object. It was also understood that a correspondence
should be opened with Manchester, London, and other
towns, with a view to obtain the co-operation of the trade
in those places. Thanks were voted to the chairman, and
the meeting separated.

CORRESPONDENCE.

EDINBURGH AND GLASGOW RAILWAY.

TO THE EDITOR OF THE LIVERPOOL ST.ANDABD.

SIR,—My attention has been directed to an article in your
paper of this morning, headed as above, which has caused
me, as a party deeply interested in the undertaking, much
regret; inasmuch as it is so glaring an attempt to puff up
the concern, that it cannot fail to do it an injury with the
public. The Edinburgh and Glasgow Railway, I believe.
needs no such artificial means to enable it to take that place
in the public estimation which it deserves; but if share-
holders, or others, are weak enough to believe that it is going
forthwith to pay a dividend of seven pc•r cent, they are
doomed to experience bitter disappointment. The following
estimate may be taken as a somewhat nearer approximation
to what may be expected as the result of the present hall-
year's working, and if it should be borne out, 1, for one,
shall be well contented ; satisfied, as 1 am, that the elements
of future gradual improvement exist on the line to as great
I an extent as on most others of the most successful of our
railways. From " A Shareholder's" statement of the re-
ceipts to the 10th inst.
deduct error discovered in the week ending the 3rd
instant, about 420

will leave 29,859
to o hich add, for seven weeks in September and
October, an average of £2,100 per week..
and for nine weeks subsequently £l,BOO per week 16,200

making a gross revenue, for the half-year, of 60,759
In estimating the expenses for the same period, we have
nothing to guide us but the result of the first four months
working, which is hardly a sufficient datum, as it is fair to
infer that the percentage will be less upon an increased re-
ceipt ; but let us err on the safe side, and assume that as a
rule. The working expenses during that period were 33 per
cent. on the gross receipts, including a mileage duty exceed-
ing seven per cent. thereon; this being now reduced to five
per cent. on passengers only, will be not much short of three
per cent. in favour of the company, and will be more than
sufficient to cover income tax, and some trifling charges
heretofore charged to capital account; therefore from £60,759
deduct 33 per cent. or

deduct also interest, estimated at .

40,709
.......... 11,G00

add balance on hand, 30th June..

29,109
1,449

will give a nett revenue of
from which deduct dividend orklB,ooo shares of £5O
each, at three per cent...
will leave a clear surplus of 3,558
to carry over to 1843.

Beliving, as I do, that the traffic is susceptible of a great
increase, I am under no apprehension as to the above rate of
dividend being maintained, and in time augmented ; and I
look upon the prospect as sufficiently flattering to induce
those who can hold their shares to do so, until they can
obtain a price more commensurate with their intrinsic value
than that now current ; at the same time, let it not be for-
gotten that they are not much lower, relatively, than the
shares in other undertakings which have stood the test of
experience ; and it is expecting rather too much to call upon
the public to give the value of a seven per cent. dividend,
for a stock which as yet has paid but five per cent. People
begin to be tired of discounting large anticipated dividends,
and puffing is nearly exploded.
16th September, 1842. PATIENCE.