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ANIMAL 8. We might now proceed immediately to the appli

ANTX STRENGTH. cation of the preceding formulæ, but it may not be

Numerical values of V (A - B) in the amiss, in the first place, to say a few words relative

Angle of inclination Effect of

equation v' =VnXV (A - B)..

of the plane to the centrifugal to the centrifugal force which takes place in the motion.

horizon. force. In order to conceive this effect, it must be observed,

When ascending.

When descending.
that the centre of gravity describes a curve, which
has for its radius of curvature the leg on which we


advance in walking. Let us denote this radius of


curvature by r, the velocity of the centre of gravity by


', and the centrifugal force by f. We have, therefore,


by Dynamics,






and, if we suppose the centrifugal force equal to gra-


vity, we shall have


f= 2 g (P + 4);




= 2g, or TV 2 gr.



The radius of the curvature is equal to about 2 feet


in a man of the most common size, therefore


v=V (30.196 x 2.5) = 8.6884 feet.


Whence we may draw the following conclusion, viz.


that a man who runs 9 feet per second, ceases entirely


to gravitate on his feet, which is conformable to what
Mr. Lambert has observed ; that is to say, that a person
running with the above velocity, remains so long in the 11. It is now only necessary to determine, from a Esperi
air, that the feet act only as they push, as it were, the course of experiments, the numerical value of n. mental
earth behind them, and have little or no effect in sup- M. Prony states, that he has frequently observed that suks.
porting the body.

a man without a load can walk on a plane nearly hori9. Let us now consider the case of the formula zontal, without fatigue, 6,000 feet in 20 minutes, viz. P + k

about 5 feet per second ; we have, therefore, in this n A B

case, 1 = 0, v' = 5; and the equation when the fatigue is the least; that is, when the effort

u = V (n X (A - B)) which a man employs in walking is sensibly the same becomes 5 = Nnx 3.8856; as that which he is able to continue without walking.

25 This condition will give k = 9, and the above equa


= 1.6559.

15.098 tion becomes

And n = 1.2868, a number by which we must n'= {n (A – B) }

multiply those in the table, in order to have the veWe may calculate, by means of the table (art. 7), locity corresponding to any proposed angle of inclinathe values of (A — B) for different inclinations of the tion. plane, agreeably to the above hypothesis, and thus Lambert has observed, that he employed, without form another table, which shall exhibit the value of n; making any uncommon effort, 13 seconds in ascendfor when A - B is known, we shall have immediately ing a ladder of 24 steps, to the height of 134 Rhenish

feet, and the angle of its slope 37°1: This gives us A - B

an hypothenuse = 21 French feet, which, divided by It is to be observed, however, that the expression 13, gives v' = 1•64 feet. A - B has only been considered, at present, as it ap 12. Now supposing it had been proposed to deter-Axa plies to the case of a man ascending; when he de- mine this velocity from the preceding table, we should of the i scends, sin 1 becomes negative, and B changes sign. have assumed 37°ļ as an arithmetical mean between Such a table, therefore, ought to exhibit two values of 350 and 40°: our tabular number would therefore have. n, one for each of the above cases.

been ):3183, which, multiplied by the above constant

value of n n = 1.2868, we should have found TABLE II. Table of ve 10. For calculating the velocities, corresponding to

r' = 1:3183 x 1.2868 = 1.696 feet; locities corresponding

different inclinations of a road, when the effort of a man which differs as little from the preceding experimental to different upon it differs not sensibly from that necessary for him to deduction as can be expected in cases of this kind. ascents. continue to the end without walking.

13. It appears, therefore, that the value n = 1.7 is

very nearly conformable to experiment, and that n = 2, Virgil was not ignorant of this fact; he says, when speaking as assumed by Lambert, is a little in excess. He deof a certain warrior,

rives this value of n by supposing that a man, jumping “ Illa vel intectæ segetis per summa volaret

vertically, with all the force he is capable of, without Gramina, nec teneras cursu læsisset aristas Vel mare per medium, fluctu sospensa tumenti

a load, can raise himself 2 feet; which is perhaps Ferret iter, celeres nec tingeret æquore plantas.” rather too much for the medium strength of mer.


n =



2 ng



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ANIMAL NMIL M. Lambert has computed a table analogous to the ascending a plane, of which the inclination was equal RENGTH. preceding, assuming n = 2; we, however, prefer to the angle formed by a tangent at that point of the

leaving this quantity indeterminate, till it shall be circumference where he is placed. It follows, therefore,

ascertained from a mean of various experiments. from what is stated above, that the most advantageous termina 14. By inspecting the descending velocities in position of that tangent will be, when it forms an angle ooi the Table II. it appears that the greatest velocity is that of 24° 6' with the horizon, in which case, the effective RELALU corresponding to 15° of inclination. But, in order to weight employed in turning the wheel, will be bacity: find the precise angle which gives the maximum velocity,

P sin 24° 6' = 0.40833 P, we must put our equation

P denoting, as before, the weight of the man. dʻ = {n (A + B)}?,

Let P + Q be the greatest effort of which a man is 2 ng sina

capable; the effort Q may be augmented by habit and

exercise, and it is liable to diminution by inaction; it 2 (1 + 3 sin’X) (1 + 3 sin’A) 3

will also undergo some modification when either great into fluxions, and equate it to zero, which will give loads are to be listed, or great swiftness is required ; 7

but in all cases the application of the effort P + Q can
sin' l =
– sin’ of 12° 44';

be only instantaneous; that is, being the greatest the

man is capable of, it can be exerted only for a moment, whence the angle answering to the greatest velocity is whether it be employed in listiog a great weight, or in 12° 44', and the corresponding value of v' is found running with a great velocity: to be 6 feet per second.

17. A man who is not loaded with any weight, whe- Time in 15. The second column of Table II. which appertains ther he merely stand upright on his fect, or walk with which the to the velocity of ascent, presents neither a maximum nor a minimum; we may, however, still arrive at either and in the first instants the force Q will remain to him out using any effort, employs, at first, only the power P, strength is

exhausted. by having regard to the time. Suppose we go from entire; but in either of the above cases this power Q one point to another in a right line, the second being will, after a time, be weakened, and will ultimately be higher than the first by a given quantity H; and if extinguished; let the time from the beginning to the denote the angle of the inclination of the road, the latter event taking place be called T. Let us suppose, H

now, that instead of the power P, the man from the length of it will be sin

first instant employed an effort P + K; there will then, Let + denote the time, and rʻ the velocity; then we which will also be extinguished after a certain time t,

in this case, remain to him a quantity of force = Q-K, shall have to find

and it is an important question to decide the ratio of

the times T and t, when the powers Q and K are given.
- a minimum,
r' sin

Lambert conceives that it is not far from the truth to or since H is constant,

assume that these times are proportional to the residual

forces, viz. by assuming that
o sin = a marimum.

T:t::Q:Q - K,
Substituting for rʻits general value given in (art. 16),

Q - K equation (3), we shall have

which gives t =

P + k
2 n g sino

This time t, being that which has passed from the

moment the man began to walk till he can, from fatigue, mar. Which being put into fluxions, and reduced, gives walk no longer, it is evident, that at this instant, he (P + k)

has passed over the greatest possible space, and con-
sino =
9 (P + 1 - 3 (P + h)

sequently that the product s = it will be a maximum.

Now we have
This result shows that the inclination which corre-

P + K
sponds to the minimum of time necessary to ascend a
given quantity, varies with the relation between the force
that we employ and the load we have to carry. Again, and multiplying this value of v' by the above expres-
since sin ?x is necessarily less than 1, we shall have sion for t, and equating the fluxion of the result to zero,
(P + k) < 9 (P +9) – 3 (P + k), or

we obtain the following values, viz.
4 (P +- k) < 9 (P + 9)?, or

2 B
2 (P + k) < 3 (P + 9).
K = } (Q – 2 P) + (P + I),


ЗА If we suppose k = 9, the above equation gives

2 B P + K = }(Q + P) +

(P + 9),

(6) sin =, or X = 24° 6';

ЗА wherefore, when a man employs in ascending, an effort


B necessary only to preserve himself erect, the most ad

(6) vantageous inclination, or that by means of which he

(P + Q) A (P + 9) B will soonest arrive at the given height, is 24° 6'; and

3 T

(1) the corresponding velocity to this inclination will be

AQ ect of a found 24 feet per second.

By means of these equations, the load , and the 16. A man employed in a walking-wheel, as in some inclination of the road being given, we shall know the Eing.

old cyanes, &c. is in similar circumstances as if he were effort P + Ķ necessary, in order to render o't, or the


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A – B) };

P +9

d' =

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in a

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P +9

mass a

ANIMAL space 8, passed over before the forces are all spent, a

Cf x AC

ANIMAL STRENGTH. maximum. We may hence also determine the mean



AE resulting velocity of this effort, and the time which passes, before fatigue prevents the man from walking the effort necessary for holding the arnı straight Call

Let us assume Ei=f: we have then f to represent any longer. Particular 18. It will be observed, that the quantity n does not

the angle AC g = y, and the weight Cg of the value of Q. enter into the formulæ of the preceding article, but, in

man =P; and we shall have
order to apply them, it is necessary that we determine

dg = Cf=P x tano,
either by hypothesis, or experiment, the quantity Q, or which, substituted in the preceding equation, gives
the greatest effort that a man can make beyond that

necessary for supporting his own weight. M. Lambert


P x tan o. supposes P=Q, which changes the above formula

AE into the following:

The medium proportions of the body of men, in general, 2 B

P + k = (P + 9),


= }; whence


f= P x tano

21 If we call f the greatest effort of which the 2 PA - (P + 9) B

arms are susceptible, T' the time necessary of con-. t=fT AQ

(c) suming this effort, and the time necessary for anniBy this means, there is now remaining only the quantity reasons to those given above, the equation

hilating the effort F-f, we shall have, for similar T to be determined experimentally, and it is, of course, subject to certain yariations according to the age and ·


T. activity of a man, his natural strength, and the habit

F acquired by practice. We may, however, without any The component Cd representing the action on the remarkable violation of probability, assume that, a man point A, which is subject to no diminution, ought to be without a load can continue walking for twelve or four

P teen hours in a day; from which assumption, the value estimated by its constant value which is the efof T becomes determined.

cos Velocity 19. Every particular load q requires a particular fort made by the man to hold himself erect on his feet; into the

velocity, in order that the man may pass over the greatest we have, therefore, maxinium. space possible before his strength is exhausted; for this

we must have

= P + 9;
og = 9

a marimum. .

that is to say, it will be the same here as would be

excited by a man carrying a load q. P+Q v* q° = q* (HA 1 B) a maximum. We might now proceed to reduce these equations to

the best practicable form for solution, as we have done Putting the second side of this equation into fluxions, in the preceding part of this article, and to consider regarding q as variable, and equating it to zero, the the effort of men employed in drawing loads, &c. but value of 9 will be determined; but those values of a we are fearful it would carry us beyond the limits that which exceed Q, it is obvious must be rejected. can be assigned to this article; we must, therefore, refer 20. Let examine now the case where a man pushes,

the reader who is desirous of pursuing the subject to a or draws; and suppose, at first, that the path he has to greater length to Prony's Architecture Ilydraulique, where go over is horizontal, as also the direction in which he will find many important analytical results. his exertion is made. (Fig. 2, Plate V, Miscella Experimental researches respecting animal strength. neous) may represent the attitude of this man

22. We have already had occasion to remark, that Expenfor the moment that he supports himself on the leg CDB. In this attitude there are two points of purely analytical investigations are of little use in such support, the one at A, the other at K: the arm KE

cases as those we have just been examining, inde- anzia being supposed extended horizontally. The efforts pendent of experimental results; we propose, theremade by a man in this case, are those necessary to

fore, before we conclude this article, to give a detail of keep his arm straight, his body erect, and that due to

a few of the best conducted experiments that have been his motion : but the actual force which enters into our

made with reference to this subject. consideration, is gravity, and particularly the weight of Desaguliers asserts, that a man can raise water, his body.

or any other weight, about 550lbs. (or one hogshead, Let the vertical Cg represent the weight of the man,

the weight of the vessel included), ten feet high in a and draw the horizontal lines Cf, dg, and complete the minute; but this statement, although he says it will parallelogram Cfdg: then the weight Cg may be re- hold good for six hours, appears, from his own facts, to presented by the components Cd, Cf. Now the effort be too high, and is certainly such as could not be conwhich exercised horizontally in the direction EK, and tinued one day after another. Mr. Smeaton considers which we shall represent by Ei, and as we may suppose this work as the effort of haste or distress; and re.t applied at the point E of the lever EA, of which of the ports, that six good English labourers will be required axis of rotation is in A, we have the proportion

to raise 21141 solid feet of sea water to the height of Ei:Cf:: AC ; AE;

four feet in four hours; in which case, the men would

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raise very little more than six cubic feet of fresh water ing on a horizontal path, with or without a load, the ANIMAL oth. each to the height of ten feet in a minute. Now, the same author concludes that the greatest quantity of STRENGTH:

hogshead containing about 8L cubic feet, Smeaton's action takes place when the men are unloaded; and it ton's allowance of work proves less than Desaguliers' in is to that of men loaded with 190lbs. nearly as seven

about the ratio of 6 to 8.1. And his good English la to four. The weight which a man ought to carry to
bourers, who can work at this rate, are estimated by produce the greatest useful effect, or that effect in
him to be equal to a double set of common workmen; which the quantity of action relative to the carrying
it appears, therefore, that with the probabilities of vo his own weight is deducted from the total effect, is
luntary interruptions, and other incidents, a man's work, 165lbs.
for several successive days, ought not to be valued at There is a particular case, which obtains with re-
more than halfa hogshead raised ten feet high in a minute. spect to burdens carried in towns, where the men,
Smeaton likewise states that two ordinary horses will after having carried their load, return home unloaded ;
do the above work in 3} hours, which is at the rate of the weight they ought to carry in this case, according
little more than two and a half hogsheads ten feet high to M. Coulumb, is about 200 lbs. Here the quantity
in a minute ; so that, if these statements can be de- of useful action, compared with that of a man who
pended upon, one horse will do the work of five men. walks freely, and without a load, is nearly as one to

According to Emerson's statement, a man of ordi- five, or, in other words, he employs to pure loss four-
nary strength, turning a roller by the handle, can act fifths of his power. By causing a man to mount a
for a whole day against a resistance equal to 30 lbs. flight of steps freely and without a burden, his quantity
weight; and if he works ten hours per day, he will of action is at least double of what he affords in any
raise a weight of 30 lbs. through 3? feet in a second other way of employing his strength.
of time; or, if the weight be greater, he will raise it to This seems to be understood by our coal merchants,
a proportional less height; so that, under all circum- who thus employ manual labour in emptying the coal
stances, 30 x 3} = 105, the momentum of his effort. vessels of their loads in the river Thames, where we
If two men work at a windlass, or roller, they can more frequently see four or five men perpetually ascending a
easily raise up 70 lbs. than one man can 30 lbs., provided step-ladder and jumping down, so as by their weight
the elbow of one of the handles be at right angles to to bring up the coals from the hold by means of a rope
that of the other. Men accustomed to bear loads, such passing over a pulley. Here the useless action is in
as porters, will carry from 150 lbs. to 200 lbs. or 250lbs., ascending, and the useful in descending:
according to their strength. A man cannot well draw When labour is applied to cultivating the ground, the
more than 70lbs. or 80lbs. horizontally; and he cannot whole quantity afforded by one man, during a day,
thrust with a greater force acting horizontally at amounts to about the same as 328 lbs. raised 1094 yards;
the height of his shoulders than 27 lbs. or 30 lbs. But one and M. Coulumb comparing this work with that of men
of the most advantageous ways in which a man can employed to carry burdens up an ascent of steps, or
exert his force is to set and pull towards him, as in at a pile-engine, finds a loss of about goth part only

of the quantity of action, which may be neglecied in reCoulumb, so well known as an accurate experimental searches of this kind. philosopher, in a memoir communicated to the French It may not be improper to observe, that in estimating Institute, states that the quantity of action which a mean results, we should not determine from experiman can produce, when during a day he is employed ments of short duration, nor should we make


dein mounting a flight of steps without a burden, is ductions from the exertions of men of more than ordidouble that which the same man could produce tf nary strength. The mean results have also a relation loaded with a weight of 223 lbs., continuing his exer to climate. M. Coulumb observes, that he has directed tions, in both cases, through the day. Hence it appears extensive works at Martinico, where Fahrenheit's therhow much, with equal fatigue and time, the total or abso. mometer is seldom less than 77°, and similar works in, lute effect may obtain different values, by varying the France; and he affirms that not more than half the combination of effort and velocity. This fact is imme. work can be done in similar cases in the one climate diately applicable to the formulæ investigated in the to what can be effected in the other. preceding part of this article.

It will of course be observed by the reader that the Feats of strength, either natural or artificial: term effect here denotes the total quantity of labour necessary to raise not only the burden but the man 24. We have already observed, that unusual strength Feats of himself; the useful effect is very ditferent, and it is is not to be considered in forming any mechanical de- strength. this, as M. Coulumb observes, which it is most im- ductions relative to the employment of animal exertion portant to determine. For instance, we have seen

as a first mover of machinery, but still any extraordithat the total effect is the greatest when without a

pary power, whether natural or artificial, cannot but be burden, but the useful effect is then nothing; it is also considered as an interesting subject for philosophical nothing when the man is so loaded as not to be able reflection, and we must not, therefore, pass over certo move; and it is between these limits that the useful tain surprising facts of this kind; but we shall confine effect is a maximum ; this we have already determined our remarks principally to those recorded by Desaguanalytically in the foregoing part of this article, but liers, of Thomas Topham, a man, at the time he exhithe above results of Coulumb will be found to change bited before the author, thirty-one vears of age, but somewhat the ultimate value; the principle, however, who had practised the same feats for five or six years remains, and other experiments are perhaps still ne- preceding that time. The exploits of this man, which cessary to arrive at a satisfactory conclusion.

Desaguliers witnessed, were as follow: 23. From an examination of the work of men walk 1. By the strength of the fingers (only rubbed in

of tax

ANIMAL cold ashes to keep them from slipping) he rolled up a cult to make a comparison between two animals whose ANT!!! STRENGTII, very large pewter dish.

powers are so differently exerted. The worst way of !?ru°o i 2. He broke seven or eight short and strong applying the strength of a horse is to make him carry pieces of tobacco-pipe with the force of his middle fin a weight up a steep hill, while the organization of man ger, having laid them on the first and third finger. fits him very well for this kind of labour. Hence, three

“ 3. Having thrust in under his garter the bowl of men climbing up such a hill, with the weight of 100lbs, a strong tobacco-pipe, his legs being bent, he broke it cach, will proceed faster than a horse with a load of to pieces by the tendons of his hams without altering 300 lbs., as was first stated, we believe, by La Hire. the bending of his legs.

We are not acquainted with any series of experi“ 4. He broke such another bowl between his first ments which have been made with a view of determining and second finger, by pressing his fingers together the weights horses can carry, when moving up sloping sideways.

roads, making given angles with the horizon; but, “ 5. He lifted a table six feet long, which had half fortunately, this deficiency is not of much consequence, a hundred weight hanging at the end of it, with his because, as we have stated, the carrying of weights is teeth, and held it in a horizontal position for a consi- far from the best manner of employing the strength of derable time. It is true, the feet of the table rested these animals. It is known, however, in general, that against his knees; but, as the length of the table was a horse, loaded with a man and his equipage, weighing, much greater than its height, that performance required at a medium, about 224 lbs., may, without being much a great strength to be exerted by the muscles of his forced, travel, in seven or eight hours, the distance of loins, those of his neck, the masseter, and temporul 43,000 yards, or about 25 miles, on a good road. (muscles of the jaws), besides a good set of teeth. When a horse travels day after day, without cessation,

“ 6. He took an iron kitchen poker, about a yard either the weight he carries, or the distance passed long, and three inches in circumference, and, holding over, must uudergo some diminution, as well as the it in his right hand, he struck upon his bare left arm, time actually employed in travelling: but we cannot between the elbow and the wrist, till he bent the poker undertake to assign a mean value of his capabilities. nearly to a right angle.

M. Amontons, in the Memoirs of the French Academy Atacante's " 7. He took such another poker, and holding the for 1703, has given some comparative observations on estigated ends of it in his hands, and the middle against the back the velocity of men and horses ; in which he states the the p.ee of his neck, he brought the two ends of it together before velocity of a horse loaded with a man, and walking, him, and, what was yet more difficult, he pulled it to be rather more than 51 feet per second, or 3 miles almost straight again: because the muscles which se per hour; and when going a moderate trot with the parate the arms horizontally from each other are not same weight, to be about 84 feet per second, or 6 so strong as those that bring them together.

miles per hour. These velocities are, however, we “ 8. He broke a rope of about two inches in cir- think, rather less than might have been safely assumed cumference, which was, in part, wound about a cylinder in these cases. of five inches in diameter, having fastened the other 26. In the same way as we have seen that the most posar's end of it to straps that went over his shoulders. But advantageous manner of applying the strength of man a renica he exerted more force to do this than any other of his is most unfavourable for a horse, so it is found that the first feats, from his awkwardness in going about it: for the most disadvantageous to the former will be the most rope yielded and stretched as he stood upon the cylin- favourable for the latter; that is, when they are emder, so that when the extensors of the legs and thighs ployed in drawing loads in carriages. A horse pirt had done their office in bringing his legs and thighs into harness, and making an effort to draw, bends straight, he was forced to raise his heels from their himself forwards, inclines his legs, and brings his bearing, and use other muscles that were weaker. But, breast nearer to the earth, and this so much the more, if the

rope had been so fixed that the part of it to be as his effort is more considerable: so that when he is broken had been short, it would have been broken employed in drawing, his effort will depend, in some with four times less difficulty.

measure, both on his own weight and that which he “ 9. I have seen him list a rolling-stone of about carries on his back. Indeed, it is highly useful to load 800 lbs. with his hands only, standing in a frame above the back of a draught horse to a certain degree, though it, and taking hold of a chain that was fastened to it. this, on a slight consideration, might be thought unBy this I reckon, he may be almost as strong again as necessarily to augment the fatigue of the animal: but those who are commonly considered as very strong it must be considered, that the mass with which the men.”-DESAGULIER's Experimental Philosophy. horse is charged vertically, is in part added to the

effort which he makes in the direction of traction, and Of the strength of horses.

thus dispenses with the necessity of his inclining so Strength of 25. Amongst quadrupeds, the most useful, as a much forward, as he must otherwise do, and may,

first mover of machinery, is the horse. The strength of therefore, in this point of view, relieve the draught
this animal is, perhaps, about six times that of a man. more than to compensate for the additional fatigue
Desagutiers states the proportion as 5 to 1, coinciding occasioned by the vertical pressure. Carmen and
with our preceding deductions from Smeaton's results. waggoners in general are aware of this, and are com-
French authors commonly reckon seven men as equiva- monly very careful to dispose of the load in such a
lent to one horse, and probably, upon the whole, I to manner that the shafts shall throw a due proportion of
6 may be stated as a fair proportion; the strength of the weight on the back of the shaft horse.
a man, at a dead pull, being therefore estimated at 27. The best disposition of the traces during the time positie
70 lbs.; that of a horse, under like circumstances, will a horse is drawing, is when they are perpendicular to the 6-3
be 420 lbs. The fact is, however, that it is very diffi- the position of the collar upon his breast and shoulders.


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