force 
moving along a curved path into a component accelera- 
tive elongation of the radius of curvature of the path 
(md-'p / M-), due to the inertia of the particle ; inertia con- 
sidered as the cause of such acceleration. If, while ;i 
wheel is revolving uniformly, a particle is suddenly re- 
leased from its periphery, this particle will (in the absence 
of forces) fly off on a tangent without change of velocity. 
The path of the particle, considered as relative to the re- 
volving wheel, is an involute of the circle. Hence, at the in- 
stant of release the direction of the relative motion of the 
particle is radial to the wheel, and it can be shown that, 
while the velocity of this motion would be null at that iu- 
stant, its acceleration would be equal to the square of the 
velocity of the particle divided by the radius of the wheel. 
It is simplest to say that this accelerative elongation of 
the radius vector always takes place, and that if, notwith- 
standing, the particle does not leave the wheel, it is be- 
cause the centrifugal acceleration due to inertia is pre- 
cisely balanced by a centripetal acceleration due to the 
forces which hold the particle in place. But the centrif- 
ugal force does not at all depend upon the principle of 
action and reaction. If a particle moves upon any curved 
path whatever, any infinitesimal part of this path is oscu- 
lated by a circle, and inertia will produce the same accel- 
erative elongation of the radius vector from the center of 
this circle as before ; and this radius vector is the radius 
of curvature of the path. As thus defined, the centrif- 
ugal force is not a true force, since it results from the 
resolution of the motion into a radial and a circular 
part, while the principle of the parallelogram of forces 
(see def. 8 (a)) forbids such a resolution of forces proper. 
Thus, if a particle moves in a circular orbit about an at- 
tracting center, since the radius of curvature is constant, 
the centrifugal force must be balanced by a precisely equal 
and opposite attracting force. But a body which was 
really subjected to two equal and opposite forces would 
move as if subjected to none that is, not in a circle, but 
in a straight line. The fact is that the only influences to 
which the body is subjected are I, its inertia, and A, the 
attraction that is, I + A. The centrifugal force is equal 
to A, and balances the attraction, but it is a part of the 
inertia, the remainder of which is I + A. (b) In an er- 
roneous use, a repulsive force causing a revolving body 
to fly away from the center of revolution. Writers on 
attractions sometimes so use the word, (c) A fictitious 
force repelling every particle of the earth from the axis 
by an amount equal to the centrifugal force in sense (a). 
With this hypothesis, and supposing the earth not to ro- 
tate, the statical effects are the same as in the actual case ; 
hut the dynamical effects are different, (d) As used by many 
high authorities, the reaction of a moving body against 
the force which makes it move in a curved path. In this 
sense it is a real force. It does not, however, act upon 
the moving body, but upon the deflecting body ; and, far 
from giving the former a tendency to fly away from the 
center, it is but an aspect of that stress which holds it to 
the curved trajectory. The centrifugal force in sense (a) 
may be regarded as that in sense (d) transferred from 
the deflecting to the deflected bodies. [These differences 
of meaning explain the apparently conflicting views of 
writers.] 
When I was about nine years old I was taken to hear a 
course of lectures, given by an itinerant lecturer in a 
country town, to get as much as I could of the second 
half of a good, sound, philosophical omniscience. . . . 
" You have heard what I have said of the wonderful cen- 
tripetal force, by which Divine Wisdom has retained the 
planets ill their orbits round the Sun. But, ladies and 
gentlemen, it must be clear to you that if there were no 
other force in action, this centripetal force would draw 
our earth and the other planets into the Sun, and univer- 
sal ruin would ensue. To prevent such a catastrophe, 
the same wisdom has implanted a centrifugal force of the 
same amount, and directly opposite," &c. I had never 
heard of Alfonso X. of Castile, but I ventured to think 
that if Divine Wisdom had just let the planets alone it 
would come to the same thing, with equal and opposite 
troubles saved. De Morgan, Budget of Paradoxes, p. 431. 
Deviating force and centrifugal force are but two differ- 
ent names for the same force, applied to it according as 
its action on the revolving body or on the guiding body is 
under consideration. Rankine, Applied Mechanics, 538. 
The student cannot be too early warned of the danger- 
ous error into which so many have fallen, who have sup- 
posed that a mass has a tendency to fly outwards from a 
centre about which it is revolving, and therefore exerts a 
centrifugal force which requires to be balanced by a cen- 
tripetal force. Tait, Encyc. Brit., XV. 682. 
Although the earth is really revolving about its axis, 
so that all problems relating to the relative equilibrium 
of the earth itself and the bodies on its surface are really 
dynamical problems, we know that they may be treated 
statically by introducing, in addition to the attraction, 
that fictitious force which we call the centrifugal force. 
Stokes, On Attractions, 1. 
Centripetal force, a force which draws a body toward a 
center. Chemical force. See chemical. Coercive or 
coercitive force. See coercive. Complex offerees, 
component of a force, congruency of forces, etc. See 
complex, component, etc. Composition of forces. See 
composition, and def. 8 (a), above. Compound force, 
in law, unlawful violence attended by another crime : dis- 
tinguished from simple force. Conservation of force. 
See the law of the conservation of energy or offeree, under 
energy. Conservative force, an attraction or repul- 
sion depending upon the relative position of the pair of 
bodies concerned. All fundamental forces are believed to 
be conservative or fixed. Whatever motion takes place un- 
der the influence of conservative forces alone might take 
place under the same forces in precisely the reverse order, 
the velocities being the same, but opposite in direction. 
A determinate order among phenomena is therefore never 
due to the action of forces, but is a result of probabili- 
ties. Corpuscular force, a force which, like cohesion 
and adhesion, acts between the molecules of a body or 
of different bodies; molecular force. Correlation of 
energies or of forces. See energy. Decomposition 
Of forces. Same as resolution of forces. Deflective 
forces. See deflective. Deviating force or tangential 
force, a force acting in a direction at right angles to that 
of the motion of the body, and producing a curvature of 
2319 
its path.- Diffusion of force. See di/usion. Distrib- 
uted force, in mtch., a force which is not applied at a 
point, but is spread over a surface or disseminated through 
a solid. All real forces are distributed. Electromotive 
force. See electromot ice. Equilibrium of forces. See 
equilibrium, i. Equivalence of force. See tgtrfn- 
leni'e. External forces, those forces which act upon 
masses of matter at sensible distances, as gravitation. 
Fine forcet. Heejinc?,l6. Fixed force. Kee fixed. 
Force Bill, in If. S. hist. : (a) A bill to enforce the 
tariff, introduced into Congress at the time of the nullifi- 
cation excitement in 1833. It became a law March 2d, 1833. 
(6) A bill for the protection of political and civil rights in 
the South. It became a law May 31st, 1870. (c) A bill similar 
to (b), but of still more stringent character, enacted April 
20th, 1871. Force of detrusion. See aetrusimi. Force 
of inertia. See momentum. In great force, exceed- 
ingly vivacious or energetic ; in effective condition : gener- 
ally applied to powers of conversation or oratory : as, he 
was in great force at the dinner or the meeting last night. 
[Colloq. ] Internal forces, forces which act only on 
the constituent particles of matter, and at insensible dis- 
tances, as cohesion. Line of force. See equipolential 
surface, under equipotential. Living force. See vis 
viva. Magne-crystalliC force. See magiie-crystallic. 
Molar force, a force producing motions in large masses 
of matter. Molecular force, a force acting between 
molecules, but insensible at sensible distances. Moment 
Of a force. See moment. Moral force, the power of 
acting on the reason in judging and determining. Mo- 
tive power or force. See motive, a. Moving force. 
See momentum. Noforcet, no matter; no consequence. 
See def. 6, above, and to make no force, below. 
No fors, quod he, tellith me al youre greef. 
Chaucer, Summoner's Tale, 1. 489. 
"Noforce," quod Merlin, "he shall do right wele; but 
take a spere, and folowe after, ye and youre brother and 
Vlfln." Merlin (E. E. T. S.), ii. 221. 
Non-conservative forces, forces which depend upon 
the velocities of the bodies between which they act. Such 
forces are alone capable of setting up rotations. Friction 
and viscosity are examples of such forces, and these are 
explained by physicists as the result of chance encounters, 
etc., among almost innumerable molecules. Other effects 
of this sort are the conduction of heat, the dissipation of 
energy, the development of livingforms. etc. pdic force, 
odyllc force. See od. Of forcet, of necessity ; neces- 
sarily ; unavoidably ; perforce. 
Good reasons must, of force, give place to better. 
Shak., J. C., iv. 3. 
This prince, of force, must be helov'd of Heaven, 
Whom Heaven hath thus preserv'd. 
Fletcher (and others), Bloody Brother, iii. 1. 
Parallelogram of forces. See def. 8 (a). Physical- 
force men. See Chartist. Reciprocating force, a 
force which acts alternately with and against the motion 
of the body, as gravity does upon an oscillating pendu- 
lum. Resolution of forces. See def. 8 (a). Simple 
force, in law, unlawful violence attended by no other 
crime: distinguished from compound force. Tangen- 
tial force. See deviating force. Thermo-electric or 
thermo-electromotive force. See thermo-electric. 
To be in force (milit.), to be prepared for action with a 
large or full force. 
The enemy was in force at Corinth, the junction of the 
two most important railroads in the Mississippi valley. 
U. S. Grant, Personal Alemoirs, I. 330. 
To hunt at forcet. See hunt. TO make, do, or give 
no forcet, to care not; consider of no importance. See 
no force, above. 
When thei here speke of the grete light and blisse of 
heven, thei make no force. Gesta Romanorum, p. 14. 
To my bettre did no reverence, 
Of my sovereyns gafnofors at al. 
Quoted in Babees Book (E. E. T. S.), p. xliii. 
Triangle of forces. See triangle. Tube of force. See 
tube. Unit Of force. See unit. =Syn. Strength, etc. 
(see power); efficacy, efficiency, potency, cogency, vir- 
tue ; Force, Compulsion, Coercion, Constraint, Restraint. 
Among these force is the most general. Compulsion and 
coercion are generally more active, pushing one onward ; 
constraint and restraint less active, the last being simply 
a holding back. The first three could be applied to a per- 
son's treatment of himself only by a lively figure ; con- 
straint and restraint express equally self-control and con- 
trol of others. Constraint upon one's self is much harder 
than restraint. 
By/orce they could not introduce these gods; 
For ten to one in former days was odds. 
Dryden, Abs. and Achit., i. 122. 
Give you a reason on compulsion ! If reasons were as 
plenty as blackberries, I would give no man a reason 
upon compulsion. Shak., 1 Hen. IV., ii. 4. 
Congress had neglected to provide measures and means 
for coercion [in dealing with the seceding States]. The 
conservative sentiment of the country protested loudly 
against everything but concession. 
The Century, XXXV. 614. 
Bitter constraint, and sad occasion dear, 
Compels me to disturb your season due. 
Stilton, Lycidas, 1. 6. 
Certain complex restraints on excesses of altruism ex- 
ist, which, in another way, force back the individual upon 
a normal egoism. H t Spencer, Data of Ethics, 96. 
force 1 (fors), v. ; pret. and pp. forced, ppr. for- 
cing. [< ME. forcen, forsen (= D.forceren = G. 
forciren = Dan. forcere = Sw. forcera), < OF. 
forcer, forcier, F. forcer = Pr. forsar = Sp. 
forzar = Pg. forgar = It. forzare, < ML. forti- 
are, force, fortify, < fortia, force, strength, etc. : 
see force*, .] I. trans. 1. To act effectively 
upon by force, physical, mental, or moral, in 
any manner ; impel by force ; compel ; con- 
strain. 
force 
A smalle sparke kyndles a great fyre if it be forste lo 
burne. Babees Book (E. E. T. S.), p. 94. 
I'll undertake to land them on our coast, 
Ami force the tyrant from his seat by war. 
Shak., 3 Hen. VI., iii. 3. 
I have been told that one hundred and sixty minnows 
have been found in a Trout's belly ; either the Trout had 
devoured so many, or the miller that gave it a friend of 
mine had forced them down his throat after he had taken 
him. /. Walton, Complete Angler, p. 95. 
Like a bow \tmgf orc'd into a curve, 
The mind, releas'd from too constraint a nerve, 
Flew to its first position with a spring. 
Couyer, Table-Talk, 1. 622. 
2. To overcome or overthrow by force ; accom- 
plish one's purpose upon or in regard to by force 
or compulsion ; compel to succumb, give way, 
or yield. 
Will he force the queen also before me in the house? 
Esther vii. 8. 
Then they flatter'd him and made him do ill things ; now 
they would force him against his Conscience. 
Selden, Table-Talk, p. 63. 
I should have/orced thee soon with other arms. 
Hilton, S. A., 1. 1096. 
When wine has given indecent language birth, 
And/orced the floodgates of licentious mirth. 
Cowper, Conversation, 1. 264. 
Some forced the breach, others scaled the ramparts. 
Prescott, Ferd. and Isa., ii. 10. 
3. To effect by effort or a special or unusual 
application of force ; bring about or promote 
by some artificial means : as, to force the pas- 
sage of a river against an enemy ; to force a 
jest. 
If you how low, may be he'll touch the bonnet, 
Or fling a f orc'd smile at you for a favour. 
Fletcher (and another), Queen of Corinth, ii. 4. 
Some twenty times a day, nay, not so little, 
Do I force errands, frame ways and excuses, 
To come into her sight. 
Middleton, Changeling, H. 1. 
A successful speculator or a "merchant prince" may 
force his way into good society in England ; he may be 
presented at court, and flourish at court-balls. 
W. H. Russell, Diary in India, II. 152. 
4. To cause to grow, develop, or mature under 
unnaturally stimulating or favorable condi- 
tions. Specifically (o) To hasten or enlarge the growth 
of, as flowers, fruits, etc., by means of artificial heat and 
shelter, as in hothouses or hotbeds, (b) To fine, as wine, 
by a short process or in a short time, (c) In general, to 
subject to unnatural stimulation or pressure, in order to 
accomplish a desired result before the usual or natural 
time, as in training the young. 
5. To impose or impress by force; compel the 
acceptance or endurance of : with on or upon : 
as, to force one's company or views on another ; 
to force conviction on the mind. 6f. To fur- 
nish with a force ; man ; garrison. 
Were they not fared with those that should be ours, 
We might have met them dareful, beard to beard, 
And beat them backward home. Shak., Macbeth, v. 5. 
7f. To put in force ; make binding ; enforce. 
8. In card-playing : (a) In whist, to compel (a 
player) to trump a trick by leading a card of a 
suit of which he has none, which trick other- 
wise would be taken by an opponent: as, to 
force one's partner. (6) To compel (a person) 
to play so as to make known the strength of his 
hand. 9f. To attach force or importance to; 
have regard to ; care for. 
I force not Philautus his fury, so I may haue Euphues his 
friendship. Lyly, Euphues, Anat. of Wit, p. 81. 
For me, I force not argument a straw, 
Since that my case is past the help of law. 
Shak., Lucrece, 1. 1021. 
Forced heir, in law : (a) An heir in whose favor the law 
provides that a part at least of the inheritance shall not 
be devised away from him. (6) In Rom. law, one obliged 
to accept a succession, however involved the estate might 
be. Forced march, sale, etc. See the nouns. To force 
one's hand, (a) In card-playing, same as 8 (b). Hence 
(!>) To compel one to disclose his intentions, plans, or 
resources. 
The potato famine in Ireland precipitated a crisis, forced 
Peel's hand, and compelled him to open the ports, which, 
once open, could not, it was clear, again be closed. 
S. Dowell, Taxes in England, IV. 13. 
= Syn. 1 and 2. To oblige, necessitate, coerce. 
II. t intrans. 1. To use force or violence; 
make violent effort ; strive ; endeavor. 
Forciny with gyfts to winne his wanton heart. 
Spenser, Shep. Cal., April. 
Howbeit, in the ende, perceiving those men did more 
fiercely force to gette up the lull. 
A'orth, tr. of Plutarch, p. 327. 
2. To be of force or importance ; be of signifi- 
cance or consequence. 
It little forceth how long a man line, but how wel and 
vertuously. J. Udall, On Mark v. 
3. To care ; hesitate; scruple. 
Your oath once broke, you force not to forswear. 
Shak., L. L. L., v. 2. 
