Ra"ti*o (r"sh* or r"sh), n. [L., fr. reri, ratus, to reckon, believe, think, judge. See Reason.] 1. (Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by or ½; of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a.

Some writers consider ratio as the quotient itself, making ratio equivalent to a number.

The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule.

2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress.

Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. -- Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

Ra`ti*oc"i*nate (rsh`*s"*nt), v. i. [L. ratiocinatus, p. p. of ratiocinari, fr. ratio reason. See Ratio.] To reason, esp. deductively; to offer reason or argument.

Ra`ti*oc`i*na"tion (-n"shn), n. [L. ratiocinatio: cf. F. ratiocination.] The process of reasoning, or deducing conclusions from premises; deductive reasoning.

Ra`ti*oc"i*na*tive (- s"*n*tv), a. [L. ratiocinativus.] Characterized by, or addicted to, ratiocination; consisting in the comparison of propositions or facts, and the deduction of inferences from the comparison; argumentative; as, a ratiocinative process.

The ratiocinative meditativeness of his character.

Coleridge.

Ra`ti*oc"i*na*to*ry (-n*t*r), a. Ratiocinative. [R.]

Ra"tion (r"shn or rsh"n), n. [F., fr. L. ratio a reckoning, calculation, relation, reference, LL. ratio ration. See Ratio.] 1. A fixed daily allowance of provisions assigned to a soldier in the army, or a sailor in the navy, for his subsistence.

Officers have several rations, the number varying according to their rank or the number of their attendants.

2. Hence, a certain portion or fixed amount dealt out; an allowance; an allotment.

Ra"tion, v. t. To supply with rations, as a regiment.

Ra"tion*al (rsh"n*al), a. [L. rationalis: cf. F. rationnel. See Ratio, Reason, and cf. Rationale.] 1. Relating to the reason; not physical; mental.

Moral philosophy was his chiefest end; for the rational, the natural, and mathematics . . . were but simple pastimes in comparison of the other.

Sir T. North.

2. Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.

It is our glory and happiness to have a rational nature.

Law.

3. Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.

4. (Chem.) Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulæ. See under Formula.

Rational horizon. (Astron.) See Horizon, 2 (b). -- Rational quantity (Alg.), one that can be expressed without the use of a radical sign, or in exact parts of unity; -- opposed to irrational or radical quantity. -- Rational symptom (Med.), one elicited by the statements of the patient himself and not as the result of a physical examination.

Syn. -- Sane; sound; intelligent; reasonable; sensible; wise; discreet; judicious. -- Rational, Reasonable. Rational has reference to reason as a faculty of the mind, and is opposed to irrational; as, a rational being, a rational state of mind, rational views, etc. In these cases the speculative reason is more particularly referred to. Reasonable has reference to the exercise of this faculty for practical purposes, and means, governed or directed by reason; as, reasonable desires or plans; a reasonable charge; a reasonable prospect of success.

What higher in her society thou find'st Attractive, human, rational, love still.

Milton.

A law may be reasonable in itself, although a man does not allow it, or does not know the reason of the lawgivers.

Swift.

Ra"tion*al, n. A rational being. Young.

Ra`tion*a"le (rsh`n*"l), n. [L. rationalis, neut. rationale. See Rational, a.] An explanation or exposition of the principles of some opinion, action, hypothesis, phenomenon, or the like; also, the principles themselves.

Ra"tion*al*ism (rsh"n*al*z'm), n. [Cf. F. rationalisme.] 1. (Theol.) The doctrine or system of those who deduce their religious opinions from reason or the understanding, as distinct from, or opposed to, revelation.

2. (Philos.) The system that makes rational power the ultimate test of truth; -- opposed to sensualism, or sensationalism, and empiricism. Fleming.

Ra"tion*al*ist, n. [Cf. F. rationaliste.] One who accepts rationalism as a theory or system; also, disparagingly, a false reasoner. See Citation under Reasonist.

{ Ra`tion*al*is"tic (-s"tk), Ra`tion*al*is"tic*al (-t*kal), } a. Belonging to, or in accordance with, the principles of rationalism. -- Ra`tion*al*is"tic*al*ly, adv.

Ra`tion*al"i*ty (-l"*t; 277), n.; pl. -ties (- tz). [F. rationalité, or L. rationalitas.] The quality or state of being rational; agreement with reason; possession of reason; due exercise of reason; reasonableness.

When God has made rationality the common portion of mankind, how came it to be thy inclosure?

Gov. of Tongue.

Well-directed intentions, whose rationalities will never bear a rigid examination.

Sir T. Browne.

Ra`tion*al*i*za"tion (rsh`n*al**z"shn), n. The act or process of rationalizing.

Ra"tion*al*ize (rsh"n*al*z), v. t. 1. To make rational; also, to convert to rationalism.

2. To interpret in the manner of a rationalist.

3. To form a rational conception of.

4. (Alg.) To render rational; to free from radical signs or quantities.

Ra"tion*al*ize, v. i. To use, and rely on, reason in forming a theory, belief, etc., especially in matters of religion: to accord with the principles of rationalism.

Theodore . . . is justly considered the chief rationalizing doctor of antiquity.

J. H. Newman.

Ra"tion*al*ly, adv. In a rational manner.

Ra"tion*al*ness, n. The quality or state of being rational; rationality.

||Ra*ti"tæ (r*t"t), n. pl. [NL., fr. L. ratis a raft; cf. L. ratitus ||marked with the figure of a raft.] (Zoöl.) An order of birds in which ||the wings are small, rudimentary, or absent, and the breastbone is ||destitute of a keel. The ostrich, emu, moa, and apteryx are examples.

Rat"i*tate (rt"*tt), a. (Zoöl.) Of or pertaining to the Ratitæ.

Rat"ite (rt"t), a. (Zoöl.) Of or pertaining to the Ratitæ. - - n. One of the Ratitæ.

{ Rat"lines, Rat"lins } (rt"lnz), n. pl. [Of uncertain origin.] (Naut.) The small transverse ropes attached to the shrouds and forming the steps of a rope ladder. [Written also ratlings, and rattlings.] Totten.

Rat"on (rt"n), n. [Cf. Raccoon.] A small rat. [Obs.] Piers Plowman.

Ra*toon" (r*tn"), n. 1. Same as Rattoon, n.

2. A rattan cane. [Obs.] Pepys.

Ra*toon", v. i. Same as Rattoon, v. i.

Rats"bane` (rts"bn`), n. [Rat + bane.] Rat poison; white arsenic.

Rats"baned` (-bnd`), a. Poisoned by ratsbane.

Rat"-tail` (rt"tl`), a. Like a rat's tail in form; as, a rat-tail file, which is round, slender, and tapering. See Illust. of File.

Rat"-tail`, n. 1. (Far.) pl. An excrescence growing from the pastern to the middle of the shank of a horse.

2. (Zoöl.) (a) The California chimæra. See Chimæra. (b) Any fish of the genus Macrurus. See Grenadier, 2.

Rat"-tailed` (-tld`), a. (Zoöl.) Having a long, tapering tail like that of a rat.

Rat-tailed larva (Zoöl.), the larva of a fly of the genus Eristalis. See Eristalis. -- Rat-tailed serpent (Zoöl.), the fer- de-lance. -- Rat-tailed shrew (Zoöl.), the musk shrew.

Rat*tan" (rt*tn"), n. [Malay rtan.] [Written also ratan.] (Bot.) One of the long slender flexible stems of several species of palms of the genus Calamus, mostly East Indian, though some are African and Australian. They are exceedingly tough, and are used for walking sticks, wickerwork, chairs and seats of chairs, cords and cordage, and many other purposes.

Rat*teen" (-tn"), n. [F. ratine.] A thick woolen stuff quilled or twilled.

Rat"ten (rt"t'n), v. t. [Prov. E. ratten a rat, hence the verb literally means, to do mischief like a rat.] To deprive feloniously of the tools used in one's employment (as by breaking or stealing them), for the purpose of annoying; as, to ratten a mechanic who works during a strike. [Trades-union Cant] J. McCarthy.

Rat"ter (-tr), n. 1. One who, or that which, rats, as one who deserts his party.

2. Anything which catches rats; esp., a dog trained to catch rats; a rat terrier. See Terrier.

Rat`ti*net" (-t*nt"), n. A woolen stuff thinner than ratteen.

Rat"ting (rt"tng), n. 1. The conduct or practices of one who rats. See Rat, v. i., 1. Sydney Smith.

2. The low sport of setting a dog upon rats confined in a pit to see how many he will kill in a given time.

Rat"tle (-t'l), v. i. [imp. & p. p. Rattled (-t'ld); p. pr. & vb. n. Rattling (-tlng).] [Akin to D. ratelen, G. rasseln, AS. hrætele a rattle, in hrætelwyrt rattlewort; cf. Gr. kradai`nein to swing, wave. Cf. Rail a bird.] 1. To make a quick succession of sharp, inharmonious noises, as by the collision of hard and not very sonorous bodies shaken together; to clatter.