proatlas 
proatlas (pro-at'las), . [NL., < I*. pro, before, 
+ NL. Hi/us : -.<( ntlii.i, :i.] A rudimentary ver- 
tebra which iu some animals precedes the atlas 
proper. Kuri/r. Brit., XX. 447. [Rare.] 
proaulion (pro-a'li-on), n. [< Gr. irpoaMiav, a 
court, a vestibule, < irp6, before, + ai~t.ii, a court, 
a hall, a chamber: see aula.] In the early 
church and in the Greek Church, the porch of a 
church. In Greek churches the proaulion is a porch at 
the west end of a church, open on three sides and of the 
same width as the narthex, into which It opens. 
The Proaulion, or porch, Is ... sometimes a lean-to 
against the west end of the narthex, but oftener It forms 
with the narthex one lean-to against the west end of the 
"e. J. II. Scale, Eastern Church, I. 215. 
probabiliorism (prob-a-bil'i-or-izm), n. [< NL. 
4741 
Itles for short periods of time. All the essential features 
of probability are exhibited ill tile case of putting into a 
bag mime black beans and some white ones, then shaking 
them well, and finally drawing out one or several at ran- 
dom. The beans must first be shaken up, so as to assimi- 
late or generalize the contents of the bag : and a similar 
result must be attained in any case In which probabil- 
be voluntarily subjected to any general conditions addi- 
tlonal to those of the course of experience of which they 
form a part. Thus, out-of-the-way ones or uppermost 
ones must not be particularly chosen. This random choice 
may be effected by machinery, If desired. If, now, a great 
number of single beans are so taken out and replaced suc- 
cessively, the following phenomenon will be found ap- 
proximately true, or, if not, a prolongation of the scries 
of drawings will render it so: namely, that If the whole 
series be separated into parts of two fixed numbers of 
probabilis, probable: see probable.] In Horn. 
Catli. theol., the doctrine that it is lawful to act 
in a certain manner only when there is a more 
probable opinion iu favor of such action than 
against it, so that when there are two equally 
probable opinions, one for aud the other against 
liberty of action, it is not lawful to accept the 
former opinion and follow one's inclinations. 
See probabilism, probabilist. 
probabiliorist (prob-a-bil'i-pr-ist), . [< NL. 
"probabiliorista, < L. probtibilior, compar. of 
probabilis, probable : see probable.] One who 
holds to the doctrine of probabiliorism. 
Probalnliorists, who hold that the law Is always to be 
obeyed unless an opinion clearly very probable (proba- 
blllor) is opposed to it. Kncyc. Brit., XIV. 6SC. 
probabilis causa (pro-bab'i-lis ka'zii). [L. : 
see probable aud cause.] A probable cause. 
Probabilis causa lltigandi, In Scot law, plausible 
ground of action or defense. 
probabilism (prob'a-bil-izm), . [= F. proba- 
bilistic = Sp. Pg. It. probabilismo = G. proba- 
bilismus, < NL. probabilismus, < L. probabilis, 
probable: see probable.] In Rom. Calh. theol., 
the doctrine that when there are two probable 
opinions, each resting on apparent reason, one 
in favor of and the other opposed to one's in- 
clinations, it is lawful to follow the probable 
opinion which favors one's inclination. See 
probabiliorism, probabilist. 
The working of the principle known as Probabilimii. 
The meaning of this principle ... is simply this: when 
a doubt arises as to the binding force of some divine or 
human precept In any given case, it Is permissible to 
abandon the opinion in favour of obedience to the law 
technically known as "safe" (tuta) opinion for that 
which favours non-compliance, provided this laxer opinion 
be "probable." And by "probable"is meant any Judg- 
ment oropinion based on some reasonable grounds, though 
with some doubt that the opposite view Is perhaps the 
true one (Gury, Theol. Mor., I. n. 51). 
Eiteye. Brit., XIV. (!3tl. 
probabilist (prob'a-bil-ist), . [= F. probabi- 
liste = Sp. Pg. It. probabilinta = G. probabilist, 
< NL. pi-obabilista,<. L. probabilis, probable: see 
probable.] 1. One who holds the doctrine of 
probabilism. 2. One who maintains that cer- 
tainty is impossible, and that probability alone 
is to govern faith and practice. 
probability (prob-a-bili-ti ),t.; pi. probabilities 
(-tiz). [= I< . probability = Sp. probabilidad = 
Pg. probabilidatle = It. probability, < L. proba- 
bifita(t-)$, probability, credibility, < probabilis, 
probable, credible: see probable.] 1. The state 
or character of being probable; likelihood; ap- 
pearance of truth ; that state of a case or ques- 
tion of fact which results from superior evi- 
dence or preponderation of argument on one 
side, inclining the mind to receive that as the 
truth, but leaving some room for doubt. 
Thus, first traditions were a proof alone. 
Could we be certain such they were, so known ; 
But, since some flaws in long descent may be, 
They make not truth, but probability. 
Dryden, Beligio Laic!, 1. 345. 
Probability is nothing but the appearance of such an 
agreement or disagreement, by the Intervention of proofs 
whose connection is not constant, . . . bat Is or appears 
for the most part to be so. . . . In which case the founda- 
tion of his assent Is the probability of the thing, the proof 
being such as for the most part carries truth with It. ... 
So that that which causes his assent to this proposition Is 
the wonted veracity of the speaker in other cases. 
Locke, Human Understanding, IV. xv. f 1. 
2. Quantitatively, that character of an argu- 
ment or proposition of doubtful truth which 
consists in the frequency with which like 
propositions or arguments are found true 
in the course of experience. Thus, if a die be 
thrown, the probability that it will turn up ace Is the fre- 
quency with which an ace would be turned up in an in- 
definitely long succession of throws. It is conceivable 
that there should be no definite probability: thus, the 
proportion of aces might so fluctuate that their frequency 
in the long run would be represented by a diverging se- 
ries. Yet even so, there would be approximate probabil 
298 
probably 
Twice the quadratures of the areas are given Iu treatises 
on probabilities as tables of the theta function of proba- 
bilities. The chief practical application of probability Is 
to insurance: and Its only significance lies In an assur- 
ance as to the average result In the long run. The theory 
of probability Is to be regarded as the logic of the physi- 
cal sciences. 
3. Anything that 1 
or truth. 
Both the rocks aud the earth are so splendent to behold 
that belter ludgements then ours might haue beene per- 
swaded they contained more then probabilities 
Quoted In Capt. John Smith'i Works, I. 115. 
4. A statement of what is likely to happen; 
a forecast: applied in the plural by Cleveland 
Abbe to his daily weather-predictions iu Cin- 
cinnati iu 1869, and subsequently adopted by 
sets of 100 will be nearly the same as the average propor- 
tion among the sets of 10,000. This Is the fundamen- 
tal proposition of the theory of probabilities we might 
say of logic since the security of all real Inference rests 
upon It. The greater the frequency with which a specific 
event occurs in the long run, the stronger Is the expec- 
tation that it will occur In a particular case. Hence, prob- 
ability has been defined as the degree of belief which 
ought to be accorded to a problematical Judgment; but 
this conceptualiiHc probability, as It Is termed, is strictly 
not probability, but a sense of probability. Probability 
may be measured in different ways. The conceptuallstic 
measure Is the degree of confidence to which a reason Is 
entitled ; it Is used in the mental process of balancing rea- 
sons pro and con. The conceptnalistlc measure Is the 
logarithm of another measure called the f</-that is, 
the ratio of the number of favorable to the number of un- 
favorable cases. But the measure which Is most easily 
guarded against the fallacies which beset the calculation 
of probabilities Is the ratio of the number of favorable 
cases to the whole number of equally possible cases, or 
the ratio of the number of occurrences of the event to the 
total number of occasions in the course of experience. 
This ratio is called the probability or chance of the event 
Thus, the probabil Ity t hat a die will turn up ace Is J. Prob- 
ablllty zero represents impossibility; probability unity, 
certainty. The fundamental rules for the calculation of 
probabilities are two, aa follows : Rule I. The probabil- 
ity that one or the other of two mutually exclusive propo- 
sitions Is true is the sum of the probabilities that one and 
the other are true. Thus, If J Is the probability that a die 
will turn up aeo, and J is the probability that it will turn up 
an even number, then, since it cannot turn up at once an 
ace and an even number, the probability that one or other 
will be turned up is A + J = ?. It follows that if p is the 
probability that any event will happen, 1 -p is the proba- 
bility that It will not happen. Rule If. The probability 
of an event multiplied by the probability, if that event 
happens, that another will happen, gives as product the 
the United States Signal Service. 
The same term had been similarly used l>y 
Leverrier in Paris since 1859. 
The whole system [of meteorological predictions! if ex- 
cellently organized and very extensive ; the official publi- 
cations embrace thepro6atai(u'< and the so-called weather- 
'"ps. Pop- S<*. Ho., XXIX. 54. 
Antecedent probability, see antecedent. Balance 
of probabilities. See balance. Calculus of proba- 
bility, a branch of mathematics teaching how to calcu- 
late probabilities by general methods. Curve Of proba- 
bility. Sec alwve. Inverse probability, the proba 
hility of a hypothesis as deduced from the comparison of 
Its consequences with observation. Thus, the following 
Is a familiar problem of Inverse probability: Suppose a 
bag contains a series of tickets numbered consecutively 
from 1 up. Snppoxe a ticket Is drawn at random, and Its 
number is 13, wnat Is the most probable number of tickets 
In the bag? The best opinion concerning Inverse proba- 
bility seems to be that it Is altogether fallacious, unless 
the antecedent probability of the hypothesis Is known. 
Some writers hold that the probability of a proposition 
about which we are completely Ignorant is ;. ; others hold 
that It is indeterminate.- Local probability. See local. 
- Old Probabilities, see old. 
probable (prob'a-bl), a. and . [< F. probable 
= Sp. probable = Pg. prurattl = It. probabile, 
< L. probabilui, that may be proved, credible, < 
probare, test, examine: see probe, prore.] I. . 
It. Capable of being proved; provable. 
It is doubtlessly probable that women are nature's pride, 
virtue's ornaments. Ford, Honour Triumphant. 
It ought to be a total fast from all things during the 
solemnity, unless it probable necessity Intervene. 
Jer. Taylor, Holy Living, Iv. 5. 
Xo man ... Is properly a heretic . . . but he who 
the probability of its being found ace up is ( x i = ,',. If 
the probability that a certain man will reach the age of 
forty Is p, and the probability, when he is forty, that he 
that the probability of A is the same whether B does or 
docs not happen, then, also, the probability of B is the 
same whether A does or docs not happen, and the events 
are said to be independent. The probability of the concur- 
rence of two Independent events Is the product of their 
separate probabilities. The probability that a general 
event, whose probability on each one of occasions Is p, 
should occur just k times among these n occasions, Is 
equal to the term containing p* | n the development of 
(P + ?>*, where q = 1 - p. Thus, suppose the event is the 
appearance of head when a coin is tossed up, so that p = 
j = }, and the coin be tossed up six times. Then the prob- 
abilities of 0, 1, 2, 3, 4, 5, e heads respectively are J,, Jf,, 
if. U. if, A. A. The most probable value of t is that 
whole number next less than ( + l)p, unless this be itself 
a whole number, when it Is equally probable. When the 
number of trials is large, the probabilities of the differ- 
ent numbers of occurrences of the given event are pro- 
portional to areas included between the so-called proba- 
bility curve, its asymptote, and ordlnates at successive dis- 
tances equal to liyZnpq. Tills probability curve, whose 
equation is = o la f (where o Is the circumference 
for unit diameter, and <r Is the Napierian base). Is repre- 
sented In the figure, where the approximate straightness 
2. Having more evidence for than against, 
or evidence which inclines the mind to belief, 
but leaves some room for doubt; lito 
I . 
:::::::::::::::: :: . 
:::::::::::::::: :: : 
::::::::::::;::: i! : 
> 
Probability Curve. 
.... . , ,, , , 
of the slope will be remarked. If it is desired to ascertain 
the probability of the occurrence from *, to t, times in- 
ihiMve in n trials of an event whose probable occurrence 
at each trial is p. the approximate value is the area inclnd- 
I do not say that the principles of religion are merely 
probable, I have before asserted them to be morally cer- 
tain. Up. Willrin*. 
That Is accounted probable which has better argument* 
producible for It than can be brought against It. South. 
1 made up a story as short and probable as I could, but 
concealed the greatest part. 
Stc\ft, Gulliver's Travels, III. 11. 
Chaucer . . . makes It possible, and even probable, that 
his motley characters should meet on a common footing. 
Lowell, Study Windows, p. 284. 
3. Rendering something likely, or showing it 
to be likely: tin, probable evidence ; a probable 
presumption. Blackstone. 4t. Plausible ; spe- 
cious; colorable. 
Make this haste as your own good proceeding, 
Strengthen'd with what apology you think 
May make it probable need. 
5*0*., All's Well, II. 4. 52. 
Probable cause. See eaute. Probable error, in at- 
Iron, and phyriet. When the value of any quantity or ele- 
ment has been determined by means of a number of Inde- 
pendent observations every one liable to a small amount of 
accidental error, the determination will also be liable to 
some uncertainty, and the probable error Is the quantity 
which Is such that there Is the same probability of the 
difference between the determination and the true abso- 
lute value of the thing to be determined exceeding or 
falling short of It. But it is to be remarked that, as so 
defined, the constant error belonging to all observations 
of the given series Is not Included In the probable error. 
Probable evidence, evidence distinguished from demon- 
strative evidence in that it admits of degrees, and of all 
variety of them, from the highest moral certainty to the 
very lowest presumption. Probable Inference. See 
inference. Probable proposition. See pnvporiKwi. 
= Syn. 2. Presumable, credible, reasonable. 
II. n. A probable opinion ; an opinion rest- 
ing upon good but not sufficient grounds. 
The casuists' doctrine of probabUt, In virtue of which a 
man may be probabiliter obligatus and probabillter deob- 
llgatus at the same time. 
Lowell, Among my Books, 2d ser. , p. 284. 
probably (prob'a-bli), a<lr. 1. With probabil- 
ity; in a probable manner; in all likelihood; 
with the appearance of truth or reality; likely: 
as, the story is probably true; the account is 
jirobnbii/ correct. 
Distinguish betwixt what may possibly and what will 
probably be done. Mr /.'. L'Estranye. 
