rule 
Gauss's Rule for finding the date of Easter. See 
Easter'. Golden rule. Scu yolden. Guldin's rule, one 
of two rules, one giving the volume and the other the 
surface of any ring formed by the revolution of any plane 
closed curve about an axis lying iu its plane. The rules are 
named after the Swiss mathematician Paul Guldin (\all- 
1643), but he obtained them from the collections of Pap- 
pus, a geometer of the fourth century. Home rule. See 
Aomi. Homa-Rule BUI. See bill . Inverse rule of 
thr.33. See inverse. Joint rule, a rule adopted by both 
houses of Congress or a legislature for the conduct of 
transactions between them. Labor-saving rule, in 
printini/, brass rules cut by system to graduated lengths, 
so that they may be easily combined. MinJmg's rule, 
a rule for the determination of the degree of an equation 
resulting from elimination, given by the Prussian mathe- 
matician E. F. A. Minding iu 1S41. Napier's rule, one 
of two mnemonic rules given by Napier, the inventor of 
logarithms, for the solution of right-angled spherical tri- 
angles. The two legs and the complements of the hypote- 
nuse and of the angles are called the parts. An angle and 
oneof the sides going to form itare said to be adjacent ; so, 
also, are the two legs. A part adjacent to both or neither 
of two parts is called, relatively to them, the middle part ; 
and if the other two are not 'adjacent to it, they are called 
opposite. Then, the two rules are that the sine of the mid- 
dle part is equal to the product of the tangents of the ad- 
jacent parts and to the product of the cosines of the oppo- 
site parts. These are equivalent to six equations of dif- 
ferent forms. Newton's rule, a certain rule for deter- 
mining a superior limit to the number of positive roots of 
an algebraic equation, and another for the negative roots. 
Let the equation be 
a^x''* + -^rs '* '< etc. = 0. 
Form a aeries of quantities A. ; , A, ... AH, by the formula 
Ar = a-r a.ri ar+i. Write down the two rows 
a ot a lt O 2 , . . . an 
AQ, A i . A , . . . AH. 
If two successive numbers in the upper row have like 
signs while the numbers under them also have like signs, 
this is called a double permanence. But if two successive 
numbers in the upper row have different signs while the 
numbers under them have like signs, this is called a varia- 
tion-permanence. The rule is that the number of negative 
roots cannot be greater than the number of double per- 
manences, nor the number of positive roots greater than 
the number of variation-permanences. One-hour rule, 
a standing rule of the United Slates House of Represen- 
tatives, first adopted in 1847, in accordance with which no 
member, except one who reports a measure from a com- 
mittee, may, without unanimous consent or permission 
given by vote, speak for more than one hour in debate on 
any subject. Parallel rule, (a) A rule for drawing paral- 
lel lines. The old form of parallel rule consisted of two 
rulers connected by two bars turning upon pivots at the 
vertices of a parallelogram. For accurate work, a triangle 
and a straight-edge are used, (b) See def. 8. Rule day, 
in legal proceedings, motion day ; the regularly appointed 
day on which to make orders to show cause returnable. 
Rule of cosst. See coss-'. Rule Of faith (regula 
fidei), the sum of Christian doctrine as accepted by the 
orthodox church in opposition to heretical sects; the 
creed : a phrase used from the second century onward. 
Rule of false (ngviaftdti), or rule of double position. 
See position, ?. Rule of intarsection, rule of six 
quantities, the proposition that, if a spherical triangle 
be cut by a transversal great circle, the product of the 
chords of the doubles of three segments which do not cut 
one another is equal to the product of the chords of the 
doubles of the other three segments. This rule was dis- 
covered by Menelaus, about A. D. 100. Rule of mixtures. 
Same as alligation, 2 Rule Of Nicomachus [named 
from Nicomachus, a Greek arithmetician who flourished 
about A. D. 100, and who is said to have been the author 
of this rule], a rule for finding the square of a small num- 
ber, as follows : subtract the number from 10 and to the 
square of the difference add 10 times the number dimin- 
ished by the difference. Thus, to find the square of 9, sub- 
tract 9 from 10, which gives 1 as the difference, the square 
of which is 1, and adding to this 10 times the excess of the 
original number, 9, over the difference, 1, which excess is 
8, we have 81 as the answer. Rule of philosophizing, 
a rule for constructing theories. Newton propounded 
certain rules of this kind. Rule Of Signs, the rule that 
any arrangement is positive or negative according as it 
contains an even or odd number of displacements. Rule 
of speech (regula scrmoni8\ the rule of false, so called be- 
cause in the use of it we " say " a quantity has a value which 
is false. Rule of supposition, the rule of false. See po- 
sition, 7. Rule of ti3 double sign, the principle that 
zero may be regarded either as positive or negative at 
pleasure, which has important applications under Budan's 
theorem. Rule Of the OCtlve. See octave. Rule Of 
the road. See road. Rule of three, the method of 
finding the fourth term of a proportion when three are 
given. The numbers being so arranged that the first is to 
the second as thi third is to the fourth, which last is the 
term required to be found, then this is found by multiply- 
ing the second and third terms together, and dividing the 
product by the first. Rule of thumb, a rule suggested 
by a practical rather than a scientific knowledge : in allu- 
sion to a use of the thumb in marking off measurements 
roughly. 
We'll settle men and things by rule of thumb, 
And break the lingering night with ancient rum. 
Sydney Smith, To B'rancis Jeffrey, Sept. 3, 1809. 
Rule of trial and error, the rule of false. See position, 
7. Rules Of a prison, certain limits outside the walls 
of a prison, within which prisoners in custody were sumi> 
times allowed to live, on giving security not to escape. 
The phrase is sometimes extended to mean the space so in- 
closed, and also the freedom thus accorded to the prisoner. 
To nid these, the prisoners took it iu turns to perambu- 
late the rules, and solicit help in money or kind. 
J. Ashton, Social Life in Reign of Queen Anne, II. 247. 
Both at the King's Bench and the Fleet debtors were al- 
lowed to purchase what were called the Rules, which en- 
331 
5265 
nbled them to live within a certain area outside the prison, 
and practically left them free. 
W. Besant, Fifty Years Ago, p. 77. 
Rules Of course, rules which are drawn up by the proper 
officers on the authority of the mere signature of counsel ; 
or, in some instances, as upon a Judge's flat, or allowance 
by the master, etc., without any signature by counsel. 
Rules which are not of course are gran table on the motion 
either of the party actually interested or of his counsel. 
Rules of practice, general rules prescribed by a court 
or other authority for the regulation of legal or other 
official procedure. See def. 2, above. Single rule. See 
def. 8. Sliding rule, a rule having one or more scales 
which slide over others for the purpose of facilitating 
calculations. Stationers' rule, a rule of considerable 
length, made of hard wood about half an inch in thick- 
ness, usually marked with inches, and having its edges 
sheathed with brass strips. It is used for measuring, and 
as a straight-edge to guide a knife in cutting thick paper, 
as drawing-paper, pasteboard, etc. The rule in Shel- 
ley's case, a much quoted doctrine of the common law, 
to the effect that wherever there is a limitation to a man 
which if it stood alone would convey to him a particular 
estate of freehold, followed by a limitation to his heirs or 
to the heirs of his body (or equivalent expressions) either 
immediately or after the interposition of one or more par- 
ticular estates, the apparent gift to the heir or heirs of the 
body is to be construed as a limitation of the estate of the 
ancestor, and not as a gift to the heir. To buy in under 
the rule. See buy. Twenty-first rule,in u. S. hist., a 
rule adopted by the House of Representatives in 1840, and 
dropped in 1844, prescribing that no abolition petitions 
should be received by the House. Waved rule. See def. 
8. =Syn. 2. Precept, etc. (see principle), law, regulation, 
formula, criterion, standard. 7. Direction, regulation, 
dominion, lordship, authority, mastery, domination. 
rule 1 (rol), t>.; pret. and pp. ruled, ppr. ruling. 
[< ME. mien, reuleii, rewlen, riwlen, < OF. ruiler, 
rieuler, rieler, reguler, reigler, regler, F. regler = 
Pr. rcglar = Sp. reglar, regular = Pg. regrar, 
regular = It. regolare = D. regelen = G. regeln 
= Dan. regulere = Sw. reglera, < LL. regutare, 
regulate, rule, < L. regula, a rule : see rule 1 , n., 
andcf. rail 1 , v., and regulate.] I. trans. 1. To 
make conformable to a rule, pattern, or stan- 
dard; adjust or dispose according to rule; regu- 
late ; hence, to guide or order aright. 
Be thise uirtne [prudence] al thet man deth and zayth 
and thength, al he dijt and let and reuleth to the lyne of 
scele [reason]. Ayenbitf, of Inwyt (E. E. T. S.), p. 124. 
Yet Pitee, through his stronge gentil might, 
Forgaf, and made Mercy passen Right, 
Through innocence and ruled curtesye. 
Chaucer, Good Women, 1. 163. 
His actions seemed ruled with a ruler. 
Lamb, South-Sea House. 
2. To settle as by a rule ; in law, to establish 
by decision or rule ; determine ; decide : thus, 
a court is said to rule a point. Burrill. 
Had he done it with the pope's licence, his adversaries 
must have been silent; for that's a ruled case with the 
schoolmen. Bp. Atterbunj. 
3. To have or exercise authority or dominion 
over; govern; command; control; manage; 
restrain. 
Let reason rule thy wyt. Babees Booi(E. E. T. S.), p. 79. 
We'll do thee homage and be ruled by thee, 
Love thee as our commander and our king. 
Shalt., T. G. of V., iv. 1. 66. 
Being not able to rule his horse and defend himselfe, 
he was tlirowne to the ground. 
Capt. John Smith, True Travels, I. 17. 
4. To prevail on ; persuade ; advise : generally 
or always in the passive, so that to be ruled by 
is to take the advice or follow the directions of. 
I think she will be ruled 
In all respects by me ; nay, more, I doubt it not. 
Shak., R. and J., iii. 4. 13. 
Nay, master, be ruled by me a little ; so, let him lean 
upon his staff. Marlowe, Jew of Malta, iv. 2. 
5. To dominate ; have a predominant influence 
or effect upon or iu. 
And God made two great lights ; the greater light to 
rule the day, and the lesser light to rule the night. 
Gen. L 16. 
Soft undulating lines rule the composition ; yet dignity 
of attitude and feature prevails over mere loveliness. 
J. A. Symonds, Italy and Greece, p. 65. 
6. To mark with lines by means of a ruler; pro- 
duce parallel straight lines in, by any means: 
as, to rule a blank book. See ruled paper, un- 
der paper. 
A singing-man had the license for printing music-books, 
which he extended to that of being the sole vendor of all 
ruled paper, on the plea that, where there were ruled lines, 
musical notes might be pricked down. 
/. It Israeli, Amen, of Lit., II. 437. 
7. To mark with or as with the aid of a ruler 
or a ruling-machine : as, to rule lines on paper. 
Age rules my lines with wrinkles in my face. 
Drat/ton, Idea, xliv. 
Ruled surface, (a) A surface generated by the motion 
of a line; a locus of lines indeterminate in one degree. 
(61 Any surface, as of paper or metal, upon which a series 
of parallel lines has been marked or cut. To rule the 
roast. See roaet. =Syn. 1 and 3. Control, Regulate, etc. 
See govern. 
ruler 
II. intrans. 1. To have power or command ; 
exercise supreme authority. 
By me princes rule, and nobles, even all the judges of 
the earth. Prov. viii. 16. 
Let them obey that know not how to rule. 
Shah., 2 Hen. VI., v. 1. 6. 
2. To prevail; decide. 
Away with scrupulous wit ! now arms must rule. 
Shak., 3 Hen. VI., iv. 7. 61. 
3. In law: (a) To decide. (6) To lay down 
and settle a rule or order of court ; order by 
rule; enter a rule. 4. In com., to stand or 
maintain a level. 
Prices generally rule low. 
The Academy, July 5, 1890, p. 15. 
rule' 2 (rbl), n. [A contracted form of revel; per- 
haps in part associated with rule in misrule 
("lord of misrule," etc.): see revel.'] Revel; 
revelry. 
What night-rule now about this haunted grove ? 
Shak., M. N. D., ili. 2. 5. 
And at each pause they kiss ; was never seen such rule 
In any place but here, at Boon-flre, or at Yule. 
Drayton, Polyolbion, xxvii. 251. 
rule 2 (rol), v. i. [Also reul; a contr. of revel. 
Cf. rule 2 , .] To revel; be unruly. Halliwell 
(under reul). [Prov. Eng.] 
rule-case (rol'kas), n. In printing, a tray or 
case with partitions provided for rules. 
rule-CUtter (rol'kut"er), n. In printing, a ma- 
chine for cutting brass rule to short lengths : 
usually a shears one blade of which is fixed and 
the other is moved by a strong lever. 
rule-driller (rol'dril"er), >i. A teacher who 
drills his pupils upon rules, or by rote, without 
teaching them the underlying principles. 
I speak to the teacher, not the rule-driller. 
De Morgan, Arith. Books, Int. , p. xxii. 
rule-joint (rol'joint), 
nature of a hinge- 
joint, whereby two 
thin flat strips may 
be so united that 
each will turn edge- 
wise toward or from 
the other, and in no 
other direction: so 
called from its gen- 
eral employment in 
folding rules and 
scales used by sur- 
veyors, engineers, 
and mechanics. Al- 
so called prop-joint. 
ruleless (roTles), a. 
lesse; < rule 1 + -less.'} 
less. 
A pivoted joint in the 
Rule- or Prop-joint. 
a and fr, prop-rods ; f, rule-joint. 
[Early mod. E. also ru- 
Being without rule ; law- 
A rulesse rout of yongmen which her woo'd, 
All slaiue with darts, lie wallowed in their blood. 
Spenser, Virgil's Gnat, 1. 431. 
rulelessness (rol'les-nes), n. [< ruleless + 
-ness.] The state or quality of being ruleless, 
or without rule or law. 
Its [the Star-Chamber's] rulelessness, or want of rules 
that can be comprehended, is curiously illustrated here. 
The Academy, July 19, 1879, p. 43. 
ruler (ro'ler), H. [< rule 1 + -er 1 .] 1. One who 
rules or governs ; one who exercises dominion 
or controlling power over others ; a person who 
commands, manages, restrains, or has part in 
the making or administration of law; one in 
authority. 
Rewlera of rewmes around all the erthe 
Were not yffoundid at the ftrist tyme 
To leue al at likynge and lust of the world, 
But to laboure on the lawe as lewde men on plowes. 
Richard the Redeless, iii. 264. 
Who made thee a ruler and a judge over us? 
Acts vii. 27. 
2. A rule; an instrument made of wood, brass, 
ivory, or the like, with straight edges or sides,by 
means of which, as a guide, straight lines may 
be drawn on paper, parchment, or other sub- 
stance, by passing a pen or pencil along the 
edge. (See rule 1 , and parallel ruler, under par- 
allel.) When a ruler has the lines of chords, 
tangents, sines, etc., it is called a scale. See 
scale 3 . 3. In engraving, a workman who oper- 
ates a ruling-machine for ruling in flat tints, 
etc. See ruling-machine. 4. In line-engrav- 
ing, a straight steel bar supported on cleats, to 
which a socket is so fitted that it slides evenly 
and steadily backward and forward. A perpen- 
dicular tube fixed to the side of the socket holds a sharp 
diamond-pointed graver which is pressed down by a 
spring. When the socket is drawn along the bar, the 
graver cuts a straight line across the plate ; but by a 
slight motion of the hand lines can be formed to suit 
the shape of any object. Marquoi's rulers, a mathe- 
