[1] In Germany the title _Intendant_ is applied to the head of public
institutions, more particularly to the high officials in charge of
court theatres, royal gardens, palaces and the like. The director of
certain civic theatres is now also sometimes styled Intendant. The
title _Generalintendant_ implies the same official duties, but higher
rank. In the German army the _Intendantur_ corresponds to the British
quartermaster-general's and financial departments of the War Office,
the French _intendance militaire_. Subordinate to these are the
_intendances_ (_Intendanturen_) under general officers commanding,
the heads of which are in Germany called _Korpsintendanten_, and in
France _intendants-generaux_, _intendants militaires_, &c. (see ARMY,
S 58).
INTENT (from Lat. _intendere_, to stretch out, extend, particularly in
the phrase _intendere animum_, to turn one's mind to, purpose), in law,
the purpose or object with which an act is done. The question of intent
is important with reference both to civil and criminal responsibility.
Briefly, it may be said that in criminal law the constituent element of
an offence is the _mens rea_ or the guilty intent. The commission of an
act without the intent is not, as a general rule, sufficient to
constitute a crime, nor, on the other hand, does the existence of a
guilty intent without commission of the act amount to the legal
conception of a crime (see CRIMINAL LAW). In the case of civil wrongs,
in general, the opposite holds good. A wrongful act done to the person
or property of another carries with it legal liability, irrespective of
the motive with which the act was done (see TORT). In reference to the
construction of contracts, wills and other documents, the question of
intention is material as showing the sense and meaning of the words
used, and what they were intended to effect.
INTERAMNA LIRENAS, an ancient town of Italy in the Volscian territory
near the modern Pignataro Interamna, 5 m. S.E. of Aquinum; the
additional name distinguishes it from Interamna Praetuttianorum (mod.
Teramo) and Interamna Nahartium (mod. Terni). It was founded by the
Romans as a Latin colony in 312 B.C. as a military base in the war
against Samnium, no fewer than 4000 colonists being sent thither. It was
among the Latin colonies which in 209 B.C. refused to supply further
contingents or money for the Hannibalic war. It became a _municipium_
with the other Latin colonies, but we hear no more of it--mainly, no
doubt, because it lay off the Via Latina. Livy's description of it as on
the Via Latina is not strictly accurate, and cannot be used as an
indication that the former course of the Via Latina was through
Interamna. The city lay on a hill on the N. bank of the Liris, between
two of its tributaries, thus lacking natural defences on the N. side
alone. Many inscriptions have been found, and there are considerable
remains of antiquity. One inscription bears the date A.D. 408, and the
site was occupied in the middle ages by a castle called Terame or
Termine. (T. As.)
INTERCALARY (from Lat. _intercalare_, to proclaim, _calare_, the
insertion of a day in the calendar), a term applied to a month, day or
days inserted between other months or days in order to adjust the
reckoning of time, based on the revolution of the earth round the sun,
the day, and of the moon round the earth, the lunar month, to the
revolution of the earth round the sun, the solar year (see CALENDAR).
From the meaning of something inserted or placed between, intercalary is
used for something which interrupts a series, or comes between two
types. In botany, the term is used of growth which is not apical but
somewhere between the apex and base of an organ, such as the growth in
length of an Iris leaf, or of the internode of a grass-haulm.
INTERCOLUMNIATION, in architecture, the distance between the columns of
a peristyle, generally referred to in terms of the lower diameter of the
column. They are thus set forth by Vitruvius (iii. 2): (a) Pycnostyle,
equal to 1(1/2) diameters; (b) Systyle, 2 diameters; (c) Eustyle, 2(1/4)
diameters (which was the proportion preferred by him); (d) Diastyle, 3
diameters; and (e) Araeostyle or wide spaced, 4 diameters, a span only
possible when the architrave was in wood. Vitruvius's definition would
seem to apply only to examples with which he was acquainted in Rome, or
to Greek temples described by authors he had studied. In the earlier
Doric temples the intercolumniation is sometimes less than one diameter,
and it increases gradually as the style developed; thus in the Parthenon
it is 1(1/4), in the Temple of Diana Propylaea at Eleusis, 1(1/4); and
in the portico at Delos, 2(1/2). The intercolumniations of the columns
of the Ionic Order are greater, averaging 2 diameters, but then the
relative proportion of height to diameter in the column has to be taken
into account, as also the width of the peristyle. Thus in the temple of
Apollo Branchidae, where the columns are slender and over 10 diameters
in height, the intercolumniation is 1(3/4), notwithstanding its late
date, and in the Temple of Apollo Smintheus in Asia Minor, in which the
peristyle is pseudodipteral, or double width, the intercolumniation is
just over 1(1/2). Temples of the Corinthian Order follow the proportions
of those of the Ionic Order.
INTERDICT (Lat. _interdictum_, from _interdicere_, to forbid by decree,
lit., interpose by speech), in its full technical sense as an
ecclesiastical term, a sentence by a competent ecclesiastical authority
forbidding all celebration of public worship, the administration of some
sacraments (baptism, confirmation and penance are permitted) and
ecclesiastical burial. From general interdicts, however, are excepted
the feast days of Christmas, Easter, Whitsunday, the Assumption and
Corpus Christi. An interdict may be either local, personal or mixed,
according as it applies to a locality, to a particular person or class
of persons, or to a particular locality as long as it shall be the
residence of a particular person or class of persons. Local interdicts
again may be either general or particular; in the latter instance they
refer only to particular buildings set apart for religious services. An
interdict is a measure which seeks to punish a population or a religious
body (e.g. a chapter) for the fault of some only of its members, who
cannot be reached separately. It is a penalty directed against society
rather than against individuals. In 869 Hincmar of Laon laid his entire
diocese under an interdict, a proceeding for which he was severely
censured by Hincmar of Reims. In the _Chronicle_ of Ademar of Limoges
(_ad ann._ 994) it is stated that Bishop Alduin introduced there "a new
plan for punishing the wickedness of his people; he ordered the churches
and monasteries to cease from divine worship and the people to abstain
from divine praise, and this he called excommunication" (see Gieseler,
_Kirchengesch_. iii. 342, where also the text is given of a proposal to
a similar effect made by Odolric, abbot of St Martial, at the council of
Limoges in 1031). It was not until the 11th century that the use of the
interdict obtained a recognized place among the means of discipline at
the disposal of the Roman hierarchy, which used it, without great
success, to bring back the secular authorities to obedience. Important
historical instances of the use of the interdict occur in the cases of
Scotland under Pope Alexander III. in 1181, of France under Innocent
III. in 1200, and of England under the same pope in 1209. So far as the
interdict is "personal," that is to say, applied to a particular
individual, it may be regarded as a kind of partial excommunication; for
instance, a bishop may, for certain faults, be interdicted from entering
the church (_ab ingressu ecclesiae_), that is, without being
excommunicated, he must not celebrate or assist at the celebration of
divine offices. Interdicts cease at the expiration of the term, or by
removal (_relaxatio_). General and local interdicts are no longer in
use.
See the canonists in tit. 39 _lib._ v., _De sententia excommun_., &c.;
L. Ferraris, _Prompta bibliotheca canonica_, &c., s.v. "Interdictum."
_Interdict_, in Scots law, is an order of court pronounced on cause
shown for stopping any proceedings complained of as illegal or wrongful.
It may be resorted to as a remedy against all encroachments either on
property or possession. For the analogous English practice see
INJUNCTION.
INTERDICTION, in Scots law, a process of restraint applied to prodigals
and others who, "from weakness, facility or profusion, are liable to
imposition." It is either voluntary or judicial. Voluntary interdiction
is effected by the prodigal himself, who executes a bond obliging
himself to do no deed which may affect his estate without the assent of
certain persons called the "interdictors." This may be removed by the
court of session, by the joint act of the interdictors and the
interdicted, and by the number of interdictors being reduced below the
number constituting a quorum. Judicial interdiction is imposed by order
of the court, either moved by an interested party or acting in the
exercise of its _nobile officium_, and can only be removed by a similar
order. Deeds done by the interdicted person, so far as they affect or
purport to affect his heritable estate, are reducible, unless they have
been done with the consent of the interdictors. Interdiction has no
effect, however, on movable property.
INTERESSE TERMINI (Lat. for "interest in a term"), in law, an executory
interest, being the right of entry which the grant of a lease confers
upon a lessee. Actual entry on the lands by the lessor converts the
right into an estate. If the lease, however, has been created by a
bargain and sale or by any other conveyance under the Statute of Uses,
which does not require an entry, the term vests in the lessee at once.
An _interesse termini_ gives a cause of action against any person
through whose action entry by the lessee or delivery of possession to
him may have been prevented. An _interesse termini_ is a right _in rem_,
alienable at common law, and transmissible to the executors of the
lessee.
INTEREST, etymologically a state or condition of being concerned in or
having a share in anything, hence a legal or other claim to or share in
property, benefits or advantages. Further developments of meaning are
found in the application of the word to the benefits, advantages,
matters of importance, &c., in which "interest" or concern can be felt,
and to the feeling of concern so excited; hence also the word is used of
the persons who have a concern in some common "interest," e.g. the
trading or commercial interest, and of the personal or other influence
due to a connexion with specific "interests." The word is derived from
the Latin _interesse_ (literally "to be between"), to make a difference,
to concern, be of importance. The form which the word takes in English
is a substantival use of the 3rd person singular of the present
indicative of the Latin verb, and is due to a similar use in French of
the older _interest_, modern _interet_. The earlier English word was
_interess_, which survived till the end of the 17th century; the
earliest example of "interest" in the _New English Dictionary_ is from
the _Rolls of Parliament_ of 1450.
These meanings of "interest" are plainly derived from the ordinary uses
of the Latin _interesse_. The origin of the application of the word to
the compensation paid for the use of money or for the forbearance of a
debt, with which, as far as present English law is concerned, this
article deals, forms part of the history of USURY and MONEY-LENDING
(q.v.). By Roman law, where one party to a contract made default, the
other could enforce, over and above the fulfilment of the agreement,
compensation based on the difference (_id quod interest_) to the
creditor's position caused by the default of the debtor, which was
technically known as _mora_, delay. This difference could be reckoned
according as actual loss had accrued, and also on a calculation of the
profit that might have been made had performance been carried out. Now
this developed the canonist doctrine of _damnum emergens_ and _lucrum
cessans_ respectively, which played a considerable part in the breaking
down of the ecclesiastical prohibition of the taking of usury. The
medieval lawyers used the phrase _damna et interesse_ (in French
_dommages et interets_) for such compensation by way of damages for the
non-fulfilment of a contract, and for damages and indemnity generally.
Thus _interesse_ and _interet_ came to be particularly applied to the
charge for the use of money disguised by a legal fiction under the form
of an indemnity for the failure to perform a contract.
At English common law an agreement to pay interest is not implied unless
in the case of negotiable instruments, when it is supported by
mercantile usage. As a general rule therefore debts certain, payable at
a specified time, do not carry interest from that time unless there has
been an express agreement that they should do so. But when it has been
the constant practice of a trade or business to charge interest, or
where as between the parties interest has been always charged and paid,
a contract to pay interest is implied. It is now provided by the Civil
Procedure Act 1833 that, "upon all debts or sums certain payable at a
certain time or otherwise, the jury on the trial of any issue or in any
inquisition of damages _may_ if they shall think fit allow interest to
the creditor at a rate not exceeding the current rate of interest, from
the time when such debts or sums certain were payable, if such debts or
sums be payable by virtue of some written instrument at a certain time;
or if payable otherwise, then from the time when demand of payment
shall have been made in writing, so as such demand shall give notice to
the debtor that interest will be claimed from the date of such demand
until the term of payment: provided that interest shall be payable in
all cases in which it is now payable by law." Compound interest requires
to be supported by positive proof that it was agreed to by the parties;
an established practice to account in this manner will be evidence of
such an agreement. When interest is awarded by a court it is generally
at the rate of 4%; under special circumstances 5% has been allowed.
INTERFERENCE OF LIGHT. S 1. This term[1] and the ideas underlying it
were introduced into optics by Thomas Young. His Bakerian lecture on
"The Theory of Light and Colours" (_Phil. Trans._, 1801) formulated the
following hypotheses and propositions, and thereby laid the foundations
of the wave theory:--
_Hypotheses._
(i.) A luminiferous aether pervades the universe, rare and elastic in
a high degree.
(ii.) Undulations are excited in this aether whenever a body becomes
luminous.
(iii.) The sensation of different colours depends on the different
frequency of vibrations excited by the light in the retina.
(iv.) All material bodies have an attraction for the aethereal medium,
by means of which it is accumulated in their substance, and for a
small distance around them, in a state of greater density but not of
greater elasticity.
_Propositions._
(i.) All impulses are propagated in a homogeneous elastic medium with
an equable velocity.
(ii.) An undulation conceived to originate from the vibration of a
single particle must expand through a homogeneous medium in a
spherical form, but with different quantities of motion in different
parts.
(iii.) A portion of a spherical undulation, admitted through an
aperture into a quiescent medium, will proceed to be further
propagated rectilinearly in concentric superfices, terminated
laterally by weak and irregular portions of newly diverging
undulations.
(iv.) When an undulation arrives at a surface which is the limit of
mediums of different densities, a partial reflection takes place,
proportionate in force to the difference of the densities.
(v.) When an undulation is transmitted through a surface terminating
different mediums, it proceeds in such a direction that the sines of
the angles of incidence and refraction are in the constant ratio of
the velocity of propagation in the two mediums.
(vi.) When an undulation falls on the surface of a rarer medium, so
obliquely that it cannot be regularly refracted, it is totally
reflected at an angle equal to that of its incidence.
(vii.) If equidistant undulations be supposed to pass through a
medium, of which the parts are susceptible of permanent vibrations
somewhat slower than the undulations, their velocity will be somewhat
lessened by this vibratory tendency; and, in the same medium, the
more, as the undulations are more frequent.
(viii.) When two undulations, from different origins, coincide either
perfectly or very nearly in direction, their joint effect is a
combination of the motions belonging to each.
(ix.) Radiant light consists in undulations of the luminiferous
aether.
In the _Philosophical Transactions_ for 1802, Young refers to his
discovery of "a simple and general law." The law is that "wherever two
portions of the same light arrive at the eye by different routes, either
exactly or very nearly in the same direction, the light becomes most
intense where the difference of the routes is a multiple of a certain
length, and least intense in the intermediate state of the interfering
portions; and this length is different for light of different colours."
This appears to be the first use of the word _interfering_ or
_interference_ as applied to light. When two portions of light by their
co-operation cause darkness, there is certainly "interference" in the
popular sense; but from a mechanical or mathematical point of view, the
superposition contemplated in proposition viii. would more naturally be
regarded as taking place without interference. Young applied his
principle to the explanation of colours of striated surfaces (gratings),
to the colours of thin plates, and to an experiment which we shall
discuss later in the improved form given to it by Fresnel, where a
screen is illuminated simultaneously by light proceeding from two
similar sources. As a preliminary to these explanations we require an
analytical expression for waves of simple type, and an examination of
the effects of compounding them.
S 2. _Plane Waves of Simple Type._--Whatever may be the character of
the medium and of its vibration, the analytical expression for an
infinite train of plane waves is
/ 2[pi] \
A cos ( -------- (Vt - x) + [alpha] ) (1),
\[lambda] /
in which [lambda] represents the wave-length, and V the corresponding
velocity of propagation. The coefficient A is called the amplitude,
and its nature depends upon the medium and may here be left an open
question. The phase of the wave at a given time and place is
represented by [alpha]. The expression retains the same value whatever
integral number of wave-lengths be added to or subtracted from x. It
is also periodic with respect to t, and the period is
[tau] = [lambda]/V (2).
In experimenting upon sound we are able to determine independently
[tau], [lambda], and V; but on account of its smallness the periodic
time of luminous vibrations eludes altogether our means of
observation, and is only known indirectly from [lambda] and V by means
of (2).
There is nothing arbitrary in the use of a circular function to
represent the waves. As a general rule this is the only kind of wave
which can be propagated without a change of form; and, even in the
exceptional cases where the velocity is independent of wave-length, no
generality is really lost by this procedure, because in accordance
with Fourier's theorem any kind of periodic wave may be regarded as
compounded of a series of such as (1), with wave-lengths in harmonical
progression.
A well-known characteristic of waves of type (1) is that any number of
trains of various amplitudes and phases, but of the _same
wave-length_, are equivalent to a single train of the same type. Thus
/ 2[pi] \
[Sigma]A cos ( --------(Vt - x) + [alpha] )
\[lambda] /
2[pi] 2[pi]
= [Sigma]A cos[alpha].cos --------(Vt - x) - [Sigma]A sin[alpha].sin --------(Vt - x)
[lambda] [lambda]
/ 2[pi] \
= P cos ( --------(Vt - x) + [phi] ) (3),
\[lambda] /
where P^2 = ([Sigma]A cos [alpha])^2 = [Sigma](A sin[alpha])^2 (4),
[Sigma](A sin[alpha])
tan[phi] = --------------------- (5).
[Sigma](A cos[alpha])
An important particular case is that of two component trains only.
/ 2[pi] \ / 2[pi] \
A cos ( --------(Vt - x) + [alpha] ) + A' cos ( --------(Vt - x) + [alpha]' )
\[lambda] / \[lambda] /
/ 2[pi] \
= P cos ( --------(Vt - x) + [phi] ),
\[lambda] /
where P^2 = A^2 + A'^2 + 2AA' cos ([alpha] - [alpha]') (6).
The composition of vibrations of the same period is precisely
analogous, as was pointed out by Fresnel, to the composition of
forces, or indeed of any other two-dimensional vector quantities. The
magnitude of the force corresponds to the amplitude of the vibration,
and the inclination of the force corresponds to the phase. A group of
forces, of equal intensity, represented by lines drawn from the centre
to the angular points of a regular polygon, constitute a system in
equilibrium. Consequently, a system of vibrations of equal amplitude
and of phases symmetrically distributed round the period has a zero
resultant.
According to the phase-relation, determined by ([alpha] - [alpha]'),
the amplitude of the resultant may vary from (A - A') to (A + A'). If
A' and A are equal, the minimum resultant is zero, showing that two
equal trains of waves may neutralize one another. This happens when
the phases are opposite, or differ by half a (complete) period, and
the effect is that described by Young as "interference."
S 3. _Intensity._--The intensity of light of given wave-length must
depend upon the amplitude, but the precise nature of the relation is
not at once apparent. We are not able to appreciate by simple
inspection the relative intensities of two unequal lights; and, when
we say, for example, that one candle is twice as bright as another, we
mean that two of the latter burning independently would give us the
same light as one of the former. This may be regarded as the
definition; and then experiment may be appealed to to prove that the
intensity of light from a given source varies inversely as the square
of the distance. But our conviction of the truth of the law is perhaps
founded quite as much upon the idea that something not liable to loss
is radiated outwards, and is distributed in succession over the
surfaces of spheres concentric with the source, whose areas are as the
squares of the radii. The something can only be energy; and thus we
are led to regard the rate at which energy is propagated across a
given area parallel to the waves as the measure of intensity; and this
is proportional, not to the first power, but to the _square_ of the
amplitude.
S 4. _Resultant of a Large Number of Vibrations of Arbitrary
Phase._--We have seen that the resultant of two vibrations of equal
amplitude is wholly dependent upon their phase-relation, and it is of
interest to inquire what we are to expect from the composition of a
large number (n) of equal vibrations of amplitude unity, and of
arbitrary phases. The intensity of the resultant will of course depend
upon the precise manner in which the phases are distributed, and may
vary from n^2 to zero. But is there a definite intensity which becomes
more and more probable as n is increased without limit?
The nature of the question here raised is well illustrated by the
special case in which the possible phases are restricted to two
_opposite_ phases. We may then conveniently discard the idea of phase,
and regard the amplitudes as at random _positive or negative_. If all
the signs are the same, the intensity is n^2; if, on the other hand,
there are as many positive as negative, the result is zero. But,
although the intensity may range from 0 to n^2, the smaller values are
much more probable than the greater.
The simplest part of the problem relates to what is called in the
theory of probabilities the "expectation" of intensity, that is, the
mean intensity to be expected after a great number of trials, in each
of which the phases are taken at random. The chance that all the
vibrations arc positive is 2^(-n), and thus the expectation of
intensity corresponding to this contingency is 2^(-n).n^2. In like
manner the expectation corresponding to the number of positive
vibrations being (n - 1) is
2^(-n).n.(n -)^2,
and so on. The whole expectation of intensity is thus
1 / n(n - 1)
----- ( 1.n^2 + n.(n - 2)^2 + -------- (n - 4)^2
2^(n) \ 1.2
n(n - 1)(n - 2) \
+ ---------------(n - 6)^2 + ... ) (1).
1.2.3 /
Now the sum of the (n + 1) terms of this series is simply n, as may be
proved by comparison of coefficients of x^2 in the equivalent forms
(e^x + e^(-x))^n = 2^n(1 + (1/2)x^2 + ... )^n
n(n - 1)
= e^(nx) + ne^[(n-2)x] + -------- e^[(n-4)x] + ...
1.2
The expectation of intensity is therefore n, and this whether n be
great or small.
The same conclusion holds good when the phases are unrestricted. From
(4), S 2, if A = 1,
P^2 = n + 2[Sigma] cos ([alpha]2 - [alpha]1) (2),
where under the sign of summation are to be included the cosines of
the (1/2)n(n - 1) differences of phase. When the phases are arbitrary,
this sum is as likely to be positive as negative, and thus the mean
value of P^2 is n.
The reader must be on his guard here against a fallacy which has
misled some high authorities. We have not proved that when n is large
there is any tendency for a single combination to give the intensity
equal to n, but the quite different proposition that in a large number
of trials, in each of which the phases are rearranged arbitrarily, the
_mean_ intensity will tend more and more to the value n. It is true
that even in a single combination there is no reason why any of the
cosines in (2) should be positive rather than negative, and from this
we may infer that when n is increased the sum of the terms tends to
vanish in comparison with the number of terms. But, the number of
terms being of the order n^2, we can infer nothing as to the value of
the sum of the series in comparison with n.
Indeed it is not true that the intensity in a single combination
approximates to n, when n is large. It can be proved (_Phil. Mag._,
1880, 10, p. 73; 1899, 47. p. 246) that the probability of a resultant
intermediate in amplitude between r and r + dr is
2
-- e^(-r^2/n) rdr (3),
n