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EQUITY is the name applied to a number of legal rules, which formerly were administered by the court of chancery. The chancellor was originally the king's secretary, and as such he had to advise the king in "matters of grace and favour"; viz. in matters in which the king's intercession was invoked for the sake of mitigating the strict rules of the common law. "When early in the reign of Edward III. the chancellor ceased to be a part of the king's personal retinue, and to follow the court, his tribunal acquired a more distinct and substantive character. ; petitions for grace and favour began to be addressed primarily to him, instead of being simply referred to him by the king, or passed on through his hands. In the twenty-second year of that king such transactions were recognised as the proper province of the chancellor, and from that time his separate and independent equitable jurisdiction began to grow into the possession of that powerful and complicated machinery which belongs to later history" (Stubbs's Const. History, ii. 269). One of the most important stages in that growth was reached when, in the reign of Richard II., the "writ of subpoena" was introduced, which enabled the chancellor to enforce obedience to his decrees by the threat of imprisonment. One of the most important matters which came under the chancellor's jurisdiction was the protection of the rights of persons possessed of "uses in land. For several reasons it had become convenient to sever the legal ownership of land from the beneficial ownership, and with that object it became customary on a transfer of ownership to enfeoff one person "to the use" of another. The firstnamed person was called the "feoffee to the use," and he was the only person whom the ordinary courts recognised; but as he was in duty and conscience bound to allow the rights of beneficial ownership to the second-named person, known by the technical name of "cestui que use," the chancellor in the exercise of his equitable jurisdiction compelled him to do so, if he wished to take advantage of his formal right. The practice in matters of this nature developed into a regular system called " equity," to distinguish it from the

(3) by a special procedure; (4) by special kinds of relief.

(1) The most conspicuous among equitable rights are the rights derived from trusts. Trusts are the modern successors of "uses," but are used on a much larger scale, and also in the case of personal property; the most familiar instances being the trusts created by wills and settlements, by which the control of certain land or certain funds is given to one or more persons for the benefit of another person or other persons. Another instance of an equit able right is the right of the mortgagor to redeem the mortgaged property, the legal right to which is vested in the mortgagee.

(2) Amongst doctrines specially belonging to the sphere of equity may be mentioned the rule that a debt may be assigned; that, in the absence of an express stipulation or necessary implication, time is not considered as of the essence of a contract, that penalties named in contracts cannot be enforced unless they partake of the nature of liquidated damages, etc.

(3) The administration of trusts and of the estates of deceased persons involves protracted inquiries and the taking of accounts, etc.; for this purpose a special procedure and a special machinery has been developed in the courts of equity, which were the only courts which had to deal with matters of this nature.

(4) Among the special kinds of relief which could be obtained with the assistance of the courts of equity, the right to claim specific performance of contracts for the sale of land, and the right to claim injunctions, i.e. orders restraining the opposite party from doing certain acts injuring the rights of the plaintiff, are the most important. The courts of equity, in granting relief of this kind, were supplying a material defect in the administration of justice, as in the courts of common law; the only remedy in the case of breach of contract or injurious acts consisted in pecuniary damages, which in many cases did not adequately compensate the injured party. The power of the courts of equity to enforce their decrees by the imprisonment of disobedient parties materially helped them in the exercise of this jurisdiction.

The Judicature Act of 1873 has merged the equity courts and the courts of common law into one high court, and the rules of equity are now administered in all courts; but as they are derived from a different source from the common law rules, and have always been treated as a separate system, the distinction is still kept up, though it has no longer any practical meaning. The matters which are specially fitted for the procedure of the chancery court, have, however, been assigned to a special chancery division which is organised in a manner appropriate to the proceedings required with regard to them.

[Spence, Equitable Jurisdiction.-H. A. Smith,

ERROR EXCEPTED. These words are frequently inserted at the end of a statement of account, and are intended to show that the accounting party wishes to reserve the right to make further claims in case any error should subsequently be discovered in the account.

E. S.

ERROR, LAW OF. When an average of a set of statistics is taken, the deviation of any one of them from the average is sometimes called an error; and the arrangement of the group about its mean, a law of error. A particular arrangement, which under certain frequently-realised conditions arises, is designated as the law of error. According to this law the figure which is likely to occur most frequently is the one which forms the average; the others are grouped symmetrically above and below the average; becoming less frequent as they are more distant from that central magnitude. In the exact language of symbols, if x1, x2, etc., are the quantities averaged, and X the average, the number of quantities comprised between 2 and a neighbouring value x+Ax is approximately = (X-x)2

1

n Ax

known constants 3.1415 and c is a constant proper to the group under consideration. This arrangement is represented

(X - x)2 by the curve Y= e €2 √ TC of observations in the neighbourhood of any point in the axis of x being proportioned to the ordinate at that point; and the number of observations comprised between two values of x being equal to the area intercepted by the ordinates at those two points, the curve, and

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the axis x. Two illustrations of this curve are given in the annexed diagrams. The curve is spread out, as in Fig. 1, when the constant c is

Q

Fig. 1.

P

large; it is gathered in, as in Fig. 2, when the

Fig. 2.

Q

Q' P'O P constant c is small. The constant c being ascertained for any group of statistics, we are able to predict what proportion of the group will probably be comprised between limits defined in terms of that constant. Thus half of the group is likely to be comprised between the limits X-4769. . . c and X+.4769 . . . c; or, in other words, it is as likely as not that an observation taken at random will be distant from the average X by an interval greater than .4769 .. c; which multiple of c is accordingly called the probable error. Again the greater part of the group is comprised between the limits X-2c, X+2c; the odds are more than 200 to 1 against any observation being at a distance greater than 2c from the average. The odds are 50,000 to 1 against the distance of any observation from the average being greater than 3c. The points P and Q (P' and Q') in the figures are intended to represent the "probable" and what may be called the improbable error (2c or more).

The condition under which the law of error is fulfilled is that each of the things averaged is dependent in the same way upon (the same function of) a great number of independently variable elements. For example add together ten or more digits obtained thus: the first is the first decimal place in any constant, e.g. π, the second addendum is the first digit in any other constant, e.g. e, and the remaining eight constituents of the sum are the first digits in almost any other unconnected constants. Form another

sum of ten digits by taking the second decimal place in each of the ten constants; and so on. The set of sums thus formed will group themselves according to the law of error; the average being 45, and the constant c being √165=13 nearly. About half the group will be found between 45 - 6 (i.e. 39) and 45+6 (i.e. 51) since .477 1656 nearly. A very small proportion of the group-less than a two-hundredth part may be expected to occur outside the limits 45±26.(26=2× √165 nearly). If the number of elements entering into each of the figures averaged had been greater than ten, e.g. twenty, the "probable" and the "improbable error would have been greater absolutely, namely 10 and 36 respectively; but less relatively to the average, now 90. Similar consequences would follow if, instead of a simple sum, we had employed almost any function.

There is reason to believe that the condition which has been indicated is frequently fulfilled; and the law of error has been observed to prevail in extensive classes of phenomena, which may thus be summarised :

1. Repeated observations of one and the same physical quantity.

2. Shots fired at the same object.

3. A series of numbers each of which is obtained by taking at random a batch of say n balls out of a bag containing white and black balls mixed up in a certain proportion, and noting the number of whites in each batch of n balls; or a series obtained by tossing coins or dies and noting the number of heads or aces; and similar series.

4. Measurements of the organs of numerous specimens of a natural species.

5. Statistics of social phenomena which do not present a progressive character, e.g. the number of births, deaths, or marriages or the rates of the same, or the ratios between the male and female rates; observed at places or times not materially distant from each other.

Illustrations of the third and fifth classes are given in the accompanying tables, the materials of which have been taken from Professor Westergaard's Theorie der Statistik. In Table I., column 1, was obtained from 100 batches of balls; each batch numbering 100 balls, which were taken at random from a bag containing black and white balls in equal proportions; the number of white balls in each batch having been noted, the number of these numbers comprised between two limits, which are defined by a multiple of the constant c, forms an entry in column 2. The corresponding limits are given in column 1. Thus twentyfive of the observations occurred between the and 50+3

limits 50-3√2

с

or 47 and 2

53, since the value of c is here √2 × 10; 40

In Table II., the first column gives limits defined by the constant c as before; the second column gives the arrangement of errors obtained by comparing the proportion of male births to all births, male and female, in Italy for each of nineteen years with the average proportion for the whole period; the third column gives the theoretical arrangement.

The applications of the law of error with which we are here concerned relate partly (I.) to practice, and partly (II.) to the investigation of causes.

(I.) It is useful, when employing an average obtained from statistics, e.g. a death-rate, or an index-number, to have the means of estimating the extent to which the figure in the case with which we are dealing is likely to differ from the average obtained in past experience. It is useless to calculate the average to a number of decimal places not warranted by the "probable error to which the figure is liable.

(II.) Under the second head two cases may be distinguished: (a) where the analogy of simple games of chance holds good; the constant c being that which would be obtained if the statistics were of the sort which forms our third class of phenomena above; and (b) where the constant is not such.

(a) In the first case we have the advantage of knowing that the given group cannot be broken up into two, or more, with widely different averages; that the analysis which is a principal object of the scientific statistician has been already pushed almost up to its limit. Our statistics cannot be like batches of balls taken from bags in which the proportion of white to black is very different; but rather are analogous to the successive numbers of white balls occurring in batches of the same size taken at random from the same bag. It would appear hopeless therefore to trace by ordinary induction the causation of any particular event of this character. It is only crazy gamblers who pretend to predict the " runs" in games of pure chance. But we are not precluded from apply. ing the law of error to detect delicate differences, such as may exist between a perfect and a slightly-loaded coin. Take for example the observation that the percentage of male compared with female births for more than a million plural births (of twins or triplets) in Prussia during a certain period of years was 104.447 (males to 100 females); whereas the corresponding ratio for all births (single as well as plural) was 106.305; the observation on which this average is based numbering several millions. Given these numbers, and knowing as we do that the phenomenon belongs to class (a), we are able to determine the constant c; which proves to be nearly 3. Thus the difference between the two averages compared, viz. 1.858, is about six times the constant, and accordingly (see above par. 1) the odds against

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the observed difference in the averages being due to accident and not to a real cause which may be expected to continue acting-are many times more than 50,000 to 1 (Duesing). We have obtained, at a stroke, a degree of evidence in favour of a law which otherwise could only be obtained by a laborious analysis of the returns. By parity of reasoning it is found that in times and places where the absolute number of births is large the proportion of males is small (ibid.).

(b) This summary method may be employed also in the second case (where the analogy with games of chance does not hold good); but not in such a clear light of foreknowledge as to the character of the causes under investigation.

Besides the exact and direct applications of the law of error, it also affords what may be called "regulative ideas" to the statistician; supplying the rationale of many received maxims that ceteris paribus an average is more worth the greater the number, and the less the divergence, of the returns averaged; that a few accurate returns may be better than many loose

ones.

[Fora general exposition, at once simple and accurate, of the law of error, see Venn, Logic of Chance, third ed. 1888, chaps. xviii. and xix. See also Jevons, Principles of Science, chap. xvii.-Bertillon, art. "Moyenne," Dictionnaire Encyclopédique des Sciences Médicales.-Quetelet, Physique Sociale. For the conditions under which the fulfilment of the law may be expected, Glaisher, Memoirs of the Astronomical Society, vol. xl. p. 104.-Galton, Philosophical Magazine, 1875, "Statistics by inter-comparison."-Edgeworth, ibid. 1892, "The Law of Error."-For the a posteriori proof, that the law is fulfilled, see Galton, Natural Inheritance.Westergaard, Grundzüge der Theorie der Statistik, chap. iii.-Edgeworth, "Empirical proof of the law of Error," Phil. Mag., 1887.-For the application of the law to practice, Dormoy, Théorie mathématique des assurances sur la vie. For the application of the law to induction, (a) where the analogy of games of chance holds good, Westergaard, op. cit.

Lexis, Massenerscheinungen.· - Duesing, Das Geschlechtsverhältniss in Preussen; (b) in general, Edgeworth, Journal of the Statistical Society, Jubilee Volume, 1885, "Methods of Statistics," ibid. December 1885, "Methods of Determining Rates." Many of these writers throw light on other parts of the subject besides those with special reference to which they have been cited. Several other authors might have been cited. Merriman has published an immense list of writers on the cognate subject of the Method of Least Squares, many of whom have touched on the law of error, and some on its applications to social phenomena (see PROBABILITIES; STATISTICS).]

F. Y. E.

ESCHEAT (historical) was a feudal term introduced by the Normans into England, and applied to the reversion of land to the lord. The ordinary cause of such reversion was the failure of heirs, when the whole estate passed into the hands of the lord. If the heir was a

minor, the phrase was escata cum hærede, when the necessities of the heir and other children were paid for out of the estate and the surplus only went to the lord, until the heir, on reaching his majority, paid a relief and obtained seisin. Escheat also took place in cases of treason or felony. If the criminal was a tenant-in-chief, the whole of his property reverted to the crown; but if he was a sub-tenant, his movables only fell to the crown, while the real estate passed to the immediate lord.

[Dialogus de Scaccario, ii. x.]

R. L.

Escheat (modern law), takes place where a person dies intestate and without an heir. The lands of such a person go to the feudal lord, but, as in the case of freehold land the right of mesne lords can in our days be established but rarely, such land generally goes to the sovereign as lord paramount. Copyhold land goes to the lord of the manor, and § 4 of the Copyhold Act provides that the right of escheat is to continue after enfranchisement; enfranchised copyhold land, though otherwise of the nature of freehold land, does not therefore escheat to the crown, but goes to a private person. Formerly the lands of felons were subject to the right of escheat, but an act passed in 1870 has repealed this rule. On the other hand the Intestate Estates Act of 1884 has made certain rights as to real property subject to escheat, which were not so subject before. The same act has enabled the crown to waive its right in certain cases. The procedure which takes place to inquire as to the right of the crown has been simplified by the Escheat (Procedure) Act of 1887.

The right of the state to acquire the property of a person dying without relations or a will exists in most countries independently of feudal rules, and seems justified by reason and convenience.

[Bentham, J. S. Mill, Godin, and other reformers, have proposed to narrow the rights of intestate succession (ie. to extend escheat) in order to correct, to some extent, the unequal distribution of wealth.]

E. S.

ESCUSADO, the name of the portion of ecclesiastical tithes made over in 1567 by the Pope to the crown of Spain.

E. Ca.

ESSART, EXART, sometimes also called ASSART. A mediæval term applied to a portion of forest land cleared and brought into cultivation. To make essarts was technically a breach of the forest law, punishable by fine. These fines, with the yearly rents levied on the essarted lands, which the maker of the essart was usually allowed to keep under cultivation, formed a considerable item in the revenues of the royal and other lords of forests in mediaval England. These rents would appear to have been fixed at the highest rate that could be maintained, a rate which will be found to be often several times as great as that paid by free or even customary tenants for other land in the same neighbourhood. In spite of these high rates, however, fresh essarts were made almost every year in England. The forest of Wirrall in Cheshire, for instance, was entirely under cultivation before the death of the Black Prince, who, in his capacity of Earl of Chester, by a formal charter of disafforestment, put his seal to the work of reclamation. The word essart has been variously derived from the old French assortir, to make smooth, or one of the low Latin terms, exertum, rooted up, sarrire, to weed, or exarare, to plough up.

[Manwood, Forest Law, London, 1596, etc.Ducange, Glossarium Media et Infima Latinitatis, ed. nova a L. Favre, Paris, 1884.-Forest accounts among the ancient records of the exchequer in the Public Record Office.] A. H.

ESTATE. A so-called owner of land has, according to English law, no absolute right of ownership; all that he has is an interest varying in extent and duration, and known in technical language as an "estate" in the land. The largest estate known to the law is an "estate in fee" (fee simple), which gives the owner as complete rights of enjoyment and alienation as the nature of the property will admit; an estate tail (see ENTAIL), being convertible into an estate in fee-by the tenant alone, if in