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shape. Although the regression equacions obtained would not L. 154. In the determination of the standard deviation proper to the accurately fit the original material, yet they would have a certain law of error (and other constants proper to other laws of frequency) correspondence thereto. What sort of correspondence may be it commonly happens that besides the inaccuracy, sa illustrated by an example in games of chance, which Professor which has been estimated, due to the paucity of the

Sheppard's

Corr Weldon kindly supplied. Three hall-dozen of dice having been

ections. data, there is an inaccuracy due to their discrete characthrown, the number of dice with ter: the circumstance that measurement, e.g. of human heights, are more than three points in that dozen given in comparatively large units, e.g. inches, while the real objects which is made up of the first and are more perfectly graduated. Mr Sheppard has prescribed a remedy the second half-dozen is taken for y, I | for this imperfection. For the standard deviation let uz be the the number of sixes in the dozen rough value obtained on the supposition that the observations made up to the first and the third are massed at intervals of unit length (not spread out continuously, half-dozen, is taken for . Thus as ideal measurements would be); then the proper value, the mean each twofold observation (xy) is the integral of deviation squared, say (uz) =

u h a, where h is the size sum of six twofold elements, each of of a unit, e.g. an inch. It is not to be objected to this correction which is subject to a law of fre that it becomes nugatory when it is less than the probable error to quency represented in fig. 13; where ! which the measurement is liable on account of the paucity of obserthe figures outside denote the num vations. For, as the correction is always in one direction, that of ber of successes of each kind, for the subtraction, it tends in the long run to be advantageous even though ordinate the number of dice with masked in particular instances by larger fluctuating errors.

more than three points (out of a cast 155. Prosessor Pearson has given a beautiful application of the FIG. 13.

of two dice), for the co-ordinate the theory of correlation to test the empirical evidence that a given number of sixes (out oi a cast of two dice, one of which is common group conforms to a proposed formula, e.g. the normal proge to the aforesaid cast); and the figures inside denote the comparative law of error.

Criterion of probabilities of each twofold value (e.g. the probability of obtain | Supposing the constants of the proposed function to

Empirical ing in the first two cast dice each with more than three points, and

be known-in the case of the normal law the arith-ve

Verification, in the second cast two sixes, is 1/72). Treating this law of fre

metic mean and modulus--we could determine the quency according to the rule which is proper to the normal law, position of any percentile, e.g. the median, say a. Now the prowe have (for the element) is the sides of the compartments each uil bability that if any sample numbering n were taken at random

from the complete group, the median of the sample, a', would lie at q=ivG/18; 09=i/v2; s=1/v20.

such a distance from a that there should be r observations between Whence for the regression-equation which gives the value of the ordinate most probably associated with an assigned value of the

e and e' is van exp-20°/n. S abscissa we have y=xX rozlo, = 0.3x; and for the other regression. equation, I=y/6. Accordingly, in Professor Weldon's statistics,

If, then, any observed set has an excess which makes the above which are reproduced in the annexed diagram, when x=3 the written integral very small, the set has probably not been formed

by a random selection from the supposed given complete group. 0 1 | 2 | 3 | 4 5 | 6 | 7 | 8 | 9 10 | 11 | 12

To extend this method to the case of two, or generally n, percentiles, forming (n + 1) compartments, it must be observed that the excesses say c and e', are not independent but correlated. To measure the

probability of obtaining a pair of excesses respectively as large as | 3 3 1

e and e', we have now (corresponding to the extremity of the pro

bability-curve in the simple case) the solid content of a certain | 171513

probability-surface outside the curve of equal probability which passes through the points on the plane ry assigned by e, e' (and the

other data). This double, or in general multiple, integral, say P, is 161 | 36 | 14 | 5

expressed by Professor Pearson with great elegance in terms of

the quadratic factor, called by him x?. which forms the exponent of 36 135 154/150| 64 | 21

the expression for the probability that a particular system of the

values of the correlated e, e', &c., should concur 7 74 | 195 260 179112 35 5

12

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most probable value of y ought to be I. And in act this expectation is verified, and y being measured along lines drawn through the centre of the compartment, which ought to have the maximum of content, representing the concurrence of one dozen with two sixes and another dozen with six dice having each more than three points, the compartment which in fact contains 254 (almost the maximum content). In the absence of observations at x= -3i or y= # 6i, the regression-equations cannot be further verified. At least they have begun to be verified by batches composed of six elements, whereas they are not verifable at all for the simple elements. The normal formula describes the given statistics as they behave, not when by themselves, but when massed in crowds: the regressionequation does not tell us that if r' is the magnitude of one member the most probable magnitude of the other member associated there. with is rx', but that if x' is the average of several samples of the first member, then rx' is the most probable average for the specimens of the other member associated with those samples. Mr Yule's proposal to construct regression-equations according to the normal rule" without troubling to investigate the normality of the distri. bution"? admits of this among other explanations. Mr Yule's own view of the subject is well worthy of attention.

1 Cl. above, par. 115. • Proc. Roy. Soc., vol. 60. p. 477. * Below, par. 168.

when n is odd; with an expression different in form, but nearly coincident in result, when n is even. The practical rule derived from this general theorem may thus be stated. Find from the given observations the probable values of the coefficients pertaining to the formula which is supposed to represent the observations. Calculate from the coefficients a certain number, say n, of percentiles; thereby dividing the given set into nti sections, any of which, according to calculation, ought to contain say m of the observations, while in fact it contains m'. Put e for m'-m; then x* = Ec/m. Professor Pearson has given in an appended table the values of P corresponding to values of n+1 up to 20, and values of x' up to 70. He does not conceal that there is some laxity involved in the circumstance that the coefficients employed are not known exactly, only inferred with probability.

156. Here is one of Professor Pearson's illustrations. The table on next page gives the distribution of 1000 shots fired at a line in a target, the hits being arranged in belts drawn on the target parallel to the line. The “normal distribution" is obtained from a normal curve, of which the coefficients are determined from the observations. From the value of x. viz. 45.8, and of (n+1). viz. 11, we deduce, with sufficient accuracy from Professor Pearson's table, or more exactly from the formula on which the table is based, that P=.000,001,5 . “In other words, if shots are distributed on a target according to the normal law, then such a distribution as that cited could only be expected to occur on an average some 15 or 16 times in 10,000,000 times."

157. "Such a distribution" in this argument must be interpreted as a distribution for which it is claimed that the The observations are all independent of each other. Suppose Criterloo that there were only 500 independent observations, the Criticized. remainder being merely duplicates of these 500. Then in the above

Just as the removal of a tax tends to be in the long run beneficial to the consumer, though the benent on any particular occasion may be masked by fluctuations of price due to other causes. 5 Phil. Mag. (July, 1900).

As shown above.. par. 103. * Loc. cit. p. 166.

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table the columns for the normal distribution and for the discrepancy These values being substituted for the coethcients in the general e should each be halved; and accordingly the column for em should formula, there results an expression which may be obtained directly be halved. Thus e'm being reduced to 22.9, Pas found from Pro by continuing to expand the expression for a term of the binomial. fessor Pearson's table is between 995 and 629. That is, such a In virtue of the second approximation a set of observations distribution might be expected to occur once on an average some | is not to be excluded from the affinity to the normal curve because, once or twice in a hundred times. If actual duplication of this sort like the curve of barometric heights, it is slightly asymmetrical. is not common in statistics,' yet in all such applications of the In virtue of the third approximation it is not excluded because,

like the group of shot-marks above examined, it is, though almost | Observed Normal Belt.

perfectly symmetrical, in other respects apparently somewhat Frequency. Distribution.

c/m.

abnormal.

160. Il the third approximation is not satisfactory there is still

available a fourth, or a still higher degree of approximation.10 0.667 The general expression for y which (multiplied by Ar)

represents the probability that an error will occur at a 10.704

* Higher 89 7.224 particular point (within a particular small interval):

Approxima.
190
162

4.839 may be written
212
242

3.719
Lidia

1
240

dl 1+2
5.400
.-ki

G -...+(-1)"k172+2)! (d) "* ... you
8.255
1.157

where % is (the norinal error-function)Jabf*2*, k is the

mean square of deviation; ki, ka,..., &c., are coefficients formed 1000

from the mean powers of deviation according to the rule that ki is the 1000

45.811

difference between the tth mean power as it actually is and what it Pearsonian criterion-and in other calculations involving the num.

would be is the (1-1)th approximation were perfectly correct. Thus ki

is the difference between the actual mean third power and what the ber of observations, in particular the determinations of probable error -a good margin is to be left for the possibility that the n observa

third power would be is the first approximation, the normal law, were

perfectly correct, that is, the difference between the actual mean tions are not perfectly independent: e.g. the accidents of wind or

third power, often written us, and zero, that is 43. Similarly kz is nerve which affected one shot may have affected other shots immediately before or after.

the difference between the actual mean fourth power of deviation, 158. (2) The Generalized Law of Error.–That the normal law of

say 4, and what that mean power would be if the second approximaerror should not be exactly fulfilled is not disconcerting to those who

tion were perfectly correct, viz. 3k". Thus kg =43-3k". The series ground the law upon the plurality of independent causes. On that

ki, k2, ks, &c., k, k, ka, &c., form each a succession of terms descendview the normal law would only be exact when the numbers of ele

ing in the order of magnitude, when each k, e.g. k, has been divided ments from which it is generated is very great. In general, when

by the corresponding power, i.e. the power (1+2) of the parameter or that number is large, but not indefinitely great, there is required a

modulus c= V (2k), which division is secured by the successive differcorrection owing to one or other of the following imperfections: that the elements do not fluctuate according to the normal law of

entiations of yo, with which each k is associated, e.g. ke with a frequency; that their fluctuations are not independent of each other;

Moreover, the first term of the odd series of k's when divided by that the function whereby they are aggregated is not linear. The correction is formed by a series of terms descending in the order

the proper power of the parameter, viz. ( is small in comparison of magnitude.

with the first term of the even series, viz. k, properly referred 159. The first term of this series may be written

divided by c? ( = 2k).

161. Whatever the degree of approximation employed, it is to be -2(k/c")</c-2x°/3c);

remembered that the law in general is only applicable to a certain where 2 is the mean square of deviation for the compound and

range of the compound magnitude here represented by also the sum of the mean squares of deviations for the component the abscissa x." The curve of error, even when general

Character elements, ki is the mean cube of deviations for the Second

ized as here proposed, coincides only with the central o

i of the compound and the sum of the mean cubes for the comportion-the body, as distinguished from the extremities

Approxima. and Third

ponents, and the clements are supposed to be such and of the actual locus; a greater or less proportion. Approxima

tion. so numerous that ki/c' is of the order 1/vn. This second tions.

162. The law thus generalized may be extended, with similar approximation, first given by Poisson, was rediscovered reservations, to two or more dimensions. For example, the second by De Forest. The present writer has obtained it by a variety of

approximation in two dimensions may be written methods. By a further extension of these methods a third and

Extension further approximations may be found. The corrected normal law

to Two or is then of the form

More where zo is (the normal error-function)

Dimeo (x-2xy +y2)

sions.

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where k = kulc. k, = k/ch, k, and c are defined as above, k, is the sum of the respective differences for each element between its mean fourth power of crror and thrice its mean square of error, and also the corresponding difference for the compound. The formula may be verified by the case of the binomial, considered as a simple case of the law of great numbers. Here

c = 2np9, k, = npg (9-p), kg = npg (1 - 6p9).

x and y are (as before) co-ordinates measured from the centre of gravity of the group as origin, each referred to (divided by its proper modulus; r is the ordinary coefficient of regression; 2.ok is the mean value of the cubes x, 2.k is the mean value of the products x'y, and so on; all these k's being quantities of an order less than unity. This form lends itself readily to the determination of a second approximation to the regression-curve, which is the locus of that y, which is the most probable value of the ordinate corresponding to an assigned value of x. Form the logarithm of the above-written expression (for the frequency-surface); and differentiate that logarithm with respect to X. The required locus is given by equating this

'It is frequent in the statistics of wages.

? See on this subject, in addition to the paper on the “ Law of Error " already cited (Camb. Phil. Trans., 1905), another paper by the present writer, on "The Generalized Law of Error," in the Journ. Siat. Soc. (September, 1906).

* The Analyst (lowa), vol. ix.
· Phil. Mag (Feb. 1896) and Camb. Phil. Trans. (1905).

The part of the third approximation affected with k? may be found by proceeding to another step in the method described (Phil. Mag., 1896, p. 96). The remaining part of the third approximation is sound by the same method (or the variant on p. 97) from the

dy i d'y new partial differential equation a nd where kz, is the difference between the actual mean fourth power of deviation and what it would be if the normal law held good." Further approximations may be obtained on the same principle.

Mi-3472 in the notation which Professor Pearson has made familiar. 7 Cl. Pearson, Trans. Roy. Soc. (1895), A, clxxxvi. 347.

XXII 7*

. Above, $ 103, referring to Todhunter, History, art. 993. The third (or second additional term of) approximation for the binomial, given explicitly by Professor Pearson, Trans. Roy. Soc. (1895), A, foot note of p. 347, will be found to agree with the general formula above given, when it is observed that the correction affecting the absolute Lerm, his yo, disappears in his formula by division.

Journ. Slal. Soc. (1899), p. 550, referring to Pearson, Trans. Roy. Soc. (1898), A.

10 Practically no doubt the law is not available beyond the third or fourth approximation, for a reason given by Pearson, with relerence to his generalized probability-curve, that the probable error incident to the determination of the higher moments becomes very great.

11 This consideration does not present the determination of the true moments from the complete set of observations if homogeneous, according as the system of elements fulfils more or less perfectly certain conditions.

differential to zero (the second differential being always negative). The resulting equation is of the form

y dx Cat Cat +Cox y-rx-T-ax? - 2Bxy-gyo,

This latter curve comprises the two others as special cases, and, so where T, a, B. are all small, linear functions of the k's. As y is far as my investigations have yet gone, practically covers all nearly equal to rx, it is legitimate to substitute rx for y, when y is homogeneous statistics that I have had to deal with. Something multiplied by a small coefficient. The curve of regression thus still more general may be conceivable, but I have found no necessity reduces to a parabola with equation of the form

for it."? The "hypergeometrical series," it should be explained, y-T=rx-9x2;

had appeared as representative of the distribution of black balls, where q is a linear function of the third mean powers and moments

in the following case. " Take n balls in a bag, of which pn are black

and on are white, and let r balls be drawn and the number of black of the given group.

be recorded. If r>pn, the range of black balls will lie between o and 163. Disseclion of certain Helerogeneous Groups.-Under the pn; the resulting frequency-polygon is given by a hypergeometrical head of law of error may be placed the case in which statistics

series."

Further reasons in favour of his construction are given by Professor relating to two (or more) different types, each separately con

Pearson in a later paper. “The immense majority, if not the total. forming to the normal law, are mixed together; for instance,

ity, of frequency distributions in homogeneous material show, when the measurements of human heights in a country comprising the frequency is indefinitely increased, a tendency to give a smooth two distinct races.

curve characterized by the following properties. (i.) The frequency

starts from zero, increases slowly or rapidly to a maximum and then In this case the quaesila are the constants in a curve of the form:

falls again to zero-probably at a quite different rate as the characy = a (1/ Vac) exp-(x-a)/c,?+B(1/V702) exp - (x - 5)/, ter for which the frequency is measured is steadily increased. This where a and B are the proportionate sizes of the two groups

is the almost universal unimodal distribution of the frequency of (a+B=I); a and b are the respective centres of gravity; and C. C,

homogeneous series .. (ii.) In the next place there is generally the respective moduli. The data are measurements each of which

contact of the frequency-curve at the extremities of the range. relates to one or other of these component curves. A splendid

These characteristics at once suggest the following of frequency solution of this difficult problem has been given by Professor Pearson. curve, il yox measure the frequency falling between x and x +år: The five unknown quantities are connected by him with the centre

dy_yírta) of gravity of the given observations, and the mean second, third,

dx F(x) ... fourth and fifth powers of their deviations from that centre of gravity, Now let us assume that F(x) can be expanded by Maclaurin's theorem. by certain rational algebraic equations, which reduce to an equation

Then our differential equation to the frequency will be in one variable of the ninth dimension. In an example worked by Professor Pearson this fundamental equation had three possible

I dy rta roots, two of which gave very fair solutions of the problem, while the

y dx bo+61x + box? +... third suggested that there might be a negalive solution, importing that Experience shows that the form (x) (“ keeping bo. b. 67, only ") the given system would be obtained by subtracting one of the normal suffices for certainly the great bulk of frequency distributions." groups from the other, but the coefficients for the negative solution 166. The “ generalized probability-curve" presents two main proved to be imaginary. “In the case of crabs' foreheads, therefore, | forms we cannot represent the frequency curve for their forehead length as

y= yo(1+xla,)v) 1 -x/a)van, the difference of two normal curves." In another case, which primâ

-v tan-x/a. facie seemed normal, Professor Pearson found that "all nine roots

and y=yoti+x?q?)-€ of the fundamental nonic lead to imaginary solutions of the problem. The best and most accurate representation is the normal curve."

When an ag, v are all finite and positive, the first form represents, 164. This laborious method of separation seems best suited to

in general, a skew curve, with limited range in both directions; in cases in which it is known beforehand that the statistics are a mix

the particular case, when a, = 2g, a symmetrical curve, with range ture of two normal groups, or at least this is strongly suggested by

limited in both directions. If y=0, the curve reduces to the two-headed character of the given group. Otherwise the less

yeyo(2+xlaquite-vs); troublesome generalized law of error may be preferable, as it is appro representing an asymmetrical binomial with v=2w2/ws, and priate both to the mixture of two not very widely different-normal 21 = 2u/-awa/uz, mu and ks. being respectively the mean second groups, and also the other cases of composition. Even when a and mean third power of deviation measured from the centre of group of statistics can be broken up into two or three frequency gravity. In the particular case, when he is sinall, this form reduces curves of the normal or not very abnormal-type, the group may to what is above called the “ quasi-normal" curve; and when ms is yet be adequately represented by a single curve of the "generalized" | zero, a, becoming infinite, to the simple normal curve. The pregnant type, provided that the heterogeneity is not very great, not great general form yields two less familiar shapes apt to represent curves enough to prevent the constants ki, kz, ks, &c., from being small. of the character shown in figs. 14 and 15-the one occu Thus, suppose the given group to consist of two normal curves each having the same modulus c, and that the distance between the centres is considerable, so considerable as just to cause the central portion of the total group to become saddle-backed. This phenomenon sets in when the distance between the centre of gravity of the system and the centre of either component = c.! Even in this case ka is only -0.125;k is 0.25 (the odd k's are zero).

Section II.-Laws of Frequency. 165. A formula much more comprehensive than the corrected normal law is proposed by Professor Pearson under the The designation of the “ generalized probability-curve." “ General

FIG. 14.

Fig. 15. The ground and scope of the new law cannot be better ized Proba. stated than in the words of the author: " The slope of bility

good number of instances, such as infant deaths, the values of houses, the normal curve is given by a relation the form

Curve." the number of petals in certain flowers; the other less familiarily I dy

illustrated by Consumptivity and Cloudiness. The second solution Jdx=

represents a skew curve with unlimited range in both directions.

Professor Pearson has successfully applied these formulae to a number The slope of the curve correlated to the skew binomial, as the of beautiful specimens culled in the most diverse fields of statis. normal curve to the symmetrical binomial, is given by a relation of tics. The flexibility with which the generalized probability-curve the form

adapts itself to every variety of existing groups no doubt gives it a i dy

great advantage over the normal curve, even in its extended form. jdx=-ct Cox

It is only in respect of a priori evidence that the latter can claim Finally, the slope of the curve correlated to the hypergeometrical

precedence. series (which expresses a probability distribution in which the 167. Skew Correlation.--Professor Pearson has extended his contributory causes are not independent, and not equally likely to give equal deviations in excess and defect), as the above curves to

Trans. Roy. Soc. (1895), A, p. 381.

3 Ibid. p. 360. their respective binomials, is given by a relation of the form

" Mathematical Contributions to the Theory of Evolution"

(Dra pers' Company Research Memoirs, Biometric Series II.), xiv. 4. iCf. Journ. Stat. Soc. (1899). lxii. 131. A similar substitution of sp. 7, loc. cil. Ibid. p. 367. the generalized law of error may be recommended in preference to Pearson, loc. cit., p. 364, and Proc. Roy. Soc. the method of translating a normal law of error (putting x=f(x). A lucid exposition of Professor Pearson's various methods is where x obeys the normal law of error) suggested by the present given by W. Palin Elderton in Frequency-curves and Correlation writer (Journ. Stai. Soc., 1898), and independently by Professor J.C (1906). Kapteyn (Skew Frequency Curves, 1903).

Journ. Slal. Soc. (1895), p. 506.

V = yo (1 + x/a)yax

method to frequency-loci of two uimensions;' constructing for "Generating Functions.". Not all parts of the book are as rewarding

as the Introduction (published separately as Essai philosophique des the curve of regression (as a substitute for the normal right

probabilités) and the fourth and subsequent chapters of the second line), in the case of “skew correlation," a parabola, with

book. Among numerous general treatises E. Czuber's Wahrscheinconstants based on the higher moments of the given group. lichkeitstheorie (1899) may be noticed as terse, lucid and abounding

168. In this connexion reference may again be made to Mr in references. Other authorities may be mentioned in relation to Yuie's method of treating skew surfaces as if they were normal.

the different parts of the subject as above divided. First principles

are discussed with remarkable acumen by J. Venn in Logic of Chance It is certainly remarkable that the correlation should be so well

(ist ed., 1876, 3rd ed., 1888) and by J. v. Kries in Principien der represented by a line-the property of a normal surface--in Wahrscheinlichkeitsrechnung (1886). As a repertory of neat probcases of which normality cannot be predicated: for instance,

lems involving the calculation of probability and expectation the statistics of the number of husbands (or wives) living at

W. A. Whitworth's Choice and Chance (5th ed., 1901), and DCC.

Exercises ... in Choice and Chance (1897) deserve mention. But this each age who have wives (or husbands) living at different ages.

advantage is afforded in nearly as great perfection by more compreIt may be suggested that though in this case there is one dominant hensive works. Bertrand's Calcul des probabilités (1889) abounds cause, the continual decrease of the population, inconsistent in choice examples, while it excels in almost every other branch with the plurality of causes postulated for the law of error, yet

of the subject. ' Special mention is also deserved by H. Poincaré's

Calcul des probabilités (leçons professes, 1893-1894). On local or there is a sufficient degree of accidental variation to realize one

geometrical probability Professor Morgan Crofton is one of the property at least of the normal locus.

highest authorities. His paper on “Local Probability" in Phil. 169. There is possibly an extensive class of phenomena of Trans. (1868), and on “ Geometrical Theorems," Proc. Lond. Math. which frequency depends largely on fortuitous causes, yet not

Soc. (1887), viii., should be read in connexion with the section on

" Local Probability" in his article on “ Probability" in the oth Relations so completely as to present the genuine law of error.)

edition of the Ency. Bril., from which section several paragraphs between This mixed class of phenomena might be amenable have been transferred en bloc to the section on Geometrical Frequency to a kind of law of frequency that would be different Applications in the present article. The topic is treated exand Proda- from. vet have some affinity to the law of error. I haustively by Czuber in Geometrische Walırscheinlichkeiten und bility

Miltelworten (1884). Czuber is also to be mentioned as the author The double character may be taken as the definition

of Theorie der Beobachtungsfehler, in which he has reproduced, often of the laws proper to the present section. The definition of with improvement, or referred to, almost everything of importance the class is more distinct than its extent. Consider for example in the work of his predecessors. A. L. Bowley's Elements of Statistics, the statistics which represent the numbers out of a million born

pt. 2 (2nd ed., 1902), forms an introduction to the law of error which that die in each year of age after thirty of forty-the latter

leads the beginner casily, yet far. References to other writers are

given in Section 1. of Part II. above. A list of writings on the cognate part of the column in a life-table. These are well represented by topic, the method of least squares, has been given by Merriman (Cona species of Professor Pearson's "generalized probability-curve,"5 necticut Trans. vol. iv.). On laws of frequency, as above defined, his type iïï. of the form

Professor Karl Pearson is the highest authority. His “ Contributions to the Mathematical Theory of Evolution," of which twelve have appeared in the Trans. Roy. Sos. (1894-1903), and others are being

published by the Drapers' Company, teem with new theories in The statistics also lend themselves to the Gompertz-Makeham | Probabilities.

(F. Y. E.) formula for the number living at the age

PROBATE, in English law, the “proving ” (Lat. probatio) of

a will. The early jurisdiction of the English ecclesiastical bs = S¢gle

courts over the probate of wills of personality is discussed under The former law, the simplest species of the “generalized | WILL. The Court of Probate Act 1857 transferred the jurisprobability-curve," may well be attributed in part to the diction both voluntary and contentious of all ecclesiastical, operation of a plexus of causes such as that which is apt to royal peculiar, peculiar and manorial courts to the court of generate the law of error. In fact, a high authority, Professor probate thereby constitutcd, created a judge and registrars of Lexis, has seen in these statistics-or continental statistics that court, abolished the old exclusive rights in testamentary in pari materiama fulfilment of the normal law of error. They matters of the advocates of Doctors' Commons, and laid down at least fulfil tolerably the generalized law of error above rules of procedure. Contentious jurisdiction was given to county described. But the Gompertz-Makeham formula is not thus to courts when the personal estate of the deceased was under £200 be accounted for; at least it is not thus that it was regarded by in value. The Judicature Act: 1873 merged the old court of its discoverers. Gompertz justifies his law? by a “ hypothetical probate in the probate divorce and admiralty division of the deduction congruous with many natural effects," such as the High Court of Justice. The division now consists of the presiexhaustion of air by a pump; and Makeham follows & in the same dent and one other judge. The practice of the division is mainly track of explanation by way of natural laws. Of course it is regulated by the rules of the Supreme Court 1883. Appeals not denied that mortality is subject to accident. But the lie to the court of appeal and thence to the House of Lords. Gompertz-Nakeham law purports to be fulfilled in spite of, not | Probate may be taken out either in common or solcmn form.

s agencies. The formula is accounted | In the former case, which is adopted when there is no dispute as for not by the interaction of fleeting causes which is character to the validity of the will, the court simply recognizes the will istic of probability, but by causes of that ordinary kind of which propounded as the last will of the deceased. This formality the investigation constitutes the greater part of natural science. is necessary to enable the executor to administer the estate of Laws of frequency thus conceived do not belong to the theory of his testator. Probate in this form is granted simply as a Probabilities.

ministerial act if the attestation clause declares that the formaliAUTHORITIES.-As a comprehensive and masterly treatment tics of the Wills Act have been complied with, or if other evidence of the subject as a whole, in its philosophical as well as mathematical to that effect is produced. Such grant is liable to revocation, character, there is nothing similar or second to Laplace's Théorie

but it is provided that any person dealing with an executor analytique des probabilités. But this " ne plus ultra of mathematical skill and power" as it is called by Herschel (Edinburgh Review, on the faith of a grant of probate in common form, shall not be 1850) is not easy reading. Much of its difficulty is connected with prejudiced by its revocation. The executor may within thirty the use of a mathematical method which is now almost superseded, years be called upon to prove in solemn form, or a person who 1" Contributions," No. xiv. (above cited).

doubts the validity of the will propounded may enter a caveat • Not the same parabola as that proposed at par. 162.

which prevents the executor proving for six months and the 3 Census of England and Wales General Repori (cod. 2174), p. 226.

caveat may be renewed each six months. The executor may Cf. p. 70, as to the rationale of the phenomenon. A good example of the suggested blend between law and chance

however take out a summons to get the caveat “subducted " or is presented by an hypothesis which Benine (in a passage referred to

withdrawn, but if an appearance to the summons is entered above, par. 97) has proposed to account for Pareto's income-curve. These initials do not apply to certain passages in the above 6." Contributions." No. ii., Phil. Trans. (1895). vol. 186, A.

article, namely, the greater part of paragraphs 41, 52, 62 and 72, and Lexis, Massenerscheinungen, $ 46. Cr. Venn, cited above, par. 124. almost the whole of the 4th section of Part. I. (pars. 76-93), which · Phil. Trans. (1-25).

have been adopted froin the article " Probability" in the oth edition • Assurance Magazine (1866), xi. 315.

I of the Ency. Brit., written by Professor Morgan Croston.

within six days to the summons the executor is then compelled | law and chancery courts (Noemen's Law of Administration, to prove in solemn form. Probate in solemn form is a judgment | $ 145). of the court in favour of the will propounded, and is only revoc- Jurisdiction as to wills and their probate as such is neither able by the discovery of a later will. In order, therefore, to included in nor excepted out of the grant of judicial power to obtain such grant proceedings have to be taken by action, and the courts of the United States (i.e. the Federal as distinguished witnesses produced in support of the will, and the action from the state courts). So far as it is ex parte and merely proceeds in the usual way.

administrative it is not conferred, and it cannot be exercised by The principal rules now obtaining as to probate are these. them at all until in a case at law or in equity its exercise becomes Probate, which since the Land Transfer Act 1897 must be taken necessary to settle a controversy by reason of the (diverse) out for wills of realty as well as wills of personalty, may be l citizenship of the parties. An action to set aside the probate of granted either in the principal or in a district registry, and a will of real estate may be maintained in a Federal court when should be obtained within six months after the testator's death. the parties on one side are citizens of a different state from the When no executor is named the will is not now invalid, as was once parties on the other side (Ellis v. Davis, 109 U.S. Reports, 485). the case, but administration cum testamento annexo is granted. Probate in solemn form, i.e. after due notice to all parties in The same course is pursued where the executor renounces or interest is the almost universal form in use in the United States. dies intestate before administering the estate of the deceased. One reason for this no doubt is that all documents affecting After probate, the probate itself (as the official copy of the will title to real estate must be recorded and probate in solemn form is called) becomes evidence, the original will being deposited in concludes all parties to the proceeding and thus tends to establish the principal registry at Somerset House, London. On grant the title to all real estate passing under the will. of probate, estate duty, denoted by a stamp on the affidavit In the United States wills of real property must be separately sworn for that purpose, is payable. It varies according to the proven in the proper probate court in each state in which the amount at which the estate of the deceased is fixed by the real property is situated, unless statute dispenses with separate oath of the executor (see EstATE DUTY). The act of 1881 probate (each state being " foreign" to every other for this enables any officer of inland revenue to grant probate where the purpose). Copies of such will and probate should be filed also personal estate does not exceed £300.

in the office of the register of decds of each county in the state Ireland.-In 1867 an act on lines similar to the English act was

in which any real property belonging to the testator is situated. passed for Ireland and under the Irish Judicature Act of 1877 the

In the state of New Jersey it has been held that an unprobated then existing court of probate was merged in the High Court of will is capable of conveying an interest in the property devised, and Justice.

when a conveyance is made under a power in the will before probate Scotland.-Confirmation includes both the probate and letters of a subsequent probate validates the conveyance (1906, Mackey V. administration of English procedure. Without confirmation by

Mackey, 63 Atl. Rep. 984). the court interference by the executor becomes a vitious intro

In Illinois a court of equity has no inherent power to entertain mission. Originally confirmation of testaments of movables fell, a bill to contest a will (1906; O'Brien v. Bonfield, 220 Ill. Rep. 219). as in England, under the cognizance of the church courts. Such

In Missouri a foreign (New York) will of real estate in Missouri, jurisdiction certainly existed at the time of regiam majestatcm.

probate of which was duly recorded in Missouri, cannot be collaterally This ecclesiastical right continued through the commissary court

attacked, and cannot be set aside by direct proceeding after being at Edinburgh (constituted by Queen Mary in 1563), and the local

filed for record more than five years in Missouri (1907; Cohen v. commissaries, until modern times when the jurisdiction of the courts

Herbert, 104 So. W. Rep. 84). was at first transferred and then abolished by a series of enactments PROBATION. The probation system. in penology, is an from the Commissary Courts Act 1823 to the Sheriff Courts Act 1876. The act of 1822 placed the commissary jurisdiction in the attempt to reform a prisoner outside prison, a special kind of sheriff courts; by the act of 1876 the sheriffs sit as sheriffs in warder-the probation officer-supervising the prisoner in the testamentary matters, no longer as commissaries. Confirmation prisoner's own home. The state of Massachusetts in America of wills where the whole estate is under 1300 is regulated by

was the first to attempt “probation," and at first (1878) in a the Customs and Inland Revenue Act 1881 and other acts. An eik is an addition to a confirmation made on discovery of

tentative manner. As success crowned the efforts of the readditional effects of the deceased after confirmation,

formers the system was developed and applied to an increasing Uniled Slates.- Probate is granted in some states by the number of cases; and gradually other American states followed ordinary chancery or common law courts, but more frequently with some variations in their plans. The probation officers by courts of special jurisdiction, such as the prerogative court attend the court and the judge ollicially gives up the prisoner in New Jersey, the surrogates' court in New York, the orphans' to the officer chosen to supervise him, generally explaining to court in Pennsylvania.

the prisoner that, if he is not obedient to all the rules made for " In a great majority of the states the original equitable juris. him by the officer, he will be returned to court and prison will diction over administrations is in all ordinary cases--without any | be his fate. An officer generally has from sixty to eighty cases special circumstances such as fraud, or without any other equitable feature such as trust-either expressly or practically abrogated.

under his care. Women officers are in charge of women and The courts of equity, in the absence of such special circumstances boys and girls under eighteen. A probation officer has a special or distinctively equitable features, either do not possess or will not area of the town allotted to him and usually gets all prisoners exercise the jurisdiction, but leave the whole matter of administra.

whole matter of administra: from that area. He acquires an intimate knowledge of the tions to the special probate tribunals"... so that " unless the case involves some special feature or exceptional circumstances

physical, economic and social surroundings in which his prisoner of themselves warranting the interference of equity, such as lives. He is therefore well fitted to watch him and to help him fraud, waste, and the like, or unless it is of such an essential to become once more a decent citizen. He gradually gives him nature that a probate court is incompetent to give adequate back his liberty and removes restrictions until he is capable of relief, or is one of which the probate court having taken living a decent life alone. The powers of the probation officer cognizance has completely miscarried and failed to do justice by its decree, the courts of equity will refuse to interpose and to are necessarily very great. The prisoner continues his work as exercise whatever dormant powers they may possess, but will before, but the officer visits his factory or workshop and arranges leave the subject matter and the parties to the statutory forum | to receive his wages each week, passing over the greater part of which the legislature plainly regarded as sufficient and intended

| them to the wife to keep up the home, giving a very small sum to be practically exclusive" (Rice's Probate Law, pp. 4 and 5).

to the prisoner for personal expenses, and retaining a small Probate courts are in most if not all the states courts of sum, which is paid back to the prisoner when he becomes a free record, having a public seal and a clerk (or the judge has authority man. to act as clerk); they issue process and execute their decrees by The advantages claimed for the probation system are these, appropriate officers in the same manner as the common law and that a number of independent well-paid probation officers, chancery courts. They sit at stated terms. They have power chosen for their knowledge of human nature and their skill to punish for contempt, and to compel obedience to their orders in reforming it, can give personal attention to individual cases; and decrees, and their judgments upon matters within their the stigma of prison is avoided, and while great care is taken jurisdiction are enforced usually by the same means as common that the prisoner shall be strictly controlled and effectively

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