Imágenes de páginas
PDF
EPUB

should (particularly when a little self-love and regard for his own memory after death are taken into the account) delude himself into the belief, that to make a false protestation of his innocence would be an offence of an extremely venial nature, if not deserving positive approbation. We must not forget the position in life and characters of [ *352 ] *the persons making these protestations, or expect them to see with the eyes of philosophy the extent of the mischiefs likely to result from the belief that an innocent man has been sacrificed by a mistaken sentence. The immediate benefit of themselves, their families, or neighbours at most, form the boundary line of their vision, while the great interests of society are lost in a distant horizon. The judicial histories of every country supply instances of the most solemn denunciations of the unjustness of their judges, or the perjury of the witnesses against them, made by criminals, whose guilt no rational being could doubt; and when we recollect the numerous cases of persons making groundless confessions of guilt, (i) we shall cease to be surprised at false asseverations of innocence.

(i) See suprà, § 258 et seq.

APPENDIX.

NOTE I.

ON THE APPLICATION OF THE CALCULUS OF PROBABILITIES TO JUDICIAL

EVIDENCE. (a)

"Most of our judgments being founded on the probability of testimony, it is of great importance to submit it to calculation. This is, no doubt, often impossible, from the difficulty of appreciating the veracity of witnesses, and the great number of circumstances accompanying the facts to which they depose. But, in many cases, problems may be solved which have considerable analogy with those in question, the solutions of which may be regarded as approximations useful for our guidance, and to protect us against the errors and dangers to which we are exposed from false reasoning." (Laplace, Essai Philosophique sur les Probabilités, p. 135. Paris, 1819.) In pursuance of this principle, and in accordance with the example of several of our most eminent writers on evidence, we propose, in this note, to state shortly the general principles of the calculus of probabilities, as applied to the subject of judicial testimony.

The calculus of probabilities had its origin in questions relative to the expectation of success or loss in games of chance; *and all problems relating to it may be represented by [ *354 ] throws with dice of different forms, or by drawing from urns or bags balls of different colours. The fundamental principle on which it rests is, that, in order to determine the probability of any event, we must take the ratio of the favourable chances or cases to all the possible cases which in our judgment may occur. Thus the probability of throwing 6 on a die is evidently; as there are 6 possible cases, only one of which gives the result required. So, again, if an urn contain 5 black, 4 white, and 2 red balls, the total number of possible cases is 11; and the probability of drawing a black ball, of a white ball, and of a red ball. So, generally, let m+n be the total number of possible cases; m represent the chances in favour of an event A, and n those of an event B; the probability of event A will be =

n

m

m+n

and that

of B = It is also evident that unity is the symbol of certitude: m+ n for, by hypothesis, one of the events must happen; and, adding the probabilities of A and B, we have

m+n

1.

m+n

* The substance of this note is taken from Laplace's Essai philosophique sur les Probabilités; Lacroix's Traité élémentaire du Calcul des Probabilités; and the title "Probability" in the Library of Useful Knowledge: to which works the reader is referred for further information on this subject.

It is stated in Art. 188 of this work, that the probability of the concurrence of independent events were not merely the sum of their simple probabilities, but their compound ratio: and we now proceed to demonstrate this, which is one of the most important principles in the science. Take first the case of two events. Let A and B represent two conflicting events; and A' and B' any other two conflicting events. Let and that of B ·; of A' =

the probability of A =

m' m' + n'

[ocr errors]

of B' =

n'
m'+n'

m

m+n

n

=

m+n

Now, as, by hypothesis, A cannot happen

with B, nor A' with B', all quantities whose factors are represented by the chances in favour of the conflicting events become impossible: and all the possible cases. are mm'+m'n+nn' — (m+n)(m'+n'). Of these, mm' are favourable to the occurrence of A and A'

nn' mn'

m'n

[ocr errors]

B and B'

A and B'

A' and B.

[355] *According to the general principles already stated,

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][ocr errors]

(m+n) (m'+n')'

the first

of which factors is the simple probability of A taken singly, and the second that of A' taken singly and so of the rest. Hence it appears that the probability of the concurrence of any two independent events is the product of the probabilities of each considered separately. It is easy to extend this theorem to any number of events A, A', A", A", &c.

When the total number of possible cases, and their ratio to the number of favourable chances, are unknown, still approximate values of the probabilities of events can be obtained, by having recourse to hypotheses framed according to the results of a certain number of trials or observed events. Formulæ, the deduction of which would occupy more space than can be afforded in a note, establish the principle, that in such cases the probability of a fresh event is obtained by calculating, according to the events already observed, the probability of the different possible hypotheses, and taking the sum of the products of these probabilities by those of the event, calculated according to each hypothesis." (Lacroix, Calcul des Probabilités, art. 81.)

The calculus of probabilities has been applied to the subject of human testimony, by supposing that, in a certain number of depositions, (say m+n), the witness has told truth in m cases, and falsehood in n cases; although, in order to determine with accuracy the probability of the fact to which he deposes, the intrinsic, or à priori probability of that fact itself must be taken into the account.

[ *356 ]

*Let there be two witnesses, A. and B.; and suppose that in m cases A. has spoken truth, and in n cases falsehood; the analogous numbers in the case of B. being m' and n': the probability of the truth of the testimony of A. is

[blocks in formation]

m

m+n'

and that of B.

[ocr errors]

If they both depose to the same fact, the probability of the truth of that fact will, according to the formulæ (A.), be

mm' mm'+nn'

mm'

(m+n) (n'+n'); and, as by hypothesis the depositions agree, the quantities m'n and mn' are impossible, and the above equation becomes By a similar process, we shall find that the probability of the falsehood of their joint The same principle can easily be extended

nn' mm'+nn'

testimony = to any number of witnesses (say p); so that, supposing the probability of the veracity of each to be the same, we shall have`m=m', n=n', and the expressions last obtained will become

[ocr errors][merged small]
[ocr errors]

mp+np

(B.), and

Suppose now that instead of witnesses we have circumstances, the probability of any fact, as, for instance, the guilt or innocence of the accused, is calculated in the same way, and will be in the compound proportion of the simple probabilities due to each of these circumstances. In estimating strictly the probability of guilt resulting from each circumstance, the probability of the truth or falsehood of the witnesses deposing to that circumstance must be taken into calculation.

It has been stated in the third Part of this work, and the proposition could be supported by numerous examples, that the degree of assurance of the guilt of an accused person, derived from a long and connected chain of presumptive evidence, may equal, and in many cases much exceed, that derived from a limited portion (and in most criminal cases it must necessarily be a very limited portion) of direct testimony. The mathematical formulæ established in this note strongly illustrate this principle.

*Suppose 2 persons, A. and B., are charged with 2 dis[ *357 ] tinct acts equally criminal, say, for instance, 2 distinct murders; and, in order to simplify the question, we will assume the probability of the principal fact to be equal in both cases. The evidence against A. is altogether direct, consisting of the positive testimony of two witnesses, E. and F. The probability of the truth of their united testimony depends on the values assignable to m and n in equations (B.) and (C.) Let us assume for the sake of illustration. that the chances of the guilt of the accused, A., arising from the evidence of each, are to the contrary chances in the proportion of 1000: 1. The effect of this is to render m = 1000, n = i, and p = 2. Substituting these values in (B,) and (C,) we shall have

[ocr errors]

mp+ny

[blocks in formation]

Let us now return to the case of B., all the evidence against whom is purely circumstantial and presumptive. Instead of 2 witnesses to the fact, there are 24 circumstances adduced in evidence. The chances of guilt, resulting from each singly, to that of innocence, we will take as low as 2:1. We then have m = = 2, n = 1, and p = 24. Substituting these values as before, we get

and

[ocr errors]

1

[ocr errors]

16777216

mp+np 16777216+1

m2+no 16777216+1 or, the probability of his guilt is to that of his innocence in a proportion exceeding 16 millions: 1.

It will, of course, be understood that these numbers are only assumed for the purpose of illustration; but the above expressions clearly shew, that, however high the credit of an eye-witness be taken, a number of circumstances may be so accumulated as to give a probability greater than any assignable.

[*358 ]

NOTE II.

CONFESSIONS OF WITCHCRAFT.

THE following are the examinations of two of the Essex witches, in 1645, taken from Howell's State Trials, Vol. 4, p. 817 et seq. :"The examination of Anne Cate, alias Maidenhead, of Much Holland, in the county aforesaid, before Sir Harbottell Grimston, Bart., one of the members of the honourable the House of Commons, and Sir Thomas Bowes, Knt., another of his majesty's justices of the peace for the county of Essex, at Mannintree, 9th May, 1645. This examinant saith that she hath four familiars, which she had from her mother about twenty-two years since; and that the names of the said imps are James, Prickeare, Robyn, and Sparrow; and that three of these imps are like mouses, and the fourth like a sparrow, which she called Sparrow. To whomsoever she sent the said imp Sparrow, it killed them presently. And that, first of all, she sent one of her three imps like mouses, to nip the knee of one Robert Freeman, of Little Clacton, in the county of Essex aforesaid, whom the said imp did so maim that he died of that lameness within half a year afterwards. Saith, that she sent the said imp Prickeare to kill the daughter of John Rawlins, of Much Holland aforesaid, who died accordingly within a short time after; and that she sent her said imp Prickeare to the house of one John Tillet, who did suddenly kill the said Tillet. Saith, that she sent her said imp Sparrow to kill the child of one George Parby, of Much Holland aforesaid, which child the said imp did presently kill; and that the offence this examinant took against the said George Parby, to kill his said child, was because the wife of the said George Parby denied to give this examinart a pint of milk. Saith, that she sent her said imp Sparrow to the

« AnteriorContinuar »