induction, we may instance that of the sex of children, which for our present purposes we may assume to be half male and half female according to observed experience. In reality the number of each sex is always equal. From this induction our knowledge is so far incomplete, that we cannot tell, when a child is about to be born, whether it will be male or female; though we can calculate with tolerable certainty that out of a thousand children, five hundred will be males, five hundred females; but we cannot tell from this knowledge which five hundred will be males and which females.

(60.) Of possible inductions, we may take in illustration the following assumed fact: amongst a thousand children one is born with six fingers, and we have no information as to the precise one which is the subject of the monstrosity. It is manifest that with this knowledge, it is possible that any one may be the subject of the disease.

(61.) The Inductions of Means is another kind of knowledge of considerable utility. This species of induction consists in ascertaining the sum of the values of a certain number of objects, when by dividing it by that number, we obtain the mean value. If we discover that four men weigh four hundred weight, then we know the mean weight of each of the four men, though we do not know in any one case the absolute weight.

(62.) The Induction of Means is much increased in value when we have the limits of variation between the different individual instances, thus a mean of 4 may be obtained between the limits of 7 and 1, 6 and 2, or 5 and 3.

(63.) There is yet one other mode of induction, which investigators frequently employ with advantage. Having a single fact earefully examined, they assume a law from it, and they examine other facts to see how far they agree or disagree with that law. This is called a Hypothetical Induction. This form of induction is most valuable if the in. vestigator never forgets that it is a mere Hypothe sis; but on the contrary, if he bends his other facts to suit the Hypothesis, then this form of induction is in the highest degree dangerous.

CHAPTER V.

ON DEDUCTION.

(64) Deduction.--(65) Perfect Deduction.-(66, 67) Imperfect Deduction.

(64.) As by the process of induction we are enabled to classify a large number of facts under one general rule; so by deduction we are enabled to apply this induced knowledge to any particular instance. As an example of a deduction, we may take, as an illustration, the deduction: "Man is mortal," or in electro-biological language, man A always suffers death Z. From this induction we rightly deduce that John A+B is liable to death, because John, contains A the properties of a man in his organization, or we may express the fact by symbols, that A + B is conjoined with Z.

(65.) Deductions are of two kinds, perfect and imperfect. In all cases of perfect deductions, the inference derived from the law is certain; thus, if I have twenty pounds, and add thereto twenty pounds, I may of certainty deduce that I shall then

have forty pounds, because I have previously learnt by induction that twenty and twenty make forty.

(66.) Imperfect deductions may be divided into several departments, for every deduction is imperfect in which the law which is sought to be applied is not absolute. From this cause it follows, that a deduction from a probable induction, or hypothetical induction, or an induction of means and limits when applied to any particular instance, is necessarily incomplete and unsatisfactory.

(67.) As an example of an imperfect deduction, I will assume as a law, that amongst great masses of children, half are boys half are girls. From this law it follows deductively, that of one thousand children we should probably have five hundred of each sex, but it by no means follows that out of ten children we should have five of each, for it might happen that the boys and girls are grouped together in masses of each, and, therefore, the law would not apply to very small numbers.

D

CHAPTER VI.

ON THE LAWS OF THOUGHT.

(68) Laws of Thought.-(69) Properties of Symbols.-(70) Laws of Symbols.-(71) Laws of Judgment.-(72) Reason.

(68.) In former chapters I have shown how every word may be expressed by a cypher; and I have pointed out the manner in which we can express all ideas by this mode of notation. These symbols when rightly arranged as a geometric series, have certain properties to which the laws of thought are obedient, and are most important to be studied and thoroughly understood, and it will be now my business to endeavour to explain them.

(69.) Each symbol expresses something in nature which does not stand alone, but has certain relations to other symbols. If we arrange these symbols as a geometrical series, each letter would comprise the properties of a part of a symbol above it, and those of two symbols below it, and differ in some condition from those beside it: thus let A