evaporated in unity of time gives the gross effect of the engine in unity of time. The result affords the means of calculating all the circumstances connected with the working of a steam-engine according to the principle of the conservation of vis viva, or, in other words, of the equality of power and effect, which regulates the action of all machines that move with a uniform or periodical velocity. This principle was first applied to the steam-engine by the Count de Pambour, and, accordingly, the formulæ of this paper only differ from those of his work in the expressions for the pressure and expansive action of the steam, which are results peculiar to the author's theory. As an illustration of the use of the formulæ, the maximum useful effect of a double-acting Cornish engine is computed, and compared with the result of the calculation of M. de Pambour for the same engine, shewing the latter to be too large by about onefifteenth.

In an Appendix are given two tables; one for calculating the volume of steam from its pressure, and vice versa, and its mechanical action at full pressure, the other for computing the amount of its action in expansive engines.

In order to shew the limit of the possible effect from the expenditure of a given quantity of heat in evaporating water under given circumstances, the maximum gross effect of unity of weight of steam, evaporated at a higher temperature, and liquefied at a lower, is computed in two examples, and compared with the heat which disappears during the action of the steam, as calculated directly. In the first example, the water is supposed to be evaporated at the pressure of four atmospheres, and condensed at that of half an atmosphere; in the second, to be evaporated at eight atmospheres, and condensed at one atmosphere.

In both these examples, the direct calculation of the heat rendered effective, agrees with the calculation from the power developed, thus verifying the methods of computation founded on the author's theory.

The heat converted, in those examples, into engine-power amounts to only about one-sixth part of the heat expended in evaporating the water, the remainder being carried off by the steam and liquid water which escape from the cylinder. In practice, the proportion of heat rendered effective is still smaller, and in some unexpansive engines amounts to only one twenty-fourth part, or even less. It is thus

shewn, that there is a waste of heat in the steam-engine, which is a necessary consequence of its nature. It can be reduced only by increasing the initial pressure of steam, and the extent of the expansive action; and to both these resources there are practical limits.

In conclusion of the present paper, the author states, that, from his equations, many additional formulæ are deducible, with respect to the specific heat of imperfect gases, to certain questions in meteorology, and to the specific heat of liquids; but from the want of sufficient experimental data, he conceives that they are not as yet capable of being usefully applied.

2. On Probable Inference. By Bishop Terrot.

The paper commenced with a suggestion, that, as the inferences of ordinary logic admitted no premises but such as were absolutely certain, and as the premises with which we have to deal in the business of life were not certain, but only probable, therefore it was highly desirable that we should have a logic, or rules for drawing inferences on the case of probable premises.

The attention of the Society was then drawn to the 15th section of the article Probabilities, in the Encyclopædia Metropolitana, and especially to the following passage: "It is an even chance that A is B, and the same that B is C; and therefore, 1 to 3 from these grounds only that A is C. But other considerations of themselves give an even chance that A is C. What is the resulting degree of evidence that A is C ?" To which query the answer in the Encyclopædia is §.

On this passage it was observed, in the first place, that the asserted ratio of 1 to 3, or the probability in the first syllogism, was true only on the hypothesis that A can be C only through the intervention of the middle term B. But that when such is not the case, when other ways are conceivable but totally unknown, the probability is not but; these two fractions representing, the one the probability of the evidence of a complete proof that A is C, the other the probability that A is C; and it was observed, that, in practical questions, it is the latter probability alone which we have an interest in determining.

It was then shewn generally, that, if the probabilities of the

If A can be C only through the intervention of B, then the proba

unknown ways, we must add together all the probabilities arising from all the combinations, the result of which addition was shewn to be,

Whence it was inferred, that if q'=2 p', or if the second premise have a probability of, each of these fractions becomes, or the probability that A is C becomes .

It was then shewn that a weak argument, that is to say, one affording a probability of less than, diminishes instead of increasing the probability arising from any previous argument or evidence; and it was proved, that even if we take for the probability arising from the first argument, the probability arising from both conjointly was not ğ but §.

The general conclusions of the paper are as follows :-

1. When the premises, which, if certain, would involve the certainty of the conclusion, are not certain, but have each a known pro

bability, the probability of the conclusion is the product of the probabilities of the premises, in those cases only where the presence of the middle term is necessary for the connexion of the major and minor terms. When this is not so, then the probability of the conclusion is the product of the probabilities of the premises, plus the sum of the probabilities arising from the other conceivable causes of connexion.

2. In a sorites of probable premises, any premise with a probability of brings the force of the argument up to that premise inclusive to a probability of .

3. When various arguments of different validities have been advanced for a proposition, or when evidence has been brought in support of argument, or argument of evidence, the resulting probability is not the sum, but the average of the several probabilities; so that a weaker argument following upon a stronger, weakens it, or rather weakens the probability produced by it.

The Hon. LORD MURRAY, V.P., in the Chair.

3. On the Ante-Columbian Discovery of America. By Dr Elton. Communicated by Dr Traill.

The object proposed by Dr Elton, is a summary of the knowledge we possess on the discovery of the Continent of America, by several adventurous European voyagers, anterior to the time of Columbus.

This subject, which has been for almost a century and a half well known to the students of northern history, was first made known to the rest of Europe by the publication of the Vinlandia Antiqua of the celebrated Torfæus in 1705; and most of the facts given by Dr Elton are extracted from that work. Torfæus proved from existing Icelandic MSS., that America was discovered, and even attempted to be colonized, by his enterprising countrymen, in the end of the tenth and beginning of the eleventh century; and the descriptions transmitted to us prove that they landed on what are now Newfoundland, Nova Scotia, Massachusetts, and Rhode Island.

The first adventurer was Leif, the son of Eirik the Red, who, in A.D. 995, when attempting to pay a visit to his father, the colonizer of Greenland, was driven by stress of weather to the coast of Newfoundland, which he named Helluland, or Rocky Land. From that he sailed south-westward, till he arrived at a country, which from be

VOL. II.

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