24. Swine-stone.-Hisinger and Berzelius have analysed various specimens of Swedish swine-stone. The following are the results of

Gehlen has proposed two alterations in the present mode of analysing minerals; and, in his analysis of prehnite, he has shown that they may be employed with advantage. 1. He substitutes carbonate of soda, instead of caustic alkali, for the original fusion of the mineral in a platinum crucible. He found that this method answers even in the analysis of corundum. 2. He substitutes carbonate of barytes for nitrate of barytes when our object is to obtain the fixed alkali which we suppose to exist in any mineral. He has found that this carbonate readily acts as a flux to minerals, and that it answers better than the nitrate of the same earth.

D

II. Geognosy.

I ought now to give a sketch of the recent improvements in this branch of science, which of late years has become a fashionable object of study in Great Britain; but I have already extended this article to such an enormous, and I fear improper length, that I must, however reluctantly, stop short here. The great object of geognosts on the Continent at present seems to be to trace to their utmost extent the formations discovered in the neighbourhood of Paris; and to extend as much as possible the transition formations in those countries hitherto considered as primitive. In this country we have no fewer than three geological societies, the Wernerian, the London, and the Cornwall. The first two have recently published each a volume of Transactions. I shall give an analysis of each of these books as speedily as possible. They contain almost all the important geological facts that have been lately ascertained in Great Britain.

ARTICLE II.

Solution of a Problem of Col. Silas Titus. (See Wallis's Algebra, Chap. 60.) By the Abbé Buée.*

SIR,

HAVING for many years considered the different algebraical methods for the solution of arithmetical problems by approximation to be deficient in their fundamental principles, I have been led to mistrust the whole science of algebra as generally taught, and am convinced that if we place an implicit faith in it we shall be involved in the most revolting absurdities. Pell's problem (see Wallis's Algebra, chap. 60, 62, &c.), and all those which can only be resolved by approximation, are examples of this kind. The absurdity belonging to the solution of these sort of problems is to represent numbers of which we know not the fundamental unity. In speculation this absurdity is not felt; but we easily perceive it when we quit speculation, and are engaged in questions respecting real beings, such as men. In this case the solution gives for units fractions as much smaller as the approximation is farther extended. If, then, the real unit be a man, the solution gives for unit a fraction of a man, which goes on always diminishing, and by that means becomes more and more absurd. In general the speculative

The following curious solution of a well-known problem was sent by the Abbé Buée to a mathematical gentleman in London, who declines communicating his name to the public. Though I do not participate in the Abbe's objections to algebraic approximation, yet I conceive the solution of the problem itself to be so curious as to be well entitled to the attention of mathematicians; and on that account I agreed without hesitation to insert it in the Annals of Philosophy. The letter which serves as an introduction to the problem is written by the Abbé Bute.-T.