anterior to the sandstone; as is pretty well shewn from the appearance of a breccia that lies on its surface, which had been interposed between it and the sandstone, before the causes which formed the glen had carried away the sandstone.' The following description of the Pitchstone, from Brodick Wood, illustrates the author's method of characterizing minerals. He seems judiciously to have adopted the style of Werner and Kirwan. PITCHSTONE, Brodick Wood. Colour.-Dirty green, but the number of distinct concretions give it a light hue. Lustre.-Greasy. Transparency. Transmits a very little light at the edges. • Fracture. Uneven, conchoidal, and sometimes splintery, with numerous distinct concretions. In the gross is often slaty. 6 Fusibility-At 75° formed a compact glazed mass, coloured red and white At 100 it forms a compact mass, having, however, in some parts the appearance of pumice*. The different species of this genus have been found to differ consi derably in their degree of fusibility, but in none so remarkably as the one now described. Mr. Kirwan, who has made the most satis factory experiments upon their fusibility, observed, that the most fusible formed an enamel at 130°, but in general were far more refractory, some refusing to melt at 1609. Widenman also found them to differ considerably in this respect. It will be difficult, then, to say with confidence, that either of the Arran stones belongs to this genus; at least, if we are to carry the character of fusibility so far as Mr. Kirwan has done in the case of the Gemeiner Kiesel Schiefer of Werner. It decomposes by the action of the weather, in the form of a white tegmen; which is often separated into layers. It is also frequently traversed with another species, which has a greater degree of lustre, and is more difficultly decomposable by the action of the weather. On account of this last circumstance, specimens of this kind, when decomposing, present a striped surface of dark gecen and white, the dark green being the undecomposed species. Gerhard, in his Mineral System, mentions a species of gneiss and granite, that contains obsidian, a stone much allied to pitchstone. Townson, in his travels through Hungary, remarks, that this gneiss is a species of obsidian, with black and white layers, containing also probably a few chrystals of adularia, and scales of mica. The stone I have now described appears to be of the same kind, and this is rendered more probable from its sometimes containing feltspar.' The Appendix, which includes observations on Peat, Kelp, and Coal, is worthy of notice. The Abbe Spallanzani, in his travels through the two Sici lies, remarks, that pumice cannot be formed from any kind of natural glassy substance; the fact mentioned above, renders this somewhat doubtful.' Peat. Peat. Mr. James on informs us, from Toffoeus, that peat was first made known to the inhabitants of Orkney and Shetland by a Norwegian called Einar; who, from that circumstance, received the name of Torf-Einar. He seems to think that peat is a substance peculiar to colder climates; and his subsequent observations appear to sanction his opinion. We refer the reader to pages 152 and 153. The author then enumerates the different undecomposed vegetable matters, which have been found in peat mosses; and at page 156, we have an account of a substance resembling the mineral tallow of Mr. Kirwan, which Mr. Jameson found in peat. Then follows the analysis of the peat from Glen-Cloy, in the island of Arran. This comprehends an examination of the matter soluble in wa ter and alkali, with a detail of experiments on the acid of peat. This acid Mr. J. imagines to be of the same nature with the suberique; and he thinks that both are compounds, of carbon and oxygen, differing from the carbonic acid only in the proportion of their constituent parts. He was led (he says) to form this opinion, as he was able to produce an acid nearly similar to the suberique, by digesting the nitrous acid on charcoal, We cannot detail these experiments: but we are not of opinion that Mr. Jameson has by any means proved theeidentity of the component parts of the carbonic and suberique acids. Our objections are founded on two facts-1. the great difficulty of freeing charcoal from hydrogen: 2. suberique acid, when exposed to the air, gradually acquires a brown colour; as is the case with vegetable matters when they lose their hydrogen. The author next considers the different theories which have been proposed to explain the origin of this substance. He notices particularly that of Dr. Anderson and Dr. Darwin; and he con cludes by stating his own conjecture, that vegetable matter is deprived of a considerable portion of its hydrogen; in which idea he coincides with an opinion delivered by Mr Hatchet in the fourth volume of the Transactions of the Linnæan Society. Kelp. We are happy to find this important article of Highland industry noticed by Mr. J.; for there can be little doubt that much is to be done towards its improvement. We defer giving our opinion of the author's observations and experiments, until he favours us with a farther detail, which is here promised. Coal. We have not room even for abridging Mr. Jameson's remarks on this substance: but we think that they are likely to be useful to those who may not have an opportunity of consulting the different works which treat on this subject. On the whole, we cannot but congratulate Mr. Jameson on the rank among successful mineralogists, and respectable REV. SEPT. 1799. writers, C writers, which his volume (short as it is) entitles him to hold; and we look with pleasing expectation for the authoria farther researches in which he may hereafter indulge. Ham...n. ART. III. A Course of Mathematics, composed, and more especially F. R. S. 2 Vols. 8vo. 15s. Boards. Robinsors. 1798. SINCE authorship has become a trade, the love of gain has operated in the literary as it has ever operated in the mer cantile world, and books have been produced in proportion to the demand for them. In former times, when the sole incitement to publish was the desire of fame, or the hope of instructing mankind, books appeared in small numbers, and were only of certain descriptions; now, since the motive which impels to authorship is different, since avarice is more active and predominant than ambition, books have been showered on us in the largest abundance; diversified in their character, and unlimited in the variety of their subjects. That evils have accompanied this abundance cannot be denied; the fears of public censure and the hopes of public applause have beeni weakened by the love of gain; some of the books which have appeared add nothing to truth, many contain falsehood, and few amply repay the toil of perusal. Such evils were indeed to be foreseen; for it would be absurd to expect that a building, erected according to the circumstances of the moment, or in the view of present gain, should have the solidity and perfection of one which was destined to last through all time. If, however, we balance opposite arguments, and compare the good with the evil that has resulted from this change of motive, mankind will appear perhaps to have gained by it. Our treatises on certain subjects may be less profound than they were formerly, but they are more numerous; and we may be allowed to hope that there is no author who will not contribute something to the common stock of knowlege. If former works contained a greater variety and richness of matter, there were few persons only to whom it could be imparted; now we have books level with every capacity, and adapted to diffuse knowlege through all ranks. The elaborate refinement and scrupulous exactness, which care and long meditation gave to the productions of past times, are now to be hoped from frequency of practice and repetition of trial; and when the experiments. are numerous beyond computation, we may allow for many failures. If we turn from the character of these literary productions to the effects of their influence on society, the advantage will evidently appear to be with modern times; for, if knowlege existed formerly in larger separate masses, it is now without doubt more generally diffused; and what moralist will deny that knowlege contains the germs of virtue and happiness? If, in the luxury of present times, the temptations to vice be increased, exhortations to goodness are more frequent; and moral depravity is assailed on every side, and under every form, in prose and in poetry, by novels and by serious essays. In past times, men were rarely impelled to the quest of knowlege, and never allured; science was difficult of access, and her features were harsh and forbidding, Now she advances to meet the student, and strives to captivate by every art; the curiosity of the inquisitive is excited, the idie are tempted to useful occupation, and the busy resort to her for relaxation.-We are wandering, however, far from our limits; substantial criticism must not vanish in the fume of delectable speculation." We have been tempted to digress, by observing how sedulously the wants of the studious are supplied; and we have been led into reflections similar to those which we expressed in a former article. The present work is one of those which are produced in the abundance of modern times, to suit the variety of capacity and disposition which is found among men: for the general objects of intellectual pursuit are not only different, but each object is pursued with different means and views; language, poetry, antiquities, mathematics, are the classes into which the objects of mental inquiry are distributed: but (to take an instance that suits our present purpose) the science of mathematics is studied under a difference of views and circumstances; for some students are ambitious of a variety of knowlege, while others only aim at correctness; some are contented with the spiritual and philosophical utility of mathematical science, others demand a gross and material utility; some seek for truth,-truth naked and abstract,- and some require that it should be clothed with power, and subservient to the purposes of common life. Adapted to the dissimilitude of taste and capacities, books have been written, which are either systematical and coherent, or familiar and illustrative; speculative, or applied to practical purposes; either exact in their logical deduction, or copious in the variety of their matter. Under what description the present treatise falls, and what are the recommendations which sanction its appearance, will be understood from the author's preface: *See Rev. July last, p. 301, &c. / A short A short and easy Course of the Mathematical Sciences has long been considered as a desideratum for the use of Students in the dif ferent schools of education: one that should hold a middle rank between the more voluminous and bulky collections of this kind, and the mere abstract and brief common place forms of principles and memorandums. For long experience in all Seminaries of Learning, and particularly in the Royal Military Academy at Woolwich, has shewn, that such a work was very much wanted, and would prove a great, and general benefit; as for want of it, recourse has always been obliged to be had to a number of other books, of different authors, selecting a part from one and a part from another, as seemed most suitable to the purpose in hand, and rejecting the other parts: a practice which occasions much expence and trouble, in procuring and keeping such a number of odd volumes, of various modes of compo sition and form; besides wanting the benefit of uniformity and reference, which are found in a regular series of composition. To remove these inconveniences, the Author of the present work has been induced, from time to time, to compose various parts of this Course of Mathematics; which the experience of many years use in the Academy has enabled him to adapt and improve to the most useful form and quantity, for the benefit of instruction. And, to render that benefit more eminent and lasting, the Master General of the Ordnance has been pleased to give it its present form, by ordering it to be enlarged and printed. As this work has been composed expressly with the intention of adapting it to the purposes of academical education, it is not designed to hold out the expectation of new inventions or discoveries: but rather to collect and arrange the most useful principles in a convenient practical form, demonstrate them in a plain and concise way, and illustrate them with suitable examples: rejecting whatever seem to be matters of mere curiosity; and retaining only such parts and branches, as have a direct tendency and application to some useful purpose in life, especially in the military profession, for which the gentlemen educated at this Academy are intended. As a work of such a nature must necessary consist of matters which have, in a manner, become common property, and in a great measure are contained, in some shape or other, in most books of this kind, it will not be imputed to the author, as a crime, that he has availed himself of the materials of some of the best books on these sciences, from whence he may have extracted, or which he may have imitated; whether they be any of his own former publications, or those of other authors. Nevertheless it is expected that something new may be found in many parts of these volumes, as well in the matter, as in the arrangement and manner of demonstration, especially in the goemetrical part of this work. And here the author hopes he will not be too severely criticised if, through a desire of rendering this branch more easy and simple, he has in some instances deviated a little from the tedious and rigid strictness of Euclid, particularly in the doctrine of ratios and proportion, which has always been so greatly |