produce this minimum, because gases move on with extraordinary slowness in metal when they are not impelled by any exterior electromotive force; to remove the last remains of them consumes on this account an extreme length of time.

To show this slowness of the gas-motion I adduce the following-Polarized plates of platinum standing in the usual aircontaining liquids apparently lose their polarization in a few hours, or even minutes, when in conducting connexion with each other. Indeed on this circumstance depended, for instance, the utility of the polarizable electrodes employed by E. du BoisReymond formerly for experiments on animal electricity. On the contrary, in a gas-free liquid polarization dies away at first, it is true, quickly, but later very slowly. I have in such a case observed in the multiplier the depolarizing current for sixteen days. From the electrolytic equivalents of the current used for the polarization of the plates and the depolarization-current afterwards still existing it followed that months must elapse ere so feeble a current as the last named was could remove the residue of the gas-charge still present.

The phenomena in polarization which are similar to those attending the residual electricity of a Leyden jar, are accounted for by the occlusion of the gases. When hydrogen is penetrating a platinum plate, if the current be interrupted a few seconds, the gas has time during this interruption to advance further into the interior, and thereby diminish its density in the superficial layers. If the circuit be closed again, the resistance to the entry of fresh hydrogen is thereby diminished, the current may become stronger. Conversely, the depolarization-current can remove the gas which has been driven to the surface; if we interrupt this current, the hydrogen slowly pressing up from within will be able to accumulate at the surface and reinforce its polarization. It is known that in a platinum plate, behind an oxygen polarization an older hydrogen polarization can exist simultaneously, which latter comes to light when the former has vanished, and vice versa.

So far as I can see, the phenomena belonging here are without difficulty explained if we assume for the onward motion of the gases occluded in metals the same laws as for the conduction of heat.

Lastly, it is to be remarked that in these cases, after the current of the condenser has passed (that is, the electricity attached only to the surface of the plates is discharged), another current can only set in in proportion as gas presses from the interior of the metal to the surface. If this takes place only very slowly, the current-intensity in the circuit becomes as good as independent of the resistance of the latter; so that, in my experi

ments, insertions of from 20 to 60 miles of telegraph-wire certainly made the needle of the multiplier go back for a few seconds, but then soon permitted it to return to its previous deflection. The resistance of the rest of the circuit amounted to only about 2 miles of the same wire; the behaviour of the permanent current-intensities which appeared in the circuit with alternating resistances was just as if there existed at the surface of the plates a passing resistance in comparison with which 40-60 miles of wire was vanishingly little. This enormous apparent transitory resistance, however, existed only for just the then present direction of the current; if a current of the opposite direction was called forth, no such resistance was present. This holds good not only for platinum electrodes polarized by a Daniell element nearly to the maximum, but also for such as have been again depolarized almost to the vanishing of the polarization, and have thus arrived as nearly as possible at their natural

state.

XIX. Notices respecting New Books.

Treatise on Practical Solid or Descriptive Geometry: embracing Orthographic Projection and Perspective or Radial Projection. By W. TIMBRELL PIERCE, Architect, late Lecturer on Geometrical Drawing at King's College, London. With 85 Plates of Original Drawings. London: Longmans, Green, and Co. 1873. THIS volume is a small quarto, consisting of the plates and a text of 86 pages. About two thirds of it are devoted to orthographic, and the remaining third to radial projection. The former part is strictly elementary, but it embraces all the points which under ordinary circumstances a student would wish to make out. After a brief view of the projection of points and lines, with a few examples, the author fairly begins the subject in the second chapter, on Straight Lines and Planes, which is in substance the same as the first section of the Géométrie Descriptive of Monge. It is followed by a good many applications-one chapter (the third) treating of the projections of the five regular solids, while the fourth shows how to determine the projections of a cube from various data, and to solve a few other problems. The remainder of this part of the work is mainly devoted to a number of questions of intersection and tangency of a plane with cylinder, cone, and sphere, and of the mutual intersection and tangency of the same solids with each other; though a few other cases are given, such as the section of an annulus by a plane, and the contact of a cone with a surface of revolution. The treatment is clear and accurate; and though the subject is not without its difficulties, the student who brings to it a moderate acquaintance with solid geometry will be able to read it without serious trouble.

The case is somewhat different in the second part, the subject

of which (radial projection) presents difficulties of a much higher order than those of orthographic projection; and Mr. Pierce's treatment by no means smooths down its asperities. Of course a reader who has worked conscientiously through the first part, has gone through a sort of preliminary discipline for the second; but even such a reader would find it, at the outset, very hard to master the first four pages and Plate I. to which they refer-a difficulty which is seriously increased by an unfortunate misprint at a critical point (line 18, p. 60), and another in the lettering of Plate I. It might perhaps be said that the author undertakes to treat the matter as a question of geometry, and therefore addresses himself to competent readers; and this, of course, justifies a severe treatment of the subject, but not unnecessary abstruseness. It is said that when Brook Taylor's treatise On the Principles of Linear Perspective' was published, it was criticised by a most competent judge as being abstruse to all and unintelligible to artists, for whom it was specially written. Brook Taylor's book is easy reading compared with this part of Mr. Pierce's; still, it may be freely allowed that a student who masters the present work will know the principles of the subject, and their application to several important and to some very difficult questions.

The plates, which form just half of the volume, are well done, and are as a rule intelligible to any one who takes proper pains to make them out. They are called on the titlepage" 85 Plates of Original Drawings;" which, we suppose, means that they are copies of drawings actually made by Mr. Pierce; of course many are substantially the same as what may be found in other works, e. g. in Mr. Bradley's Elements of Practical Geometry,' a work to which our author refers in his preface.

That descriptive geometry is a subject of great importance in the constructive arts is much more commonly recognized than it was a few years ago; and works of merit exist on the subject in English, particularly Mr. Bradley's, mentioned above; but their number is not large, and the present is likely to be of great value to the student. It contains, in a convenient form and moderate compass, what all who take up the subject ought to know, and as much as most students would wish to learn*. We do not doubt that a second edition will be called for ere long; and in that case Mr. Pierce would greatly increase its value by suggesting exercises for the student to work out. To some extent this want has been anticipated by a very good but unpretending little volume by Messrs. Edgar and Pritchard, Note-book on Descriptive Geometry.' However, it is much better for a student to have in a single text-book all he requires; and the want could be easily supplied. As it is he finds in the plates a complete solution to every question in the book, and is never thrown on his own resources. There are a few misprints in the book which will doubtless dis

Mr. Pierce proposes to show in a future work the application of the subject to the several arts of construction.

appear in the second edition. We have already mentioned two; a third occurs in the second paragraph of Art. 61, p. 39, where the word "plane" is dropped out. Moreover the substance of the paragraph is not strictly correct, even when the printer's error has been set right.

Catalogue of Stars observed at the United-States Naval Observatory during the years 1845 to 1871. Prepared for publication by Professor M. YARNALL, U.S.N. Washington, 1873.

This Catalogue, which forms Appendix III. of the Washington Observations for 1871, contains the places in right ascension and declination of 10,658 stars observed during a period of more than a quarter of a century with the transit instrument, meridian circle, prime vertical, mural circle, and equatorial of the observatory. The preliminary matter treats principally of the methods employed for the reduction, throughout the Catalogue, to the Besselian epoch 1860-0, when the sun's longitude was 280°. The Catalogue gives:the designations or numbers of the stars observed as they stand in the catalogues named, with the magnitudes, the mean right ascension 1860-0 with the mean year of observation; the number of observations of each star with its annual precession in 1860; the mean declination, mean year of observation, number of observations, and annual precession in 1860.

The Catalogue contains a large number of small stars which were observed in consequence of Mr. James Ferguson, who had charge of the equatorial, requiring many for comparison with the objects observed by him. Mr. Ferguson having observed the stars of the Pleiades with the equatorial, and those in Præsepe having been observed with the same instrument by Professor Hall, many in both clusters were reobserved with the transit instrument and mural circle. The resulting right ascensions and declinations are inserted separately from those determined with the equatorial. We cordially recommend this Catalogue to the attention of amateurs, and the more so as so many telescopes of large aperture are now in active work in this country.

XX. Intelligence and Miscellaneous Articles.

ON A NEW DETERMINATION OF THE MECHANICAL EQUIVALENT OF HEAT. BY H. SERRANO Y FATIGATI.

THE mechanical equivalent of heat had not, until now, been determined by the relation which subsists between the work expended to turn the disk of a Ramsden electrical machine and the electrostatic decompositions produced. The following are, in brief, the process I have employed to resolve the problem and the results which I have obtained.

To turn the disk and measure the work, I wound round the handle of the disk of a Ramsden machine two strings passing over two pulleys and carrying each a weight at its extremity—the one

of 17 kilogr., and the other of 22. These weights descended near two graduated rules. I have deducted from the calculated work (1) the work equivalent to the vis viva retained by the weights at the end of their fall, (2) the work consumed by the friction of the strings against the handle and in the pulleys.

On the other hand, I estimated as exactly as possible the heat developed by the cushions,-first by employing a good mercurial thermometer, and then by means of a thermoelectric pile compared with the preceding indications, and measuring approximately the specific heat of the cushions and the disk, taking into consideration the losses in the air. The quantity thus obtained was likewise deducted from the calculated work.

Finally, to measure the electrolyzation, I took two large testtubes, graduated and furnished with platinum wires extending to their bottom, one of which was connected with the machine, while the other was in communication with the earth. These tubes were immersed in a large receiver containing acidulated water, and united by means of a long string wetted to serve as a conductor to the electricity without producing sparks.

The following are the mean results obtained in twenty-eight operations :

I should be glad to have these results controlled by other physicists. Bibliothèque Universelle, Archives des Sciences Phys. et Nat. Nov. 1873, pp. 252, 253.

ON THE EXPANSIBILITY OF EBONITE BY HEAT.

BY F. KOHLRAUSCH.

Accidentally repeated observations that ebonite lids stuck fast in glass vessels, or even cracked them, led me to the idea that this material might have a considerable expansibility by heat. Expectation was exceeded by reality; for it was found to be about three times as expansible as zinc.

The coefficient for 1° was found to be

0.0000770 measured between 16°.7 and 25°.3,