266 



NA TURE 



{Feb. 4, 1875 



metrical law of generation was described and the position 

 and aspect of its principal elements indicated on the 

 paper.* Its indication was then complete, and the re- 

 presentation of any points or lines upon it was then 

 reduced to the devices of practical geometry. The 

 principle simply was that a surface might be regarded 

 as completely known when we had indicated a method 

 of taking an infinite number of sections of it. In the 

 simplest case, these would be parallel plane sections, as 

 in the ordinary drawings of a ship, but Monge's method 

 was not trammelled by this restriction. 



Like most large subjects, it is one which it is very 

 difficult to know how to treat with advantage to the 

 student. An exhaustive treatise is out of the question for 

 any learner who is not prepared to make it an exclusive 

 or principal study, and it is a matter of very nice judg- 

 ment what to select and how much to present to the 

 pupil ; and this is the more emphatically so, inasmuch as 

 it is really the only good introduction to a practical 

 insight into the geometrical properties of space. 



Viewed in this light, the treatise before us is an 

 exceedingly good one. With great clearness and pre- 

 cision, it covers a considerable extent of ground, and 

 that by no means baldly ; and yet it is not too long. 

 It has, moreover, a very valuable adjunct, and one which, 

 we believe, is quite new — a series of stereoscopic drawings 

 exhibiting the actual construction in solido of thirty-six of 

 the principal problems. To the ordinary student this will 

 be of immense assistance ; for it is well known to teachers 

 of geometry and of mechanics, that want of imagination 

 on the part of the student is one of the principal obstacles 

 they have to deal with in endeavouring to impart to 

 him accurate conceptions of space and of motion. These 

 drawings have been very clearly and judiciously executed 

 by Prof. Saint Loup (of Paris), and slight colouring has 

 been introduced in some of the examples of intersection 

 with marked advantage and success. 



We notice some peculiarities of language in which 

 English usage is slightly departed from, as in writing 

 ■warped surfaces instead of skew surfaces, in spelling the 

 word directery^\C[\. two c's instead of " director," and in the 

 use of the word raccoi d to express that two surfaces have 

 a line of contact. Some of these, having regard to the 

 unsettled English nomenclature of an imported subject, 

 are not blemishes, and none of them detract from the 

 really high value of the book. 



Some account is also given of the leading spherical 

 projections, especially the orthographic and the stereo- 

 graphic. These are important additions to the treatise, 

 and although we would gladly have seen some others 

 described, particularly the gnomonic projection, we think 

 the author has done wisely in not unduly extending this 

 part of his treatise. 



The book is of convenient size, clearly printed, and well 

 arranged, with a good table of contents. Altogether, we 

 think it one of the best books upon the subject which we 

 have yet seen, especially in English, and we think it does 

 the highest credit to the distinguished American professor 

 who is its author. 



* It is certain that Monge did a great deal to systematise and complete the 

 method ; but some of its principles were certainly known, although carefully 

 kept secret, in some of the higher French schools- In consequence of this 

 secrecy, it will probably never be known exactly how much is due to Monge ; 

 but we may well believe that Monge did for this science what NewtOD and 

 Leibnitz did for the iafinitesimal calculus. 



PHILLIPS' ''ELEMENTS OF METALLURGY" 



Eh'inents of Metallurgy : a Practical Treatise on the Art 

 of Extracting Metals from their Ores. By J. Arthur 

 Phillips, M. inst. C.E., F.G.S., F.C.S., &c. (London : 

 Charles Griffin and Co., 1874.) 



OF all the sciences, Metallurgy is the one whose his- 

 tory extends into the most remote antiquity, and 

 there is abundant evidence to show that even compli- 

 cated metallurgical operations were performed empiri- 

 cally long before the physical sciences existed. 



Until within comparatively recent times the number of 

 eminent chemists who devoted themselves to metallur- 

 gical work was more commensurate with the importance 

 of the subject than at the present day, when, we venture 

 to think, too many are lured away by the attractions of 

 organic chemistry and abstract speculations as to the 

 existence of matter. Notwithstanding this, within the 

 last few years the science of metallurgy has made great 

 advances, but the works on the subject published in this 

 country have been singularly few ; Dr. Percy's admirable 

 work is still incomplete, and, with the exception of 

 the translation of Kerl's " Metallurgy" by Crookes and 

 Rohrig, there is no work which is even fairly compre- 

 hensive. The edition of Mr. Phillips' " Manual of 

 Metallurgy " published in 1858 has become almost use- 

 less, but the volume just issued is an important addition 

 to this branch of literature. 



The physical properties of metals are fully and care- 

 fully treated, and eighty pages are devoted to the con- 

 sideration of fuel. The description of iron ores is very 

 good, tlie author having closely followed Bauerman, and 

 no pains have been spared to render the portion of 

 the work which treats of iron as complete as possible. 

 Among the numerous carefully executed engravings are 

 drawings of roasting and calcining kilns, and of the blow- 

 ing engine and blast cylinder at Dowlais. 



The next important metal, copper, is discussed at some 

 length, and the description of the " wet methods " of 

 extracting this metal is specially valuable, as the author 

 writes from long experience of operations which have been 

 conducted under his own direction. It is interesting 

 to note that processes such as those carried on at Widnes, 

 Alderley Edge, and Jarrow-on-Tyne, are applications, on 

 a manufacturing scale, of methods ordinarily used by the 

 chemist in his laboratory, and, as such, they afford singu- 

 larly important evidence of the progress of metallurgical 

 science. 



Lead is treated at some length, special attention being 

 devoted to the extraction of this metal by means of rever- 

 bcratory furnaces. Excellent drawings are given of those 

 employed in the works at Couiiron, where galena asso- 

 ciated with carbonate of lead is partially converted into 

 oxide and sulphate by roasting, which subsequently react, 

 at a more elevated temperature, on the undecomposed 

 sulphide in the charge, producing metallic lead. 



The articles on silver and gold are condensed from the 

 author's well-known work on the mining and metallurgy 

 of these metals, some new matter being added ; they 

 leave little to be desired, but the forms of apparatus for 

 assaying which are described, are ^not in all cases the 

 most perfect. 



Fifteen metals are treated in the work, and these are 



