Septemheu 14, 18S3.] 



SCIENCE. 



3o5 



treatise. The purely geometrical method comes 

 out most clearly in the chapters added in the 

 revision, particularly in two (xvii., xviii.), in 

 which, after going over the ground of practical 

 perspective, Professor Ware sums up, first the 

 principles and relations, and tiien the chief 

 problems, in the most abstract and generalized 

 form. This portion is, therefore, scientifically' 

 the essence of the book, and is that which a 

 reader versed in pure mathematics, but unac- 

 quainted with perspective, might properly- read 

 first. Such a reader would find pleasure in 

 ,its neatness and comprehensiveness of state- 

 ment, and in the skilful way in which the whole 

 sui)ject is cast in condensed and logical form ; 

 every phenomenon or process being first i)re- 

 sented in its most general aspect, — • against the 

 usual habit of books on perspective, — and 

 particular eases deduced from it afterwards. 

 These chapters make a sort of inner treatise, 

 whose appeal will be to the geometer and tlie 

 special student. The}' are probably too ab- 

 stract and too concise to be acceptable to the 

 ordinary student, and he may be left to skip 

 them. 



The methods of the book are naturally those 

 of descriptive geometr3\ We could wish Pro- 

 fessor AVare had held to the received termin- 

 ology when he names the perspective of the 

 vanishing-line of a plane its ' trace,' and diverts 

 the word from its received sense as the inter- 

 section of the plane with the plane of projection. 

 What in descriptive geometry is called the 

 trace, Jlr. Ware calls the ' initial line ' of the 

 plane : the point where a line pierces the pic- 

 ture-plane, which might by proper analogy be 

 called the trace of the line, he calls its ' initial 

 point.' The use of 'horizon' for the actual 

 vanishing-line of any^systeni of planes is hap- 

 pier. The subscript notation emplojcd is the 

 author's own, and is cleverly contrived to suit 

 the manner of his exposition. It contains in 

 itself a symmetrical record of the princi|)al 

 data and relations, and its neatness and efti- 

 ciencj' make one the more regret that the 

 author has not cared to follow an accepted 

 terminology where there is one. 



The phenomena of planes in perspective are 

 first discussed, according to the author's uni- 

 formly analytical metiiod : first oblique planes, 

 then parallel and normal. So much of the 

 pers[)ective i)lienomena of lines is accounted 

 for by treating them as intersections of planes, 

 that their separate consideration is much short- 

 ened by anticipation ; and by the time the 

 point is reached, its discussion is reduced to a 

 minimum. In like manner, instead of confin- 

 ing the discussion of points of distance, as is 



common, to points in the horizon-line, or the 

 prime vertical, the most general case is first 

 considered, and the circular locus of all the 

 points of distance of a given line is determined. 

 We miss the categorical statement, — implied, 

 to be sure, but wortli making distinctlj', — that 

 the points of distance are tlie same for all par- 

 allel lines ; as in another place it is apparently 

 taken to go without saying, that the vanishing- 

 jioint of a line, or the vanishing-line of a plane, 

 is enough to determine problems relating to its 

 direction, even when its position is unknown. 

 Tiie chapter of abstract problems presents 

 pretty much all the problems of descriptive 

 geometry, so far as concerns planes and right 

 lines, ajiplied in perspective, and therefore 

 covers, e.Kccpt for a few special cases, all the 

 elements of perspective practice. Here, again, 

 generalization and condensation are carried 

 ver^- far : some, indeed, of the problems in 

 which manj- alternatives are groupeil together 

 are perhaps too succinct and comprehensive to 

 be satisfying to the student. 



The same method and (juality are found in 

 the other chapters of the book, so far as suits 

 with its practical purpose. Thus parallel per- 

 spective, usuall3- taken first, is postponed, and 

 treated as a special case. There is throughout 

 a watchful eye to the needs of the architectural 

 draughtsman and the painter. The work is 

 made interesting liy observation of natural and 

 ])ictorial i)henomena, many of which are, so far 

 as we know, new to the books. Some special 

 topics which are taken up in the advanced 

 treatises are here liardh- mentioned, — tlie per- 

 spective of curved surfaces and of solids of 

 revolution, for instance; even vaulting being 

 left untouched, and the problems not going 

 beyond plane figures and solids with plane 

 faces. But within its limits, the discussion is 

 very complete ; and some subjects are enlarged 

 u|)on wliich it is usual to dismiss with slight 

 mention, — the perspective of reflections, and 

 of shadows by hotii parallel and divergent light, 

 and especially the chapters on the perspective 

 of the circle, and on perspective distortions and 

 corrections. The method of the perspective 

 plan is made much of, as it deserves ; and some 

 space is given to ^I. Adhemar's ingenious 

 devices for avoiding remote vanishing-points, 

 and carrying on all the operations on a small 

 sheet by means of what Mr. Ware calls ' small- 

 scale data,' — -points of fractional distance, 

 scales of depth, marginal co-ordiuates, and the 

 like, — a method which is much less known than 

 it deserves to be. Mr. Ware adds an ingen- 

 ious alternative for M. Adh<;mar's device of 

 enlarging the remote parts of the perspective 



