May 9, 1 901] 



NA TURE 



27 



to the particular set of natural conditions under which 

 it grows are facts which are seldom absent from his mind, 

 and as a consequence there is a freshness and reality 

 about much which he has written that are often absent 

 from the writings of the laboratory and museum worker. 



Dr. Fowler's accounts of the Hydromedusfc and Scy- 

 phomedusa: are, in our opinion, the least satisfactory 

 portions of the volume. The style is too concentrated 

 and concise to make the writing effective, and intellectual 

 interest has been entirely sacrificed in an attempt to in- 

 troduce every available fact and to deposit it in a properly 

 labelled compartment. The result resembles the syllabus 

 of an advanced course of lectures on the groups dealt 

 with rather than an intelligible account of those groups. 



In the chapters on Anthozoa and Ctenophora, Mr. 

 Bourne presents us with an excellent series of detailed 

 descriptions of particular types, together with a clearly 

 stated and well-marshalled body of facts concerning the 

 groups as a whole. His work will undoubtedly prove of 

 great value to both teachers and students. We, however, 

 fail to find in these two sections that originality of treat- 

 ment and originality of thought which characterise Prof 

 Minchin's section on the Ponfera. 



The whole work is well illustrated, being in this respect 

 a great improvement on the volume of the treatise pre- 

 viously published (Part III. Echinoderma). The figures 

 for which Prof Minchin and Mr. Bourne are responsible, 

 many of which are original, are specially worthy of 

 praise. 



THE GRAPHICAL MENSURATION OF 

 VAULTS. 

 II Cakolo Grafico applicato alia Misura delle Volte. 

 Prof Ernesto Breglia. 5th serie, vol. i. (Atti del 

 Reale Istituto d'Incoraggiamento di Napoli, 1899.) 

 /'"^ R.APHIC.AL methods are used to a certain extent in 

 the solution of engineering problems, although per- 

 haps their employment is not so extended as their neat- 

 ness and simplicity merit. In some cases, it is true, 

 where the simplification is great and the application easy, 

 they are used practically to the exclusion of other methods. 

 But in other cases where a graphical treatment would effect 

 almost as great a simplification the methods have never 

 been very generally applied. The reason lies, we think, 

 in the fact that it requires greater ingenuity to treat a 

 problem graphically than analytically. Problems such as 

 occur in practice, even though they may be complicated, 

 can generally be hammered out by analytical means. 

 A good mathematician, no doubt, will Ije able to find a 

 short cut to the solution, but the engineer, whose ready 

 stock of mathematical knowledge on which he can draw 

 with ease amounts to little more than the algebra he 

 learnt at school and an acquaintance with the principles of 

 the calculus, will be able to work out the solution by dint 

 of determined plodding. With graphical methods it is 

 difterent. To begin with, the geometrical training which 

 an English engineer receives at school is a hindrance 

 rather than a help, so that w-hen he comes to study 

 graphical systems he finds himself in a region unknown 

 to him and is obliged to disembarrass himself of the 

 Euclidean notions acquired in his youth. We are 

 afraid that the Englishman will never be quite happy 

 NO. 1645, ■^'OL. 64] 



in using geometrical methods until the groundwork of 

 his knowledge is laid with some more suitable text-book 

 than Euclid's Elements. In addition to this, with these 

 methods each new problem requires somewhat different 

 treatment ; it is hard, and often impossible, to lay down 

 very definitely the lines on which to proceed. The in- 

 genuity which is consequently required can only be 

 obtained, by any except the born mathematician, by the 

 habitual use of the system. 



Prof. E. Breglia's paper illustrates what we have been 

 saying. The method that he has worked out for measur- 

 ing the volumes of arches and vaults is extremely neat. 

 In the simpler cases it is, as is natural, very much easier 

 to follow and apply, and the ease of doing so is such that 

 it should commend itself to all who have need to make 

 such measurements. In the cases of vaults of more com- 

 plicated shape the method becomes also more complex ; 

 artifices have to be used in order to " dodge " the more 

 important difficulties. It is just these artifices that are 

 so difficult to find when a new problem is attacked. To 

 apply Prof Breglia's method to the determination of the 

 volume of a vault similar in shape to one of those he has 

 examined in the paper before us would be fairly simplei 

 even though the shape might be very complicated ; to 

 apply it to the case of a vault of quite a different shape 

 would not be nearly so easy. Prof Breglia has, how- 

 ever, examined a great variety of cases in a thorough 

 manner, and has thus rendered his paper very valuable. 



Prof Breglia's system has other advantages besides a 

 simplicity which enables the volume of a vault of com- 

 plicated shape to be found without the use of advanced 

 mathematics. The accuracy can be increased practically 

 at will by varying the number of sections into which the 

 vault is divided ; with analytical methods high accuracy 

 is often only attainable by undue complication of the 

 mathematics. We are inclined to think, also, with Prof 

 Breglia that error is less likely to occur in its use, as 

 should any mistake be made it will show itself directly ; 

 but this is an advantage that must not be given too great 

 weight, as graphical methods possess possibilities of error, 

 especially in the interpretation of the results, which are 

 not to be met with in other methods. The system is, 

 however, a very useful one, and the paper is worthy the 

 careful attention of all those interested in the subject. 



OUR BOOK SHELF. 

 E.xperitnental Chemistry. By Lyman C. Newell, Ph.D. 



Pp. XV -I- 410. (Boston : Heath and Co., 1900 ) 



Price 5^'. 

 Dr. Newell has added one more to the already formid- 

 able array of elementary science text-books, each of 

 which, according to their respective authors, has been 

 written to supply a long-felt need. In the present in- 

 stance, the object is to promote the more efficient teach- 

 ing of chemistry by modern methods ; and in writing his 

 book Dr. Newell has been actuated by "a desire to pro- 

 vide a course of study which shall be a judicious 

 combination of the inductive and deductive methods." 



We fail to see in what way Dr. Newell's book 

 superior to a hundred others of a similar kind. The 

 ideal that the author has set before him is a very high 

 one, and we should be the last to deprecate any attempts 

 to improve upon modern methods of teaching experi- 

 mental science. It is obvious that the time at the dis- 

 posal of the average student is so limited that it would be 



