6io 



NATURE 



[October 26, 1893 



subject to its fullest development must consult vol. ii. of 

 Mr. Love's " Elasticity," which has recently appeared. 



Kirchoff's Kinetic Analogue between this Elastica 

 and the motion of a Top, makes the same analysis serve 

 for both ; thus, as pseudo-elliptic solutions, we may 

 mention that tortuous Elasticas are given by : — 



(i. ) r'<..2'W+P») = ^i/- -\c{\- 4^ )«2;. ^\r"- + i( I - 2r) ( r - 4f )a^} 



(ii.) , 3,3/(.>+,,) ^ <;.5 + ( , _^) (2 _ 3^)a?|. ^/j^ _ (2^ _ ,^»)^;. 



+ (•(2 - 3f ) s/ ; - ?-^ - ( I - r) ( I - y)d'r'' + ( I - cy{2c - 3^ -)a^} ; 



corresponding to parameters a^ + \u,^ and a^ + l<"3 of 

 the related Elliptic Integrals of the third kind. 



Here a determines the scale of the figure, and c is an 

 arbitrary parameter, upon which / depends ; and it is 

 curious that in case (ii.) the value f = ^ makes/) vanish, 

 and then (u^ = ^/(- 3)<»i. 



Other interesting applications of the Theory of the 

 Bending of Rods, requiring Bessel Functions, are the 

 investigations of the greatest height consistent with 

 stability to which a vertical wire or mast can be carried, 

 or to which a tree can grow, without drooping over 

 under its own weight ; we can thus supply the analysis 

 required in the old German proverb, quoted by Goethe, 

 " Es ist dafiir gesorgt, dass die Baiime nicht in den 

 Himmel wachsen." 



The third part, on Asiatics, is intimately bound up 

 with the distribution in space of Poinsot's central axis 

 for a system of forces ; or with Sir Robert Ball's in- 

 vestigation on Screws. A great analogy e.xists with the 

 an.ilysis required in the distribution of principal axes in 

 space. A problem which might well find a place here is, 

 " The moment of inertia of a body of mass M about any 

 generating line of the hyberloloid of one sheet 



x"- V- 2^ 



a' + Ii 0' + Ii c' + fi 

 confocal with the ellipsoid of gyration 



a- b- c^ 

 is constant, and equal to 



M(a- + l)"- + c- + 2m)." 

 Dr. Routh has now completed his work on " Analytical 

 Statics," and the two volumes form an indispensable 

 addition to the library of the mathematical student. 



A. G. Greenhill. 



MOLESWORTH'S POCKET-BOOK. 

 Pocket-Book of Useful Fonnidce and Memoranda for 

 Civil and Mechanical Engineers. By Sir Guilford L. 

 Molesworth, K.C.I, E., M.Inst.C.E., and Robert 

 Bridges Molesworth, M.A., Assoc.M.Inst.C.E. 23rd 

 edition. (London: E and F. N. Spon, 1893.) 



OF all the many books published for the assistance of 

 engineers generally there is none so well known 

 to the profession as " Molesworth." This pocket-book 

 is to be found in the possession of every engineer, and 

 rightly so, because it is certainly the most useful and 

 accurate of the many to be obtained. 



Any work which has reached the 23rd edition requires 

 no praise to verify its position. This edition is said to 

 contain new and important information on recent 

 NO. 1252. VOL. 4S] 



engineering and industrial developments, many of them 

 entirely new, and much of the matter in previous editions 

 has been revised. "Molesworth" treats with nearly all 

 the various branches of engineering, and so extensively 

 has this been carried out that it is impossible to notice 

 but slightly its contents ; besides the many purely tech- 

 nical formulae there is to be found a collection of most 

 useful tables applying generally to engineering. There 

 are, however, a few mistakes in the mass of matter 

 brought together in this book, and in some instances 

 statements are made which would have been better 

 omitted. 



On page 254 we read that Vickers' straight steel axles 

 should have an ultimate tensile strength of not more than 

 23 tons per square inch, and that this test can only be 

 made by destroying the tested axle. Crank axles should 

 also have a maximum tensile strength of 23 tons. There 

 is either a typographical error or gross mistake in this 

 statement. Had the maximum limit been given 33 tons 

 it would have been nearer the mark ; 23 tons is absurd. 

 Probably the best tensile tests for steel axles would be 

 30 tons per square inch, 25 per cent, extension measured 

 over a length of three inches, and 40 per cent, contraction 

 of area at point of fracture. The author omits to state 

 that straight a.xles are tested under the tup, and that it is 

 this test which destroys them. It is usual to take the 

 tensile sample from this axle. Again, in the tests for steel 

 tyres given on page 255, we notice that a tensile strength 

 of 47 tons is required, but no extension or contraction of 

 area is specified. This is all very well, but tyres have 

 been known to stand the tup test and give the proper 

 tonnage in the tensile test, still the extension has only 

 been 5 to 8 per cent, on three inches, when 16 per cent, 

 is the lowest limit safety demands. 



On p. 410, under ihe head of workshop recipes, there 

 are several mixtures given for case-hardening of wrought 

 iron. The first recipe is used by a few people, but the 

 majority use ordinary charcoal mixed with about 2 per 

 cent, of soda ash. This gives a very uniform and close- 

 grained casing. The author gives no.time-allowance for 

 the articles to remain in the furnace ; this is all-important, 

 because the time governs the depth of the casing. Further 

 on, at p. 41S, we find some recipes to prevent the in- 

 crustation of boilers. One cannot help being amused to 

 discover in "Molesworth" of 1S93 that potatoes, j^jlh 

 the weight of water in the boiler, when put in prevent 

 adherence of scale. Twelve remedies are given, but the 

 only one a man having any regard for his boiler would 

 use is that of frequent blowing off. 



When dealing with the question of the proportions of 

 locomotive boilers on p. 453, the statement is made that — 

 (l) no fixed rule can be established as to the best relative 

 proportions of grate, fire-box, and tube surfaces. (2) 

 Length of tube does not affect economic result. (3) 

 Diameter of tube is a matter of indifference. 



These conclusions are, to say the least of it, very dog- 

 matical. Given the class of fuel to be consumed and the 

 work to be done, then the question of the design of 

 boiler is not very difficult, and the general practice in 

 this respect may be said to be uniform. This practice is 

 certainly approaching a fixed rule. Given the conditions, 

 the design, or we should say the proportions, becomes 

 an easy matter to designers worthy of the name. 



