82S 



SCIENCE. 



[Vol.. II., No. 47. 



if f, riy f, denote linear functions of Uie co-oiilinalrs 

 (;c, y. z, w), suclj that identically 



X + y + z + 5 +17+ f=0. 



ax + by + cz+fi +gv + hi;—0 



(where af = bg ~ ch = 1), then the quartic surface, 



\Jx^ + \Jyv + y/zf = 0, 

 is a sisteen-nodal surface. Prof. Cayley has previously 

 given the equation of this surface under the form 



\/x (X - 10) + y/y(T-w) + s/z [Z-w) = 0, 

 where X= a{y'yi'y — [3' (3" z), etc.. and a + /3 + y = 0, 

 etc. ; the other relations being obtained by cyclical 

 interchange of the letters, and by advancing the 

 accents. The object of the present paper is the direct 

 identification of these two forms of the equation of 

 the surface. — {Journ. reine anq. math., xciv.) t. c. 



[541 

 Elliptic functions. — M. Hermite has given a 

 simple and direct demonstration of an interesting 

 relation discovered by Prof. Cayley. The relation is 

 as follows: if n, v, r, s, are four quantities connected 

 by the relation u + u + r + s = 0, then we have — 

 — fc'2 sn u sn B sn }• sns + en « en u en r en .s — 

 1 k'-' 



J.., dn M dn t) dn r dn s = — ,..r- 



This remarkable i-elation is shown by M. Hermite 

 to be easily derived by means of certain formulas 

 which he has long used in his course in the Sor- 

 bonne. The formulas are those which give the 

 decomposition into simple factors of the three quan- 

 tities sua; sn (x + a), cnx en (x + a), dnx dn (x + a). 

 The decomposition of the first of these products is 

 a known fundamental relation between Jacobi's Z- 

 functions: the decomposition of the other two prod- 

 ucts is given by M. Hermite; and by aid of them 

 Pi'of. Cayley's formula is proved. — [Ada math., i. ) 

 T. c. [542 



ENGINEERING. 



The two-cylinder compound engine. — Pro- 

 fessor S. W. Robinson furnishes Van Nostrand's 

 inaf/azine a paper on the working of steam in this 

 engine in its various forms, and traces the method 

 of distribution in the two cylinders and the effect of 

 such methods on the theoretical efficiency. He gives 

 the general method of representing the action of steam 

 grapliically, and shows how diagrams made from the 

 two cylinders are combined. The effect of the re- 

 ceiver is exhibited, and the result of the introduction 

 of various conditions, as clearance, etc. — (Van Nos- 

 trand's mag., Oct.) E. H. T. [543 



Spherical steam-engines. — Messrs. Heenan & 

 Proude of Manchester, G.B., recently exhibited at 

 the Engineering and metal trades exhibition, Lou- 

 don, their 'Tower' spherical engine, driving an 

 Edison dynamo. The steam-cylinder is a sphere hav- 

 ing two cylindrical projections cast upon it. Each 

 of these carries a sliaft, only one of which transmits 

 power from the engine, the other having merely to 

 guide the hinged piston nearest it. The pistons divide 

 the interior of the sphere into four i^ortions, which 

 at times are four equal quadrants of the sphere, but 

 which are capable of variation of volume with change 



of piston position; and, this being effected by the 

 action of the steam which is let into the several spaces 

 at proper times by the action of the rotating valves 

 which are set in the cylindrical projections, the shafts 

 are turned, and power is produced and transmitted to 

 the mechanism of transmission. 



The engine worked silently and well, and indicated 

 IS-horse power at 600 revolutions per minute, with 

 steam at SO pounds (O5 atmos. ). Its diameter was 

 but 7 inches (17. S centimetres). — {London engineer, 

 July.) K. 11. T. [544 



Steel castings. — Mr. W. Parker has collected 

 facts bearing upon the value of steel castings in marine- 

 engine construction. He observes that forged iron 

 shafts and other heavy parts are very unsafe, and that 

 mild steel is taking the place of wrought iron for all 

 such uses. About a hundred and twenty steel ships 

 are in progress in Great Britain, constructed of low 

 steel. The testimony of steel-makers and tests of 

 the material show that steel castings can be made of 

 homogeneous character and thoroughly reliable. 

 Jessop & Co. use crucible steel for this purpose, and 

 think that good castings can only be obtained with 

 certainty by the crucible process. Spencer & Sons 

 use both crucibles and the open-hearth process, and 

 get equally good results from both. The Steel com- 

 pany of Scotland use the Siemens furnace and process, 

 and adopt the silicide of manganese as a flux to insure 

 soundness. The luternal stresses due to variation In 

 rate of cooling are avoided either by very slow cooling 

 or by annealing. Pourcel of Terre Noire, France, 

 tempers in oil, with, as is claimed, very gre.it advan- 

 tage. The tenacity is thvis increased sometimes thirty 

 per cent, and the elongation at rupture remains un- 

 reduced, while the grain of the steel is greatly im- 

 proved. Sir Joseph Whitworth compresses his ingots 

 of steel, while solidifying, by applying the pressure of 

 a large hydraulic press. Messrs. Vickers & Co. make 

 many large crank-shafts for steamships, adopting a 

 mild steel of a tenacity of about fifty-five thousand 

 pounds per square inch. The castings are improved by 

 liammering or rolling, thirty per cent. — {Scient. 

 Amer., Oct. 20.) K. H. T. [545 



CHEMISTRY. 



{General, physical, and inorganic.) 



Bleaching. — ' Oxygenated water,' a comtnon name 

 for peroxide of hydrogen, has within the last few years 

 attracted a good deal of attention as a bleaching and 

 purifying agent, and has been successfully employed 

 as a substitute for chlorine. It is now stated that 

 Mr. P. Ebell of Pfungstadt, near Darmstadt, has 

 succeeded in preparing economically a product, pure, 

 stable, and of constant strength, capable of being 

 easily transported for long distances, and kept for 

 years without losing its bleaching-properties. Among 

 other applications of this product, that of the decolor- 

 ation of anim.al fibres is the most Important, as it 

 does not contain some of the disadvantages of other 

 bleaching-agents. For wool or silk, it is advisable, 

 before bleaching, to cleanse the materials thoroughly, 

 so as to eliminate all the greasy substances and im- 

 purities. For this purpose, Mr. Ebell recommends a 



