Sept. 23, 1875] 



NATURE 



463 



diameter. This confirms the assertion that the rate of wave-pro- 

 gress varies direcUy as the square root of the wave length ; be- 

 cause the rate of recurrence must vary as the rate of progression 

 divided by the path . 



Experiment shows that a wave of I meter wave length would 

 travel 83 -07 meters in one minute if it did not alter its wave 

 length, and moved automatically. A cylindrical trough of water 

 more than, say, 5cxj millimeters deep and I'gSS meters in 

 diameter, will, in the latitude of London, undulate in seconds, 

 and will remain isochronous with the London seconds* pendulum 

 wherever tliey travel together. 



In rectangular troughs, the wave progress is hindered. The 

 rates of recurrence of phase in rectangular troughs are slower 

 than in circular troughs when the wave lengths are the same ; 

 and this difference is greater when the wave length is greater. 

 Both circular and rectangular troughs accept mononodal undula- 

 tion. The rate of progress between parallel walls of a wave 

 I meter long is found to be 747, and this is independent of the 

 distance of the walls apart. The mononodal undulations in 

 circular and rectangular troughs have also been examined. 



The comparative empirical mean constants in minute-milli- 

 meters are — 



Circular. Kectangiilar. 



Mononodal. Binodal. Mononodal. Binodal. 



_ (a) (*) _ (r) (rf) 



«\/<J'= 1 762-56 2613-24; «v'^ = 1594-16 2360-04. 



where d is the diameter of the circular trough and e the length 

 of the rectangular one. 



The water in a circular trough can also undulate with two per- 

 pendicular rectilinear nodes. 



Taking the same trough, it is found that the number of undu- 

 lations per minute, when (a) the circular binodal, {b) the mono- 

 nodal, and (c) the binodal rectangular systems were established, 

 were — 



a = 106-9 i5 = 7i"6 c = 94. 



These numbers a and c agree well in ratio with those of a 

 circular elastic plate in similar vibration. The details of this 

 communication were laid before the Physical Society in June 

 last. They will, I hope, appear in [part in the Philosophical 

 Magazine for October. 



SECTION B— Chemical Science 



Prof. Cayley read a paper On the Analytical Forms called 

 Trees, with application to the theory of chemical combinations, 

 before a good audience composed to a considerable extent of 

 mathematicians. 



The author in commencing stated that the subject he was 

 about to consider was more mathematical than chemical, but as 

 the results bore considerably upon the latter subject he had intro- 

 duced it in this Section. The problem to be solved was to find 

 the theoretic number of the hydrocarbons CnHj^ + g. 



The only assumptions are that an atom of hydrogen can link 

 itself to one other atom, and an atom of carbon to four other 

 atoms. A combination of n carbon atoms can then link itself on 

 to 2„ + J hydrogen'atoms at most, but this number is only attained 

 when the carbon atoms are linked together without cycles, or so 

 as to forma "tree": given the tree, the hydrogen atoms can 

 be linked on in one way only, and the question thus is to find 

 the number of trees which can be formed with « carbon atoms. 

 The atoms, or dots representing them, are termed " knots," the 

 lines joining two knots are termed "branches" — the trees in 

 question are such that from each knot there proceed at most four 

 branches ; but this limitation is in the first instance disregarded. 

 A tree may be considered as springing from any one of its knots 

 as its root, and trees which are chemically the same thus present 

 themselves under different forms. For the treatment of the 

 chemically distinct forms it is necessary to introduce the notions 

 of a "centre " and a "bicentre" (due to Prof. Sylvester) ; and 

 the question is reduced to that of finding the number of the 

 central trees with « knots : this is solved by the method of gene- 

 rating functions, viz., the number of the central trees of altitude 

 iVis given by a series of the form — 



/**+' -f{/,/«}^*+» +{/,/»,/3]x^+» +, &c. 



where the numerical coefficient of any term /«^^ + ^ shows the 

 number of trees of a main branches and N + fi knots. The final 



result as regards the carbon-trees, or say the hydrocarbons 

 C^Hgn + 2 is given by the following table : — 



so that theoretically for the body whose formula is CjgHjg there 

 exist 799 isomeric bodies. 



It is worthy of remark that the mathematical theory agrees 

 with experiments for the first five bodies, thus affording strong 

 confirmation of the truth of the remainder. 



The Professor also drew attention to the fact that any number 

 is sometimes rather more and sometimes rather less than double 

 the preceding number. 



Prof. Armstrot»g suggested that probably a" large number of 

 these isomers would be unstable, illustrating his meaning by the 

 two isomeric di-nitro-phenols, one whose melting-point was 

 76" C. readily passing into the other whose melting-point was 

 116° C, which was objected to on the ground that it was not 

 fair to compare the action of bodies as complicated as the 

 phenols with the simple hydrocarbons. 



Prof. Clifford also made some remarks on the bodies repre- 

 sented by C„H2n + A - 2x. ^^^ stated that it would be found 

 that X represented the number of cycles that would occur in the 

 trees. 



Mr. P. Braham made some remarks on some further experi- 

 ments on Crystallisation of Metals by Electricity, in which he 

 stated that he had placed the positive and negative electrodes of 

 a battery in a vessel containing a mixed solution of copper and 

 zinc, and that with terminals of copper he obtained a dull 

 crystallisation proceeding from the negative pole of mixed 

 crystals of copper and zinc, and beyond this, crystals of 

 copper alone. With terminals of zinc he got a mixture of 

 crystals as before, and in front of these, crystals of zinc alone. 

 But if terminals of brass (a compound of zinc and copper) are 

 used, there is a dull crystallisation of zinc across the field. 

 He also observed that with zinc terminals, by increasing the 

 battery power, the crystallisation is broken up ; but not so when 

 the terminals are copper or brass, but then the crystallisation 

 extends above and beyond the positive pole. 



Mr. Gatehouse read a paper On Stiver Nitrtte, giving the 

 results of some investigations into the causes of what is termed 

 by photographers " woolliness " in their negative baths. 



The five methods given of preparing the nitrite were as 

 follows : — 



1. By mixing solutions of potassium nitrite and silver nitrate. 



2. By sensitising a collodion film and evaporating to dryness 

 a mixture of nitrite and nitrate is obtained. 



3. By fusing silver nitrate with organic matter. 



4. By electrolysis of silver nitrate with platinum electrode. 



5. By means of metals placed in neutral solution of silver 

 nitrate. 



By this last method he found that metals which produced 

 reduction, viz., K, Na, Bi, Hg, As, Th, did not produce nitrite, 

 but those which did not produce reduction, viz., Fe, Ni, Co, 

 Mg, Zn, Cu, Pb, Sn, Sb, did produce nitrite. The former, it 

 was observed, hare an uneven equivalency, and the latter an 

 even equivalency, with the exception of Ilg and Sb, the latter of 

 which may, like Fe, be tetratomic. The physical forms of the 

 crystals were observed to vary from modular masses to filiform 

 crystals. 



Mr. A. H. Allen, in making some remarks On a Method of 

 effecting the Solution of difficultly-soluble Substances, stated that he 

 had found that many so-called insoluble substances could, when 

 heated with fuming hydrochloric acid in sealed combustion tubes, 

 be either completely dissolved or decomposed with separation of 

 silica. In some cases where hydrochloric acid failed, sulphuric 

 acid succeeded. The heating of the tubes was generally done 

 by means of a water bath, but for some substances a cliloride of 

 calcium bath must be used. 



Mr. J. C. Melliss read an account of the method of purifica- 

 tion of a river by precipitation, at present adopted at Coventry. 

 He stated that 2,000,000 gallons of sewage liquor, contaminated 

 by dye, refuse, &c., were daily passed through these works and 

 completely purified. The process employed is briefly the follow- 



