284 



NATURE 



\_Feb. 7, 1878 



8 cm. from the primary. Reverse the wires in the 

 secondary circuit, reverse the wires in the primary circuit, 

 how you please, the mercury always moves towards the 

 point of the capillaiy. 



8. Shouting or singing (excepting the above-mentioned 

 note) produces no visible effect under the conditions 

 mentioned in Experiments 5, 6, and 7. 



9. If the secondary coil be now moved close up, so as 

 to cover as completely as possible the primary, talking to 

 the telephone with the ordinary voice, i.e. with moderate 

 strength and at any pitch, produces a definite movement 

 of the mercury column for each word, some sounds of 

 course giving more movement than others, but the move- 

 ment is always towards the end of the capillary. Singing 

 the note mentioned in Experiments 5, 6, and 7 loudly, 

 produces a movement too large to be measured with the 

 electrometer. 



Reversing the poles of the magnet in the telephone does 

 not alter the results of Experiments 5, 6, 7, and 9. 



On mentioning the above results to Dr. Burdon San- 

 derson, he suggested that the apparently anomalous 

 behaviour of the electrometer might be accounted for, by 

 supposing that the mercury moved quicker Wcioxi a current 

 passed towards the point of the capillary than when it 

 flowed in the opposite direction ; so that if a succession 

 of rapidly alternating currents be passed through the 

 instrument, the mercury will always move towards the 

 point of the capillary, the movement away from the point 

 being masked by the sluggishness of the instrument in 

 that direction. That this explanation is the correct one 

 is proved by the following experiment : — The current 

 from two Grove's cells is sent through a metal reed 

 vibrating 100 times a second, the contact being made and 

 broken at each vibration, the primary wire of a Du Bois 

 Reymond's induction-coil is also included in the circuit ; on 

 connecting the electrometer with the secondary coil placed 

 at an appropriate distance the mercury always moves to 

 the point of the tube whatever be the direction of the 

 current. F. J. M. Page 



Physiological Laboratory, University College, 

 London, February 2 



Note.— On February 4 Prof. Graham Bell kindly 

 placed at my disposal a telephone much more powerful 

 than any of those I had previously used. On speaking to 

 this instrument, the electrometer being in the circuit, 

 movements of the mercury column as considerable as 

 those in Experiment 9 were observed. — F. J. M. P. 



CHEMISTRY AND ALGEBRA 

 T T may not be wholly without interest to some of the 

 ■*• readers of Nature to be made acquainted with 

 an analogy that has recently forcibly impressed me 

 between branches of human knowledge apparently so 

 dissimilar as modern chemistry and modern algebra. I 

 have found it of great utility in explaining to non-mathe- 

 maticians the nature of the investigations which alge- 

 braists are at present busily at work upon to make out 

 the so-called Grtmdfornien or irreducible forms appurte- 

 nant to binary quantics taken singly or in systems, and I 

 have also found that it may be used as an instrument of 

 investigation in purely algebraical inquiries. So much is 

 this the case that I hardly iever take up Dr. Frankland's 

 exceedingly valuable "Notes for Chemical Students," 

 which are drawn up exclusively on the basis of Kekule's 

 exquisite conception of valence^ ■^\\}a^Q\x\. deriving sugges- 

 tions for new researches in the theory of algebraical 

 forms. I will confine myself to a statement of the grounds 

 of the analogy, referring those who may feel an interest 

 in the subject and are desirous for further information 

 about it to a memoir which I have written upon it for the 

 new American Journal of Pure and Applied Mathe- 

 matics, the first number of which will appear early in 

 February. 



The analogy is between atoms and binary quantics 

 exclusively. 



I compare every binary quantic with a chemical atom. 

 The number of factors (or rays, as they may be regarded 

 by an obvious geometrical interpretation) in a binary 

 quantic is the analogue of the number of bonds, or the 

 valence, as it is termed, of a chemical atom. 



Thus a linear form may be regarded as a monad atom, 

 a quadratic form as a duad, a cubic form as a triad, and 

 so on. 



An invariant of a system of binary quantics of various 

 degrees is the analogue of a chemical substance composed 

 of atoms of corresponding valences. The order of such 

 invariant in each set of coefficients is the same as the 

 number of atoms of the corresponding valence in the 

 chemical compound, 



A CO- variant is the analogue of an (organic or inorganic) 

 compound radical. The orders in the several sets of co- 

 efficients corresponding, as for invariants, to the respective 

 valences of the atoms, the free valence of the compound 

 radical then becomes identical with the degree of the 

 co-variant in the variables. 



The weight of an invariant is identical with the number 

 of the bonds in the chemicograph of the analogous 

 chemical substance, and the weight of the leading term 

 (or basic differentiant) of a co-variant is the same as the 

 number of bonds in the chemicograph of the analogous 

 compound radical. Every invariant and covariant thus 

 becomes expressible by a graph precisely identical with a 

 Kekuldan diagram or chemicograph. But not every 

 chemicograph is an algebraical one. I show that by an 

 application of the algebraical law of reciprocity every 

 algebraical graph of a given invariant will represent the 

 constitution in terms of the roots of a quantic of a type 

 reciprocal to that of the given invariant of an invariant 

 belonging to that reciprocal type. I give a rule for the 

 geometrical multipUcation of graphs, i.e. for constructing 

 a graph to the product of in- or co variants whose separate 

 graphs are given. I have also ventured upon a hypothesis 

 which, whilst in nowise interfering with existing chemico- 

 graphical constructions, accounts for the seeming anomaly 

 of the isolated existence as "monad molecules" of 

 mercury, zinc, and arsenic — and gives a rational explana- 

 tion of the " mutual saturation of bonds." 



I have thus been led to see more clearly than ever I 

 did before the existence of a common ground to the new 

 mechanism, the new chemistry, and the new algebra. 

 Underlying all these is the theory of pure colligation, 

 which apphes undistinguishably to the three great 

 theories, all initiated within the last third of a century or 

 thereabouts by Eisenstein, Kekule, and Peaucellier. 



Baltimore, January i J. J. Sylvester 



PALMEN ON THE MORPHOLOGY OF THE 

 TRACHEAL SYSTEM 



DR. PALMEN, of Helsingfors, 'has recently published 

 an interesting memoir on the tracheal system of 

 insects. He observes that although the gills of cer- 

 tain aquatic larvae are attached to the skin very near to 

 the points at which the spiracles open in the mature 

 insects, and though spiracles and gills do not co-exist in the 

 same segment, yet the point of attachment of the gills 

 never exactly coincides with the position of the future 

 spiracle. Moreover, he shows that even during the larval 

 condition, although the spiracles are not open, the struc- 

 ture of the stigmatic duct is present, and indeed that it 

 opens temporarily at each moult, to permit the inner 

 tracheal membrane to be cast, after which it closes 

 again. In fact, then, he urges, the gills and spiracles do 

 not correspond exactly, either in number or in position, 

 and there can therefore be between them no genetic 

 connection. He concludes that the insects with open 

 tracheae are not derived from ancestors provided with gills, 



