72 



NATURE 



[July 21, 1910 



radius ratio ; but so that there is developed at the icosa- 

 hedral centre, a deficit or gravitative pull equal exactly to 

 the hydrogen mean weight by H, : O, viz. i'0076l. 



1 

 ;V = 2l2[=I'OS9462 • •]-M-oo76i. 



(ii) The vortex compensating the ratio of cube-edge to 

 octahedral-edge — i.e. he.x- : ocf- — both having a common 

 or equal circum-radius, unravels down the cube-edge to its 

 7th root, and at '^J'u becomes an icosahedral compensation 

 vortex ; the octahedral-edge becomes or equals the icosa- 

 hedral circum-radius ; and the hydrogen pull is developed 

 at the icosahedral centre ; but at H, : O max. i'00777. 

 Cases (iii), (iv), and (v), and all the coalition permutations 

 (see below), are to be interpreted like (i) and (ii), though 

 more complex. 



In cases (i), (ii), (iii), and (iv) we have severally H' " ' ■" ; 

 and, similarly, in the coalition formulae ic or H are 

 never in excess by more than the valency numbers i to 4 

 — 1 to S in the cross-formula (No. 4).' This, probably, is 

 attributable to the multiple radial lines. For we are con- 

 cerned with powers, not multiples. Each central vortex 

 does not need to pull against the sum of all its surrounding 

 vortices as isolated units, because these latter too are them- 

 selves centres, and correspondingly weakened. The contrac- 

 tion of the crystalline ratios under heat is consistent with the 

 cntropic or adiabatic phenomena of H,0 ; and for many 

 reasons it is believed that the weight deviations are a 

 function of entropy. When (see below) the line is crossed, 

 the signs change, contraction becomes expansion, and 

 along the lines of the pari passu increase of exponents, 

 the ^'D, entropically disturbed, gradually becomes constant. 



Morley's ranges are severally +o.oooi6, +0-00033, 

 + 0-0007, 3nd (means) 0-00004- By coalition of the frac- 

 tures of the main formulae, we derive the following, 11? 

 all -which formulae, +x being high, the mean is attained, 

 and the maxima and minima ivhen ±x is low; so that the 

 formulae can never transcend the experimental range, and 

 always tend to its means. (Compare entropy) : — 



A comprehensive deduction from the general formula is 

 the following : 



H ( I -00761 ) X "." =,-—,= ; -„ &c. 



,(fir_ O ct*' 

 ic' hex 3 hex 5" 

 Provisionally, upon examination of four out of the eight 

 combinable groups, the elemental weights are found ex- 



pressible in like Ir-rms to these, i.e. the elemental 

 weights are such that, multiplied into the simple volution 

 of one or more of the symmetry line-ratios, they yield 

 accurately the simple volution of one or more othe/ 

 symmetry line-ratios, each expression having its exact 

 cquational variant, like elements yielding to like expression, 

 hut not mechanically so (see Chcm. News, April 22, May 6, 

 and June 10). This is deduced from the basal-equations 

 with .V as I • - 8, the formula not being constructed (or 

 rather discovered) empirically to yield any given weight, 

 but rationally to meet the whole problem of weight com- 

 pensation. That, X being i, the H weights were with 

 perfect exactitude obtained, chanced to be a fact almost 

 the last discovered. 



Considering the hydrogen solution alone, the rational 

 postulate of vortex compensation for inequidistance (as 

 contrasted with the crude Democritan hard-atom hypo- 

 thesis) hits precisely — with the odds 100. onn to i against 

 each hit — in the four corners of the basal-equation, the 

 four means of hydrogen ; and by coalition, all their 

 deviations. The postulate is thus, nn the one element, 

 proved true hy the odds 100,000-* (lO"") to 1. 



Corroboration is glimpsed in the spectrum-line ratios. 

 H. Newman Howard. 



Electrical Discharge Figures. 



Mr. a. \V. Porter gave in Nati-re of March 31 (vol. 

 Ixxxiii., p. 142) an account of his experiments on electric 

 discharges over photographic plates, made in order to 

 ascertain what is due to the luminosity of the discharge 

 and what to the discharge itself. Knowing that the dis- 

 ruptive discharge carries metallic particles from the elec- 

 Irodes, and that in the silvering of mirrors by the wet 

 processes the silver begins to set at every metallic particle 



NO. 2125, VOL. 84] 



Electrical discharge figure developed by wet 



which clings to the surface of the glass because of the action 

 of local couples, I ventured to develop the invisible inrage 

 of the discharge on a clean glass plate by the silvering 

 solution. 



The elTect was a very striking one ; instead of the broad 

 band ot the trunk discharge, a clean band was_ left, 

 surrounded by two sharp, dense lines of deposited silver. 

 The thin ramifications were still visible, but the splendid 

 display of surrounding figures is lacking. The two un- 

 satisfactory paper prints that I send [one is here repro- 

 duced] were made from developed plates, and are there- 

 fore negatives. It is impossible to get better results now, 

 because the laboratory is closed for the summer holidays. 



The acid intensifier for the collodion plates, acting in 

 the same way as the wet silvering mixture, was also tried 

 by me, but the result was worse. 



■\V. Lermaxtoff. 



University of St. Petersburg, Russia. 



