September 29, 1892] 



NA TURE 



513 



The first nitrogen would be too heavy, if it contained residual 

 -oxygen. But on this hypothesis something like i per cent, 

 would be required. I could detect none whatever by means of 

 alkaline pyrogallate. It may be remarked the density of this 

 nitrogen agrees closely with that recently obtained by Leduc, 

 using the same method of preparation. 



On the other hand, can the ammonia-made nitrogen be too 

 light from the presence of impurity? There are not many gases 

 lighter than nitrogen, and the absence of hydrogen, ammonia, 

 and water seems to be fully secured. On the whole it seemed 

 the more probable supposition that the impurity was hydrogen, 

 which in this degree of dilution escaped the action of the copper 

 oxide. But a special experiment appears to exclude this 

 explanation. 



Into nitrogen prepared by the first method, but before its 

 passage into the furnace tubes, one or two thousandths by 

 volume of hydrogen were introduced. To effect this in a uniform 

 manner the gas was made to bubble through a small hydrogen 

 generator, which could be set in action under its own electro- 

 motive force by closing an external contact. The rate of hydro- 

 gen production was determined by a suitable galvanometer 

 enclosed in the circuit. But the introduction of hydrogen had 

 not the smallest effect upon the density, showing that the copper 

 oxide was capable of performing the part desired of it. 



Is it possible that the difference is independent of impurity, 

 the nitrogen itself being to some extent in a different (dissociated) 

 state ? 



I ought to have mentioned that during the fillings of the 

 globe, the rate of passage of gas was very uniform, and about 

 I litre per hour. Rayleigh. 



Terling Place, Witham, September 24. 



Recent Spectroscopic Determinations. 



In the September number of the Philosophical Magazine Mr. 

 Michelson has published determinations, by a most interesting 

 method, of very close double and multiple lines. In any at- 

 tempt to interpret his results, it is neccesary to bear in mind the 

 profound modifications which the internal motions of a ;;as — the 

 rectilinear motions of the molecules between their encounters, 

 as well as the motions going on within each molecule — had 

 undergone within the Geisler's tubes upon which he experi- 

 mented. 



In a gas under ordinary circumstances the rectilinear journeys 

 of the molecules take place indifferently in all directions, and 

 where this is the case it follows from the well-known relation 

 between the surface of a sphere and that of its circumscribing 

 cylinder, that the effect of the velocities which happen to lie be- 

 tween V and y + 5v is to substitute for each line of the spectrum 

 of the gas a band of uniform intensity and without nebulous 

 edges, the width of which can be calculated. This width, for 

 example, is 04 of an Angstrom or Rowland unit (the tenthet- 

 metre), in the yellow part of the spectrum and for velocities of 

 the molecules which lie in the neighbourhood of two kilometres 

 per second, which is about the average velocity of molecules of 

 hydrogen at atmospheric temperatures. Hence with all the 

 velocities that prevail among the molecules, the effect of the 

 rectilinear motions under ordinary circumstances is that each 

 line will be symmetrically widened and rendered nebulous. To 

 this effect Mr. Michelson calls attention. 



But in the residual gas of a Geisler's tube through which 

 electricity is passing, the case is altogether different. Here the 

 rectilinear motions of the molecules are not alike in all directions, 

 but preponderate in some : a state of things which must at least 

 double the lines, and may introduce greater complications. 



Moreover, different lines may be differently affected, since the 

 behaviour of the gas varies according to its position between the 

 electrodes ; as is evidenced by the observed differences in the 

 form and colouring of the striae, &c., in the several parts of a 

 Geisler's tube. 



We must also be on our guard in another respect, when we 

 attempt to interpret the results, since the distribution of the 

 heat energy of a gas between the rectilinear motions of its 

 molecules and the motions within the molecules, which in the 

 case of ordinary gas is a fixed ratio, is certainly largely departed 

 from in gas through which electricity is passing. Until the laws 

 of the new distribution are understood, the temperature of the 

 gas, judged of by its behaviour to neighbouring bodies, will give 

 us little information. 



It is to such events as are referred to above, or others which 



like thtm may aiise from the special circumstances under which 

 the vapour of sodium was in Mr. Michelson's experiments, that 

 we must apparently turn for an explanation of the doubling of 

 the corstituerts of the principal pair of sodium lines which he 

 has delected ; since he found that "the width of the lines, 

 their distances apart, and their relative intensities vary rapidly 

 with changes in temperature and pressure." 



The method of investigation which Mr. Michelson has so 

 successfully ppplied appears to be by far the most searching 

 means yet discovered of experimentally investigating the intricate 

 and obscure phenomena which present themselves in Geisler's 

 tubes, and we seem justified in hoping for great results from it. 

 G. Johnstone Stoney. 



9, Palmerston Park, Dublin, September 22. 



Printing Mathematical Symbols. 

 Everyone who has had to correct printers' proofs of mathe- 

 matical formulae must be painfully alive to the pitfalls into 

 which the non-mathematical compositor continually blunders. 

 To such as know the extreme difficulty of getting such formulae 

 properly set up, there have doubtless occurred from time to 

 time suggestions for such simplifications of notation as shall 

 render the composition less liable to derangement. One most 

 sensible step of the kind I allude to is the introduction by 

 Sir G. Stokes of the solidus notation for quotients, whereby 



f^ is now written dyldx. 



The immediate purpose of this letter is not to propound any 

 wholesale scheme of reform, but to advocate one other simple 

 step, and to induce some of my confreres to give the world their 

 own suggestions. 



Exponentials are a continual stumbling-block to the com- 

 positor, and to the printer's reader, who, when he comes to an 

 expression like 



does his best to make it look a little straighter and turns it into 



Ae - ax, 

 or into 



Ae- ax, 

 or perhaps worse. 



The reform I advocate is to write the thing as follows : — 



A exp\ - ou:], 



the square brackets being possibly omitted in all cases when 

 their omission would occasion no confusion. One gain in this 

 notation is the reduction of the whole of the symbols to one 

 level, so not breaking the line of type. 



Another useful reform, though one on which I fear the 

 probability of agreement is less likely, is the use of the Conti- 

 nental notation for inverse trigonometrical functions, writing, 

 for example, 



arc tan x, 

 instead of 



tan-i jr 



for the angle whose tangent is x. Our notation is not only liable 

 to continual misprinting, but is very confusing to Continental 

 readers, who again and again read the ktter expression as mean- 

 ing 



(tan x) - 1, or cotan x. 



I have even seen it reprinted in a German technical journal ns 

 tan - i.r. 



SiLVANus P. Thompson. 

 Technical College, Finsbury, September 22. 



A so-called Thunderbolt. 

 During a short storm in Liverpool this summer, I noticed 

 one flash as peculiarly sharp and noisy, and subsequently in the 

 correct bearing from my house the ground was reported as 

 having been struck by a thunderbolt. I examined the place, 

 which was on the greensward of a lake, where the ground was 

 penetrated by a number of fairly clean-cut almost vertical holes 

 down which a walking-stick could be thrust. People sheltering 

 near the lake repotted a ball of fire and a great splash up of the 



NO. II 96, VOL. 46] 



