October 22, 1903] 



NATURE 



599 



with demy quarto, and the printed page is too large to 

 allow of the paper being cut down to demy or even medium 

 iictavo size. The Atti of the Lincei Academy may be cited 

 IS an important example. Fortunately, hovvever, such ex- 

 < ptions are comparatively few in number, and they include 

 nune of the main English journals in which original papers 

 are published on mathematics or physics. 



It is my hope that by again directing attention to this 

 n\atter further uniformity may be secured in the sizes of 

 proceedings and transactions by the gradual elimination of 

 inconvenient sizes, and by the avoidance of further 

 divergences. The size of the new number of London 

 -Mathematical Proceedings is peculiarly unfortunate, as it 

 is not uniform even with those outstanding foreign journals 

 which do not conform to the recommendations of the com- 

 "1 it tee. G. H. Bryan. 



Expansion Curves. 



Mr. Stoddart's method of finding points on the curve 

 /7"= constant, to which Prof. Perry directed attention on 

 October S (p. 548), is interesting, but it does not give a 

 great number of convenient points on the curve. If the 

 points A, E, . . . are called {v„ />,), {v^, />,), . . ., the 

 values of v and p form two series of quantities in continued 

 proportion, i.e. such that vjv.,=v.lv = . . ., and 



A modification of the method, bringing out more clearly 

 its essential simplicity, and, moreover, far easier in practice, 

 would be to calculate the positions of two points A, E 

 instead of finding A and the specially related angles a, /3. 



It will then be seen from the diagram, by drawing the 

 lines needful to find a third point (say for definiteness in 



r 



the direction of increasing v and decreasing />), that the 

 method advocated is only that of finding the above two series 

 of continued proportionals, and that any angles would serve 

 the purpose, all that is necessary being that all the con- 

 struction lines like JH must be parallel to each other, and 

 similarly all the lines like BC parallel to each other. But 

 no modification of the method will give more than the 

 points I have indicated. 



By drawing the tangents at the points so found, the 

 accurate construction of the curve would evidently be facili- 

 tated. This can be neatly done by taking care in the choice 

 of the first two points ; for in these curves the gradient is 

 -p-rvin, so that the tangent at the point (y,p) cuts the 

 axis of -v at the point the abscissa of which is v(i + i In). 

 Hence if we choose the first two points (f,, p^) and {v^, p^) 

 so that "j,,=i;,(i+i/n), the tangent at the first point will 

 pass through the foot of the second ordinate, and similarly 

 the tangent at the second point will pass through the foot 

 of the third ordinate, and so on. 



NO. 1773. VOL. 6^] 



Or, if we take Vj=Vi'^{i + i/n}, so that Vj = i',(i+i/n), 

 the first tangent will pass through the foot of the third 

 ordinate, and so on. 



This happens to be approximately the case in Prof. Perry's 

 diagram, which for convenience has been reproduced here 

 with a set of additional construction lines. 



Coopers Hill. Alfred Lodge. 



Rocket Lightning. 



A PECULIAR species of lightning, bearing a strong re- 

 semblance to ascending rockets, was witnessed on the even- 

 ing of July 22 by two of the professors in Sibpur Engineer- 

 ing College, Hovvrah, near Calcutta, one of whom wrote 

 me the following careful account in a letter dated the next 

 day. I wrote back suggesting local inquiry in the direc- 

 tion in which the phenomenon appeared, and sending some 

 extracts from Hann's " Lehrbuch der Meteorologie " bear- 

 ing on the subject. The reply, dated September i, shows 

 that the suggested inquiry is impracticable. 



II Leopold Road, Ealing, W. J. D. Everett. 



We saw some strange lightning yesterday evening at 

 about 9 p.m. It was a clear, moonless night, with just 

 a bank of cloud very low in the S.S.W., with a well-marked 

 edge, height say from horizon (flat) to 5° up. There was 

 a misty cloud above this. These clouds we could only see 

 properly when the flashes came. Stars were visible at 

 about 10° above the horizon at this point, and the sky was 

 quite clear all over elsewhere. Now and then flashes showed 

 from behind the lower cloud (the flashes themselves were 

 mostly hidden, and thunder was not audible). The flashes 

 were not so frequent as usual, say one per minute or so. 

 Generally here they are almost incessant during thunder- 

 storms. 



At intervals of three minutes or so, immediately after a 

 flash — which, as common here, was mostly multiple, lasting 

 a second or so altogether — a luminous trail 

 shot straight up to 15° or so, about as fast 

 as, or rather faster than, a rocket, and of 

 very similar appearance, but with minute 

 waves, like ribbon lightning. It was hardly 

 as bright as most lightning. S. and I 

 saw it repeated seven times, and Prof. 

 Bruhl (physics) three or four times after we 

 directed his attention to it. He was equally 

 surprised at the novelty, and he has been 

 out here some eighteen years. One of the 

 trails turned off, as shown ; the others were 

 about vertical as seen from here. Each 

 grew up steadily from below, and then dis- 

 appeared at once. The upper end was 

 definite, and did not branch or spread. 



In each case it followed immediately on 

 a vivid flash or set of flashes. It was 

 certainly not fireworks of any kind. It 

 terminated in apparently clear' sky. Its appearance as a 

 uniformly and very bright ribbon was different from any 

 fireworks. It was somewhat yellowish, not purple as 

 lightning often is. It was much too far off for fireworks 

 to be so high and bright. Xo thunder was audible. 



July 23. W. H. Everett. 



Thanks for trouble of making extracts from Hann re 

 lightning, which, as you say, describe phenomena different 

 from what we saw. 



Peake is in charge of the Meteorological Office for India, 

 and did not hear about it, nor did I see anything in the 

 Calcutta newspapers. 



There would be practically no Europeans or any com- 

 petent observers nearer the lightning than we were ; as it 

 must have occurred at a spot above the Sunderabunds, a 

 wilderness of waterways and jungle. And there are probably 

 not a score of men in all Bengal who would take serious 

 interest in such lightning if they did happen to see it. I 

 was lucky to have Briihl as a witness, he being an old 

 resident, and one who keeps his eyes open. 



It was not like a string of fireballs, for it was of uniform 

 width. But it had, as Hann says of globular lightning, 

 doubtless some connection with the breaking down of the 

 air by the volleys of discharges. \V. H. E. 



September i. 



