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♦ KNOWLKDGE * 



[August 1, 1889. 



A History of the Study of Mathematics at Cambridge. 

 By W. W. E.OUSE Ball, Fellow and Lecturer of Trinity 

 College, Cambridge. Univei-sity Press. 1889.) — This is a 

 most interesting little book, containing in its 260 small 8vo. 

 pages au immense amount of information with respect to 

 life at the university in the Middle Ages, and other matters 

 which only bear incidentally on the study of mathematics. 

 The book is only too much compressed, one would con- 

 tinually like to be a.sking its author for further information 

 which he must possess in order to be able to give the many 

 genei-al summaries of facts for which the book is remark- 

 able. Here is au example : " The hour of dining gradually 

 grew later. In 1570 it was at 9.0, or at Trinity at 10.0. 

 By 1755 it had got shifted to noon. In 1800 it was at 2.15 

 at Trinity, and at 1.30 at most other colleges, and the 

 senior members of the university began to complain that 

 the afternoon attendance at the schools was in consequence 

 much diminished. A few years later dinner was usually 

 served at 3 0, but until 1850 the hour did not, I think, 

 get later than 5.0. Since then the same movement has 

 gone on, and now (1889) dinner at Trinity is at 7.30." 

 Sir Isaac Newton is much too summarily dealt with, and 

 the controversy with Leibnitz is dismissed thus : — " From 

 what I have read of the voluminous Uterature on the ques- 

 tion, I think, on the whole, it points to the fact that 

 Leibnitz obtained the idea of the differential calculus fi-om 

 a manuscript of Newton's which he saw in 1673." A 

 judgment with which Professor de Morgan certainly would 

 not have concuiTcd. One would like to know to what Mr. 

 Ball refers when he says of Newton, " During the eaily half 

 of his life he was parsimonious, if not stingy, and he was 

 never liberal in money matters." It is true that during 

 the early and brilliantly fruitful part of his life he was 

 poor, but he was certainly not mean either to his cousin or 

 to hLs mother. Su- David Brewster gives many stories 

 (some perhaps doubtful) of his freehandedness in money 

 matters in after life. The book is one for reference, and 

 fortunately Mr. Ball has provided his readers with an 

 excellent index. 



A USEFUL CEMEST. 

 The following mixture has been used with the gi-eatest 

 possible success for the cementing of iron railing tops, iron 

 gi-atings to stoves, &c. : in fact, with such effect as to resist 

 the blows of a sledge-hammer. This mixture is composed 

 of equal parts of sulphur and white lead, with about one- 

 sixth proportion of borax, the thi-ee being thoroughly in- 

 corporated together so as to form one homogeneous mass. 

 When the application is to be made of this composition, it 

 is wet with strong sulphuric acid, and a thin layer of it 

 is placed between the two pieces of iron, these being at once 

 pressed together. In five days it will be perfectly dry, all 

 traces of the cement having vanished, and the work having 

 every appearance of welding. — Tlie American Artisan. 



The Editor does not hold himself responsible for the opinions or 

 statements of correspondents.] 



PHOTOGRAPHS OF LIGHTNING. 



To the Editor of Knowledge. 



Dear Sir, — I wa.s much interested by the article in the July 



number of Knowledge on lightning photograjjhs. I think 



none of the conjectures hit the nail on the head. When I saw 



Mr. Shepherd's dark flash in the Photographic Exhibition 



nearly two years ago, at the first moment I thought of solari- 

 sation, but that was immeduately negatived by the considera- 

 tion that on that supposition the edges ought to be light. 

 It then occurred to me — and I mentioned it to one of the 

 photographers as I went out — that a flash had struck very 

 shortly before the camera had been uncapped, and had left 

 a tube of au- containing nitrous acid gas in its path, and 

 that a subsequent flash illuminated the cloud behind, and 

 where the dispersed light on its way to the camera had to 

 pass through the tube the actinic rays were absorbed. Till 

 about a month ago I thought that this was the true theory, 

 though six or seven weeks ago I received an experimental 

 photogiaph from Mr. Wimshurst that was puzzling on this 

 view, and I suggested some experiments further to test the 

 view. But after the delivery of the Rede lecture on June 12 

 my friend the Eev. G. B. Atkinson showed me a photo- 

 graph obtained by him in the great thunderstorm of June 6, 

 which showed me that the absorption theory could not be 

 maintained. The action must be direct ; and I thought the 

 result would be accounted for by the known undoing action 

 of the less refrangible rays. An explanation pointing in 

 the same dii'ection has been brought before the Physical 

 Society by Mr. Clayden, who has since obtained some re- 

 markable experimental results. The experiments are in 

 progress. — Yours very truly, G. G. Stokes. 



Lensfield Cottage, Cambridge: July 10, 1889. 



DARK LIGHTNING FLASHES. 

 To the Editor of Knowledge. 



Sir, — I notice that you have recently devoted very con- 

 siderable space to the discussion of the various phenomena 

 exhibited in photogi-aphs of lightning. Among th&se the 

 most obscure is probably the existence of dark images, the 

 so-called dark flashes, and a variety of different theories 

 have been brought forward in the attercpt to explain them. 

 It so happened that I was fortunate enough to secure an 

 example of such images among some photographs which I 

 took during the storm on June 6. From certain observa- 

 tions in connection with this plate I was led on to some 

 experiments which I think sufficiently prove that dai-k 

 flashas are merely a photographic eflect produced by the 

 subsequent, or possibly simultaneous, illumination of the 

 clouds. 



I have already described some of these experiments in 

 a short note read before the Physical Society, but as that 

 account maj' not meet the eye of some of your readers, 

 perhaps it may be of interest to describe them again. My 

 dark-flash plate shows four of the dai-k images and one 

 bright one, as well as another faint but normal image. I 

 felt certain that a paiticularly fine flash had impressed itself 

 nearly vertically down the middle of the plate, which was 

 exposed altogether to six flashes, and to the diffused light 

 from several others which were either hidden in the clouds 

 or else were out of the field of view. 



When I came to develope the plat« I at once found that it 

 was greatly over-exposed, and had to treat it very carefully. 

 I was much surprised to find only one triple flash in the 

 corner. The fine vertical flash seemed to be absent ; but on 

 inspecting the plate after tLxing, I discovered that its image 

 was reversed. Yet the reversal was not complete. Three 

 flashes printed quite dark, so did the branches and upper 

 portion of the vertical one ; but the lower part of its main 

 stem (if such a phrase is allowable) showed an unreversed 

 core. Now it was evident that the reversal was due in 

 some way or other to the fact that the plate had been ex- 

 posed too long. Other photogi-aphs taken on the same 

 evening showed no such effect, and they were exposed much 

 less. Hence I conceived that it ought to be possible to 



