78 



NA TURE 



[May 25, 1905 



follows an investigation of coUineation in a plane, com- 

 prising perspective transformations, and the linear 

 transformations qf translation, rotation, and dilata- 

 tion, with combinations of these. The intiniate relation 

 that exists between projective and descriptive geometry 

 is shown. Tlie third chapter gives the general theory 

 of conies, the projective properties of the circle being 

 extended to conies by perspective transformations. The 

 next chapter deals with pencils and ranges of conies 

 and their products, and especially with cubics, the 

 latter being classified under the five standard types by 

 the help of the Steinerian transformation. Through- 

 out the book analytical and geometrical methods are 

 employed side by "side, some portions of the subject 

 being 'better suited to the former treatment; moreover, 

 the analvsis affords excellent illustrations of modern 

 analytical geometry. The main purpose of the author 

 has been to develop the subject in regard to its prac- 

 tical applications in mechanics, and the last chapter is 

 devoted to such examples. Thus we find problems in 

 graphic statics, plane stresses, and in the stress ellipse 

 of an elastic material, and there is an interesting ac- 

 count of various linkages by means of which linear and 

 perspective transformations can be mechanically ob- 

 tained. The book is excellently got up in every way, 

 and the diagrams are quite perfect and may well serve 

 as models of what such figures ought to be. The author 

 is a verv clever draughtsman, and his skill as a writer 

 is equally pronounced. 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can lie undertake 

 to return, or to correspond with the ivriters of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Fictitious Problems in Mathematics. 



In my younger days it was well recognised that such 

 statements as " perfectly smooth " and the like were 

 mere conventional phrases for designating an idea! state 

 of matter, which was assumed to exist for the purpose 

 of simplifying the mathematical conditions as far as 

 possible. Nobody can learn mathematics without working 

 out a large number of problems and examples, and in 

 order to make these sufficiently easy for the beginner, 

 various fictitious hypotheses have to be introduced. 



Similar objections would apply to the phrase " friction- 

 less liquid"; but it would be impossible for anyone to 

 learn hydrodynamics without first studying the mathe- 

 matical theory of this fictitious form of matter. In fact, 

 the introduction of viscosity leads to such formidable 

 difficulties, that nobody has yet succeeded in solving such 

 a simple problem as the motion due to a doublet situated 

 at the centre of a sphere ; and the solution, if it could 

 be obtained, would throw much light on the mode of 

 attacking more difficult problems. A. B. Basset. 



Mav 28. 



In X.^tl-re of May iS the wording of a problem set 

 near the beginning of my " Rigid Dynamics " is rather 

 adversely commented on. In the problem a man is de- 

 scribed as walking along a perfectly rough board which 

 rests on a smooth table, and the criticism is that the two 

 suppositions are inconsistent ; but this depends on what 

 is meant by the words used, and perhaps I may be allowed 

 to make an explanation. 



When bodies are said to be perfectly rough, it is usually 

 meant that they are so rough that the amount of friction 

 necessary to prevent sliding in the given circumstances 

 can certainly be called into play. In art. 156 of the 

 treatise on dynamics, just after the laws of friction have 

 been discussed, the words " perfectly rough " are defined 

 to have this meaning. The board in question has there- 

 fore no special peculiarity. All that is stated is that the 



NO. 1856, VOL. 72] 



coefficient of friction between the man and the board 

 exceeds a certain finite quantity. 



The board rests on a smooth table, but the coefficient 

 of friction now depends on both the board and the table, 

 and this mav be quite different from that between the 

 man and the' board. There is nothing amiss in supposing 

 this coefficient to be zero. One way of effecting this 

 experimentallv would be to polish the table and remove 

 all roughnesses from it. This was the plan indicated. 



Where, then, is the inconsistency? 



By using the ordinary abbreviations of language, the 

 wording of the question has been made concise, and thus 

 attention was specially directed to the dynamical principle 

 involved in the solution. 



The problem has been understood by so many students 

 in the sense above described, and worked without a single 

 objection having been raised, that I think the meaning 

 must be perfectly clear. Indeed, I cannot imagine what 

 other meaning it could have. E. J. Roi'TH. 



May 20. • 



On the Spontaneous Action of Radio-active Bodies 

 on Gelatin Media. 



In the course of some experiments on the formation of 

 unstable molecular aggregates, notably in phosphorescent 

 bodies, I was led to try W7hether such dynamically unstable 

 groupings could be produced by the action of radium upon 

 certain organic substances. It will scarcely be necessary 

 to enter here into an account of the many speculative ex- 

 periments which I have at one time or another tried, but 

 it will suffice if I describe, as briefly as possible, the ex- 

 periment which, amongst others, has led to a very curious 

 result, and that is the effect of radium chloride and 

 radium bromide upon gelatin media, such as those 

 generally used for bacterial cultures. 



An extract of meat of i lb. of beef to i litre of water, 

 together with i per cent, of Witter peptone, i per cent, 

 of sodium chloride, and 10 per cent, of gold labelled 

 gelatin, was slowly heated in the usual way, sterilised, 

 and then cooled. The gelatin culture medium thus pre- 

 pared, and commonly known as bouillon, is acted upon by 

 radium salts and some other slightly radio-active bodies in 

 a most remarkable manner. 



In one experiment the salt was placed in a small 

 hermetically sealed tube, one end of which was drawn out 

 to a fine point, so that it could be easily broken. 

 This was inserted in a test-tube containing the gelatin 

 medium. The latter was stopped up with cotton wool in 

 the usual way with such experiments, and then sterilised 

 at a temperature of about 130° C. under pressure for about 

 thirty minutes. Controls without radium were also at 

 various times thus similarly sterilised. 



When the gelatin had stood for some time and become 

 settled, the fine end of the tube containing the radium salt 

 was broken, from outside, without opening the test-tube, 

 by means of a wire hook in a side tube. 



The salt, which in this particular experiment consisted 

 of 2^ milligrams of radium bromide, was thus allowed to 

 drop upon the surface of the gelatin. 



After twenty-four hours or so in the case of the 

 bromide, and about three or four days in that of the 

 chloride, a peculiar culture-like growth appeared on the 

 surface, and gradually made its way downwards, until 

 after a fortnight, in some cases, it had grown fully a 

 centimetre beneath the surface. 



If the medium was sterilised several times before the 

 radium was dropped on it, so that its colour was altered, 

 probably by the inversion of the sugar, the growth was 

 greatly retarded, and was confined chiefly to the surface. 



It was found that plane polarised light, when transmitted 

 through the tube at right angles to its axis, was rotated 

 left-handedly in that part of the gelatin containing the 

 growth, and in that part alone. 



The controls showed no contamination whatever, and 

 no rotation. The test-tubes were opened and microscopic 

 slides examined under a twelfth power. They presented 

 the appearance shown in Fig. i. At first sight these 

 seemed to be microbes, but as they did not give sub- 

 cultures when inoculated in fresh' media they could 

 scarcely be bacteria. The progress of any of the sub- 

 cultures after a month was extremely small, and certainly 



