May 26, 1904] 



NA TURE 



with either cylinder wire, were surrounded by brass tubes 

 connected with the earth. The sensitiveness of the electro- 

 meter was such as to produce for a aV of 001 \', a shifting 

 ul about 7 mm. on the scale. The connection of the 

 cylinder wires with the earth was brought about by touch- 

 ing them with brass wires connected with the earth. In 

 the whole there was not on the path from the cylinder 

 wire to the electrometer any contact of two different metals. 

 The cylinder was charged, as a rule, to 100 V by a battery 

 of storage cells. 



During the progress of these experiments a very interest- 

 ing phenomenon presented itself. It was found that when 

 either of the cylinders is connected with the earth, the wire 

 enclosed within it, after being disconnected from the earth, 

 immediately begins to get electrified, i.e. the electrometer 

 thereupon indicates a rise of a potential, which continually 

 increases during a certain interval of time, some hours in 

 the main, before reaching a limiting value. (The electrifi- 

 cation was observed when the mud was removed from the 

 cylindeis.) The wire contained in the zinc cylinder becomes 

 positively electrified, whilst that in the brass cylinder 

 becomes negatively electrified. Having remarked such a 

 phenomenon, we introduced into the brass cylinder which 

 opened from beneath, a zinc cylinder, placed coaxially so as 

 to enclose the wire. This cylinder was in metallic connec- 

 tion with the surrounding brass one. In this case, too, the 

 wire acquired a potential, but it was opposite in sign to 

 that it acquired without such a zinc cylinder being merely 

 enclosed in the brass cylinder, i.e. it became positively 

 electrified. The maximum value of the potential produced 

 in the wire amounted in our observations to 02 V. This 

 maximum value depends, it seems, upon the degree of 

 ionisation of the air in the cylinder. 



\\"e also replaced the zinc cylinder at the interior of the 

 great brass cylinder by others of lead, aluminium, iron and 

 silver, with the effect that the two former acted in the same 

 direction as the zinc cylinder ; the lead cylinder, which, by 

 the bye, proved very radio-active, gave the strongest effect 

 (about 035 V), whilst aluminium toolc the last place, zinc 

 remaining in the middle. The iron and the silver 

 cylinders, on the contrary, exerted the same action as the 

 main brass cylinder, giving a negative electrification, but 

 to a less degree. 



The phenomenon we have observed seems to be in corre- 

 spondence with effects produced in metals by air ionised 

 with Rdntgen rays (I. Borgmann and A. Gerchun, C. R., 

 cxxii. p. 378, 1896; Minchin, the Electrician, March 27, 

 i8g6 ; Rutherford, Pliil. Mag., xliii. p. 241, 1897). It may 

 perhaps give the explanation of atmospheric electricity ; and 

 it is also of interest in the fact that here we take electrical 

 energy directly from the air. I. Borgmann. 



Physical Institute, The University, St. Petersburg, May 9. 



Graohic Methods in an Educational Course on 

 Mechanics. 



It is difficult to reconcile Mr. Milne's opening statement 

 (N.ATURE, May 5, p. 5) with the rest of his letter. He 

 begins by venturing to think that no one will gainsay Mr. 

 W. Larden's main contention (Nature, April 28, p. 607) 

 that " analytical methods give a grasp of the principles 

 of statics while graphical methods disguise them," and 

 he goes on to give half a dozen instances confuting it. 

 Mr. Larden wrote to elicit opinions from those who have 

 taught mechanics, and as I have had only one pupil, a 

 very troublesome one, namely, myself, I cannot think that 

 my opinions are invited. But when Mr. Milne thinks that 

 no one will gainsay the contention, the challenge is a wide 

 one, and I deny it emphatically, and know that there are 

 hundreds of men who will agree with me. These men are 

 not teachers or mathematicians, but those who have to 

 use mathematics for their profession or trade. 



I have the highest admiration for all those to whom 

 science is an end in itself. I fully appreciate the attitude 

 of mind (the butt of so many jokes) which feels that mathe- 

 matics and other sciences become degraded by useful appli- 

 cations. But for one true mathematician there are a 

 thousand men to whom mathematics are but a means to an 



NO. 1804, VOL. 70] 



end. Many of these, like myself, are not mathematically 

 minded (as Mr. Larden probably counts mathematics), and 

 with the exception of Maxwell's " reciprocal figures " and 

 a few others, we have had to work out graphical methods 

 mainly for ourselves. Teachers are now coming round, or 

 as Mr. Larden would put it, giving way, or as I would 

 put it, waking up, and are recognising that analytical 

 language, powerful as it is for research, is not paramount 

 for explanation. " I believe," wrote Prof. J. Perry in 

 his " Spinning Tops," " that there are very few mathe- 

 matical explanations of phenomena which may not be given 

 in quite ordinary language to people who have an ordinary 

 amount of experience. In most cases the symbolical 

 algebraic expression must be given first by somebody, and 

 then comes the time for its translation into ordinary 

 language." 



I agree with the whole of Mr. Milne's letter except the 

 first few words, and, like him, " I believe the best results 



nethods are used side by 

 about one in five prefer 



will be obtained when the two 

 side." Of my own acquaintanc 



analytical methods, but the others have a diagram in their 

 heads, if not before them on paper as a guide to bring it 

 vividly before the mind (to borrow Mr. Larden's words). 

 Mr. Larden concludes, " graphical work consumes an 

 amount of time that seems out of proportion to the mental 

 training and knowledge of principles gained." The title 

 of his letter shows that he has " an educational course " in 

 view, and qua education, " mental training and knowledge 

 of principles " is the true and only object. His pupils 

 should emerge as mathematicians. But those who have to 

 use statics professionally would not hesitate to consume 

 twice or thrice the time on a graphical method if it carries 

 conviction of truth with it, as it does to two or three at 

 least out of five of my acquaintances. 



Mr. Larden dates his letter from Devonport, and this 

 suggests that some of his pupils hope to become naval 

 officers and not wranglers ; that mathematics will be used 

 by them in after life as a means to an end. \\'ould he 

 deny the use of a piece of string on a globe to explain 

 " great circle sailing," or does he use a formula applicable 

 generally to figures of revolution, of which the earth and 

 Saturn's ring are particular cases? Sumner's method may 

 be disguised in algebra, but it must be confessed that the 

 famous " line " as discovered by him was a bit of pure 

 graphics. 



It may be impossible for Mr. Larden to appreciate the 

 geometrical point of view, for my contentions are exactly 

 the opposite of his first and fourth. For us non-mathe- 

 maticians, " graphical methods give a grasp of the 

 principles of statics, while analytical methods disguise 

 tfcem," and " analytical methods confuse learners of 

 statics." The second contention, " Analytical methods 

 must be mastered in any case," needs the addition of the 

 words " by the help of diagrams." If there be any truth 

 in the third contention, that " analytical methods connect 

 statics with dynamics," it is of small importance if they 

 fail to elucidate dynamics. Nature herself gainsays these 

 contentions with the parabola of the fountain, the ripple 

 of the pond, and the slope of the sand hill. 



A. P. Trotter. 



8 Richmond Terrac;, Whitehall, S.W., May 13. 



.Aw educational course in mechanics should undoubtedly 

 be based first of all on experiment. If such is the case, it 

 is practically impossible for any student using " graphical 

 methods " to make the wild " shots " referred to by Mr. 

 Larden (vol. I.xix. p. 607), who seems to have been very 

 unfortunate in the kind of boy he has received from " a pre- 

 paratory school " ; or is it the boy who has been unfortunate 

 in his previous training? Has Mr. Larden considered the 

 possibility of the " method of teaching " adopted being wrong 

 in the aforesaid school? Surely there is no inherent quality 

 in " graphical methods " to cause these wildest of " shots." 

 The writer's experience goes entirely against this idea, and 

 supports the contentions set forth by Mr. Milne. 



Mr. Larden writes : — " If then, there be not time for 

 both, it is the latter (Graphics) that should be sacrificed." 

 If time is so short that some sacrifice must be made, the 



