June 2, 1904] 



NA TURE 



The proper name of the idiomorph would be a binomial, 

 the name of the superspecies being inserted when advisable, 

 iu-it as subereneric names are inserted, within brackets. 



T. D. A. COCKERELL. 



Colorado Springs, Colorado, U.S.A., May 7. 



Graphic Methods in an Educational Course in 

 Mechanics. 



I .AM glad to have succeeded in calling forth some corre- 

 spondence on this subject. But since I have evidently failed 

 to make my views clear, may I briefly restate my conten- 

 tion ? 



By an educational course in mechanics, I mean a course 

 intended to teach a beginner the principles of mechanics ; a 

 course that will leave him properly equipped for more 

 technical work. 



By " analytical methods " I mean those methods in which 

 we resolve forces and take moments about axes. Working 

 diagrams and plotted curves (as is cjuite clearly implied or 

 stated in my former letter) would accompany such work, and 

 would not come under the head of graphic statics. 



By " graphic methods " I mean those methods that depend 

 on accurate drawing only, there being no calculation ; 

 methods in which " resolution " is replaced by the drawing 

 of force polygons, and " taking moments " by the drawing 

 of funicular polygons. 



I advocated the exclusive use of the former methods in 

 bringing the beginner up to the desired point at which there 

 would no longer be danger of confusion of ideas as to 

 principles. Such methods demand the use of simple equa- 

 tions and of a little elementary trigonometry. 



Mr. .Milne, I see, agrees with me in the main. I cannot, 

 however, agree with him in his view that the employment 

 of analytical methods implies that the teaching is not to be 

 experimental, or leads to impressing on the pupil the idea 

 that " statics is practically useless." Surely he would find 

 " resolving " and " taking moments " more practical than 

 drawing polygons of forces and funicular polygons in intro- 

 ducing a beginner to the action of machines, to matters of 

 friction, to the nature of bending moments and shearing 

 forces, to the torsion of shafts, and, indeed, to most of the 

 problems of practical mechanics. 



Even in the case of " statics of structures," if we limit 

 curselves (as I do here) to such a range as will be sufficient 

 to make the principles clear, there is much to be said for 

 the analytical " method of sections " ; and if this be em- 

 ploved there is less temptation to present to the beginner 

 the unpractical " weightless frame, loaded at the joints 

 onlv." However, in this branch of mechanics, graphic 

 methods must be employed sooner or later when the learner 

 passes beyond the simpler forms of structures. 



Mr. Trotter has quite misunderstood me ! He speaks 

 much about (or against?) mathematics; says that my pupils 

 should " emerge as mathematicians " ; and refers (depre- 

 catingly?) to " wranglers." 



I cannot see that the employment, with beginners, of 

 the methods of resolution and taking moments would pro- 

 duce a race of wranglers, any more than that the employ- 

 ment of graphic methods would produce a race of 

 geometricians or artists. 



Further, he considers me as opposed to the use of 

 diagrams, and as preferring formute to explanations given 

 in " quite ordinary language "; and he asks (indignantly?) 

 whether I " would deny the use of a piece of string on a 

 globe to explain great circle sailing? " I may state briefly 

 that I am not a mathematician, that I am fond of diagrams, 

 that I delight in simple language, and that I would give 

 two pieces of string to any pupil. who had serious aims in 

 view. I do not think that the above were quite reasonable 

 deductions from my letter. 



I do not wish in my turn to misunderstand Mr. Trotter. 

 But I gather from the second paragraph of his letter (vol. 

 Ixx. p. 81) that he claims the use of " quite ordinary 

 language " as the prerogative of those teachers who use 

 graphic methods in preference to the analytical methods of 

 " resolution " and " taking moments "? I gather also, 



from the last paragraph, that, in his opmion, to resolve 

 forces and to take moments about axes " confuse learners 

 of statics "; and that these analytical methods are a failure 

 when applied to dynamics? Certainly there is here a real 

 difference of opinion between Mr. Trotter and myself. 

 Devonport, May 28. '\'\"- Larden. 



The graphic methods are the complement of the 

 analytical and a mind brought up on either to the exclusion 

 of the other is but half trained. I agree with Mr. Mdne 

 that the best results are obtained when the two methods 

 are used side by side. But there is another and potent 

 reason for including graphic methods in an elementary 

 course ; they can to a great e.xtent be used at an earlier 

 stage and before the student has proceeded far in his mathe- 

 matical training. The triangle of forces is practically the 

 only principle involved, and if this is satisfactorily taught, 

 so that in any practical application the student can write 

 out clearly an explanation of his diagram showing what 

 the different lines represent, he will then proceed naturally 

 to the analytical methods of resolving and taking moments. 

 But he wi'll never abandon the graphic methods, which 

 should now be developed simultaneously with the analytical. 

 His mastery of the two, with the analytical, as I think, 

 resting on the graphic, will give him greater resourceful- 

 ness than he would be likely to obtain from an exclusive 

 use of one method. 



I want to see the study of mechanics, even in its elemen- 

 tary stages, brought into' closer union with practical require- 

 ments, and the barrier which usually separates theoretical 

 from applied mechanics to a considerable extent removed. 

 The inclusion of graphic methods tends to prevent the dis- 

 cussion of fantastical problems invented by the mathe- 

 matician from usurping the consideration of the more 

 practical kinds required by the engineer. In the elementary 

 work it is not usual to take account of the internal forces 

 which are called into play when any solid is in equilibrium 

 under external forces. I think that the stresses induced 

 in a bar of no appreciable weight by forces applied at its 

 extremities should be considered at a very early stage, and 

 then the student may work easy problems on the equilibrium 

 of simple frames. Of course these problems are all more 

 or less idealised, but they will serve to show him that he 

 is at work upon something of practical value, and he will 

 not fail to grasp and appreciate it. W. J. Dobbs. 



East Putney, May 27. 



The Drumming of the Snipe. 



It is disputed whether the snipe's drumming— a curious 

 noise, suggestive of a miniature threshing machine— is made 

 by the bird with its wings or by its tail, or by both \vings 

 and tail. Some recent observations incline me strongly to 

 believe that the tail plays at any rate the more important 

 part. During the performance the bird flies at a great 

 height round and round in a wide sweeping circle. At 

 intervals he makes a sudden and rapid descent, holding his 

 wings partly flexed and his tail spread to its full extent. 

 The outermost tail feather on either side points outward 

 at a greater angle than those adjoining it, so that when 

 the bird is watched through a good field glass daylight 

 shows between it and the next ; and, if I am right in my 

 view the drumming sound is due to the rush of air against 

 this isolated feather. The snipe's tail feathers seem so 

 punv that it is at first difficult to believe that they can pro- 

 duce so great a result. But if an outer one be taken— it 

 is slightly scimitar-shaped with the outer web much re- 

 duced—and swung rapidly through the air, the drumming 

 noise may be distinctly heard, though it seems but a very 

 faint echo of the loud throbbing hum that startles one 

 when it suddenly descends from an ethereal height, and the 

 small bird is descried, hardly more than a speck to the 

 naked eye, circling round in wild career, and now and 

 then swooping headlong downwards and thrilling the air 

 with his weird music. F. W. He.wlev. 



Haileybury. 



NO. 1805, VOL. 70] 



