2l8 



NA TURE 



[July 8, 1897 



is to obtain the necessary stiffness with a narrow tube, 

 as horizontal space is valuable at this part. Doubt has 

 been expressed by cyclists upon the safety of D tubes 

 when thus used. They will be glad to hear from Mr. 

 Sharp, or to calculate for themselves if they like, as he 

 has shown them how, that the D-tube is stiffer than a 

 round tube of equal width and weight by rather less than 

 I per cent. Mr. Sharp, however, advocates the use of 

 tubes of rectangular section for this part of the machine, 

 for they are roughly 33 per cent, stiffer than elliptical 

 tubes of the same depth, breadth and weight. 



In the chapter on the strength of materials, a result 

 is given which will surprise those who do not realise 

 the importance of depth in a beam, but who only con- 

 sider tensile strength and density. Steel is so en- 

 ormously strong for its weight that, with the exception 

 possibly of some of the new alloys, it is the one material 

 on which the designer of strong and light structures 

 depends. Now in the case of solid beams of the same 

 length, breadth and weight, a light material, such as wood, 

 may be made so enormously deeper than one of steel, that 

 the stiffness which depends upon the cube of the depth 

 actually exceeds that of steel. For this reason a wooden 

 cycle rim is lighter than a solid steel rim of the same 

 width and strength. It probably is not lighter than a 

 hollow steel rim of the same outer shape and weight, any 

 more than a solid wooden beam would be lighter than 

 a compound beam made of steel of the same width, 

 weight and strength in which nearly all the material is 

 at the upper and lower surfaces. 



The concluding chapter of Part i. deals with the 

 strength of materials. In this there are two sections of 

 special interest to cyclists. The first relates to the 

 " helical tubing " of the Premier Company. This is an 

 ingenious composite tube made by rolling band steel in 

 a helix, so that at no point has it less than two thicknesses, 

 and then brazing all together. By this method of con- 

 struction a higher grade of steel can be employed than 

 any used in drawn tubes, and a gain of about 50 per 

 cent obtained in tenacity. This, of course, is at the 

 expense of ductility, so that while a frame built of helical 

 tube will be stiffer for its weight than one of solid drawn 

 tubing, it will, or perhaps it is better to say it should, 

 give way suddenly to accidental stresses which would 

 merely bend an ordinary tube. 



The other interesting point is the effect of repeated 

 small stresses of an amount which applied even many 

 hundred times would be quite incapable of damaging a 

 material. Certain parts of a bicycle are subject to alter- 

 nate stresses in ordinary use, while others are constantly 

 pulled in the same direction. The latter may therefore 

 be made with a somewhat lower factor of safety than the 

 former. 



Part ii. is partly historical. This will be welcomed 

 by readers very differently, according to their individual 

 cycling experience. Those who have ridden since the 

 'seventies, or have followed the progress of the cycle, 

 more especially in the last fifteen years, may turn over 

 these pages with a certain melancholy interest, while 

 those who have only recently joined the ranks of cyclists 

 will probably be tempted by curiosity to learn something 

 about the machines which so recently they despised. In 

 the writer's opinion, the first fifty pages of this part is 

 NO. 14-45, VOL. 56] 



not likely to seriously interest any one for whom the 

 really new and valuable part of the book has been 

 written. 



With Chapter xvii. the valuable portion of Part ii. 

 begins. This is upon the stability of cycles. The 

 author explains the bicycle balance by supposing the 

 rider to steer unconsciously in such a curve that the 

 centrifugal force balances the tendency to overturn. All 

 that can be said of this is that when the rider is following 

 a curved path he must lean over to the angle which every 

 one knows, for this is what may be called the dynamical 

 vertical ; but small variations from this have to be 

 counteracted just as much as small variations from the 

 real vertical when a straight path is to be followed. Mr. 

 Sharp speaks of the lateral oscillations that are neces- 

 sary for stability as being pendular, so that a high 

 bicycle has a slower period than a low. This, no doubt, 

 is true in a way, but the essential difference between 

 a hanging and an inverted pendulum are not pointed 

 out. The former has a natural period— that is, it 

 takes the same time to reach the vertical from any 

 moderate inclination ; but the inverse is not the case, 

 an inverted pendulum has no natural time to fall from 

 the vertical to any definite inclination, but only from one 

 inclination to another, and the comparison of the periods 

 between high and low machines can only be made when 

 these inclinations are the same for both. The main point 

 is that there is no natural period for the inverted pen- 

 dulum, the time becoming greater as the start is made 

 from a truer vertical, and also greater as the angle of fall 

 becomes greater. For this reason it would seem that the 

 more correct view is that the bicycle balance consists in 

 merely running the wheel so as to bring the line of con- 

 tact with the ground vertically under the centre of gravity, 

 the vertical being the dynamical vertical for the particular 

 speed and average radius of path. 



There is one section in this very interesting part which 

 is at variance with the supposed experience and almost 

 universal belief of riders. This is upon the effect of pedal 

 pressure upon side slip. Page 215 rather unnecessarily 

 traces the forces upon the frame and wheel in consequence 

 of pressure upon one pedal. Obviously no sustained pres- 

 sure by the rider upon the pedal can produce a lateral 

 force upon the tyres, however much riders may think the 

 contrary ; but is it not possible that this lateral force may 

 exist, and to a more than perceptible extent, in con- 

 sequence of the fact that it need not be sustained, that it 

 is not one of the entirely balanced internal forces, but is 

 unbalanced, the lateral momentum of the rider's body 

 supplying the force which is external to the frame? This 

 depends for its possibility upon its not being sustained, 

 for if it were the rider would move laterally off the 

 machine ; as it is he begins to acquire a lateral velocity, 

 which is pulled up and reversed at the next half-turn. 

 This is the lateral equivalent of the objectionable vertical 

 swaying of the body, which enables the rider to exert an 

 effort on the pedal greater at the time that it is useful 

 than that which the vertical force due to his mere weight 

 would allow. In the middle of the stroke the vertical 

 acceleration of the body is made a maximum, and so the 

 position is at its lowest. At this time, therefore, a greater 

 pressure is available ; at the ends of the stroke, where 

 pressure is less useful, less is applied, and gravity is 



