16 



MECHANICS. 



" Comparing from these, and other 

 experiments, the momentum of friction 

 of rotation of the point of different 

 pivots against a plane of agate, he found 



that the quantity which varies as that 



momentum, was, for a pivot of 45, aiW; 

 a pivot of 15, TaW ; a pivot of 6, B 4i.J 



" After this, Coulomb varied the 

 charge in his experiments, and deter- 

 mined the relative momentum of fric- 

 tion of pivots under different pressures. 

 But without going further into detail, 

 we may give the following as the prin- 

 cipal deductions from the whole. 



" 1. That the friction of pivots is inde- 

 pendent of the velocities, being merely 

 as a function of the pressure. 



" 2. That the friction of granite is less 

 than that of glass. 



" 3. That the figure of the point of the 

 pivot, as to acuteness, affects the quan- 

 tity of friction ; in such manner that when 

 we cause to whirl, upon the point of a 

 needle, a body weighing more than 5 or 6 

 drachms, the most advantageous angle 

 for that point appeared to be from 30 

 to 45 ; under a less pressure, the angle 

 might be progressively diminished,with- 

 out the friction being perceptibly aug- 

 mented : it may even without great in- 

 convenience be reduced to 10 or 12 

 with good steel, when the charge does 

 not exceed 100 grains, an important 

 consideration in the suspension of light 

 bodies upon cheeks or sockets. 



" These rules may be useful to the 

 makers of chronometers." 



CHAPTER V. On the Rigidity of 

 Cordage. 



(22.) IN considering the effects of cor- 

 dage in our second treatise, we assumed 

 that it possessed perfect flexibility. In 

 cases where experiments are instituted 

 on a small scale, with light weights and 

 moderate tensions, fine silken threads, 

 or even thin packthread, may be used, 

 without any consideration of their rigi- 

 dity, because in these cases the flexibi- 

 lity is so great that no sensible effect is 

 produced by stiffness. But in most 

 cases which occur in actual practice, 

 where great resistances are to be over- 

 come, or considerable weights to be 

 elevated, ropes are used whose thickness 

 and strength necessarily produce consi- 

 derable rigidity ; and if we would know 

 the real and practical power of the ma- 

 chines we use, it is necessary to be able 



to determine the effects of the stiffness 

 of the cordage with which we work. 



Although the theory of the rigidity of 

 cordage is much more satisfactory and 

 more conformable to experiment than 

 any which has yet been invented re- 

 specting friction, yet it is more difficult 

 to explain it in a simple and popular 

 manner. The stiffness of a rope de- 

 pends on the elements by which it is 

 determined in a manner which is veiy 

 easily explained to one that is familiar 

 with the elements of algebra, but ex- 

 tremely difficult to express in ordinary 

 language. 



To explain the manner in which the 

 rigidity of a rope obstructs the action 

 of a machine, let the equal weights A, B, 

 (fig. 5,) be supposed to be connected by 



Fig. 5. 



a rope ACDB passing over a fixed pul- 

 ley, O. By adding a small weight to A, 

 the wheel will be turned in the direction 

 DKC. That part of the rope which has 

 been applied to the semicircle DKC 

 will, by reason of its rigidity, have a 

 tendency to retain the semicircular form, 

 and to resist any effort to disturb that 

 form. Let us suppose that it actually 

 retains that form during a small motion 

 of the wheel. The part DCK of the 

 rope will then continue to be applied to 

 the wheel, but the points C and D will 

 be moved to the position C', D'. For 

 the same reason that the part DCK of 

 the rope endeavours to retain its semi- 

 circular form, the parts DB and CA 

 will endeavour to retain their rectilinear 

 form, and also their position with re- 

 spect to the part DCK. Let us also 

 suppose that during the small motion 

 already mentioned, they actually do 

 maintain both their figure and relative 

 position, and that, consequently, at the 



