162 GEOLOGY OF THE COMSTOOK LODE. 



mic curve is great when the number of movable slieets is small, but wlien 

 this number is great the eftect of y" on the locus is imperceptible. If, for 

 example, m ^z 1.4 and n zr 25, 



i„ = Anr" = A 1.4-=' zz 0.()()022^, 



which on ordinary scales would be scarcely visible. The value taken for m 

 is one which has been noted in experiments to be described on a succeeding 

 page. If 0.0001^ is regarded as a negligible quantity, then the locus of 

 the edges of the sheets may be regarded as coincident with the logarithmic 

 curve y =r Am~^ when for the first fixed sheet P„ 



logm 



Logarithmic distribution of energy. — Tlic force cxcrtcd at cacli coutact of a system 

 of sheets is that of friction, and when the friction is uniform throughout 

 the system, only the distance through which the force acts at each contact 

 varies with its distance from the first contact. If on the contact P„P„ + i the 

 surfaces are such as to present a greater or smaller number of opposing 

 projections per linear unit than exists upon other contacts, the force or friction 

 would also diflfer. But the energy received by P„ would be unaftected by 

 this difference, and the ratio of the energy expended upon the contact 

 Pn Pn+i to that transmitted to subsequent contacts will depend not upon the 

 number of projections but upon tlie physical (elastic) properties of the 

 material of which the sheets are composed. By Morin's law the friction, 

 and therefore also this ratio, are unaffected by the velocity, and the same 

 amount of work will consequently be done on the contact P„ Pn+i ^s if the 

 friction were the same as on other contacts. If the wliole energy applied 

 to the system is E, and if the frictional resistance on the successive con- 

 tacts is/, /i, /a, etc., 



The absolute movements of the slieets will be dependent upon the total 

 energy and upon the different resistances, and so also will be tlie curve or 

 broken line assumed by the edges of the sheets; but any term 



fAK-K,r) 



