1895.] Investigation of the Laws of Attrition. 27 



Fig. 2. 



paper, that the weight attrited may be considered proportional to the 

 force briuging the cylinders together. 



We can thus say that the weight attrited from any given area is 

 proportional to the pressure, although we may not know the value of 

 the pressure itself. For we can express the weight removed thus. 

 W = K.V.T.JPfZA, since the integral is equal to the force in question. 

 We assume here that the effect is simply proportional to the dis- 

 placement Vl\ thus neglecting all terms involving higher powers of 

 the velocity.* 



I have called the value of the constant K, when the two surfaces 

 are of the same material, the coefficient of attrition or the attritivity 

 of the substance. In this way arbitrariness in definition is avoided, 

 such as would be introduced, say, in assuming all bodies to be 

 attrited with one standard substance — by diamond, for instance — : 

 and we arrive at a so-called absolute unit. The dimension of attri- 

 tivity will be seen to be the inverse square of a velocity [K] = 

 [T 2 x Ir 2 ]. 



It might be thought that the coefficient here introduced did 

 riot refer to anything which could properly be looked upon or 

 advisedly classed as one of the properties of a substance, but its 

 importance may perhaps be better seen further down, where it is 

 shown that with bodies harder than itself the amount attrited from 

 a given substance can practically be considered as depending only on 

 its own value of the coefficient. 



Elsewhere (' Brit. Assoc. Report,' Leeds, 1890) this coefficient has 



* In none of the experiments made was any difference observed due to running 

 the apparatus at different rates ; but no great difference in the rates of rotation 

 could be tried owing to the apparatus not working smoothly at higher speeds. 



