GENERAL PRINCIPLES 53 



of energy. These frictions or passive resistances can either be 

 due to a continuous sliding or rolling contact, ( 14) or else to a 

 contact of very short duration, as in impact, or, lastly, to 

 friction against a magnetic field. Thus the work done by a 

 copper disc, which turns between the poles of an electro-magnet 

 is transformed into heat (Foucault's currents). The friction 

 produced by sliding and rolling shows that the surfaces of 

 bodies are never perfectly polished ; they present roughnesses, 

 from which ensues a veritable adhesion of the molecules in con- 

 tact, causing a resistance called the force of friction capable of 

 opposing movement. When a surface slides or a cylinder rolls on 

 another surface, which is horizontal, the friction will be propor- 

 tional to the pressure of the body and will vary according to the 

 substances employed. Let <J> (phi, Greek letter) be the friction of 

 sliding of a body whose weight is P ; the friction per kilogramme 

 will be : 



this is the unit or the co-efficient of friction of sliding bodies. 

 Let $', in the same way, be the friction of a rolling cylinder of 

 weight P ; then : 



this is the unit or the co-efficient of friction of rolling bodies. 

 For instance : 



Co-efficients of 



_ ____ ^A ^ 



sliding. rolling. 



Wood on wood (dry) ...... ... / = 0'40 9 = 0'002 



Metals on metals ......... = (H9 = 0'002 



It is clear that the effort necessary to overcome the friction is 

 larger in sliding than in rolling. Also, 9 diminishes in proportion 

 as the radius of the rolling body increases. For a displacement /, 

 the work done in sliding or rolling will be : 



*X/=/XPX/ or >'X/ = *X PX/. 



These are the values of vibratory energy changed into heat 

 (32). If there is sufficient friction between a moving surface 

 and a fixed surface it will not only retard but stop the movement. 



Such is the case of the slipper or shoe which is applied to the rim 

 of a wheel and serves as a brake, and it is also the case of brakes 

 in general, of which the classic type is Prony's brake. In this 

 friction is produced on the shaft A of an engine (fig. 68) by a brake 

 band C provided with blocks of wood and terminated by lever of 

 a length L. In practice the belt encircles a pulley keyed on the 

 shaft, and in tightening the screws e, e, the brake band C is forced 



