213 



beetles spring up by their own elasticity and that of the linen, 

 and are overtaken by the wipers in their ascent, their whole 

 weight does not resist. Indeed Dr. Robinson is not aware of 

 any unexceptionable mode, except Prony's brake, which can 

 exhibit the actual amount of actual force transmitted by a 

 machine. This instrument is well known to consist of a ring 

 clamped on a revolving cylinder, and tightened till its friction 

 constrains the shaft to revolve at a given speed. That friction 

 must equal the resistance of any other kind of work which pro- 

 duces the same speed; and it can be directly measured by weights 

 hung on the extremity of a lever attached to the ring. Let 

 R be the distance of the weight from the centre of the shaft, 

 r the radius of the brake, n the revolutions which it makes in 

 a minute, IV the weight applied + that of the lever reduced 

 to the same distance R ; w the friction produced by the ring 

 and its appendages. Then the effect is expressed by the 

 equation. 



2irr X < + w>xn 



E = 



33,000 



In this instance — = 19, and r = 0-56. The weight of the 



lever reduced to R = 50 lbs ; and as the pressure of the brake, 

 &c., = 202 lbs, while, from the abrading nature of the action,* 

 the coefficient of friction must have been at least one-fifth, the 

 quantity iv may be taken at 40 lbs. These give the formula 



E={w + 52-132) x/ix 0-002015. 



In the first trial, the weight JV= 280lb. ; the depth on the 

 overfall = 4-75 inches ; the mean depth from the datum plane 



* This was so severe, owing to the rubbing surface being too small, that 

 it was necessary to have the upper part of the brake wade a cistern, which 

 was kept full of water, and communicated with the rubbing parts by several 

 apertures. The water boiled violently from the heat evolved. 



