JManchcstcr Memoirs, Vol. xliv. ( i CS99), A'^. 5. 1 7 



do rather with the rate (//) at which energy is expended 

 than with the force F itself. The relation is 



H=FV (11), 



so that in place of (10) 



H=KSV^%\xC~a (12). 



Or, again, since in many cases the power that might be 

 expended is proportional to the weight lifted, we may 

 conveniently write 



H^WU (13). 



From these equations we derive 



^=7SH^7SU ^^^^' 



kSH" kSU' , , 



and it is possible so to determine V and a that, with a 

 given U and a given S, any weight IV can be supported. 

 As JV increases, J^ must be greater and o smaller. The 

 same is true, in an enhanced degree, if it be //that is given 

 in place of U. 



According to what has been shown (6), (7), {S),F/o-, (i), 

 we have in C.G.S. measure 



».-sin 5° = -25 X -00085, 

 so that 



;:=-0024 (16). 



In the case of a very elongated plane the value of k 

 would be a little higher. We must remember that V is 

 reckoned in centimetres per second, 5" in square centi- 

 metres, and the normal force in dynes. 



The conclusion that a weight, however great, may be 

 supported with a given J) and a given U, or even a given 

 H, is unpractical for more than one reason. There must 



