196 MISCELLANEOUS I.XAM1 1 



about which awheel and axle tu 

 16 axle, but nt with the axis of the \vi. 

 lin reatest and least ratios of the power ami w< 



Miilibrium, neglecting the weight of the ma- 



ohi 



8. In the system of pullies where each strin 



to the weight, let one of the strings be nailed i" the Mock 

 through which it passes, then shew that tin- pwrr mav 

 increased up to a certain limit without producing mntinn. 

 tlinv. be, three, pullies, and the action dt' th.- middle one 

 be checked in the manner described, find the tension of each 

 string for given values of P and 1 1 '. 



9. A weight w is supported on an inclined plane by two 

 forces, each equal to , one of which acts parallel to the 

 base. Shew that equilibrium may be possible when the in- 



' ; clination of the plane is not greater than 2 tan' 1 (-) , n b< ' 

 a positive integer. 



10. A w.-i-^ht is suspended from the two ends of a str; 

 lever without weight whose length is 5 feet, by strings \\ i 

 lengths are 3 and 4 feet. Find the position of the fulcrum 

 that the lever may rest in a horizontal position. 



At a distance 3J feet from that end of the lever to 

 which the longer string is fastened. 



11. A uniform steelyard AB, having a constant \ 

 and a scale-pan of weight kP, suspended at B and A respec- 



vcly, is used as a balance by moving the rod backwards and 

 forwards upon the fulcrum (7, on which the wlmle j, 

 JShew that the beam must be graduated by the formula 





the weight of the rod being k P, and n being each of the 

 natural numbers 1, 2, 3, ... taken in succession. 



