P U L 



Table shewing 1 the length of the meridian on the projection for every de- 

 gree of latitude ; in like manner it may be constructed for every minute, 

 Such a table is called a table of Meridional Parts. 



This projection is of great use in navigation, on account of its being 

 constructed by right lines only j the rhumb lines or lines of azimuth be- 

 ing also straight lines. 



Suppose for example a ship wants to go from any place A to B laid 

 down upon Mercator's map, and it is required to find the rhumb or point 

 of the compass it must sail upon j we have only to join A B, and that is 

 the rhumb. Now to determine what rhumb this is, there is always in 

 these maps one or more points, from which are drawn 32 straight lines, 

 representing the 32 points of the compass. Apply .*. one edge of a par- 

 allel ruler to the line A B, and bring the other edge over the point from 

 which the lines of the compass are drawn, and it immediately gives the 

 direction in which the ship must sail. 



PULLEY. 



1. In the single fixed pulley, there is an equilibrium when the power 

 and weight are equal. 



2. In the single moveable pulley whose strings are parallel, P '. W :: 



1 :2. 



3. In a system where the same string passes round any number of pul- 

 lies, 1 and the parts of it between the pullies are parallel, P .* W : : \ '. n y 

 n being the number of strings at the lower block. 



* Cor. If we consider the weight of the pullies, it is only requisite to add 

 the weight of the lower block ; hence if a be this block, 



W n P a. 



4. In general in the single moveable pulley, P : W :.' rad. '. 2 cosine of 

 the angle which either string makes with the direction in which the 

 weight acts ; or : : sin. angle which the two strings make with each 

 other : sin. of the whole angle. 



5. In a system where each pulley hangs by a separate string, and the 

 strings are parallel, P : W ; : 1 : 2 n where n is the number of moveable 

 pullies. 



Cor. 1. Hence W =2 n P. If the weight of the pullies be taken into 

 the account, and a = weight of each, W =2 n P a (2 n 1) j hence the 

 weight W is less as a is greater. 



Cor. 2. When the strings are not parallel, P : W ;; (rad.) w : 2 X 

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