148 MACHINE FOR SAVING PERSONS Sec. 



combination of perpendicular and lateral movements may 

 alfo be applied to many other valuable purpofes. 



Perpendicular lines being dropt from the point G to 

 the bafe, the fquares of thefe, and the fquares of the 

 diftances of their ends from the foot of the rope, are 

 jointly equal to the fquare of the rope. The fquare of 

 EG is likevvife equal to thofe of its fmes. When the 

 fhaft is drawn up, the perpendicular height of the rope 

 differs from the joint heights of the lliaft and pulleys 

 by the cofme of DEG j and when the Ihaft is down, 

 it is equal to the height of this piece, joined to the cofme 

 of the reverfed angle. The fines of thefe angles are equal 

 to the diftances between the ends of the faid perpen- 

 diculars and the center of the trunks bottom. Taking 

 the value of the rope in the two cafes, gives this 

 equation: a a^ -{- afliaft. y. aa = 

 2aEx cos. DE "J) 



-|- 2/h X COS. rev. ang. > EG. 



+ 2 fl H X Sin. DEG— Sin. rev. a. ) 



This will guide the choice of angles, proportion of EG, 

 and pofition of the rope. 



jiD/f. 



