90 Statics. 



conclude, therefore, that the tension p is to the tension ^, as -the 

 143 sine XV '& is to the sine of p VX. 



If a heavy cord now be considered as an infinite number of 

 small weights uniformly distributed along the axis of this eord, 



x Fig. 65. jt will be seen, that if T* represent the point where the power is 

 applied to the cord, and g that in which this cord is attached to 

 a machine, the action exerted by the power upon the point g will 



V be transmitted in the direction p V of a tangent to the curve 



representing the figure which the cord assumes by the action of 

 g rav ity* This action it not equal to that of the power w, except 

 wnen tne vertical, drawn through the point of meeting Fbf the two 



is simply d.frr, extreme tangents, bisects the angle p V w; and in general the action 

 of the power w, namely, that which it would transmit, if the cord 

 were destitute of weight, is to that which it transmits in conjunc- 

 tion with the weight of the cord, as the sine of p VX is to the sine 



Fig. 



155. We remark, that strictly speaking, whatever force is 

 employed to stretch a cord p w, this cord can never be made 

 perfectly straight, except it be in a vertical position p -a'. Let 

 Fig. 66. MS suppose the cord r Ap, destitute of gravity, to support the 

 weight 9, by means of the two equal powers p, r, the directions of 

 which are such as to form an angle approaching infinitely near 

 to 18tt, we shall have 



143. q : p :: sin CAD : sin CAB; 



Trig 13 OI Y J ^ being produced, 



q : p : : sin CAS : sin | CAD ; 



but the angle CAS is by supposition infinitely small, and i CAD 

 approaches infinitely near to a right angle ; therefore q must be 

 infinitely small with respect to p ; and even where the weight q is 

 infinitely small, the two parts of the cord still make an angle with 

 each other, and are not, strictly speaking, in the same straight line. 

 It may hence be inferred, that a very small force q will cause 

 a very great tension in the cords Ap, A r, when the angle rAp 

 formed by them is very obtuse. 



We are able, also, upon the same principle, to explain why, 

 Fig. 67. in blowing through a tube A a, into a flexible bag a EEC a, the 



Sine* *<- ef^l )7Tt~ 



