22G i-.LE OTRr 



section of the string at P, and p the density at P; let T be tin- 



tension of the string at P : thm T * , T 7 ^, and T^ arc 



the resolved parts of T parallel to the co-ordinate axes ; ,-md 

 the resolved parts of the tension at Q parallel to the axes 

 be, by Taylor's Theorem, 



r dz j. d 



1 T" -r - - 

 da ds da 



Let XpKs, YpicSs, ZpicSs be the external forces which act 

 on the element PQ parallel to the axes. The equilibrium 

 of the element will not be disturbed by supposing it to 

 become rigid; hence, by Art. 27, the sum of the forces 

 parallel to the axis of a; must vanish ; thus 



or -T+ Xpic = ultimately. 



Similarly 



The product Kp may be conveniently replaced by m, so 

 that if m be constant ml represents the mass of a length I 

 of the string, and therefore m the mass of a unit of length 

 of the string. If m be not constant, cr>: re i string L 

 its length equal to the unit of length and its section and 

 density throughout the same as those of the given string at 



