/ 



SIMPLE PENnCLUM. 478 



v'l— «' 3 3 ' 



v'l—u'~' 3.5 ~3.5' 



7i\\ii c— 3.3mVi— «' jy 



/ 11 (111 



3.5.7 3.6.7' 



by virtue of which, the integral of the preceding expres- 

 sion is 



la'i ^^ u 7.QC' ,, 9.1 1. 13/)' ,, , . 



the diff'^rence between two vahies of wliich corrcspondinG; to 

 given values h. h' o{ x will give the time taken by the oscilla- 

 ting point to describe a portion of the curve, corresponding 

 to the vertical height h — //'. 



If we extend the intcgial from X—p to x=q, and conse- 

 quently from u= — 1 to ?/=!, we shall have the time (t) which 

 the oscillating point requires to descend from the hit;;hest 

 point P on ihc s[)herical surface to the lowest point Q. and 

 vice versa. In this case, the integral .] becomes siiii|)ly 



-, (tt being [)ut for the semicircumfercnce of a circle to radius 



= 1,) the integrals B, C, D, ts:c. l)ecome respeeiivrly .7. 3.?, 

 D-Z.nA, ^c. and the integrals A,B, C',IJ, i^c. all vanish. 

 We shall therefore have 



TOL. II. 3 Q 



