VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 



(5) 



(") 



(7) 



1 r\ -li"\~i\_ 



2 r in |_3/' 



cos 6 



AT_1 r, Amfr, 

 T 



This may be written: 



1 r, AmTr, 1 



■9 r ^rLsr" COS "J 



* t = fs cos ±A / : 



t^ cos^-24^ j;;J 



which is the equation of a family of circles (or circular cylinders), the variable parameter being 

 -fwc a—; that is, a given flaw m will produce the same change in period T if located anywhere on 

 one of these circles. The distance of the center of these circles from P is evidently: 



D=j£r lii _ +r li ,_ ir J=jj»' 



JT 



The condition that -?p- = gives r t — 3r cos as the equation of the locus of a flaw which will 



have no effect on the period. This is evidently a circle tangent to the inner cir lumference at P; 

 if Am is positive and located insidt of this circle it will decrease T; if outside, it will increase it. 

 A question more to the point is that of the resultant effect of a number of flaws for different 

 positions of the knife-edge. 



It will simplify matters to transfer tne origin to the center of the. ring, using the variables /' 

 and <f>, which are determined by: 



/', cos d— r-\-r' cos (j> 



/\ = \ / r'' 2 +r' i +2?'' cos 

 Making this substitution, equation (6) becomes: 



z/T_l A 



m [- 2+ [0+? COS <* " 



