286 



A. TANAKADATE 



The gcnernl expression foi' the force is 

 h- 





b — y 



{b - yy + {a — xf [b - yf + (a + xf 



b + y , l> + y 



If, now, we make 



.r = 

 y = 



a b 



p = X — =y — 



we obtain the expressions 



(^ + y)- + {n - tV (/> + yf + {a + x)- 



snccessive])^ 



F = 

 F = 

 F = 



8 b {)•'' + x'') 



(a) along .r-axis 



8 h {7 



T7J iß) 



4br'' . 4 b 



1 + 



(y) 



2/-axis 

 diao'onal 



?•' + ?"' p' + p r^ — p'- 

 The maxima and minima of these are given hy 

 X = 

 .r = ± ^r{-r±ta) 



respectively 



y = + y/ r {r ±'1 a) 



(O 



{ß') 



p=0 



p = r (others being imaginary) ( y') 



from whicli we see that the pairs of maxima are superposed at the 



origin if »— 2«, Avhich is equivalent to 0=3-. The minima along 



the //-axis at 2/=±Vr(r + 2a) are always real for any ratio of ajr. 



In tlie present case, the values become ±2j-^b. Substituting this 



value of // in [ß] we get the value of F there =— gZ^V It will be 



