12 ART. 3. — AICHI AND TANAKADATE : THEORY OF 



then the final form is 



I ( dx dy cos- -~\ x' + y' — xd{x + y) \ 



Putting -'^=^'(4-)' ^=Kf)' ' = K^)^ 



and y' = — y' in the latter half, 



then applying the well-known sequence equation of the Bessel's 



function 



i!^=_i_|j,(,,0+j.(,„)| , 



this can le reduced to the form 



r [dx'dy'coÂ>:'-' + y''--x'd{x' + y')\ U2\y' {^' + v')\+^^![^' i^' + y')V\ , 



which is almost intractable for practical calculation. 



If we transform the variables cp, (/' to :v, y which are given 

 by .'f = ^cos9^, y = (psin(/', and then integrate with respect to y, we 

 arrive at the expression 



l^>/^^^^) = -^J d{.x)^(,<py-(,xy/%y.d + y.x) . (40 



- 7. <P 



This form is most advantageous for the numerical calculation of 

 F by means of mechanical quadrature. 



5. Case where the visual angle of the drop is 

 not negligible. 



In the preceding article we neglected the visual angle of 

 the dro}), i.e. r as compared with the observers distance, but 



