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



such term as V {y^^J—i', this expression for F must be taken 



as nearly true. 



Tlius tlie maxima and minima of Fi are given by 



and to determine whether they correspond to maxima or minima, 

 we have to consider the sign of 



This being given by the directions of the tangents to the curve 

 of/- (PL T) at the points y-9 + x-^\ and y-'^—yA\ we see at once that 

 when tlie intervals of the consecutive maxima or minima are 

 greater than ^'I', maxima of /" correspond to maxima of F, but 

 when >f'I* exceeds the intervals of tiie consecutive maxima or 

 minima, the maxima of /^ correspond to minima of F. 



The maxima and minima not only interchange places at 

 certain points, but the interval l3etween the maxima and minima 

 slightly increases, as a consequence that the first maximum be- 

 ing displaced towards 6 = 0, while the higher maxima, showing 

 the same tendency, are displaced by smaller amounts. In Pul- 

 frich's experiment, where he takes the third maximum as 

 standard, the first and second are displaced slightly toward 

 ^ = 0, and the other to the opposite side, as compared with 

 Airy's values of p. This displacement may be partly due to 

 the breadth of the slit. 



8. Numerical calculation. 



Fur iHimerical calculation we must have recourse to mecha- 

 nical (piad rature. The method of procedure is as follows : — 

 Draw a circle having the centre at xO and radius e(pial to y'^*, 



