583 



however that tliis rotation» whit'li is incomprehensibly denied bv 

 Legros does not set in before the month lias reached its minimal 

 size, consequently in the middle of the period of the metamorphosis. 

 In consequence of this rotation the rostral rim of the mouth of the 

 larva becomes right-rim, whilst at the same time the posterior rim 

 becomes left-rim. 



The mouth-opening having become velaropening lies now sym- 

 metrically with regard to the median plane, but the nerves, that 

 surround it, indicate that it continues to be an organ of the 

 leftside. 



In the higher animals the middle-ear originates from the first 

 gill-pouch, whilst amphioxus lacks the auditive organ entirely. If 

 we wish to express ourselves in a popular way, we may say, as 

 I did already on a former opportunity: Amphioxus cannot hear; 

 he eats however with the left ear, and has consequently lost the 

 mouth. 



Mathematics. — "Applications of Sonine'.s- extension of Abel'.s^ 

 inte(/r(iIequation." By Dr. J. G. Rutgers. (Communicated bv 

 Prof. W. Kapteyn). 



(Communicated in tlie meeting of September 27, 1913), 



SoNi.NK ') has given to Abel's integralequation an extension which 

 comes to the following. 



The unknown function u in the equation 



.(• 



/[,■) = j iyf,v~^)n{^)d^ (1«) 



ii 

 is dctermino<l by 



"(•'■)= jöO'-— I) ./'(^M5 (2a) 



a 



where we suppose ƒ(,/■) to be Unite and continuous, /\.r) finite, 

 a<.T<b, and ƒ (a) ^ 0. Moreover <j and tp are connected in the 

 following way : 

 Suppose 



''•■ 1 CO 



'tin) = — '■», Vm , -— - = ^ 'In'/", 



1) Acta Matem. 4; 1884. 



