( i'-i ) 



EXPLANATION OF FIGURES. 



Fig. 1. Scalpellum rostratum, Darwin. Seen from the right side. 

 „ 2. Scalpellum rillosum, Leach. Seen from the right side. 

 „ 3. PoUicipes sertus, Darwin. Seen from the right side. 



(Fig. 1 — 3 after Darwin, Monograph on the Girripedia. Lepadidae. 1851). 

 „ 4. ScalpeUum polUcipedoides, n. sp. Seen from the left side. Magnified 



1 1 diameters. 

 „ 5. Same species, abnormal specimen, a the additional values, h the com- 



plemental male. Magnified 11 diameters. 

 , G. The complemenlal male of Sc. polUcipedoides. Magnified 180 diameters. 



Physics. — ''On the function -for niultijylemirtures." By 'Mr.B.'M. 

 VAN Dalfsen. (Commnnieated by Prof. .1. D. van der Waals) . 



The quantities a and b appearing in this quotient are the constant 



quantities of the equation of condition of van der Waals, applied 



a 

 to a multiple mixture. Tiie quantity - then represents an expression 



b 



proportional to the critical temperature of the undivided mixture. 

 We imagine the mixture determined by the molecular fractions 

 .I'l, i\, . . . , x,i, where .i'^ -{- x\^ -{-... -{- v„ = 1 and all xs are positive 

 quantities. Further we assume for a and tj homogeneous quadratic 

 functions of the ,vs, so that 



and 



b = 'V \^ bfjfj .^•^ Xq. ^) 



t^ ^ 



For the quantity a we must arrive, it is clear, at a quadratic 



function, as we have to do with attraction of the molecules two b}^ 



two ; for h we can suffice ^) with a quadratic function as long as 



simultaneous collisions of more molecules are neglected. 



Our particular business now is to find out whether there are 



a 

 mixtures for which - is stationarv. 

 b 



The constitutions of those mixtures we find out of 



1) Here apq=' a^p and bpq=^ bqp. For Opp and bpp we put in the sequel ordinarily 

 Op and bp. 



2) Gomp. H. A. LoRENTz, Wied. Ann. 12, p. 134. 



