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Physics. — ''Some rainnrk.s on Dr. Ph. Kohn«tamm's last papei's.^^ 

 By J. J. VAN Laau. (Communicated by Prof. H. A. Lorentz). 



i. With interest and Cull a})pro\'al 1 read Dr. Kohnstamm's three 

 papers on the osmotic pressure ^). From them it appeared to me that, 

 practically', he perfectly agreed with me. Only with regard to a few 

 points there are differences of opinion — only in appearance, howeveVy 

 as I shall show in what follows. 



On pages 723 — 729 1. c, namely, Kohnstamm gives also a thenno- 



dynamic derivation of the osmotic pressure, which seems to lead to 



a somewhat diffei'ent result from mine. He finds, namely, in the 



dh 

 numerator finally the cjuantity Vi — oc—~ instead of v^. \\ use here 



dx ^ 



my notation ; v^ is the molecular volume of the pure solvent (Kohn- 



stamm's v,I), Vx that of the solution, in wdiich the dissolved substance 



is present with a concentration x (K.'s z^J]. But here he overlooks 



that according to his approximations v^ may be written for the 



latter. P^or on page 726 an integral is neglected, among others 



on the strength of the fact that Vx — b approaches to 0. He puts 



dh , dh 



therefore v^ = b, in consequence of which Vx — cc — = — x — = 



dx dx 



= Z> — x{b.j — b^)::^b^. This however, is the value of b or z;, when 

 X = 0, so Vq. 



So Kohnstamm finds exactly the same thing as I found already in 

 1894 in a much simpler way. In my method no integral need be 

 split into three parts, and we need not neglect anything but tlie 

 compressibility of the liquid (which is of course also done by 

 Kohnstamm), so that my result (the compressibility excepted) is per- 

 fectly accurate, which cannot be said of that of Kohnstamm. 



2. The above mentioned method has been repeatedly published 

 by me. [Z. f. Ph. Ch. XV, 1894; Arch. Teyler (Theorie générale), 

 1898; Lehrbuch der math. Chemie, 1901; Arch. Teyler (Quelques 

 reraarques sur la theorie des solutions non-diluées), 1903; and recently 

 in the "Chemisch Weekblad", 1905, N". 9]. The derivation may 

 follow here once more. 



If there is namely, equilibrium between the solution with the 

 concentration x under a pressure p, with the pure solvent with a 

 concentration under the arbitrary pressure j^o (c-g- that of the 

 saturated vapour, or of tiie atmosphere etc.), the molecular potentials 



1) These Proc. VII, 723-751. 



Proceedings Royal Acad. Amsterdam. Vol. VIII. 



