480 



J. H. vair't Hoff on the Origin 



On the right side the osmotic pressure P is chosen equal 

 to P ; the cylinder is semipermeable and plunged in water, 



Fig. 2. 



^.UP 



the increase in volume, again AY, then corresponds (for 

 dilute solutions where the heat of dilution is zero) only to the 

 external work PAY. Now here the same lowering of tem- 

 perature dT must correspond to the same work Y<iP , so that 

 we have d¥ = dP. Incidentally it may be remarked that 

 such cycles take a very simple form when Y is so great that 

 AY produces no appreciable change of pressure. On the 

 other hand, dV is so small compared with AY, that the course 

 of the adiabatic may be neglected. 



This result, Gay-Lussac's law for dilute solutions, was 

 quite in agreement with the available numerical data, although 

 it could not be asserted that it was sufficient to constitute a 

 proof. A glance at the table containing Pfeffer's results with 

 a 1 per cent, sugar-solution shows this. 



But there is also a second relationship, the full significance 

 of which was almost recognized by Pfeffer, viz., that the 

 osmotic pressure in dilute solutions is proportional to the 

 concentration ; that is to say, that Boyle's as well as Gay- 

 Lussac's law is applicable to dilute solutions. The mathe- 

 matical expression for both laws is 



PY=BT, 



and with its help I was enabled to prove the above thermo- 

 dynamical formula, and so my goal was reached. 



On calculating the value of R, however, the result was 

 quite unexpected. It is well-known that for kilogramme- 

 molecules of gases the value of R is constant and equal to 

 about 846, provided that P is expressed in kilogrammes per 

 square metre and Y in cubic centimetres. We have already 



