DIFFUSION AND OSMOSIS. 917 



a column of mercury gives 760 X 0.65 = 494 mms. This figure expresses 

 the osmotic pressure of a 1 per cent, solution of cane-sugar when dialyzed 

 against pure water through a membrane impermeable to the sugar molecules. 

 In such an experiment water would pass to the sugar side until the hydro- 

 static pressure on this side was increased by an amount equal to the pres- 

 sure of a column of mercury 494 mms. high. Certain additional calculations 

 that it is necessary to make for the temperature of the solution need not be 

 specified in this connection. If, however, we wish to apply this method 

 to the calculation of the osmotic pressure of a given solution of an electro- 

 lyte, it is necessary first to ascertain the degree of dissociation of the electro- 

 lyte into its ions, since, as was said above, dissociation increases the num- 

 ber of parts in solution and to the same extent increases osmotic pressure. 

 In the body the liquids that concern us contain a variety of substances in 

 solution, electrolytes as well as non -electrolytes. In order, therefore, to 

 calculate the osmotic pressure of such complex solutions it is necessary to 

 ascertain the amount of each substance present, and, in the case of electro- 

 lytes, the degree of dissociation. Under experimental conditions such a 

 calculation is practically impossible, and recourse must be had to other 

 methods. One of the simplest and most easily applied of these methods 

 is the determination of the freezing point of the solution. 



Determination of Osmotic Pressure by Means of the Freezing Point. 

 This method depends upon the fact that the freezing point of water is low- 

 ered by substances in solution, and it has been discovered that the amount 

 of lowering is proportional to the number of parts (molecules and ions) 

 present in the solution. Since the osmotic pressure is also proportional to 

 the number of parts in solution, it is convenient to take the lowering of the 

 freezing point of a solution as an index or measure of its osmotic pressure. 

 In practice a simple apparatus (Beckmann's apparatus) is used, consisting 

 essentially of a very delicate and adjustable differential thermometer. By 

 means of this instrument the freezing point of pure water is first ascertained 

 upon the empirical scale of the thermometer. The freezing point of the 

 solution under examination is then determined, and the number of degrees 

 or fractions of a degree by which its freezing point is lower than that of pure 

 water is noted. The lowering of the freezing point in degrees centigrade 

 is expressed usually by the symbol A- For example, mammalian blood- 

 serum gives A = 0.56 C. A 0.95 per cent, solution of NaCl gives the same 

 A ,* hence the two solutions exert the same osmotic pressure, or, to put it in 

 another way, a 0.95 per cent, solution of NaCl is isotonic or isosmotic with 

 mammalian serum. The A of any given solution may be expressed in terms 

 of a gram-molecular solution by dividing it by the constant 1.87, since a 

 gram-molecular solution of a non-electrolyte is known to lower the freezing 

 point 1.87 C. Thus, if blood-serum gives A = 0.56 C., its concentration in 



terms of a gram-molecular solution will be -r^,, or 0.3. In other words, 



. lo/ 



blood-serum has 0.3 of the osmotic pressure exerted by a gram-molecular 

 solution of a non-electrolyte, that is, 22.32 X 0.3, or 6.696 atmospheres. 



Remarks upon the Application of the Foregoing Facts in Physiol- 

 ogy. In the body water and substances in solution are continually pass- 

 ing through membranes, for example, in the production of lymph, in the 

 absorption of water and digested foodstuffs from the alimentary canal, in 

 the nutritive exchanges between the tissue elements and the blood or lymph, 

 in the production of the various secretions, and so on. In these cases it is a 

 matter of the greatest difficulty to give a satisfactory explanation of the 

 forces controlling the flow to and fro of the water and dissolved substances, 

 but there can be little doubt that in all of them the physical forces of fil- 

 tration, diffusion, and osmosis take an important part. Whatever can be 

 learned, therefore, concerning these processes must in the end have an im- 

 portant bearing upon the explanation of the nutritive exchanges between 

 the blood and tissues. Some additional facts may be mentioned to indicate 

 the applications that are made of these processes in explaining physiological 

 phenomena. 



Osmotic Pressure of Proteins. The osmotic pressure exerted by crys- 



