OSMOTIC PRESSURE OF EXPRESSED VEGETABLE SAPS 
77 
A — inconsistencies which for the most part result in variations of P 
less than those attributable to experimental error. In computing 
the accompanying table we have employed the formula of Lewis^ 
quoted by Morgan.^ To quote from Lewis^ 
" The osmotic pressure may be obtained at once from the freezing point by 
means of the equation 
TT = I2.O6A — 0.02IA2, 
where tt is the osmotic pressure in atmospheres and A is the lowering of the freezing 
point in centigrade degrees. From this equation the osmotic pressure of any solution 
up to 10 or 15 times normal may be obtained with an accuracy which depends only 
upon the precision of the freezing point determinations and upon the accuracy of 
the value used for the heat of fusion of ice. Since the error in the latter quantity is 
probably not more than o.i per cent, it is obvious that except for the most dilute 
solutions osmotic pressures may be found in this way with an accuracy which is more 
than ten times as great as Morse and Frazer claim for their direct measurements." 
The osmotic pressures corresponding to depressions of hundredths 
of degrees may be read directly from the table. Furthermore for all 
practical purposes the first differences X o.i may be taken as 0.012, 
hence pressures when A is read to thousandths of a degree may be at 
once determined. Thus suppose A to be 1.244°. For A = 1.24° 
P = 14.92°. 14.92 + (4 X 0.012) = 14.968. The exact value by 
direct computation is 14.970. Or again, A = 1.248°; P = 14.92 + 
(8 X 0.012) = 15.016 as compared with the exact value 15.018.^^ 
' Lewis, G. N. Loc. cit. 
* Morgan, J. L. R. " Elements of Physical Chemistry," 4th ed., 1908, p. 180. 
^ Lewis, G. N. Loc. cit., pp. 670-671. 
Since the biologist's error in the determination of A may be at least 0.001° C. 
which affects P in the second decimal place, it is idle to write down the pressures to 
more than four significant figures. The entries in the tables were, of course, cal- 
culated to a sufficient number of places to avoid the possibility of arithmetical error. 
In copying off the table the final figure has been modified where needful. 
