io8 
Yeast  (jYowth. 
(Am.  Jour.  Pharm. 
\     February,  1920. 
Lack  of  fermentable  sugar,  which  also  acts  as  a  food  for  the  yeast, 
may  be  the  limiting  factor  which  finally  prevents  further  growth. 
A  discussion  of  this  typical  case  will  show  on  what  factors  yeast 
crops  depend. 
During  the  logarithmic  period  of  growth  the  yeast  growth  N 
during  the  time  in  which  S  grams  of  sugar  disappear  (by  growth 
and  fermentation)  is  connected  with  K  the  constant  of  growth  and 
F  the  fermentative  activity  of  the  yeast  by  the  equation  N/S  = 
dN 
K/F.    During  any  other  periods  of  growth  the  relationship    = 
dS 
—  holds  good  for  small  increments  in  N  and  corresponding  decre- 
ments  in  S.    We  have  therefore  N  =  —  dS,  that  is.  the  yeast  crop 
from  a  small  seeding  is  determined  by  the  value  of  the  integral  be- 
tween the  limits  S  =  initial  concentration  of  the  sugar  to  S  —  o. 
The  ratio  K/F  and  its  variation  with  different  sugar  concentra- 
tions determines  the  amount  of  yeast  a  given  medium  can  produce. 
If  K/F  is  constant  (which  is  approximately  the  case,  for  both  K 
and  F  are  independent)  the  sugar  concentration,  except  when  the 
solutions  are  dilute,  the  growth  and  the  initial  sugar  concentration 
will  be  proportional.  H.  T.  Brown  (1914,  226)  finds  that  2.3  grams 
maltose  disappear  when  io^°  yeast  cells  are  produced. 
Yeast  growth  may  cease,  owing  to  the  production  of  large  amounts 
of  alcohol.  The  crop  under  these  conditions  is  determined  by  the 
way  the  ratio  K/F  varies  with  different  concentrations  of  alcohol, 
and  the  same  method  can  be  used  to  calculate  the  yeast  growth. 
The  integral  is,  in  fact,  of  general  application  whatever  the  final 
limiting  factor  is. 
The  ratio  K/F  is  independent  of  the  number  of  yeast  cells 
present.  It  follows,  therefore,  that  with  a  medium  of  given  composi- 
tion the  total  possible  growth  is  a  constant,  the  crop  being  equal  to 
the  sum  of  the  seeding  and  the  growth.  A.  L.  Stern  (1901),  in  a 
series  of  careful  experiments  on  the  point,  has  proved  this  experi- 
mentally in  the  case  of  a  Burton  yeast  growing  in  a  solution  contain- 
ing glucose,  asparagin  and  mineral  salts. 
A.  J.  Brown's  previous  observation  (1892)  that  large  seedings 
of  yeast  in  wort  refuse  to  bud  is  contrary  to  this  general  conclusion 
