﻿Balanced 
  Crosses 
  299 
  

  

  vated, 
  disregarding 
  always 
  the 
  reverting 
  off- 
  

   spring. 
  At 
  the 
  end 
  I 
  counted 
  the 
  progeny 
  of 
  

   the 
  sixth 
  and 
  seventh 
  generations 
  and 
  found 
  

   figures 
  for 
  their 
  three 
  groups 
  of 
  descendants, 
  

   which 
  exactly 
  correspond 
  to 
  Mendel's 
  formula. 
  

  

  Until 
  now 
  we 
  have 
  limited 
  ourselves 
  to 
  the 
  

   consideration 
  of 
  single 
  differentiating 
  units. 
  

   This 
  discussion 
  gives 
  a 
  clear 
  insight 
  into 
  the 
  

   fundamental 
  phenomena 
  of 
  hybrid 
  fertilization. 
  

   It 
  at 
  once 
  shows 
  the 
  correctness 
  of 
  the 
  assump- 
  

   tion 
  of 
  unit-characters, 
  and 
  of 
  their 
  pairing 
  in 
  

   the 
  sexual 
  combinations. 
  

  

  But 
  Mendel's 
  law 
  is 
  not 
  at 
  all 
  restricted 
  to 
  

   these 
  simple 
  cases. 
  Quite 
  on 
  the 
  contrary, 
  it 
  

   explains 
  the 
  most 
  intricate 
  questions 
  of 
  hybrid- 
  

   ization, 
  providing 
  they 
  do 
  not 
  transgress 
  the 
  

   limits 
  of 
  symmetrical 
  unions. 
  But 
  in 
  this 
  realm 
  

   nearly 
  all 
  results 
  may 
  be 
  calculated 
  beforehand, 
  

   on 
  the 
  ground 
  of 
  the 
  principle 
  of 
  probability. 
  

   Only 
  one 
  more 
  assumption 
  need 
  be 
  discussed. 
  

   The 
  several 
  pairs 
  of 
  antagonistic 
  characters 
  

   must 
  be 
  independent 
  from, 
  and 
  uninfluenced 
  by, 
  

   one 
  another. 
  This 
  premise 
  seems 
  to 
  hold 
  good 
  

   in 
  the 
  vast 
  majority 
  of 
  cases, 
  though 
  rare 
  excep- 
  

   tions 
  seem 
  to 
  be 
  not 
  entirely 
  wanting. 
  Hence 
  

   the 
  necessity 
  of 
  taking 
  all 
  predictions 
  from 
  Men- 
  

   del's 
  law 
  only 
  as 
  probabilities, 
  which 
  will 
  prove 
  

   true 
  in 
  most, 
  but 
  not 
  necessarily 
  in 
  all 
  cases. 
  

  

  