^puS^S?'}        Plant  Morphology  and  Taxonomy.  405 
clear  definitions,  but  to  recognize  a  certain  symmetry  in  the  forms  of 
stems  and  leaves.  It  was  not,  however,  until  the  time  of  Schimper 
(1834)  and  Braun  (1835)  that  mathematical  conceptions  with  regard  to 
plant  members  were  formulated  and  made  the  basis  of  morphological 
study.  Schimper  introduced  a  system  of  phyllotaxy,  known  as  the 
spiral  theory,  the  principal  feature  of  which  was  the  assumption  of 
the  spiral  arrangement  of  leaves,  While  the  theory  is  a  beautiful 
one  on  paper,  it  has  been  found  in  practice  to  have  a  limited  applica- 
tion, and  can  not  be  said  to  account  for  the  factors  which  influence 
the  arrangement  of  leaves,  as  pointed  out  by  Hofmeister,  Its  chief 
value  lies  in  the  fact  that  it  directed  attention  to  the  study  of  the 
relative  position  of  organs  and  caused  botanists  to  inquire  into  the 
factors  influencing  their  form,  position,  and  arrangement  on  the 
plant.  It  possibly  also  led  to  the  application  of  mathematical  and 
mechanical  principles  in  the  study  not  only  of  the  disposition  of 
organs  but  also  in  the  distribution  of  tissues  as  illustrated  in  later 
years  in  the  work  of  Schwendener  and  his  students,  At  any  rate  it 
is  interesting  to  make  mention  here  of  Schwendener's  great  work  on 
the  mechanics  of  growth,  which  must  be  looked  upon  as  a  most  im- 
portant contribution  to  the  study  of  the  fundamental  principles  of 
morphology, 
We  now  come  to  a  period  which  was  marked  by  a  series  of 
brilliant  investigations,  and  which  has  been  one  of  the  most  fruit- 
ful in  the  history  of  botanical  science.  In  1838  Schleiden  announced 
the  fact  that  the  cell  is  the  fundamental  unit  in  plants  and  showed 
that  all  the  different  tissues  of  the  plants  are  combinations  of  cells, 
Several  years  previous  (183 1)  Robert  Brown  had  discovered  the 
nucleus  in  the  epidermis  of  the  orchids,  and  it  remained  for  Von  Mohl 
(1846)  to  give  the  first  accurate  description  of  protoplasm  and  to 
establish  its  fundamental  nature. 
In  contrast  to  the  cellular  theory  established  by  Schleiden  and  his 
followers,  which  appeared  to  be  all-sufficient  for  so  long,  we  now 
(1 892- 1 895)  have  the  conception  that  the  energids  are  the  funda- 
mental units  in  the  plant  structure  ;  an  energid,  according  to  Sachs, 
being  composed  of  a  single  nucleus  and  the  protoplasm  which  it 
dominates.  Thus  a  cell  may  be  monergic  or  polyergic,  depending 
upon  the  number  of  nuclei  which  it  contains. 
It  was  also  during  the  middle  period  of  the  last  century  that 
Nageli  carried  on  his  splendid  researches  on  the  development  of 
