514  PRE-CAMBR1AN    ROCKS    OF    NORTH    AMERICA.  [bull. 86, 
tained,  but  usually  it  is  too  complex  to  be  fully  covered  by  a  formula, 
Just  so  each  geological  force  wheu  more  accurately  known  will  be  found 
to  involve  an  irregular  rate  of  change.  The  increment  in  an  individual 
case  for  a  certain  length  of  time  may  be  added  or  substracted,  but  it  is 
not  probable  in  any  case  that  the  addition  or  substraction  will  fully 
cover  the  real  law,  although  this  may  be  a  second  approximation  to  the 
truth  as  the  so-called  law  of  uniformity  was  a  first  approximation.  If 
we  go  far  enough  back  a  geological  force  may  have  been  multiplied  or 
divided  by  two  or  three  or  a  larger  number.  Igneous  rocks  are  now  a 
far  less  abundant  geological  product  than  are  sedimentary  rocks. 
That  these  relations  are  true  for  all  past  time  can  no  more  be  assumed 
than  it  can  that  organic  and  mechanical  sediments  have  the  same 
relative  volume  for  the  pre-Cambrian  that  they  have  for  the  Creta- 
ceous or  Tertiary.  If  the  generally  accepted  hypothesis  as  to  the  origin 
of  the  globe  represents  the  facts,  in  all  probability  rocks  of  igneous 
origin  must  become  relatively  more  important  in  very  ancient  times.^ 
If  we  but  go  back  far  enough  they  may  become  predominant;  and  in 
still  earlier  time  for  continental  areas  they  may  be  the  only  rocks. 
The  problem  then  of  the  stratigraphy  of  the  pre-Cambrian  elastics  is 
a  problem  to  be  treated  precisely  as  that  of  the  Paleozoic.  It  is,  upon 
the  whole,  a  more  difficult  problem ;  for,  while  in  any  particular  locality 
it  can  not  be  premised  from  the  degree  of  crystallization  that  the  rocks 
are  pre-Cambrian  or  post-Cambrian;  taking  the  world  as  a  whole,  thd 
rocks  become  more  crystalline  in  passing  to  lower  series;  so  that  it 
is  to  be  expected  and  is  the  fact  that  a  greater  proportion  of  pre-Cam- 
brian rocks  than  of  the  Paleozoic  are  highly  crystalline.  This,  howi 
ever,  is  not  the  most  serious  difficulty  with  which  pre-Cambrian  strata 
graphy  has  to  contend ;  it  is  the  sparseness  of  the  remains  of  life  in 
definitely  recognizable  forms.  It  has  been  seen  that  a  beginning  of  a 
pre-Cambrian  fauna  has  already  been  found,  and  when  it  is  rememberedj 
how  rapidly  definite  paleoiitological  knowledge  has  extended  down-j 
ward  in  the  past  decade  it  may  be  reasonably  hoped  that  before  lon^ 
assistance  will  be  derived  from  paleontology  in  the  classification  of  the 
pre-Cambrian  rocks,  but  it  can  not  be  expected  that  fossils  will  ever  bej 
so  important  and  controlling  a  guide  as  in  the  post-Cambrian ;  forj 
probably  the  farther  we  go  back  from  the  Cambrian  the  sparser  and 
sparser  will  the  recognizable  life-remains  become. 
As  a  result  of  the  average  greater  crystalline  character  of  the  pre-i 
Cambrian  rocks,  and  the  frequency  in  them  of  secondary  structures^ 
the  principles  of  working  out  stratigraphy  in  regions  in  which  cleav-1 
age  foliation  occurs  with  partial  or  total  obliteration  of  stratification 
are  of  the  utmost  importance.  The  failure  to  clearly  recognize  and 
apply  these  principles  has  left  the  crystalline  Cambrian  and  post- 
Cambrian  series  of  the  Appalachians  in  a  state  of  confusion  for  many 
years.  Within  the  last  decade,  by  a  recognition  and  a  close  applica- 
tion of  them  a  new  start  has  been  made  in  the  study  of  this  difficult 
region. 
