Torsional  Stress  in  Solutions  of  Gelatine. 
453 
the  curve  shown  in  figure  4,  which  represents  final  stress 
against  concentration.  This  curve  in  the  region  4*4  per  cent, 
concentration  is  very  steep,  and  a  small  change  of  concentration 
makes  a  comparatively  large  change  in  the  elastic  limit. 
Returning  now  to  figure  3,  it  will  be  seen  that  the  curves 
are  not  quite  horizontal  alter  the  break  has  been  reached ; 
that  is  to  say,  the  elasticity  still  gradually  diminishes. 
Possibly  this  may  be  accounted  for  by  the  fact  that  during  each 
experiment  the  temperature  was  slowly  rising,  which  condition 
would  tend  to  decrease  the  elastic  limit  of  the  specimen. 
No  type  of  equation  has  been  found  which  will  fit  all  the 
•curves,  but  an  equation  of  the  form  W  =  a  log  (pt  +  1)  fits 
the  4*5  per  cent,  curve  with  considerable  exactness  This 
particular  curve  is  of  the  same  type  as  those  for  lead  wire 
treated  in  a  similar  manner  ("  On  the  stretching  and  torsion 
•of  lead  wire  beyond  its  elastic  limit,"  Phil.  Mag.  Oct.  1904), 
for  not  only  do  equations  of  the  same  form  approximately 
represent  the  curves,  but  both  curves  show  similar  departures 
from  those  equations.  The  above  equation  also  satisfactorily 
represents  all  curves  corresponding  to  higher  concentrations 
than  4*5  per  cent. ;  these  are  not  shown  in  the  diagram. 
It  is  noticeable  also  that  the  dotted  curve  passing  through 
the  points  of  breakage  of  the  four  upper  curves  is  of  like 
Fig.  4. 
100 
50 
shape,  being  fairly  represented  b\ 
=  W0-alog(>*  +  l). 
shows    the    final  weight 
GfffiMS  Of  OflAT/NE 
P£/P  /OO    ">/!Tr/? 
an   equation  of  the  form 
Figure    - 
which    is   of    con  rse 
