454       Decay  of  Torsional  Stress  in  Solutions  of  Gelatine. 
proportional  to  the  couple,  plotted  against  concentration,  and, 
if  we  regard  each  specimen  as  being  elastic  to  the  extent 
shown,  it  indicates  that  as  the  concentration  increases  the 
elastic  limit  increases  more  and  more  rapidly. 
The  elastic  limits  and  the  times  at  which  they  are  reached 
are  shown  in  the  following  table  : — ■ 
Concentration,    i     Elastic  Limit. 
Time  of  reaching 
limit. 
3-4 
4-0 
4-2 
4-4 
.37  gr.  wt. 
72      „ 
80      „ 
106      „ 
0-114  hour. 
0274     „ 
0-496     „ 
2-160  hours. 
IV.    Conclusions. 
The  following  conclusions  may  be  drawn  from  the  results 
of  these  experiments  : — 
1.  That  any  specimen,  the  concentration  of  which  exceeds 
some  fixed  limit,  is  capable  of  permanently  supporting  a 
certain  stress. 
2.  That  the  nature  of  the  variation  of  stress  for  constant 
strain  depends  on  the  amount  by  which  the  limiting  stress  is 
exceeded.  Thus  we  see  that  the  curves  of  the  3'4,  4"0,  and 
4*2  per  cent,  concentrations  differ  in  kind  from  that  repre- 
senting the  4*5  per  cent,  concentration;  that  is  to  say,  they  are 
not  represented  by  equations  of  the  type  W=  a  log  (pt  +  1). 
Owing  to  the  smallness  of  the  time  scale  it  is  impossible  to 
reasonably  fit  equations  to  them,  and  it  is  intended  to  repeat 
these  determinations  using  a  more  quickly  moving  drum,  in 
order  to  obtain  a  more  open  scale.  But  the  4*4  per  cent, 
curve  is  not.  of  the  same  type  as  the  4*5  per  cent.  No 
equation  of  the  form  suitable  to  the  latter  fits  it.  It  appears 
to  partake  of  the  shape  of  both  upper  and  lower  curves.  We 
conclude,  therefore,  that  for  specimens  of  greater  concen- 
tration, i.  e.  those  in  which  the  elastic  preponderates  over  the 
viscous,  the  variation  of  stress  under  constant  strain  follows 
the  logarithm  law  W  =  W0—  a  log  (pt  + 1)  just  as  in  the  case 
oE  lead  ;  on  the  other  hand,  if  the  concentration  is  low  and 
viscosity  is  the  more  prominent  property,  some  other  law  is 
followed,  and  solutions  of  intermediate  strength  are  governed 
by  a  combination  of  these  laws. 
3.  That,  in  some  cases  at  least,  the  whole  of  the  excess 
