On  Cayley's  solution  of  Riccati's  Equation.  433 
the  molecule  consists  of  an  atom  of  hydrogen  combined  only  with 
an  atom  of  potassium ;  but  in  the  molecule  of  caustic  potash  they 
are  so  firmly  held  together  that  they  remain  in  combination  even 
at  a  red  heat.  Neither  the  potassium  nor  the  hydrogen  can  go 
off  with  its  share  of  the  oxygen ;  the  latter  is  indivisible,  binding- 
together  the  two  other  atoms. 
KOH. 
If,  however,  the  atom  of  oxygen  be  replaced  by  an  equivalent 
quantity  of  chlorine  (that  is,  two  atoms),  then  the  atoms  of  po- 
tassium and  hydrogen, 
KC1 
C1H, 
are  separated,  each  going  off  in  combination  with  an  atom  of 
chlorine. 
Neither  does  he  attempt  to  explain  the  cause  of  isomerism, 
which  is  so  well  done  by  the  notion  of  the  existence  of  atoms  as- 
sociated in  different  relative  positions.  Perhaps  Dr.  Wright 
will  yet  explain  how  he  accounts  for  the  differences  between  iso- 
meric bodies. 
It  has  now  been  shown,  I  submit,  that,  notwithstanding  the 
author's  assertion  that  the  (i  conceptions  involved  in  the  atomic 
hypothesis  are  both  unnecessary  and  insufficient,"  he  yet  makes 
consistent  use  of  it  in  all  his  fundamental  positions.  This  evi- 
dence in  favour  of  the  theory  is  doubtless  unconscious ;  but  it  is 
not  the  less  weighty  on  that  account. 
LTV.  On  the  Relations  between  the  particular  Integrals  in  Cay- 
ley's  solution  0/ Riccati's  Equation.  Bij  J.  W.  L.  Glaisher, 
B.A.j  F.R.A.S.,  Fellow  of  Trinity  College,  Cambridge*. 
IN  the  Philosophical  Magazine  for  November  1868  (S.  4. 
vol.  xxxvi.  p.  348)  Professor  Cayleyhas  given  the  solution 
<of  Riccati's  equation  in  series  which  consist  of  a  finite  number 
of  terms  in  the  integrable  cases. 
\Vriting  the  transformed  Riccati's  equation  in  the  form 
g_**-»*=0, (1) 
it  is  shown  that  the  four  following  series  are  particular  integrals  : 
*  Communicated  bv  the  Author. 
Phil.  Mag.  S.  4.  Vol.  43.  No.  288.  June  1872.         2  F 
