Chap.  ii.  is  devoted  to  groups  of  screws.  He  discusses  in  detail  groups  con
taining  three  members,  investigating  some  special  cases  not  dwelt  on  before.  He
then  gives  the  formulae  for  what  are  termed  "Oblique  Co-ordinates."

In  Chap.  in.  the  application  of  the  Theory  of  Screws  to  mechanics  is  discussed
and  the  leading  parts  of  the  Theory  of  Screws  in  relation  to  dynamical  problems
with  freedom  of  the  «th  order  are  set  forth,  and  he  adds,  "The  lack  of  books  on  the
Theory  of  Screws  both  in  Russia  and  abroad  makes  us  hope  that  our  work  will  be
received  with  indulgence."

BALL  (R.  S.)  —  The  Theory  of  Permanent  Screws.     Ninth  Memoir.     Transactions  of
the  Royal  Irish  Academy,  Vol.  xxix.,  pp.  613  —  652.     1890.
Using  Screw-chain  co-ordinates  an  emanent  (see  Salmon's  Higher  Algebra,
§  125,  or  Elliott's  Algebra  of  Qualities)  is  here  shown  to  vanish.  This  involves  a
general  property  of  the  function  T  which  expresses  the  kinetic  energy.
dT  dT

Xl-j  --  b  ...  +  XH  -j  —  =  0.
CtOC-^  CvXft

It  is  shown  that  for  the  permanent  screw-chains,


The  special  cases  for  the  different  degrees  of  freedom  of  a  single  rigid  body  are
considered  in  detail.  If  the  rigid  body  has  three  degrees  of  freedom  then  there
are  three  permanent  screws,  about  any  one  of  which  the  body  will  continue  to
twist  if  once  set  twisting.
In  general,  if  the  body  be  set  twisting  about  a  screw  6,  a  restraining  wrench
on  some  other  screw  rj  would  be  necessary  if  the  motion  were  to  continue  as  a  twist
about  0.
