308  Notices  respecting  New  Boohs, 
many  examples  are  given;  these  are  needed  in  an  elementary- 
treatise,  to  render  the  work  independent  of  a  separate  volume 
of  examples.  So  far  as  we  have  examined  them  they  seem  well 
chosen,  and  in  many  cases  are,  in  fact,  interesting  theorems : — 
e.  g.>  "  Prove  that  the  points  of  intersection  of  a  curve  of  the  fourth 
degree  with  its  asymptotes  lie  on  a  conic ;"  and  "  Prove  that  every 
curve  of  the  third  degree  is  capable  of  being  projected  into  a  central 
curve,"  &c. 
New  Theory  of  the  Figure  of  the  Earth,  considered  as  a  Solid  of  Re- 
volution; founded  on  the  direct  employment  of  the  Centrifugal  Force 
instead  of  the  Common  Principles  of  Attraction  and  Variable  Den- 
sity. By  William  Ogilby,  Esq.,  M.A.  Trin.  Coll.  Camb.,  Fellow 
of  the  Geological  and  Zoological  Societies  of  London  and  Dublin, 
Member  of  the  Moyal  Irish  Academy,  &c.  London  :  Longmans, 
Green,  and  Co.     1872.     (4to,  pp.  104.) 
Mr.  Ogilby  in  his  preface  enumerates  seven  "  principal  fallacies 
and  hypotheses  invoked  in  this  artificial  p.  e.  the  usual]  mode  of 
treatment "  of  the  question  of  the  figure  of  the  earth.  The  first  two 
are  these : — "First,  while  it  is  universally  acknowledged  that  the 
spheroidal  figure  is  due  to  the  action  of  the  centrifugal  force,  the 
efficient  cause  of  the  phenomenon  is  sedulously  ignored  in  the  inves- 
tigation of  its  effects,  and  the  question  treated  on  the  principle  of 
attraction,  as  if  it  were  a  case  of  elliptic  motion.  Secondly,  this 
pretended  attraction,  though  professing  to  be  the  resultant  of  the  in- 
dividual attractions  of  all  the  particles,  must  not  be  confounded  with 
terrestrial  gravity  ;  inasmuch  as  gravity  varies  directly  as  the  square 
of  the  sine  of  the  latitude,  acts  in  the  normal,  and  is  consequently  di- 
rected to  a  different  centre  at  every  point  on  the  surface,  while  the 
assumed  attraction  tends  to  a  fixed  centre  of  force,  and  varies  inversely 
as  the  square  of  the  distance  &c."  (p.  viii).  We  should  be  sorry 
to  hold  Mr.  Ogilby  tightly  to  what  he  says;  but  if  we  did,  it  would 
follow  that  the  force  of  gravity  at  the  equator  is  zero.  Anyhow  it 
is  pretty  plain  from  the  above  extract  that  he  is  not  a  believer  in 
universal  gravitation;  nor,  indeed,  if  he  is  not  satisfied  with  the  evi- 
dence, is  there  any  reason  why  he  should  be ;  only,  if  so,  it  is  a 
little  strange  that  his  object  is  to  employ  mathematical  reasoning 
"in  imitation  of  Newton"  (p.  xii),  and  that,  with  reference  to 
applied  science,  he  should  speak  of  Newton  as  "  the  great  master" 
(p.  2).  The  chief  offender  in  this  matter  of  the  figure  of  the  earth 
is  Laplace,  who  says  that  the  law  of  gravity  on  the  earth's  surface 
depends  on  the  form  of  the  terrestrial  spheroid,  and  this  in  turn  on 
the  law  of  gravity,  and  that  this  mutual  dependence  of  the  two  un- 
known quantities  renders  the  investigation  of  the  figure  of  the  earth 
very  difficult.  This  is  no  more  than  might  have  been  expected  from 
Laplace ;  but  that  in  writing  thus  he  should  only  be  following  up  a 
line  of  inquiry  begun  by  Newton  demands  explanation  ;  and  here  is 
the  explanation  supplied  by  Mr.  Ogilby  (p.  14): — "  It  is  difficult  to 
account  for  all  these  arbitrary  assumptions,  unless  by  supposing 
that  the  mind  of  Newton  was  so  completely  absorbed  in  his  grand 
