834  Notices  respecting  Neic  Books. 
Proclus.  In  a  most  interesting  discussion  of  the  definitions  and 
postulates  on  which  the  theory  of  parallels  is  based,  Mr.  Frankland 
shows  that  this  early  commentator  of  the  Elements  came  very- 
close  to  the  true  view  historically  associated  with  the  name  of 
Lobachewski. 
Kummers  Quartic  Surface.     By  B.  W.  H.  T.  Hudson,  M.A.,  D.Sc. 
Cambridge  University  Press.  1905. 
Every  reader  of  this  remarkably  compact  book  will  recognize  what 
a  heavy  loss  the  mathematical  world  suffered  when  Mr.  Hudson 
met  his  tragic  death  mountaineering  in  Wales.  From  Mr.  H.  F. 
Baker's  preface  we  learn  that  the  earlier  sheets  only  were  seen  by 
the  author  in  proof;  but  that  the  editors  (Mr.  Baker  and  Mr. 
Bateman)  were  able  to  complete  the  book  by  following  the 
author's  manuscript  unaltered  throughout.  It  is  not  possible  to 
give  even  a  general  description  of  the  extraordinary  amount  that 
is  contained  in  the  xviii.  chapters.  Enough  to  say  that  the 
shape  of  the  surface  is  first  described  in  terms  of  the  singularities. 
The  powerful  methods  of  Line  Geometry  are  then  invoked;  and 
after  some  particular  forms  are  discussed  in  detail,  the  surface  is 
treated  as  a  two-dimensional  field  in  which  certain  algebraic  curves 
may  be  drawn.  This  leads  to  the  introduction  of  theta  functions, 
whose  properties  are  used  to  investigate  the  properties  of  these 
algebraic  curves.  The  book  is  characterized  by  great  brevity  of 
statement  and  demonstration.  Had  it  been  written  in  the  diffuse 
style  practised  by  some  authors  it  might  easily  have  been  doubled 
or  tripled  in  size.  But  its  conciseness  is  a  charm,  there  being 
little  danger  of  the  reader  losing  sight  of  the  forest  because  of  the 
trees.  He  has,  indeed,  frequently  to  fill  in  proofs  whose  steps  are 
indicated  in  broad  outline. 
Notions    cVtilectricite  :     Son     Utilisation    clans    V Industrie,.       Par 
Jacques  Geileaeme.  Paris :  Gauthier-Yillars.  1905. 
This  work  has  growTn  out  of  lecture  notes  prepared  by  the 
author  in  his  capacity  of  lecturer  to  the  Federation  nationale  des 
Chauffeurs,  Conducteurs,  Mecaniciens,  Automobilistes  de  toutes  in- 
dustries, and  is  primarily  addressed  to  the  artisan  class  of  reader. 
It  covers  an  enormous  extent  of  ground,  dealing  with  practically 
all  the  more  important  technical  applications  of  electromagnetism. 
The  treatment  is  necessarily  very  brief,  but  the  author  is  successful 
in  presenting  the  leading  features  of  the  various  subjects  dealt 
with  clearly  and  concisely;  the  diagrams  are  excellent.  In  a 
work  of  this  kind,  with  its  entire  absence  of  mathematical  reasoning, 
there  must  be  a  fair  amount  of  dogmatic  teaching;  yet  the  author 
has  skilfully  contrived  not  to  make  this  too  obtrusive.  The  book 
should  become  very  popular  among  those  who  desire  to  acquire 
a  general  smattering  of  electro-technology,  but  who  object  to 
anything  in  the  nature  of  a  mathematical  symbol.  The  author 
confines  his  attention  to  French  practice — wisely,  we  think,  in 
view  of  the  purpose  which  the  book  is  intended  to  serve  ;  but  we 
are  altogether  unable  to  understand  the  uncalled-for  patriotic 
flourish  in  which  he  allows  himself  to  indulge  in  the  Preface. 
