Notices  respecting  New  Books.  831 
across  from  the  opposite  electrode  "  B."  As  perforation  of 
the  diaphragm  only  took  place  when  "  B  "  was  positive,  it  is 
to  be  supposed  that  the  particles  that  caused  the  perforation 
were  minute  fragments  of  carbon  dislodged  from  "  B  "  by 
the  sand-blast  action  of  the  negative  carriers  from  "A." 
On  replacing  the  aluminium  diaphragm  by  one  made  of 
fine  brass  wire  gauze  having  150  wires  each  *003  inch 
diameter  to  the  inch,  it  was  found  that  the  Faraday  cylinder 
immediately  attained  a  potential  of  several  volts,  the  potential 
being  positive  or  negative  as  the  opposite  electrode  was  made 
respectively  positive  or  negative. 
It  would  therefore  appear  that  though  the  carriers  of  both 
positive  and  negative  electricity  in  the  arc  are,  under  the 
conditions  described,  incapable  of  passing  through  thin 
aluminium-foil  provided  the  latter  remains  intact,  they  are 
able  to  pass  freely  through  apertures  of  very  minute  dimen- 
sions in  an  earthed  metallic  screen  without  parting  with  the 
whole  of  their  electric  charges. 
LXXVIII.  Notices  respecting  New  Books. 
Cambridge  Tracts  in  Mathematics  and  Mathematical  Physics. — 
No.  1.  Volume  and  Surface  Integrals  used  in  Physics,  by  J.  G. 
Leatheat,  M.A.  No.  2.  The  Integration  of  Functions  of  a  Single 
Variable,  by  Gr.  H.  Hardy,  M.A.      Cambridge  University  Press. 
1905. 
rFHESE  are  the  first  two  of  a  projected  series  of  tracts  which  should 
prove  of  great  interest  and  value  to  mathematical  students. 
Professor  "Whittaker  is  associated  with  Mr.  Leathern  in  the  general 
editing  of  the  series.  One  feature  of  the  discussion  of  Aroliune  aud 
surface  integrals  is  the  examination  of  the  validity  of  the  process 
when  the  attracting  matter  is  of  discontinuous  structure,  a  point 
which  is  generally  ignored  by  writers  on  potentials  and  attractions. 
There  is  also  a  careful  examination  of  the  conditions  under  which 
a  volume  or  surface  integral  is  convergent  or  semiconvergent  when 
taken  through  a  region  or  over  a  surface  including  points  at 
infinity.  The  argument  is  illustrated  by  a  few  familiar  examples 
in  gravitation  potential  and  magnetism.  Elaborating  as  it  does 
just  those  points  which  are  either  assumed  or  at  any  rate  very 
briefly  referred  to  in  standard  treatises  on  mathematical  physics, 
this  tract  should  be  read  and  digested  by  every  real  student  of  the 
subjects  involved.  The  second  tract  should  appeal  to  all  students 
who,  familiar  enough  with  the  various  processes  and  "  tricks  "  of 
integration  expounded  in  our  recognized  textbooks,  wish  to  get  a 
clear  grasp  of  the  general  principles  underlying  these,  so  far  at 
least  as  such  general  principles  have  been  discovered.  The  treat- 
ment is  developed  in  six  main  sections,  of  which  the  fourth,  fifth, 
and  sixth  discuss  respectively  the  integration  of  rational  functions, 
algebraic  functions,  and  transcendental  functions.  There  is  a 
valuable   appendix    of    references  to    the   original   memoirs  and 
