Skip to main content

Full text of "A budget of paradoxes"

See other formats 


<te^ 

J^  ^9 


MO139  Q3dlAIVlS  SV  3HQ 


enp  04  joud  sAop 
t7  epouu  eq  ADUU  seBjoqoej  puo  sp/v\eue^j 

dldN  04.  s>iooq 
BujBuuq  Aq  peBjoqoej  eq  ADUU  SUDOI  JD0A-[ 


Aq  peMGuej  eq  ADUU  SUDOI 
SAVQ  L  d31dV  Q311VO3d  39  AVIAI  S>iOO9  11V 


969F-K)9t76  VO  ' 
Djujo-npo  jo 

Pl^jd  puouugoi^j  'OOF  '6p|g 
lVNOI03d  Nd3HidON 
jo 

DIUJOJIPO  jo 
AUD  jo  >isep  uoijDinojp  egj  oi 


AilllOVd 


A  BUDGET  OF  PARADOXES 


BY 


AUGUSTUS  DE  MORGAN, 

F.R.A.S.   AND  C.P.S.  OF  TRINITY  COLLEGE,  CAMBRIDGE. 


REPRINTED,  WITH  THE   AUTHOR'S  ADDITIONS,   FROM  THE   ATHEN-EUM 


SECOND  EDITION 

EDITED  BY 

DAVID  EUGENE  SMITH. 


"UT  AGENDO  SURGAMUS  ARGUENDO    GUSTAMUS." 

— PTOCHODOKIARCHUS    ANAGRAMMATISTES. 


VOLUME  I. 


THE  OPEN  COURT  PUBLISHING  CO. 

CHICAGO  LONDON 

1915 


AUTHORIZED  EDITION 

COPYRIGHT  IN  GREAT  BRITAIN  UNDER  THE  ACT  OF  191  I 
AND  COPYRIGHT  IN  THE  UNITED  STATES  BY 

THE  OPEN  COURT  PUBLISHING  COMPANY 
1915 


PREFACE  TO  THE  FIRST  EDITION. 

(1872) 

It  is  not  without  hesitation  that  I  have  taken  upon  my- 
self the  editorship  of  a  work  left  avowedly  imperfect  by 
the  author,  and,  from  its  miscellaneous  and  discursive  char- 
acter, difficult  of  completion  with  due  regard  to  editorial 
limitations  by  a  less  able  hand. 

Had  the  author  lived  to  carry  out  his  purpose  he  would 
have  looked  through  his  Budget  again,  amplifying  and 
probably  rearranging  some  of  its  contents.  He  had  col- 
lected materials  for  further  illustration  of  Paradox  of  the 
kind  treated  of  in  this  book ;  and  he  meant  to  write  a 
second  part,  in  which  the  contradictions  and  inconsisten- 
cies of  orthodox  learning  would  have  been  subjected  to  the 
same  scrutiny  and  castigation  as  heterodox  ignorance  had 
already  received. 

It  will  be  seen  that  the  present  volume  contains  more 
than  the  Athenceum  Budget.  Some  of  the  additions  formed 
a  Supplement  to  the  original  articles.  These  supplementary 
paragraphs  were,  by  the  author,  placed  after  those  to  which 
they  respectively  referred,  being  distinguished  from  the  rest 
of  the  text  by  brackets.  I  have  omitted  these  brackets  as 
useless,  except  where  they  were  needed  to  indicate  subse- 
quent writing. 

Another  and  a  larger  portion  of  the  work  consists  of 
discussion  of  matters  of  contemporary  interest,  for  the 
Budget  was  in  some  degree  a  receptacle  for  the  author's 
thoughts  on  any  literary,  scientific,  or  social  question.  Hav- 


337853 


IV  A  BUDGET  OF  PARADOXES. 

ing  grown  thus  gradually  to  its  present  size,  the  book  as 
it  was  left  was  not  quite  in  a  fit  condition  for  publication, 
but  the  alterations  which  have  been  made  are  slight  and 
few,  being  in  most  cases  verbal,  and  such  as  the  sense 
absolutely  required,  or  transpositions  of  sentences  to  secure 
coherence  with  the  rest,  in  places  where  the  author,  in  his 
more  recent  insertion  of  them,  had  overlooked  the  con- 
nection in  which  they  stood.  In  no  case  has  the  meaning 
been  in  any  degree  modified  or  interfered  with. 

One  rather  large  omission  must  be  mentioned  here.  It 
is  an  account  of  the  quarrel  between  Sir  James  South  and 
Mr.  Troughton  on  the  mounting,  etc.  of  the  equatorial  tele- 
scope at  Campden  Hill.  At  some  future  time  when  the 
affair  has  passed  entirely  out  of  the  memory  of  living 
Astronomers,  the  appreciative  sketch,  which  is  omitted  in 
this  edition  of  the  Budget,  will  be  an  interesting  piece  of 
history  and  study  of  character.1 

A  very  small  portion  of  Mr.  James  Smith's  circle-squar- 
ing has  been  left  out,  with  a  still  smaller  portion  of  Mr.  De 
Morgan's  answers  to  that  Cyclometrical  Paradoxer. 

In  more  than  one  place  repetitions,  which  would  have 
disappeared  under  the  author's  revision,  have  been  allowed 
to  remain,  because  they  could  not  have  been  taken  away 
without  leaving  a  hiatus,  not  easy  to  fill  up  without  damage 
to  the  author's  meaning. 

I  give  these  explanations  in  obedience  to  the  rules  laid 
down  for  the  guidance  of  editors  at  page  15.2  If  any 
apology  for  the  fragmentary  character  of  the  book  be 
thought  necessary,  it  may  be  found  in  the  author's  own 
words  at  page  281  of  the  second  volume.3 

1  See  Mrs.  De  Morgan's  Memoir  of  Augustus  De  Morgan,  Lon- 
$tfi,  1882,  p.  61. 

"In  the  first  edition  this  reference  was  to  page  11. 

3  In  the  first  edition  this  read  "at  page  438,"  the  work  then  ap- 
pearing in  a  single  volume. 


PREFACE  TO  THE  FIRST  EDITION.  V 

The  publication  of  the  Budget  could  not  have  been  de- 
layed without  lessening  the  interest  attaching  to  the  writer's 
thoughts  upon  questions  of  our  own  day.  I  trust  that,  in- 
complete as  the  work  is  compared  with  what  it  might  have 
been,  I  shall  not  be  held  mistaken  in  giving  it  to  the  world. 
Rather  let  me  hope  that  it  will  be  welcomed  as  an  old 
friend  returning  under  great  disadvantages,  but  bringing  a 
pleasant  remembrance  of  the  amusement  which  its  weekly 
appearance  in  the  Athenaum  gave  to  both  writer  and 
reader. 

The  Paradoxes  are  dealt  with  in  chronological  order. 
This  will  be  a  guide  to  the  reader,  and  with  the  alphabet- 
ical Index  of  Names,  etc.,  will,  I  trust,  obviate  all  difficulty 
of  reference. 

SOPHIA  DE  MORGAN. 
6  MERTON  ROAD,  PRIMROSE  HILL. 


PREFACE  TO  THE  SECOND  EDITION. 

If  Mrs.  De  Morgan  felt  called  upon  to  confess  her  hesi- 
tation at  taking  upon  herself  the  labor  of  editing  these  Para- 
doxes, much  more  should  one  who  was  born  two  genera- 
tions later,  who  lives  in  another  land  and  who  was  reared 
amid  different  influences,  confess  to  the  same  feeling  when 
undertaking  to  revise  this  curious  medley.  But  when  we 
consider  the  nature  of  the  work,  the  fact  that  its  present 
rarity  deprives  so  many  readers  of  the  enjoyment  of  its  de- 
licious satire,  and  the  further  fact  that  allusions  that  were 
commonplace  a  halfcentury  ago  are  now  forgotten,  it  is 
evident  that  some  one  should  take  up  the  work  and  perform 
it  con  amore. 

Having  long  been  an  admirer  of  De  Morgan,  having 
continued  his  work  in  the  bibliography  of  early  arithmetics, 
and  having  worked  in  his  library  among  the  books  of  which 
he  was  so  fond,  it  is  possible  that  the  present  editor,  what- 
ever may  be  his  other  shortcomings,  may  undertake  the 
labor  with  as  much  of  sympathy  as  any  one  who  is  in  a 
position  to  perform  it.  With  this  thought  in  mind,  two 
definite  rules  were  laid  down  at  the  beginning  of  the  task: 
(1)  That  no  alteration  in  the  text  should  be  made,  save  in 
slightly  modernizing  spelling  and  punctuation  and  in  the 
case  of  manifest  typographical  errors ;  (2)  That  when- 
ever a  note  appeared  it  should  show  at  once  its  authorship, 
to  the  end  that  the  material  of  the  original  edition  might 
appear  intact. 

In  considering,  however,  the  unbroken  sequence  of  items 


PREFACE  TO  THE  SECOND  EDITION.  Vll 

that  form  the  Budget,  it  seems  clear  that  readers  would  be 
greatly  aided  if  the  various  leading  topics  were  separated 
in  some  convenient  manner.  After  considerable  thought  it 
was  decided  to  insert  brief  captions  from  time  to  time  that 
might  aid  the  eye  in  selecting  the  larger  subjects  of  the 
text.  In  some  .parts  of  the  work  these  could  easily  be  taken 
from  the  original  folio  heads,  but  usually  they  had  to  be 
written  anew.  While,  therefore,  the  present  editor  accepts 
the  responsibility  for  the  captions  of  the  various  subdivi- 
sions, he  has  endeavored  to  insert  them  in  harmony  with 
the  original  text. 

As  to  the  footnotes,  the  first  edition  had  only  a  few, 
some  due  to  De  Morgan  himself  and  others  to  Mrs.  De 
Morgan.  In  the  present  edition  those  due  to  the  former 
are  signed  A.  De  M.,  and  those  due  to  Mrs.  De  Morgan 
appear  with  her  initials,  S.  E.  De  M.  For  all  other  foot- 
notes the  present  editor  is  responsible.  In  preparing  them 
the  effort  has  been  made  to  elucidate  the  text  by  supplying 
such  information  as  the  casual  reader  might  wish  as  he 
passes  over  the  pages.  Hundreds  of  names  are  referred  to 
in  the  text  that  were  more  or  less  known  in  England  half 
a  century  ago,  but  are  now  forgotten  there  and  were  never 
familiar  elsewhere.  Many  books  that  were  then  current 
have  now  passed  out  of  memory,  and  much  that  agitated 
England  in  De  Morgan's  prime  seems  now  like  ancient  his- 
tory. Even  with  respect  to  well-known  names,  a  little  in- 
formation as  to  dates  and  publications  will  often  be  wel- 
come, although  the  editor  recognizes  that  it  will  quite  as 
often  be  superfluous.  In  order,  therefore,  to  derive  the 
pleasure  that  should  come  from  reading  the  Budget,  the 
reader  should  have  easy  access  to  the  information  that  the 
notes  are  intended  to  supply.  That  they  furnish  too  much 
here  and  too  little  there  is  to  be  expected.  They  are  a 
human  product,  and  if  they  fail  to  serve  their  purpose  in  all 
respects  it  is  hoped  that  this  failure  will  not  seriously  inter- 
fere with  the  reader's  pleasure. 


Vlll  A  BUDGET  OF  PARADOXES. 

In  general  the  present  editor  has  refrained  from  ex- 
pressing any  opinions  that  would  strike  a  discordant  note 
in  the  reading  of  the  text  as  De  Morgan  left  it.  The  temp- 
tation is  great  to  add  to  the  discussion  at  various  points, 
but  it  is  a  temptation  to  be  resisted.  To  furnish  such  in- 
formation as  shall  make  the  reading  more  pleasant,  rather 
than  to  attempt  to  improve  upon  one  of  the  most  delicious 
bits  of  satire  of  the  nineteenth  century,  has  been  the  editor's 
wish.  It  would  have  been  an  agreeable  task  to  review  the 
history  of  circle  squaring,  of  the  trisection  problem,  and 
of  the  duplication  of  the  cube.  This,  however,  would  be  to 
go  too  far  afield.  For  the  benefit  of  those  who  wish  to  in- 
vestigate the  subject  the  editor  can  only  refer  to  such  works 
and  articles  as  the  following:  F.  Rudio,  Archimedes,  Huy- 
gens,  Lambert,  Legendre, — mit  einer  Uebersicht  iiber  die 
Geschichte  des  Problemes  von  der  Quadrat  ur  des  Z  irk  els, 
Leipsic,  1892;  Thomas  Muir,  "Circle,"  in  the  eleventh  edi- 
tion of  the  Encyclopedia  Britannica;  the  various  histories 
of  mathematics ;  and  to  his  own  article  on  "The  Incommen- 
surability of  ?r"  in  Prof.  J.  W.  A.  Young's  Monographs  on 
Topics  of  Modern  Mathematics,  New  York,  1911. 

The  editor  wishes  to  express  his  appreciation  and  thanks 
to  Dr.  Paul  Carus,  editor  of  The  Monist  and  The  Open 
Court  for  the  opportunity  of  undertaking  this  work ;  to 
James  Earl  Russell,  LL.D.,  Dean  of  Teachers  College,  Co- 
lumbia University,  for  his  encouragement  in  its  prosecution  ; 
to  Miss  Caroline  Eustis  Seely  for  her  intelligent  and  pains- 
taking assistance  in  securing  material  for  the  notes ;  and  to 
Miss  Lydia  G.  Robinson  and  Miss  Anna  A.  Kugler  for  their 
aid  and  helpful  suggestions  in  connection  with  the  proof- 
sheets.  Without  the  generous  help  of  all  five  this  work 
would  have  been  impossible. 

DAVID  EUGENE  SMITH. 

TEACHERS  COLLEGE,  COLUMBIA  UNIVERSITY. 


INTRODUCTORY. 

IF  I  had  before  me  a  fly  and  an  elephant,  having  never  seen 
more  than  one  such  magnitude  of  either  kind ;  and  if  the 
fly  were  to  endeavor  to  persuade  me  that  he  was  larger  than 
the  elephant,  I  might  by  possibility  be  placed  in  a  difficulty. 
The  apparently  little  creature  might  use  such  arguments 
about  the  effect  of  distance,  and  might  appeal  to  such  laws 
of  sight  and  hearing  as  I,  if  unlearned  in  those  things,  might 
be  unable  wholly  to  reject.  But  if  there  were  a  thousand  flies, 
all  buzzing,  to  appearance,  about  the  great  creature ;  and,  to 
a  fly,  declaring,  each  one  for  himself,  that  he  was  bigger  than 
the  quadruped ;  and  all  giving  different  and  frequently  con- 
tradictory reasons ;  and  each  one  despising  and  opposing  the 
reasons  of  the  others — I  should  feel  quite  at  my  ease.  I 
should  certainly  say,  My  little  friends,  the  case  of  each  one 
of  you  is  destroyed  by  the  rest.  I  intend  to  show  flies  in  the 
swarm,  with  a  few  larger  animals,  for  reasons  to  be  given. 

In  every  age  of  the  world  there  has  been  an  established 
system,  which  has  been  opposed  from  time  to  time  by  iso- 
lated and  dissentient  reformers.  The  established  system  has 
sometimes  fallen,  slowly  and  gradually:  it  has  either  been 
upset  by  the  rising  influence  of  some  one  man,  or  it  has  been 
sapped  by  gradual  change  of  opinion  in  the  many. 

I  have  insisted  on  the  isolated  character  of  the  dissen- 
tients, as  an  element  of  the  a  priori  probabilities  of  the  case. 
Show  me  a  schism,  especially  a  growing  schism,  and  it  is 
another  thing.  The  homeopathists,  for  instance,  shall  be,  if 
any  one  so  think,  as  wrong  as  St.  John  Long ;  but  an  organ- 


2  A  BUDGET  OF  PARADOXES. 

ized  opposition,  supported  by  the  efforts  of  many  acting  in 
concert,  appealing  to  common  arguments  and  experience, 
with  perpetual  succession  and  a  common  seal,  as  the  Queen 
says  in  the  charter,  is,  be  the  merit  of  the  schism  what  it 
may,  a  thing  wholly  different  from  the  case  of  the  isolated 
opponent  in  the  mode  of  opposition  to  it  which  reason  points 
out. 

During  the  last  two  centuries  and  a  half ,  physical  knowl- 
edge has  been  gradually  made  to  rest  upon  a  basis  which  it 
had  not  before.  It  has  become  mathematical.  The  question 
now  is,  not  whether  this  or  that  hypothesis  is  better  or  worse 
to  the  pure  thought,  but  whether  it  accords  with  observed 
phenomena  in  those  consequences  which  can  be  shown  neces- 
sarily to  follow  from  it,  if  it  be  true.  Even  in  those  sciences 
which  are  not  yet  under  the  dominion  of  mathematics,  and 
perhaps  never  will  be,  a  working  copy  of  the  mathematical 
process  has  been  made.  This  is  not  known  to  the  followers 
of  those  sciences  who  are  not  themselves  mathematicians 
and  who  very  often  exalt  their  horns  against  the  mathemat- 
ics in  consequence.  They  might  as  well  be  squaring  the 
circle,  for  any  sense  they  show  in  this  particular. 

A  great  many  individuals,  ever  since  the  rise  of  the  math- 
ematical method,  have,  each  for  himself,  attacked  its  direct 
and  indirect  consequences.  I  shall  not  here  stop  to  point  out 
how  the  very  accuracy  of  exact  science  gives  better  aim  than 
the  preceding  state  of  things  could  give.  I  shall  call  each  of 
these  persons  a  paradoxer,  and  his  system  a  paradox.  I  use 

v  the  word  in  the  old  sense :  a  paradox  is  something  which  is 
apart  from  general  opinion,  either  in  subject-matter,  method, 
or  conclusion. 

Many  of  the  things  brought  forward  would  now  be 
called  crotchets,  which  is  the  nearest  word  we  have  to  old 
paradox.  But  there  is  this  difference,  that  by  calling  a  thing 

^  a  crotchet  we  mean  to  speak  lightly  of  it ;  which  was  not  the 
necessary  sense  of  paradox.  Thus  in  the  sixteenth  century 
many  spoke  of  the  earth's  motion  as  the  paradox  of  Coper- 


INTRODUCTORY.  O 

nicus,  who  held  the  ingenuity  of  that  theory  in  very  high 
esteem,  and  some,  I  think,  who  even  inclined  towards  it.  In 
the  seventeenth  century,  the  depravation  of  meaning  took 
place,  in  England  at  least.  Phillips  says  paradox  is  "a  thing 
which  seemeth  strange" — here  is  the  old  meaning:  after  a 
colon  he  proceeds — "and  absurd,  and  is  contrary  to  com- 
mon opinion,"  which  is  an  addition  due  to  his  own  time. 

Some  of  my  readers  are  hardly  inclined  to  think  that  the 
word  paradox  could  once  have  had  no  disparagement  in  its 
meaning;  still  less  that  persons  could  have  applied  it  to 
themselves.  I  chance  to  have  met  with  a  case  in  point 
against  them.  It  is  Spinoza's  Philosophia  Scriptures  Inter- 
pres,  Exercitatio  Paradoxa,  printed  anonymously  at  Eleu- 
theropolis,  in  1666.  This  place  was  one  of  several  cities  in 
the  clouds,  to  which  the  cuckoos  resorted  who  were  driven 
\  away  by  the  other  birds ;  that  is,  a  feigned  place  of  printing, 
adopted  by  those  who  would  have  caught  it  if  orthodoxy 
could  have  caught  them.  Thus,  in  1656,  the  works  of  So- 
cinus  could  only  be  printed  at  Irenopolis.  The  author  de- 
serves his  self-imposed  title,  as  in  the  following:1 

"Quanto  sane  satius  fuisset  illam  [Trinitatem]  pro  mys- 
terio  non  habuisse,  et  Philosophise  ope,  antequam  quod  esset 
statuerent,  secundum  verae  logices  prsecepta  quid  esset  cum 
Cl.  Kleckermanno  investigasse ;  tanto  fervore  ac  labore  in 
profundissimas  speluncas  et  obscurissimos  metaphysicarum 
speculationum  atque  fictionum  recessus  se  recipere  ut  ab  ad- 
versariorum  telis  sententiam  suam  in  tuto  collocarent.  Pro- 

1  "Just  as  it  would  surely  have  been  better  not  to  have  considered 
it  (i.e.,  the  trinity)  as  a  mystery,  and  with  Cl.  Kleckermann  to  have 
investigated  by  the  aid  of  philosophy  according  to  the  teaching  of 
true  logic  what  it  might  be,  before  they  determined  what  it  was ; 
just  so  would  it  have  been  better  to  withdraw  zealously  and  indus- 
triously into  the  deepest  caverns  and  darkest  recesses  of  metaphys- 
ical speculations  and  suppositions  in  order  to  establish  their  opinion 
beyond  danger  from  the  weapons  of  their  adversaries. ..  .Indeed  that 
great  man  so  explains  and  demonstrates  this  dogma  (although  to 
theologians  the  word  has  not  much  charm)  from  the  immovable 
foundations  of  philosophy,  that  with  but  few  changes  and  additions 
a  mind  sincerely  devoted  to  truth  can  desire  nothing  more." 


4  A  BUDGET  OF  PARADOXES. 

fecto  magnus  ille  vir. . .  .dogma  illud,  quamvis  apud  theo- 
logos  eo  nomine  non  multum  gratise  iniverit,  ita  ex  im- 
motis  Philosophise  fundamentis  explicat  ac  demonstrat,  ut 
paucis  tantum  immutatis,  atque  additis,  nihil  amplius  animus 
veritate  sincere  deditus  desiderare  possit." 

This  is  properly  paradox,  though  also  heterodox.  It 
supposes,  contrary  to  all  opinion,  orthodox  and  heterodox, 
that  philosophy  can,  with  slight  changes,  explain  the  Atha- 
nasian  doctrine  so  as  to  be  at  least  compatible  with  ortho- 
doxy. The  author  would  stand  almost  alone,  if  not  quite ; 
and  this  is  what  he  meant.  I  have  met  with  the  counter- 
paradox.  I  have  heard  it  maintained  that  the  doctrine  as 
it  stands,  in  all  its  mystery  is  a  priori  more  likely  than  any 
other  to  have  been  Revelation,  if  such  a  thing  were  to  be ; 
and  that  it  might  almost  have  been  predicted. 

After  looking  into  books  of  paradoxes  for  more  than 
thirty  years,  and  holding  conversation  with  many  persons 
who  have  written  them,  and  many  who  might  have  done  so, 
there  is  one  point  on  which  my  mind  is  fully  made  up.  The 
manner  in  which  a  paradoxer  will  show  himself,  as  to  sense 
or  nonsense,  will  not  depend  upon  what  he  maintains,  but 
upon  whether  he  has  or  has  not  made  a  sufficient  knowledge 
of  what  has  been  done  by  others,  especially  as  to  the  mode  of 
doing  it,  a  preliminary  to  inventing  knowledge  for  himself. 
That  a  little  knowledge  is  a  dangerous  thing  is  one  of  the 
most  fallacious  of  proverbs.  A  person  of  small  knowledge 
is  in  danger  of  trying  to  make  his  little  do  the  work  of  more ; 
but  a  person  without  any  is  in  more  danger  of  making  his 
no  knowledge  do  the  work  of  some.  Take  the  speculations 
on  the  tides  as  an  instance.  Persons  with  nothing  but  a 
little  geometry  have  certainly  exposed  themselves  in  their 
modes  of  objecting  to  results  which  require  the  higher  math- 
ematics to  be  known  before  an  independent  opinion  can  be 
formed  on  sufficient  grounds.  But  persons  with  no  geom- 
etry at  all  have  done  the  same  thing  much  more  completely. 


INTRODUCTORY.  D 

There  is  a  line  to  be  drawn  which  is  constantly  put  aside 
in  the  arguments  held  by  paradoxers  in  favor  of  their  right 
to  instruct  the  world.  Most  persons  must,  or  at  least  will, 
like  the  lady  in  Cadogan  Place,1  form  and  express  an  im- 
mense variety  of  opinions  on  an  immense  variety  of  sub- 
jects; and  all  persons  must  be  their  own  guides  in  many 
things.  So  far  all  is  well.  But  there  are  many  who,  in  car- 
rying the  expression  of  their  own  opinions  beyond  the  usual 
tone  of  private  conversation,  whether  they  go  no  further 
than  attempts  at  oral  proselytism,  or  whether  they  commit 
themselves  to  the  press,  do  not  reflect  that  they  have  ceased 
to  stand  upon  the  ground  on  which  their  process  is  defen- 
sible. Aspiring  to  lead  others,  they  have  never  given  them- 
selves the  fair  chance  of  being  first  led  by  other  others  into 
something  better  than  they  can  start  for  themselves  ;  and  that 
they  should  first  do  this  is  what  both  those  classes  of  others 
have  a  fair  right  to  expect.  New  knowledge,  when  to  any 
purpose,  must  come  by  contemplation  of  old  knowledge  in 
every  matter  which  concerns  thought ;  mechanical  contrivance 
sometimes,  not  very  often,  escapes  this  rule.  All  the  men  who 
are  now  called  discoverers,  in  every  matter  ruled  by  thought, 
have  been  men  versed  in  the  minds  of  their  predecessors,  and 
learned  in  what  had  been  before  them.  There  is  not  one 
exception.  I  do  not  say  that  every  man  has  made  direct 
acquantance  with  the  whole  of  his  mental  ancestry;  many 
have,  as  I  may  say,  only  known  their  grandfathers  by  the 
report  of  their  fathers.  But  even  on  this  point  it  is  remark- 
able how  many  of  the  greatest  names  in  all  departments  of 
knowledge  have  been  real  antiquaries  in  their  several  sub- 
jects. 

I  may  cite,  among  those  who  have  wrought  strongly  upon 
opinion  or  practice  in  science,  Aristotle,  Plato,  Ptolemy,  Eu- 
clid, Archimedes,  Roger  Bacon,  Copernicus,  Francis  Bacon, 
Ramus,  Tycho  Brahe,  Galileo,  Napier,  Descartes,  Leibnitz, 
Newton,  Locke.  I  take  none  but  names  known  out  of  their 
1  Mrs.  Wititterly,  in  Nicholas  Nickleby.—A.  De  M. 


6  A  BUDGET  OF   PARADOXES. 

fields  of  work;  and  all  were  learned  as  well  as  sagacious. 
I  have  chosen  my  instances:  if  any  one  will  undertake  to 
show  a  person  of  little  or  no  knowledge  who  has  established 
himself  in  a  great  matter  of  pure  thought,  let  him  bring 
forward  his  man,  and  we  shall  see. 

This  is  the  true  way  of  putting  off  those  who  plague 
others  with  their  great  discoveries.  The  first  demand  made 
should  be — Mr.  Moses,  before  I  allow  you  to  lead  me  over  the 
Red  Sea,  I  must  have  you  show  that  you  are  learned  in  all 
the  wisdom  of  the  Egyptians  upon  your  own  subject.  The 
plea  that  it  is  unlikely  that  this  or  that  unknown  person 
should  succeed  where  Newton,  etc.  have  failed,  or  should 
show  Newton,  etc.  to  be  wrong,  is  utterly  null  and  void.  It 
was  worthily  versified  by  Sylvanus  Morgan  (the  great  her- 
ald who  in  his  Sphere  of  Gentry  gave  coat  armor  to  " Gentle- 
man Jesus,"  as  he  said),  who  sang  of  Copernicus  as  follows 
(1652): 

"If  Tellus  winged  be, 

The  earth  a  motion  round; 

Then  much  deceived  are  they 

Who  nere  before  it  found. 

Solomon  was  the  wisest, 

His  wit  nere  this  attained; 

Cease,  then,  Copernicus, 

Thy  hypothesis  is  vain." 

Newton,  etc.  were  once  unknown ;  but  they  made  them- 
selves known  by  what  they  knew,  and  then  brought  forward 
what  they  could  do ;  which  I  see  is  as  good  verse  as  that  of 
Herald  Sylvanus.  The  demand  for  previous  knowledge  dis- 
poses of  twenty-nine  cases  out  of  thirty,  and  the  thirtieth 
is  worth  listening  to. 

I  have  not  set  down  Copernicus,  Galileo,  etc.  among  the 
paradoxers,  merely  because  everybody  knows  them;  if  my 
list  were  quite  complete,  they  would  have  been  in  it.  But 
the  reader  will  find  Gilbert,  the  great  precursor  of  sound 
magnetical  theory ;  and  several  others  on  whom  no  censure 
can  be  cast,  though  some  of  their  paradoxes  are  inadmissible, 


INTRODUCTORY.  / 

some  unprovoked,  and  some  capital  jokes,  true  or  false:  the 
author  of  Vestiges  of  Creation  is  an  instance.  I  expect  that 
my  old  correspondent,  General  Perronet  Thompson,  will  ad- 
mit that  his  geometry  is  part  and  parcel  of  my  plan ;  and 
also  that,  if  that  plan  embraced  politics,  he  would  claim  a 
place  for  his  Catechism  on  the  Corn  Laws,  a  work  at  one 
time  paradoxical,  but  which  had  more  to  do  with  the  aboli- 
tion of  the  bread-tax  than  Sir  Robert  Peel. 

My  intention  in  publishing  this  Budget  in  the  Athenaeum 
is  to  enable  those  who  have  been  puzzled  by  one  or  two  dis- 
coverers to  see  how  they  look  in  a  lump.  The  only  question 
is,  has  the  selection  been  fairly  made  ?  To  this  my  answer  is, 
that  no  selection  at  all  has  been  made.  The  books  are,  with- 
out exception,  those  which  I  have  in  my  own  library ;  and  I 
have  taken  all — I  mean  all  of  the  kind :  Heaven  forbid  that 
I  should  be  supposed  to  have  no  other  books !  But  I  may 
have  been  a  collector,  influenced  in  choice  by  bias?  I  an- 
swer that  I  never  have  collected  books  of  this  sort — that  is, 
I  have  never  searched  for  them,  never  made  up  my  mind  to 
look  out  for  this  book  or  that.  I  have  bought  what  happened 
to  come  in  my  way  at  show  or  auction ;  I  have  retained  what 
came  in  as  part  of  the  undescribed  portion  of  miscellaneous 
auction  lots ;  I  have  received  a  few  from  friends  who  found 
them  among  what  they  called  their  rubbish ;  and  I  have  pre- 
served books  sent  to  me  for  review.  In  not  a  few  instances 
the  books  have  been  bound  up  with  others,  unmentioned  at 
the  back ;  and  for  years  I  knew  no  more  I  had  them  than  I 
knew  I  had  Lord  Macclesfi eld's  speech  on  moving  the  change 
of  Style,  which,  after  I  had  searched  shops,  etc.  for  it  in 
vain,  I  found  had  been  reposing  on  my  own  shelves  for 
many  years,  at  the  end  of  a  summary  of  Leibnitz's  philos- 
ophy. Consequently,  I  may  positively  affirm  that  the  fol- 
lowing list  is  formed  by  accident  and  circumstance  alone, 
and  that  it  truly  represents  the  casualties  of  about  a  third 
of  a  century.  For  instance,  the  large  proportion  of  works 


g  A  BUDGET  OF  PARADOXES. 

on  the  quadrature  of  the  circle  is  not  my  doing:  it  is  the 
natural  share  of  this  subject  in  the  actual  run  of  events. 

[I  keep  to  my  plan  of  inserting  only  such  books  as  I  pos- 
sessed in  1863,  except  by  casual  notice  in  aid  of  my  remarks. 
I  have  found  several  books  on  my  shelves  which  ought  to 
have  been  inserted.  These  have  their  titles  set  out  at  the 
commencement  of  their  articles,  in  leading  paragraphs ;  the 
casuals  are  without  this  formality.1] 

Before  proceeding  to  open  the  Budget,  I  say  something 
on  my  personal  knowledge  of  the  class  of  discoverers  who 
square  the  circle,  upset  Newton,  etc.  I  suspect  I  know  more 
of  the  English  class  than  any  man  in  Britain.  I  never  kept 
any  reckoning ;  but  I  know  that  one  year  with  another — and 
less  of  late  years  than  in  earlier  time — I  have  talked  to  more 
than  five  in  each  year,  giving  more  than  a  hundred  and  fifty 
specimens.  Of  this  I  am  sure,  that  it  is  my  own  fault  if  they 
have  not  been  a  thousand.  Nobody  knows  how  they  swarm, 
except  those  to  whom  they  naturally  resort.  They  are  in  all 
ranks  and  occupations,  of  all  ages  and  characters.  They 
are  very  earnest  people,  and  their  purpose  is  bona  fide  the 
dissemination  of  their  paradoxes.  A  great  many — the  mass, 
indeed — are  illiterate,  and  a  great  many  waste  their  means, 
and  are  in  or  approaching  penury.  But  I  must  say  that 
never,  in  any  one  instance,  has  the  quadrature  of  the  circle, 
or  the  like,  been  made  a  pretext  for  begging;  even  to  be 
asked  to  purchase  a  book  is  of  the  very  rarest  occurrence — 
it  has  happened,  and  that  is  all. 

These  discoverers  despise  one  another :  if  there  were  the 
concert  among  them  which  there  is  among  foreign  mendi- 
cants, a  man  who  admitted  one  to  a  conference  would  be 
plagued  to  death.  I  once  gave  something  to  a  very  genteel 
French  applicant,  who  overtook  me  in  the  street,  at  my  own 
door,  saying  he  had  picked  up  my  handkerchief :  whether  he 
picked  it  up  in  my  pocket  for  an  introduction,  I  know  not. 

*The  brackets  mean  that  the  paragraph  is  substantially  from 
some  one  of  the  Athen&um  Supplements. — S.  E.  De  M. 


INTRODUCTORY. 

But  that  day  week  came  another  Frenchman  to  my  house, 
and  that  day  fortnight  a  French  lady ;  both  failed,  and  I  had 
no  more  trouble.  The  same  thing  happened  with  Poles.  It 
is  not  so  with  circle-squarers,  etc.:  they  know  nothing  of 
each  other.  Some  will  read  this  list,  and  will  say  I  am  right 
enough,  generally  speaking,  but  that  there  is  an  exception, 
if  I  could  but  see  it. 

I  do  not  mean,  by  my  confession  of  the  manner  in  which 
I  have  sinned  against  the  twenty-four  hours,  to  hold  myself 
out  as  accessible  to  personal  explanation  of  new  plans.  Quite 
the  contrary :  I  consider  myself  as  having  made  my  report, 
and  being  discharged  from  further  attendance  on  the  sub- 
ject. I  will  not,  from  henceforward,  talk  to  any  squarer  of 
the  circle,  trisector  of  the  angle,  duplicator  of  the  cube,  con- 
structor of  perpetual  motion,  subverter  of  gravitation,  stag- 
nator  of  the  earth,  builder  of  the  universe,  etc.  I  will  receive 
any  writings  or  books  which  require  no  answer,  and  read 
them  when  I  please :  I  will  certainly  preserve  them — this  list 
may  be  enlarged  at  some  future  time. 

There  are  three  subjects  which  I  have  hardly  anything 
upon ;  astrology,  mechanism,  and  the  infallible  way  of  win- 
ning at  play.  I  have  never  cared  to  preserve  astrology.  The 
mechanists  make  models,  and  not  books.  The  infallible  win- 
ners— though  I  have  seen  a  few — think  their  secret  too  val- 
uable, and  prefer  mutare  quadrata  rotundis — to  turn  dice 
into  coin — at  the  gaming-house:  verily  they  have  their  re- 
ward. 

I  shall  now  select,  to  the  mystic  number  seven,  instances 
of  my  personal  knowledge  of  those  who  think  they  have 
discovered,  in  illustration  of  as  many  misconceptions. 

1.  Attempt  by  help  of  the  old  philosophy,  the  discoverer 
not  being  in  possession  of  modern  knowledge.  A  poor  school- 
master, in  rags,  introduced  himself  to  a  scientific  friend  with 
whom  I  was  talking,  and  announced  that  he  had  found  out 
the  composition  of  the  sun.  "How  was  that  done?" — "By 
consideration  of  the  four  elements."— "What  are  they?"— 


10  A  BUDGET  OF  PARADOXES. 

"Of  course,  fire,  air,  earth,  and  water."— "Did  you  not  know 
that  air,  earth,  and  water,  have  long  been  known  to  be  no 
elements  at  all,  but  compounds?" — "What  do  you  mean, 
sir?  Who  ever  heard  of  such  a 'thing?" 

2.  The  notion  that  difficulties  are  enigmas,  to  be  over- 
come in  a  moment  by  a  lucky  thought.  A  nobleman  of  very 
high  rank,  now  long  dead,  read  an  article  by  me  on  the 
quadrature,  in  an  early  number  of  the  Penny  Magazine.  He 
had,  I  suppose,  school  recollections  of  geometry.     He  put 
pencil  to  paper,  drew  a  circle,  and  constructed  what  seemed 
likely  to  answer,  and,  indeed,  was — as  he  said — certain,  if 
only  this  bit  were  equal  to  that ;  which  of  course  it  was  not. 
He  forwarded  his  diagram  to  the  Secretary  of  the  Diffusion 
Society,  to  be  handed  to  the  author  of  the  article,  in  case  the 
difficulty  should  happen  to  be  therein  overcome. 

3.  Discovery  at  all  hazards,  to  get  on  in  the  world.  Thirty 
years  ago,  an  officer  of  rank,  just  come  from  foreign  service, 
and  trying  for  a  decoration  from  the  Crown,  found  that  his 
claims  were  of  doubtful  amount,  and  was  told  by  a  friend 
that  so  and  so,  who  had  got  the  order,  had  the  additional 
claim  of  scientific  distinction.  Now  this  officer,  while  abroad, 
had  bethought  himself  one  day,  that  there  really  could  be 
no  difficulty  in  finding  the  circumference  of  a  circle:  if  a 
circle  were  rolled  upon  a  straight  line  until  the  undermost 
point  came  undermost  again,  there  would  be  the  straight 
line  equal  to  the  circle.    He  came  to  me,  saying  that  he  did 
not  feel  equal  to  the  statement  of  his  claim  in  this  respect, 

,but  that  if  some  clever  fellow  would  put  the  thing  in  a 
proper  light,  he  thought  his  affair  might  be  managed.  I  was 
clever  enough  to  put  the  thing  in  a  proper  light  to  himself, 
to  this  extent  at  least,  that,  though  perhaps  they  were  wrong, 
the  advisers  of  the  Crown  would  never  put  the  letters  K.C.B. 
to  such  a  circle  as  his. 

4.  The  notion  that  mathematicians  cannot  find  the  circle 
for  common  purposes.    A  working  man  measured  the  alti- 
tude of  a  cylinder  accurately,  and — I  think  the  process  of 


INTRODUCTORY.  1 1 

Archimedes  was  one  of  his  proceedings — found  its  bulk. 
He  then  calculated  the  ratio  of  the  circumference  to  the 
diameter,  and  found  it  answered  very  well  on  other  modes 
of  trial.  His  result  was  about  3 . 14.  He  came  to  London, 
and  somebody  sent  him  to  me.  Like  many  others  of  his  pur- 
suit, he  seemed  to  have  turned  the  whole  force  of  his  mind 
upon  one  of  his  points,  on  which  alone  he  would  be  open  to 
refutation.  He  had  read  some  of  Kater's  experiments,  and 
had  got  the  Act  of  1825  on  weights  and  measures.  Say  what 
I  would,  he  had  for  a  long  time  but  one  answer — "Sir !  I  go 
upon  Captain  Kater  and  the  Act  of  Parliament."  But  I 
fixed  him  at  last.  I  happened  to  have  on  the  table  a  proof- 
sheet  of  the  Astronomical  Memoirs,  in  which  were  a  large 
number  of  observed  places  of  the  planets  compared  with 
prediction,  and  asked  him  whether  it  could  be  possible  that 
persons  who  did  not  know  the  circle  better  than  he  had 
found  it  could  make  the  calculations,  of  which  I  gave  him 
a  notion,  so  accurately?  He  was  perfectly  astonished,  and 
took  the  titles  of  some  books  which  he  said  he  would  read. 

5.  Application  for  the  reward  from  abroad.  Many  years 
ago,  about  twenty-eight,  I  think,  a  Jesuit  came  from  South 
America,  with  a  quadrature,  and  a  cutting  from  a  news- 
paper, announcing  that  a  reward  was  ready  for  the  discovery 
in  England.  On  this  evidence  he  came  over.  After  satis- 
fying him  that  nothing  had  ever  been  offered  here,  I  dis- 
cussed his  quadrature,  which  was  of  no  use.  I  succeeded 
better  when  I  told  him  of  Richard  White,  also  a  Jesuit,  and 
author  of  a  quadrature  published  before  1648,  under  the 
name  of  Chryscespis,  of  which  I  can  give  no  account,  having 
never  seen  it.  This  White  (Albius)  is  the  only  quadrator 
who  was  ever  convinced  of  his  error.  My  Jesuit  was  struck 
by  the  instance,  and  promised  to  read  more  geometry — he 
was  no  Clavius — before  he  published  his  book.  He  relapsed, 
however,  for  I  saw  his  book  advertised  in  a  few  days.  I 
may  say,  as  sufficient  proof  of  my  being  no  collector,  that  I 
had  not  the  curiosity  to  buy  his  book;  and  my  friend  the 


12  A  BUDGET  OF   PARADOXES. 

Jesuit  did  not  send  me  a  copy,  which  he  ought  to  have  done, 
after  the  hour  I  had  given  him. 

6.  Application  for  the  reward  at  home.  An  agricultural 
laborer  squared  the  circle,  and  brought  the  proceeds  to  Lon- 
don. He  left  his  papers  with  me,  one  of  which  was  the  copy 
of  a  letter  to  the  Lord  Chancellor,  desiring  his  Lordship  to 
hand  over  forthwith  100,000  pounds,  the  amount  of  the 
alleged  offer  of  reward.  He  did  not  go  quite  so  far  as  M. 
de  Vausenville,  who,  I  think  in  1778,  brought  an  action 
against  the  Academy  of  Sciences  to  recover  a  reward  to 
which  he  held  himself  entitled.  I  returned  the  papers,  with 
a  note,  stating  that  he  had  not  the  knowledge  requisite  to 
see  in  what  the  problem  consisted.  I  got  for  answer  a  letter 
in  which  I  was  told  that  a  person  who  could  not  see  that  he 
had  done  the  thing  should  "change  his  business,  and  appro- 
priate his  time  and  attention  to  a  Sunday-school,  to  learn 
what  he  could,  and  keep  the  litle  children  from  durting  their 
close"  I  also  received  a  letter  from  a  friend  of  the  quad- 
rator,  informing  me  that  I  knew  his  friend  had  succeeded, 
and  had  been  heard  to  say  so.  These  letters  were  printed — 
without  the  names  of  the  writers — for  the  amusement  of  the 
readers  of  Notes  and  Queries,  First  Series,  xii.  57,  and  they 
will  appear  again  in  the  sequel. 

[There  are  many  who  have  such  a  deep  respect  for  any 
attempt  at  thought  that  they  are  shocked  at  ridicule  even  of 
those  who  have  made  themselves  conspicuous  by  pretending 
to  lead  the  world  in  matters  which  they  have  not  studied. 
Among  my  anonyms  is  a  gentleman  who  is  angry  at  my 
treatment  of  the  "poor  but  thoughtful"  man  who  is  described 
in  my  introduction  as  recommending  me  to  go  to  a  Sunday- 
school  because  I  informed  him  that  he  did  not  know  in  what 
the  difficulty  of  quadrature  consisted.  My  impugner  quite 
forgets  that  this  man's  "thoughtfulness"  chiefly  consisted 
in  his  demanding  a  hundred  thousand  pounds  from  the  Lord 
Chancellor  for  his  discovery ;  and  I  may  add,  that  his  great- 
est stretch  of  invention  was  finding  out  that  "the  clergy" 


INTRODUCTORY.  13 

were  the  means  of  his  modest  request  being  unnoticed.  I 
mention  this  letter  because  it  affords  occasion  to  note  a  very 
common  error,  namely,  that  men  unread  in  their  subjects 
have,  by  natural  wisdom,  been  great  benefactors  of  man- 
kind. My  critic  says,  "Shakspeare,  whom  the  Pror  (sic) 
may  admit  to  be  a  wisish  man,  though  an  object  of  con- 
tempt as  to  learning. ..."  Shakespeare  an  object  of  con- 
tempt as  to  learning!  Though  not  myself  a  thoroughgoing 
Shakespearean — and  adopting  the  first  half  of  the  opinion 
given  by  George  III,  "What!  is  there  not  sad  stuff?  only 
one  must  not  say  so" — I  am  strongly  of  opinion  that  he  throws 
out  the  masonic  signs  of  learning  in  almost  every  scene,  to 
all  who  know  what  they  are.  And  this  over  and  above  every 
kind  of  direct  evidence.  First,  foremost,  and  enough,  the 
evidence  of  Ben  Jonson  that  he  had  "little  Latin  and  less 
Greek" ;  then  Shakespeare  had  as  much  Greek  as  Jonson 
would  call  some,  even  when  he  was  depreciating.  To  have 
any  Greek  at  all  was  in  those  days  exceptional.  In  Shake- 
speare's youth  St.  Paul's  and  Merchant  Taylor's  schools 
were  to  have  masters  learned  in  good  and  clean  Latin  litera- 
ture, and  also  in  Greek  if  such  may  be  gotten.  When  Jonson* 
spoke  as  above,  he  intended  to  put  Shakespeare  low  among 
the  learned,  but  not  out  of  their  pale ;  and  he  spoke  as  a  rival 
dramatist,  who  was  proud  of  his  own  learned  sock ;  and  it 
may  be  a  subject  of  inquiry  how  much  Latin  he  would  call 
little.  If  Shakespeare's  learning  on  certain  points  be  very 
much  less  visible  than  Jonson's,  it  is  partly  because  Shake- 
speare's writings  hold  it  in  chemical  combination,  Jonson's 
in  mechanical  aggregation.] 

7.  An  elderly  man  came  to  me  to  show  me  how  the  uni- 
verse was  created.  There  was  one  molecule,  which  by  vibra- 
tion became  —  Heaven  knows  how!  —  the  Sun.  Further 
vibration  produced  Mercury,  and  so  on.  I  suspect  the  nebu- 
lar hypothesis  had  got  into  the  poor  man's  head  by  reading, 
in  some  singular  mixture  with  what  it  found  there.  Some 
modifications  of  vibration  gave  heat,  electricity,  etc.  I  lis- 


14  A  BUDGET  OF  PARADOXES. 

tened  until  my  informant  ceased  to  vibrate — which  is  always 
the  shortest  way — and  then  said,  "Our  knowledge  of  elastic 
fluids  is  imperfect."  "Sir!"  said  he,  "I  see  you  perceive 
the  truth  of  what  I  have  said,  and  I  will  reward  your  atten- 
tion by  telling  you  what  I  seldom  disclose,  never,  except  to 
those  who  can  receive  my  theory — the  little  molecule  whose 
vibrations  have  given  rise  to  our  solar  system  is  the  Logos 
of  St.  John's  Gospel!"  He  went  away  to  Dr.  Lardner, 
who  would  not  go  into  the  solar  system  at  all — the  first 
molecule  settled  the  question.  So  hard  upon  poor  discov- 
erers are  men  of  science  who  are  not  antiquaries  in  their 
subject!  On  leaving,  he  said,  "Sir,  Mr.  De  Morgan  re- 
ceived me  in  a  very  different  way!  he  heard  me  attentively, 
and  I  left  him  perfectly  satisfied  of  the  truth  of  my  system." 
I  have  had  much  reason  to  think  that  many  discoverers,  of 
all  classes,  believe  they  have  convinced  every  one  who  is 
not  peremptory  to  the  verge  of  incivility. 

My  list  is  given  in  chronological  order.  My  readers  will 
understand  that  my  general  expressions,  where  slighting 
or  contemptuous,  refer  to  the  ignorant,  who  teach  before 
they  have  learned.  In  every  instance,  those  of  whom  I  am 
able  to  speak  with  respect,  whether  as  right  or  wrong,  have 
sought  knowledge  in  the  subject  they  were  to  handle  before 
they  completed  their  speculations.  I  shall  further  illustrate 
this  at  the  conclusion  of  my  list 

Before  I  begin  the  list,  I  give  prominence  to  the  follow- 
ing letter,  addressed  by  me  to  the  Correspondent  of  October 
28,  1865.  Some  of  my  paradoxers  attribute  to  me  articles 
in  this  or  that  journal ;  and  others  may  think — I  know  some 
do  think — they  know  me  as  the  writer  of  reviews  of  some 
of  the  very  books  noticed  here.  The  following  remarks  will 
explain  the  way  in  which  they  may  be  right,  and  in  which 
they  may  be  wrong. 


INTRODUCTORY. 


THE  EDITORIAL  SYSTEM. 


15 


"SiR, — I  have  reason  to  think  that  many  persons  have  a 
very  inaccurate  notion  of  the  Editorial  System.  What  I  call 
by  this  name  hc.s  grown  up  in  the  last  centenary — a  word  I 
may  use  to  signify  the  hundred  years  now  ending,  and  to 
avoid  the  ambiguity  of  century.  It  cannot  conveniently  be 
explained  by  editors  themselves,  and  edited  journals  gen- 
erally do  not  like  to  say  much  about  it.  In  your  paper 
perhaps,  in  which  editorial  duties  differ  somewhat  from 
those  of  ordinary  journals,  the  common  system  may  be 
freely  spoken  of. 

"When  a  reviewed  author,  as  very  often  happens,  writes 
to  the  editor  of  the  reviewing  journal  to  complain  of  what 
has  been  said  of  him,  he  frequently — even  more  often  than 
not — complains  of  'your  reviewer/  He  sometimes  presumes 
that  'you'  have,  'through  inadvertence'  in  this  instance,  'al- 
lowed some  incompetent  person  to  lower  the  character  of 
your  usually  accurate  pages.'  Sometimes  he  talks  of  'your 
scribe,'  and,  in  extreme  cases,  even  of  'your  hack.'  All  this 
shows  perfect  ignorance  of  the  journal  system,  except  where 
it  is  done  under  the  notion  of  letting  the  editor  down  easy. 
But  the  editor  never  accepts  the  mercy. 

"All  that  is  in  a  journal,  except  what  is  marked  as  from 
a  correspondent,  either  by  the  editor  himself  or  by  the  cor- 
respondent's real  or  fictitious  signature,  is  published  entirely 
on  editorial  responsibility,  as  much  as  if  the  editor  had  writ- 
ten it  himself.  The  editor,  therefore,  may  claim,  and  does 
claim  and  exercise,  unlimited  right  of  omission,  addition, 
and  alteration.  This  is  so  well  understood  that  the  editor 
performs  his  last  function  on  the  last  revise  without  the 
'contributor'  knowing  what  is  done.  The  word  contributor 
is  the  proper  one ;  it  implies  that  he  furnishes  materials  with- 
out stating  what  he  furnishes  or  how  much  of  it  is  accepted, 
or  whether  he  be  the  only  contributor.  All  this  applies  both 
to  political  and  literary  journals.  No  editor  acknowledges 


16  A  BUDGET  OF  PARADOXES. 

the  right  of  a  contributor  to  withdraw  an  article,  if  he  should 
find  alterations  in  the  proof  sent  to  him  for  correction  which 
would  make  him  wish  that  the  article  should  not  appear.  If 
the  demand  for  suppression  were  made — I  say  nothing  about 
what  might  be  granted  to  request — the  answer  would  be,  It 
is  not  your  article,  but  mine ;  I  have  all  the  responsibility ;  if 
it  should  contain  a  libel,  I  could  not  give  you  up,  even  at 
your  own  desire.  You  have  furnished  me  with  materials, 
on  the  known  and  common  understanding  that  I  was  to  use 
them  at  my  discretion,  and  you  have  no  right  to  impede  my 
operations  by  making  the  appearance  of  the  article  depend 
on  your  approbation  of  my  use  of  your  materials/ 

"There  is  something  to  be  said  for  this  system,  and  some- 
thing against  it — I  mean  simply  on  its  own  merits.  But  the 
all-conquering  argument  in  its  favor  is,  that  the  only  prac- 
ticable alternative  is  the  modern  French  plan  of  no  articles 
without  the  signature  of  the  writers.  I  need  not  discuss  this 
plan ;  there  is  no  collective  party  in  favor  of  it.  Some  may 
think  it  is  not  the  only  alternative ;  they  have  not  produced 
any  intermediate  proposal  in  which  any  dozen  of  persons  have 
concurred.  Many  will  say,  Is  not  all  this,  though  perfectly 
correct,  well  known  to  be  matter  of  form?  Is  it  not  prac- 
tically the  course  of  events  that  an  engaged  contributor 
writes  the  article,  and  sends  it  to  the  editor,  who  admits  it 
as  written — substantially,  at  least?  And  is  it  not  often  very 
well  known,  by  style  and  in  other  ways,  who  it  was  wrote 
the  article?  This  system  is  matter  of  form  just  as  much 
as  loaded  pistols  are  matter  of  form  so  long  as  the  wearer 
is  not  assailed ;  but  matter  of  form  takes  the  form  of  matter 
in  the  pulling  of  a  trigger,  so  soon  as  the  need  arises.  Edi- 
tors and  contributors  who  can  work  together  find  each  other, 
out  by  elective  affinity,  so  that  the  common  run  of  events 
settles  down  into  most  articles  appearing  much  as  they  are 
written.  And  there  are  two  safety-valves ;  that  is,  when 
judicious  persons  come  together.  In  the  first  place,  the  edi- 
tor himself,  when  he  has  selected  his  contributor,  feels  that 


INTRODUCTORY.  17 

the  contributor  is  likely  to  know  his  business  better  than  an 
editor  can  teach  him ;  in  fact,  it  is  on  that  principle  that  the 
selection  is  made.  But  he  feels  that  he  is  more  competent 
than  the  writer  to  judge  questions  of  strength  and  of  tone, 
especially  when  the  general  purpose  of  the  journal  is  con- 
sidered, of  which  the  editor  is  the  judge  without  appeal.  An 
editor  who  meddles  with  substantive  matter  is  likely  to  be 
wrong,  even  when  he  knows  the  subject;  but  one  who  prunes 
what  he  deems  excess,  is  likely  to  be  right,  even  when  he 
does  not  know  the  subject.  In  the  second  place,  a  contrib- 
utor knows  that  he  is  supplying  an  editor,  and  learns,  with- 
out suppressing  truth  or  suggesting  falsehood,  to  make  the 
tone  of  his  communications  suit  the  periodical  in  which  they 
are  to  appear.  Hence  it  very  often  arises  that  a  reviewed 
author,  who  thinks  he  knows  the  name  of  his  reviewer,  and 
proclaims  it  with  expressions  of  dissatisfaction,  is  only 
wrong  in  supposing  that  his  critic  has  given  all  his  mind. 
It  has  happened  to  myself  more  than  once,  to  be  announced 
as  the  author  of  articles  which  I  could  not  have  signed,  be- 
cause they  did  not  go  far  enough  to  warrant  my  affixing  my 
name  to  them  as  to  a  sufficient  expression  of  my  own  opin- 
ion. 

"There  are  two  other  ways  in  which  a  reviewed  author 
may  be  wrong  about  his  critic.  An  editor  frequently  makes 
slight  insertions  or  omissions — I  mean  slight  in  quantity  of 
type — as  he  goes  over  the  last  proof ;  this  he  does  in  a  com- 
parative hurry,  and  it  may  chance  that  he  does  not  know  the 
full  sting  of  his  little  alteration.  The  very  bit  which  the 
writer  of  the  book  most  complains  of  may  not  have  been  seen 
by  the  person  who  is  called  the  writer  of  the  article  until 
after  the  appearance  of  the  journal ;  nay,  if  he  be  one  of  those 
— few,  I  daresay — who  do  not  read  their  own  articles,  may 
never  have  been  seen  by  him  at  all.  Possibly,  the  insertion 
or  omission  would  not  have  been  made  if  the  editor  could 
have  had  one  minute's  conversation  with  his  contributor. 
Sometimes  it  actually  contradicts  something  which  is  al- 


18  'A  BUDGET  OF  PARADOXES. 

lowed  to  remain  in  another  part  of  the  article;  and  some- 
times, especially  in  the  case  of  omission,  it  renders  other 
parts  of  the  article  unintelligible.  These  are  disadvantages 
of  the  system,  and  a  judicious  editor  is  not  very  free  with 
his  unus  et  alter  pannus.  Next,  readers  in  general,  when 
they  see  the  pages  of  a  journal  with  the  articles  so  nicely 
fitting,  and  so  many  ending  with  the  page  or  column,  have 
very  little  notion  of  the  cutting  and  carving  which  goes  to 
the  process.  At  the  very  last  moment  arises  the  necessity 
of  some  trimming  of  this  kind ;  and  the  editor,  who  would 
gladly  call  the  writer  to  counsel  if  he  could,  is  obliged  to 
strike  out  ten  or  twelve  lines.  He  must  do  his  best,  but  it 
may  chance  that  the  omission  selected  would  take  from  the 
writer  the  power  of  owning  the  article.  A  few  years  ago, 
an  able  Opponent  of  mine  wrote  to  a  journal  some  criticisms 
upon  an  article  which  he  expressly  attributed  to  me.  I  re- 
plied as  if  I  were  the  writer,  which,  in  a  sense,  I  was.  But 
if  any  one  had  required  of  me  an  unmodified  'Yes'  or  'No' 
to  the  question  whether  I  wrote  the  article,  I  must,  of  two 
falsehoods,  have  chosen  'No':  for  certain  omissions,  dictated 
by  the  necessities  of  space  and  time,  would  have  amounted, 
had  my  signature  been  affixed,  to  a  silent  surrender  of  points 
which,  in  my  own  character,  I  must  have  strongly  insisted 
on,  unless  I  had  chosen  to  admit  certain  inferences  against 
what  I  had  previously  published  in  my  own  name.  I  may 
here  add  that  the  forms  of  journalism  obliged  me  in  this 
case  to  remind  my  opponent  that  it  could  not  be  permitted  to 
me,  in  that  journal,  either  to  acknowledge  or  deny  the 
authorship  of  the  articles.  The  cautions  derived  from  the 
above  remarks  are  particularly  wanted  with  reference  to  the 
editorial  comments  upon  letters  of  complaint.  There  is  often 
no  time  to  send  these  letters  to  the  contributor,  and  even 
when  this  can  be  done,  an  editor  is — and  very  properly — 
never  of  so  editorial  a  mind  as  when  he  is  revising  the  com- 
ments of  a  contributor  upon  an  assailant  of  the  article.  He 
is  then  in  a  better  position  as  to  information,  and  a  more 


INTRODUCTORY.  19 

critical  position  as  to  responsibility.  Of  course,  an  editor 
never  meddles,  except  under  notice,  with  the  letter  of  a  cor- 
respondent, whether  of  a  complainant,  of  a  casual  informant, 
or  of  a  contributor  who  sees  reason  to  become  a  correspond- 
ent. Omissions  must  sometimes  be  made  when  a  grievance 
is  too  highly  spiced.  It  did  once  happen  to  me  that  a  wag- 
gish editor  made  an  insertion  without  notice  in  a  letter 
signed  by  me  with  some  fiction,  which  insertion  contained 
the  name  of  a  friend  of  mine,  with  a  satire  which  I  did 
not  believe,  and  should  not  have  written  if  I  had.  To  my 
strong  rebuke,  he  replied —  'I  know  it  was  very  wrong ;  but 
human  nature  could  not  resist/  But  this  was  the  only  occa- 
sion on  which  such  a  thing  ever  happened  to  me. 

"I  daresay  what  I  have  written  may  give  some  of  your 
readers  to  understand  some  of  the  pericula  et  commoda  of 
modern  journalism.  I  have  known  men  of  deep  learning 
and  science  as  ignorant  of  the  prevailing  system  as  any  un- 
educated reader  of  a  newspaper  in  a  country  town.  I  may 
perhaps  induce  some  writers  not  to  be  too  sure  about 
this,  that,  or  the  other  person.  They  may  detect  their  re- 
viewer, and  they  may  be  safe  in  attributing  to  him  the  gen- 
eral matter  and  tone  of  the  article.  But  about  one  and 
another  point,  especially  if  it  be  a  short  and  stinging  point, 
they  may  very  easily  chance  to  be  wrong.  It  has  happened 
to  myself,  and  within  a  few  weeks  to  publication,  to  be 
wrong  in  two  ways  in  reading  a  past  article — to  attribute 
to  editorial  insertion  what  was  really  my  own,  and  to  at- 
tribute to  myself  what  was  really  editorial  insertion." 

What  is  a  man  to  do  who  is  asked  whether  he  wrote  an 
article?  He  may,  of  course,  refuse  to  answer;  which  is  re- 
garded as  an  admission.  He  may  say,  as  Swift  did  to  Ser- 
jeant Bettesworth,  "Sir,  when  I  was  a  young  man,  a  friend 
of  mine  advised  me,  whenever  I  was  asked  whether  I  had 
written  a  certain  paper,  to  deny  it;  and  I  accordingly  tell 
you  that  I  did  not  write  it."  He  may  say,  as  I  often  do, 


20  A   BUDGET  OF  PARADOXES. 

when  charged  with  having  invented  a  joke,  story,  or  epi- 
gram, "I  want  all  the  credit  I  can  get,  and  therefore  I  always 
acknowledge  all  that  is  attributed  to  me, truly  or  not;  the 
story,  etc.  is  mine."  But  for  serious  earnest,  in  the  matter  of 
imputed  criticism,  the  answer  may  be,  "The  article  was  of 
my  material,  but  the  editor  has  not  let  it  stand  as  I  gave  it ; 
I  cannot  own  it  as  a  whole."  He  may  then  refuse  to  be 
particular  as  to  the  amount  of  the  editor's  interference.  Of 
this  there  are  two  extreme  cases.  The  editor  may  have  ex- 
punged nothing  but  a  qualifying  adverb.  Or  he  may  have 
done  as  follows.  We  all  remember  the  account  of  Adam 
which  satirizes  woman,  but  eulogizes  her  if  every  second  and 
third  line  be  transposed.  As  in : 

"Adam  could  find  no  solid  peace 

When  Eve  was  given  him  for  a  mate, 
Till  he  beheld  a  woman's  face, 
Adam  was  in  a  happy  state." 

If  this  had  been  the  article,  and  a  gallant  editor  had  made 
the  transpositions,  the  author  could  not  with  truth  acknowl- 
edge. If  the  alteration  were  only  an  omitted  adverb,  or  a 
few  things  of  the  sort,  the  author  could  not  with  truth  deny. 
In  all  that  comes  between,  every  man  must  be  his  own  casuist. 
I  stared,  when  I  was  a  boy,  to  hear  grave  persons  approve 
of  Sir  Walter  Scott's  downright  denial  that  he  was  the 
author  of  Waverley,  in  answer  to  the  Prince  Regent's  down- 
right question.  If  I  remember  rightly,  Samuel  Johnson 
would  have  approved  of  the  same  course. 

It  is  known  that,  whatever  the  law  gives,  it  also  gives 
all  that  is  necessary  to  full  possession;  thus  a  man  whose 
land  is  environed  by  land  of  others  has  a  right  of  way 
over  the  land  of  these  others.  By  analogy,  it  is  argued  that 
when  a  man  has  a  right  to  his  secret,  he  has  a  right  to  all 
that  is  necessary  to  keep  it,  and  that  is  not  unlawful.  If, 
then,  he  can  only  keep  his  secret  by  denial,  he  has  a  right  to 
denial.  This  I  admit  to  be  an  answer  against  all  men  except 
the  denier  himself ;  if  conscience  and  self-respect  'will  allow 


INTRODUCTORY.  21 

it,  no  one  can  impeach  it.  But  the  question  cannot  be  solved 
on  a  case.  That  question  is,  A  lie,  is  it  malum  in  se,  without 
reference  to  meaning  and  circumstances  ?  This  is  a  question 
with  two  sides  to  it.  Cases  may  be  invented  in  which  a  lie 
is  the  only  way  of  preventing  a  murder,  or  in  which  a  lie 
may  otherwise  save  a  life.  In  these  cases  it  is  difficult  to 
acquit,  and  almost  impossible  to  blame;  discretion  intro- 
duced, the  line  becomes  very  hard  to  draw. 

I  know  but  one  work  which  has  precisely — as  at  first 
appears — the  character  and  object  of  my  Budget.  It  is  the 
Review  of  the  Works  of  the  Royal  Society  of  London,  by 
Sir  John  Hill,  M.D.  (1751  and  1780,  4to.).  This  man 
offended  many :  the  Royal  Society,  by  his  work,  the  medical 
profession,  by  inventing  and  selling  extra-pharmacopoeian 
doses ;  Garrick,  by  resenting  the  rejection  of  a  play.  So 
Garrick  wrote: 

"For  physic  and  farces  his  equal  there  scarce  is ; 
His  farces  are  physic ;  his  physic  a  farce  is." 

I  have  fired  at  the  Royal  Society  and  at  the  medical  pro- 
fession, but  I  have  given  a  wide  berth  to  the  drama  and  its 
wits ;  so  there  is  no  epigram  out  against  me,  as  yet.  He  was 
very  able  and  very  eccentric.  Dr.  Thomson  (Hist.  Roy. 
Soc.)  says  he  has  no  humor,  but  Dr.  Thomson  was  a  man 
who  never  would  have  discovered  humor. 

Mr.  Weld  (Hist.  Roy.  Soc.)  backs  Dr.  Thomson,  but 
with  a  remarkable  addition.  Having  followed  his  prede- 
cessor in  observing  that  the  Transactions  in  Martin  Folkes's 
time  have  an  unusual  proportion  of  trifling  and  puerile  pa- 
pers, he  says  that  Hill's  book  is  a  poor  attempt  at  humor, 
and  glaringly  exhibits  the  feelings  of  a  disappointed  man. 
It  is  probable,  he  adds,  that  the  points  told  with  some  effect 
on  the  Society ;  for  shortly  after  its  publication  the  Trans- 
actions possess  a  much  higher  scientific  value. 

I  copy  an  account  which  I  gave  elsewhere. 

When  the  Royal  Society  was  founded,  the  Fellows  set 


22  A  BUDGET  OF  PARADOXES. 

to  work  to  prove  all  things,  that  they  might  hold  fast  that 
which  was  good.  They  bent  themselves  to  the  question 
whether  sprats  were  young  herrings.  They  made  a  circle 
of  the  powder  of  a  unicorn's  horn,  and  set  a  spider  in  the 
middle  of  it;  "but  it  immediately  ran  out."  They  tried 
several  times,  and  the  spider  "once  made  some  stay  in  the 
powder."  They  inquired  into  Kenelm  Digby's  sympathetic 
powder.  "Magnetic  cures  being  discoursed  of,  Sir  Gilbert 
Talbot  promised  to  communicate  what  he  knew  of  sympa- 
thetical  cures ;  and  those  members  who  had  any  of  the 
powder  of  sympathy,  were  desired  to  bring  some  of  it  at 
the  next  meeting." 

June  21,  1661,  certain  gentlemen  were  appointed  "cura- 
tors of  the  proposal  of  tormenting  a  man  with  the  sympa- 
thetic powder" ;  I  cannot  find  any  record  of  the  result.  And 
so  they  went  on  until  the  time  of  Sir  John  Hill's  satire,  in 
1751.  This  once  well-known  work  is,  in  my  judgment,  the 
greatest  compliment  the  Royal  Society  ever  received.  It 
brought  forward  a  number  of  what  are  now  feeble  and 
childish  researches  in  the  Philosophical  Transactions.  It 
showed  that  the  inquirers  had  actually  been  inquiring;  and 
that  they  did  not  pronounce  decision  about  "natural  knowl- 
edge" by  help  of  "natural  knowledge."  But  for  this,  Hill 
would  neither  have  known  what  to  assail,  nor  how.  Mat- 
ters are  now  entirely  changed.  The  scientific  bodies  are  far 
too  well  established  to  risk  themselves.  Ibit  qui  zonam 
perdidit : 

"Let  him  take  castles  who  has  ne'er  a  groat." 

These  great  institutions  are  now  without  any  collective 
purpose,  except  that  of  promoting  individual  energy;  they 
print  for  their  contributors,  and  guard  themselves  by  a  gen- 
eral declaration  that  they  will  not  be  answerable  for  the 
things  they  print.  Of  course  they  will  not  put  forward 
anything  for  everybody;  but  a  writer  of  a  certain  reputa- 
tion, or  matter  of  a  certain  look  of  plausibility  and  safety, 


INTRODUCTORY.  23 

will  find  admission.  This  is  as  it  should  be ;  the  pasturer  of 
flocks  and  herds  and  the  hunters  of  wild  beasts  are  two  very 
different  bodies,  with  very  different  policies.  The  scien- 
tific academies  are  what  a  spiritualist  might  call  "publishing 
mediums,"  and  their  spirits  fall  occasionally  into  writing 
which  looks  as  if  minds  in  the  higher  state  were  not  always 
impervious  to  nonsense. 

The  following  joke  is  attributed  to  Sir  John  Hill.  I 
cannot  honestly  say  I  believe  it ;  but  it  shows  that  his  con- 
temporaries did  not  believe  he  had  no  humor.  Good  stories 
are  always  in  some  sort  of  keeping  with  the  characters  on 
which  they  are  fastened.  Sir  John  Hill  contrived  a  com- 
munication to  the  Royal  Society  from  Portsmouth,  to  the 
effect  that  a  sailor  had  broken  his  leg  in  a  fall  from  the 
mast-head ;  that  bandages  and  a  plentiful  application  of  tar- 
water  had  made  him,  in  three  days,  able  to  use  his  leg  as 
well  as  ever.  While  this  communication  was  under  grave 
discussion — it  must  be  remembered  that  many  then  thought 
tarwater  had  extraordinary  remedial  properties — the  joker 
contrived  that  a  second  letter  should  be  delivered,  which 
stated  that  the  writer  had  forgotten,  in  his  previous  com- 
munication, to  mention  that  the  leg  was  a  wooden  leg! 
Horace  Walpole  told  this  story,  I  suppose  for  the  first  time  ; 
he  is  good  authority  for  the  fact  of  circulation,  but  for 
nothing  more. 

Sir  John  Hill's  book  is  droll  and  cutting  satire.  Dr. 
Maty,  (Sec.  Rpyal  Society)  wrote  thus  of  it  in  the  Journal 
Britannique  (Feb.  1751),  of  which  he  was  editor: 

"II  est  facheux  que  cet  ingenieux  Naturaliste,  qui  nous 
a  deja  donne  et  qui  nous  prepare  encore  des  ouvrages  plus 
utiles,  emploie  a  cette  odieuse  tache  une  plume  qu'il  trempe 
dans  le  fiel  et  dans  1'absinthe.  II  est  vrai  que  plusieurs  de 
ses  remarques  sont  fondees,  et  qu'a  1'erreur  qu'il  indique,  il 
joint  en  meme  terns  la  correction.  Mais  il  n'est  pas  tou- 
jours  equitable,  et  ne  manque  jamais  d'insulter.  Que  peut 


24  A  BUDGET  OF  PARADOXES. 

apres  tout  prouver  son  livre,  si  ce  n'est  que  la  quarante- 
cinquieme  partie  d'un  tres-ample  et  tres-utile  Recueil  n'est 
pas  exempte  d'erreurs?  Devoit-il  confondre  avec  des  Ecri- 
vains  superficiels,  dont  la  Liberte  du  Corps  ne  permet  pas  de 
restreindre  la  fertilite,  cette  foule  de  savans  du  Premier 
ordre,  dont  les  Ecrits  ont  orne  et  ornent  encore  les  Trans- 
actions? A-t-il  oublie  qu'on  y  a  vu  frequemment  les  noms 
des  Boyle,  des  Newton,  des  Halley,  des  De  Moivres,  des 
Hans  Sloane,  etc.?  Et  qu'on  y  trouve  encore  ceux  des 
Ward,  des  Bradley,  des  Graham,  des  Ellicot,  des  Watson, 
et  d'un  Auteur  que  Mr.  Hill  prefere  a  tous  les  autres,  je 
veux  dire  de  Mr.  Hill  lui-meme?"1 

This  was  the  only  answer ;  but  it  was  no  answer  at  all. 
Hill's  object  was  to  expose  the  absurdities ;  he  therefore  col- 
lected the  absurdities.  I  feel  sure  that  Hill  was  a  benefactor 
of  the  Royal  Society;  and  much  more  than  he  would  have 
been  if  he  had  softened  their  errors  and  enhanced  their 
praises.  No  reviewer  will  object  to  me  that  I  have  omitted 
Young,  Laplace,  etc.  But  then  my  book  has  a  true  title. 
Hill  should  not  have  called  his  a  review  of  the  "Works." 

It  was  charged  against  Sir  John  Hill  that  he  had  tried  to 
become  a  Fellow  of  the  Royal  Society  and  had  failed.  This 
he  denied,  and  challenged  the  production  of  the  certificate 
which  a  candidate  always  sends  in;  and  which  is  preserved. 

1"It  is  annoying  that  this  ingenious  naturalist  who  has  already 
given  us  more  useful  works  and  has  still  others  in  preparation,  uses 
for  this  odious  task,  a  pen  dipped  in  gall  and  wormwood.  It  is  true 
that  many  of  his  remarks  have  some  foundation,  and  that  to  each 
error  that  he  points  out  he  at  the  same  time  adds  its  correction.  But 
he  is  not  always  just  and  never  fails  to  insult.  After  all,  what  does 
his  book  prove  except  that  a  forty-fifth  part  of  a  very  useful  review 
is  not  free  from  mistakes?  Must  we  confuse  him  with  those  super- 
ficial writers  whose  liberty  of  body  does  not  permit  them  to  restrain 
their  fruitfulness,  that  crowd  of  savants  of  the  highest  rank  whose 
writings  have  adorned  and  still  adorn  the  Transactions?  Has  he 
forgotten  that  the  names  of  the  Boyles,  Newtons,  Halleys,  De  Moi- 
vres, Hans  Sloanes,  etc.  have  been  seen  frequently?  and  that  still  are 
found  those  of  the  Wards,  Bradleys,  Grahams,  Ellicots,  Watsons, 
and  of  an  author  whom  Mr.  Hill  prefers  to  all  others,  I  mean  Mr. 
Hill  himself?" 


INTRODUCTORY.  25 

But  perhaps  he  could  not  get  so  far  as  a  certificate — that  is, 
could  not  find  any  one  to  recommend  him ;  he  was  a  likely 
man  to  be  in  such  a  predicament.  As  I  have  myself  run  foul 
of  the  Society  on  some  little  points,  I  conceive  it  possible  that 
I  may  fall  under  a  like  suspicion.  Whether  I  could  have 
been  a  Fellow,  I  cannot  know;  as  the  gentleman  said  who 
was  asked  if  he  could  play  the  violin,  I  never  tried.  I  have 
always  had  a  high  opinion  of  the  Society  upon  its  whole  his- 
tory. A  person  used  to  historical  inquiry  learns  to  look  at 
wholes  ;  the  Universities  of  Oxford  and  Cambridge,  the  Col- 
lege of  Physicians,  etc.  are  taken  in  all  their  duration.  But 
those  who  are  not  historians — I  mean  not  possessed  of  the 
habit  of  history — hold  a  mass  of  opinions  about  current 
things  which  lead  them  into  all  kinds  of  confusion  when  they 
try  to  look  back.  Not  to  give  an  instance  which  will  offend 
any  set  of  existing  men — this  merely  because  I  can  do  with- 
out it — let  us  take  the  country  at  large.  Magna  Charta  for 
ever !  glorious  safeguard  of  our  liberties  !  Nullus  liber  homo 
capiatur  out  imprisonetur.  . .  .aut  aliquo  modo  destruatur, 
nisi  per  judicium  parium . . . . 1  Liber  homo ;  frank  home ;  a 
capital  thing  for  him — but  how  about  the  villeins'?  Oh, 
there  are  none  now\  But  there  were.  Who  cares  for  vil- 
lains, or  barbarians,  or  helots  ?  And  so  England,  and  Athens, 
and  Sparta,  were  free  States ;  all  the  freemen  in  them  were 
free.  Long  after  Magna  Charta,  villains  were  sold  with 
their  "chattels  and  offspring,"  named  in  that  order.  Long 
after  Magna  Charta,  it  was  law  that  "Le  Seigniour  poit 
rob,  naufrer,  et  chastiser  son  villein  a  son  volunt,  salve  que 
il  ne  poit  luy  maim."2 

The  Royal  Society  was  founded  as  a  co-operative  fcody, 
and  co-operation  was  its  purpose.  The  early  charters,  etc. 
do  not  contain  a  trace  of  the  intention  to  create  a  scientific 
distinction,  a  kind  of  Legion  of  Honor.  It  is  clear  that  the 

1  Let  no  free  man  be  seized  or  imprisoned  or  in  any  way  harmed 
except  by  trial  of  his  peers." 

"The  master  can  rob,  wreck  and  punish  his  slave  according  to 
his  pleasure  save  only  that  he  may  not  maim  him." 


26  A  BUDGET  OF  PARADOXES. 

qualification  was  ability  and  willingness  to  do  good  work 
for  the  promotion  of  natural  knowledge,  no  matter  in  how 
many  persons,  nor  of  what  position  in  society.  Charles  II 
gave  a  smart  rebuke  for  exclusiveness,  as  elsewhere  men- 
tioned. In  time  arose,  almost  of  course,  the  idea  of  distinc- 
tion attaching  to  the  title;  and  when  I  first  began  to  know 
the  Society,  it  was  in  this  state.  Gentlemen  of  good  social 
position  were  freely  elected  if  they  were  really  educated 
men ;  but  the  moment  a  claimant  was  announced  as  resting 
on  his  science,  there  was  a  disposition  to  inquire  whether  he 
was  scientific  enough.  The  maxim  of  the  poet  was  adopted ; 
and  the  Fellows  were  practically  divided  into  Drink-deeps 
and  Taste-nots. 

I  was,  in  early  life,  much  repelled  by  the  tone  taken  by 
the  Fellows  of  the  Society  with  respect  to  their  very  mixed 
body.  A  man  high  in  science — some  thirty-seven  years  ago 
(about  1830) — gave  me  some  encouragement,  as  he  thought. 
"We  shall  have  you  a  Fellow  of  the  Royal  Society  in  time," 
said  he.  Umph !  thought  I :  for  I  had  that  day  heard  of  sonic 
recent  elections,  the  united  science  of  which  would  not  have 
demonstrated  I.  1,  nor  explained  the  action  of  a  pump. 
Truly  an  elevation  to  look  up  at!  It  came,  further,  to  my 
knowledge  that  the  Royal  Society — if  I  might  judge  by  the 
claims  made  by  very  influential  Fellows — considered  itself 
as  entitled  to  the  best  of  everything:  second-best  being  left 
for  the  newer  bodies.  A  secretary,  in  returning  thanks  for 
the  Royal  at  an  anniversary  of  the  Astronomical,  gave  rather 
a  lecture  to  the  company  on  the  positive  duty  of  all  present 
to  send  the  very  best  to  the  old  body,  and  the  absolute  right 
of  the  old  body  to  expect  it.  An  old  friend  of  mine,  on  a 
similar  occasion,  stated  as  a  fact  that  the  thing  was  always 
done,  as  well  as  that  it  ought  to  be  done. 

Of  late  years  this  pretension  has  been  made  by  a  Presi- 
dent of  the  Society.  In  1855,  Lord  Rosse  presented  a  con- 
fidential memorandum  to  the  Council  on  the  expediency  of 
enlarging  their  number.  He  says,  "In  a  Council  so  small  it 


INTRODUCTORY.  27 

is  impossible  to  secure  a  satisfactory  representation  of  the 
leading  scientific  Societies,  and  it  is  scarcely  to  be  expected 
that,  under  such  circumstances,  they  will  continue  to  publish 
inferior  papers  while  they  send  the  best  to  our  Transact  ions." 
And,  again,  with  all  the  Societies  represented  on  the 
Council,  "even  if  every  Science  had  its  Society,  and  if  they 
published  everything,  withholding  their  best  papers  [i.  e., 
from  the  Royal  Society],  which  they  would  not  be  likely  to 
do,  still  there  would  remain  to  the  Royal  Society. .  ."  Lord 
Rosse  seems  to  imagine  that  the  minor  Societies  themselves 
transfer  their  best  papers  to  the  Royal  Society ;  that  if,  for 
instance,  the  Astronomical  Society  were  to  receive  from  A. B. 
a  paper  of  unusual  merit,  the  Society  would  transfer  it  to 
the  Royal  Society.  This  is  quite  wrong:  any  preference  of 
the  Royal  to  another  Society  is  the  work  of  the  contrib- 
utor himself.  But  it  shows  how  well  hafted  is  the  Royal 
Society's  claim,  that  a  President  should  acquire  the  notion 
that  it  is  acknowledged  and  acted  upon  by  the  other  Socie- 
ties, in  their  joint  and  corporate  capacities.  To  the  preten- 
sion thus  made  I  never  could  give  any  sympathy.  When  I 
first  heard  Mr.  Christie,  Sec.  R.  S.,  set  it  forth  at  the  anni- 
versary dinner  of  the  Astronomical  Society,  I  remembered 
the  Baron  in  Walter  Scott : 

"Of  Gilbert  the  Galliard  a  heriot  he  sought, 
Saying,  Give  thy  best  steed  as  a  vassal  ought." 

And  I  remembered  the  answer: 

"Lord  and  Earl  though  thou  be,  I  trow 
I  can  rein  Buck's-foot  better  than  thou." 

Fully  conceding  that  the  Royal  Society  is  entitled  to  pre- 
eminent rank  and  all  the  respect  due  to  age  and  services,  I 
could  not,  nor  can  I  now,  see  any  more  obligation  in  a  con- 
tributor to  send  his  best  to  that  Society  than  he  can  make  out 
to  be  due  to  himself.  This  pretension,  in  my  mind,  was 
hooked  on,  by  my  historical  mode  of  viewing  things  already 
mentioned,  to  my  knowledge  of  the  fact  that  the  Royal  So- 


28  A  BUDGET  OF  PARADOXES. 

ciety — the  chief  fault,  perhaps,  lying  with  its  President,  Sir 
Joseph  Banks — had  sternly  set  itself  against  the  formation 
of  other  societies ;  the  Geological  and  Astronomical,  for  in- 
stance, though  it  must  be  added  that  the  chief  rebels  came 
out  of  the  'Society  itself.  And  so  a  certain  not  very  defined 
dislike  was  generated  in  my  mind — an  anti-aristocratic  affair 
— to  the  body  which  seemed  to  me  a  little  too  uplifted.  This 
would,  I  daresay,  have  worn  off ;  but  a  more  formidable  ob- 
jection arose.  My  views  of  physical  science  gradually  ar- 
ranged themselves  into  a  form  which  would  have  rendered 
F.R.S.,  as  attached  to  my  name,  a  false  representation  sym- 
bol. The  Royal  Society  is  the  great  fortress  of  general  phys- 
ics :  and  in  the  philosophy  of  our  day,  as  to  general  physics, 
there  is  something  which  makes  the  banner  of  -the  R.S.  one 
under  which  I  cannot  march.  Everybody  who  saw  the  three 
letters  after  my  name  would  infer  certain  things  as  to  my 
mode  of  thought  which  would  not  be  true  inference.  It 
would  take  much  space  to  explain  this  in  full.  I  may  here- 
after, perhaps,  write  a  budget  of  collected  results  of  the 
a  priori  philosophy,  the  nibbling  at  the  small  end  of  om- 
niscience, and  the  effect  it  has  had  on  common  life,  from 
the  family  parlor  to  the  jury-box,  from  the  girls'-school  to 
the  vestry-meeting.  There  are  in  the  Society  those  who 
would,  were  there  no  others,  prevent  my  criticism,  be  its 
conclusions  true  or  false,  from  having  any  basis;  but  they 
are  in  the  minority. 

There  is  no  objection  to  be  made  to  the  principles  of 
philosophy  in  vogue  at  the  Society,  when  they  are  stated  as 
principles;  but  there  is  an  omniscience  in  daily  practice 
which  the  principles  repudiate.  In  like  manner,  the  most 
retaliatory  Christians  have  a  perfect  form  of  round  words 
about  behavior  to  those  who  injure  them ;  none  of  them  are 
as  candid  as  a  little  boy  I  knew,  who,  to  his  mother's  admo- 
nition, You  should  love  your  enemies,  answered — Catch  me 
at  it! 

Years  ago,  a  change  took  place  which  would  alone  have 


INTRODUCTORY.  29 

put  a  sufficient  difficulty  in  the  way.  The  co-operative  body 
got  tired  of  getting  funds  from  and  lending  name  to  persons 
who  had  little  or  no  science,  and  wanted  F.R.S.  to  be  in 
every  case  a  Fellow  Really  Scientific.  Accordingly,  the  num- 
ber of  yearly  elections  was  limited  to  fifteen  recommended 
by  the  Council,  unless  the  general  body  should  choose  to 
elect  more;  which  it  does  not  do.  The  election  is  now  a 
competitive  examination :  it  is  no  longer — Are  you  able  and 
willing  to  promote  natural  knowledge;  it  is — Are  you  one 
of  the  upper  fifteen  of  those  who  make  such  claim.  In  the 
list  of  candidates — a  list  rapidly  growing  in  number — each 
year  shows  from  thirty  to  forty  of  those  whom  Newton  and 
Boyle  would  have  gladly  welcomed  as  fellow-laborers.  And 
though  the  rejected  of  one  year  may  be  the  accepted  of  the 
next — or  of  the  next  but  one,  or  but  two,  if  self-respect  will 
permit  the  candidate  to  hang  on — yet  the  time  is  clearly  com- 
ing when  many  of  those  who  ought  to  be  welcomed  will  be 
excluded  for  life,  or  else  shelved  at  last,  when  past  work, 
with  a  scientific  peerage.  Coupled  with  this  attempt  to 
create  a  kind  of  order  of  knighthood  is  an  absurdity  so  glar- 
ing that  it  should  always  be  kept  before  the  general  eye. 
This  distinction,  this  mark  set  by  science  upon  successful 
investigation,  is  of  necessity  a  class-distinction.  Rowan 
Hamilton,  one  of  the  greatest  names  of  our  day  in  mathe- 
matical science,  never  could  attach  F.R.S.  to  his  name — he 
could  not  afford  it.  There  is  a  condition  precedent — Four 
Red  Sovereigns.  It  is  four  pounds  a  year,  or — to  those  who 
have  contributed  to  the  Transactions — forty  pounds  down. 
This  is  as  it  should  be:  the  Society  must  be  supported. 
But  it  is  not  as  it  should  be  that  a  kind  of  title  of  honor 
should  be  forged,  that  a  body  should  take  upon  itself  to 
confer  distinctions  for  science,  when  it  is  in  the  background 
— and  kept  there  when  the  distinction  is  trumpeted — that 
the  wearer  is  a  man  who  can  spare  four  pounds  a  year.  I 
am  well  aware  that  in  England  a  person  who  is  not  gifted 
either  by  nature  or  art,  with  this  amount  of  money  power, 


30  A  BUDGET  OF  PARADOXES. 

is,  with  the  mass,  a  very  second-rate  sort  of  Newton,  what- 
ever he  may  be  in  the  field  of  investigation.  Even  men  of 
science,  so  called,  have  this  feeling.  I  know  that  the  scien- 
tific advisers  of  the  Admiralty,  who,  years  ago,  received 
100  pounds  a  year  each  for  his  trouble,  were  sneered  at  by 
a  wealthy  pretender  as  "fellows  to  whom  a  hundred  a  year 
is  an  object."  Dr.  Thomas  Young  was  one  of  them.  To 
a  bookish  man — I  mean  a  man  who  can  manage  to  collect 
books — there  is  no  tax.  To  myself,  for  example,  40  pounds 
worth  of  books  deducted  from  my  shelves,  and  the  life-use 
of  the  Society's  splendid  library  instead,  would  have  been  a 
capital  exchange.  But  there  may  be,  and  are,  men  who  want 
books,  and  cannot  pay  the  Society's  price.  The  Council 
would  be  very  liberal  in  allowing  books  to  be  consulted. 
I  have  no  doubt  that  if  a  known  investigator  were  to  call 
and  ask  to  look  at  certain  books,  the  Assistant-Secretary 
would  forthwith  seat  him  with  the  books  before  him,  ab- 
sence of  F.R.S.  not  in  any  wise  withstanding.  But  this  is 
not  like  having  the  right  to  consult  any  book  on  any  day, 
and  to  take  it  away,  if  farther  wanted. 

So  much  for  the  Royal  Society  as  concerns  myself.  I 
must  add  that  there  is  not  a  spark  of  party  feeling  against 
those  who  wilfully  remain  outside.  The  better  minds  of 
course  know  better;  and  the  smaller  savants  look  compla- 
cently on  the  idea  of  an  outer  world  which  makes  elite  of 
them.  I  have  done  such  a  thing  as  serve  on  a  committee 
of  the  Society,  and  report  on  a  paper:  they  had  the  sense 
to  ask,  and  I  had  the  sense  to  see  that  none  of  my  opinions 
were  compromised  by  compliance.  And  I  will  be  of  any 
use  which  does  not  involve  the  status  of  homo  trium  lite- 
rarum;  as  I  have  elsewhere  explained,  I  would  gladly  be 
Fautor  Realis  Scientice,  but  I  would  not  be  taken  for  Falsa 
Rationis  Sacerdos. 

Nothing  worse  will  ever  happen  to  me  than  the  smile 
which  individuals  bestow  on  a  man  who  does  not  groove. 
Wisdom,  like  religion,  belongs  to  majorities ;  who  can  won- 


INTRODUCTORY.  31 

der  that  it  should  be  so  thought,  when  it  is  so  clearly  pictured 
in  the  New  Testament  from  one  end  to  the  other? 

The  counterpart  of  paradox,  the  isolated  opinion  of  one 
or  of  few,  is  the  general  opinion  held  by  all  the  rest ;  and  the 
counterpart  of  false  and  absurd  paradox  is  what  is  called  the 
"vulgar  error,"  the  pseudodox.  There  is  one  great  work  on 
this  last  subject,  the Pseudodoxia  Epidemica  of  Sir  Thomas 
Browne,  the  famous  author  of  the  Rellgio  Medici ;  it  usually 
goes  by  the  name  of  Browne  "On  Vulgar  Errors"  ( 1st  ed. 
1646;  6th,  1672).  A  careful  analysis  of  this  work  would 
show  that  vulgar  errors  are  frequently  opposed  by  scientific 
errors ;  but  good  sense  is  always  good  sense,  and  Browne's 
book  has  a  vast  quantity  of  it. 

As  an  example  of  bad  philosophy  brought  against  bad 
observation.  The  Amphisbsena  serpent  was  supposed  to 
have  two  heads,  one  at  each  end;  partly  from  its  shape, 
partly  because  it  runs  backwards  as  well  as  forwards.  On 
this  Sir  Thomas  Browne  makes  the  following  remarks: 

"And  were  there  any  such  species  or  natural  kind  of 
animal,  it  would  be  hard  to  make  good  those  six  positions 
of  body  which,  according  to  the  three  dimensions,  are  as- 
cribed unto  every  Animal ;  that  is,  infra,  supra,  ante,  retro, 
dextrosum,  sinistrosum:  for  if  (as  it  is  determined)  that  be 
the  anterior  and  upper  part  wherein  the  senses  are  placed, 
and  that  the  posterior  and  lower  part  which  is  opposite 
thereunto,  there  is  no  inferior  or  former  part  in  this  Animal ; 
for  the  senses,  being  placed  at  both  extreams,  doth  make 
both  ends  anterior,  which  is  impossible ;  the  terms  being 
Relative,  which  mutually  subsist,  and  are  not  without  each 
other.  And  therefore  this  duplicity  was  ill  contrived  to  place 
one  head  at  both  extreams,  and  had  been  more  tolerable  to 
have  settled  three  or  four  at  one.  And  therefore  also  Poets 
have  been  more  reasonable  than  Philosophers,  and  Geryon 
or  Cerberus  less  monstrous  than  Amphisbana" 


32  A  BUDGET  OF   PARADOXES. 

There  may  be  paradox  upon  paradox:  and  there  is  a 
good  instance  in  the  eighth  century  in  the  case  of  Virgil, 
an  Irishman,  Bishop  of  Salzburg  and  afterwards  Saint,  and 
his  quarrels  with  Boniface,  an  Englishman,  Archbishop  of 
Mentz,  also  afterwards  Saint.  All  we  know  about  the  matter 
is,  that  there  exists  a  letter  of  748  from  Pope  Zachary,  citing 
Virgil — then,  it  seems,  at  most  a  simple  priest,  though  the 
Pope  was  not  sure  even  of  that — to  Rome  to  answer  the 
charge  of  maintaining  that  there  is  another  world  (mundus) 
under  our  earth  (terra),  with  another  sun  and  another 
moon.  Nothing  more  is  known :  the  letter  contains  threats 
in  the  event  of  the  charge  being  true;  and  there  history 
drops  the  matter.  Since  Virgil  was  afterwards  a  Bishop 
and  a  Saint,  we  may  fairly  conclude  that  he  died  in  the  full 
flower  of  his  orthodox  reputation.  It  has  been  supposed — 
and  it  seems  probable— that  Virgil  maintained  that  the  earth 
is  peopled  all  the  way  round,  so  that  under  some  spots  there 
are  antipodes ;  that  his  contemporaries,  with  very  dim  ideas 
about  the  roundness  of  the  earth,  and  most  of  them  with 
none  at  all,  interpreted  him  as  putting  another  earth  under 
ours — turned  the  other  way,  probably,  like  the  second  piece 
of  bread-and-butter  in  a  sandwich,  with  a  sun  and  moon 
of  its  own.  In  the  eighth  century  this  would  infallibly  have 
led  to  an  underground  Gospel,  an  underground  Pope,  and 
an  underground  Avignon  for  him  to  live  in.  When,  in  later 
times,  the  idea  of  inhabitants  for  the  planets  was  started,  it 
was  immediately  asked  whether  they  had  sinned,  whether 
Jesus  Christ  died  for  them,  whether  their  wine  and  their 
water  could  be  lawfully  used  in  the  sacraments,  etc. 

On  so  small  a  basis  as  the  above  has  been  constructed  a 
companion  case  to  the  persecution  of  Galileo.  On  one  side 
the  positive  assertion,  with  indignant  comment,  that  Virgil 
was  deposed  for  antipodal  heresy,  on  the  other,  serious  at- 
tempts at  justification,  palliation,  or  mystification.  Some 
writers  say  that  Virgil  was  found  guilty ;  others  that  he  gave 
satisfactory  explanation,  and  became  very  good  friends  with 


INTRODUCTORY.  33 

Boniface:  for  all  which  see  Bayle.  Some  have  maintained 
that  the  antipodist  was  a  different  person  from  the  canon- 
ized bishop :  there  is  a  second  Virgil,  made  to  order.  When 
your  shoes  pinch,  and  will  not  stretch,  always  throw  them 
away  and  get  another  pair :  the  same  with  your  facts.  Ba- 
ronius  was  not  up  to  the  plan  of  a  substitute :  his  commen- 
tator Pagi  (probably  writing  about  1690)  argues  for  it  in 
a  manner  which  I  think  Baronius  would  not  have  approved. 
This  Virgil  was  perhaps  a  slippery  fellow.  The  Pope  says 
he  hears  that  Virgil  pretended  licence  from  him  to  claim 
one  of  some  new  bishoprics :  this  he  declares  is  totally  false. 
It  is  part  of  the  argument  that  such  a  man  as  this  could  not 
have  been  created  a  Bishop  and  a  Saint :  on  this  point  there 
will  be  opinions  and  opinions.1 

Lactantius,  four  centuries  before,  had  laughed  at  the  an- 
tipodes in  a  manner  which  seems  to  be  ridicule  thrown  on 
the  idea  of  the  earth's  roundness.  Ptolemy,  without  refer- 
ence to  the  antipodes,  describes  the  extent  of  the  inhabited 
part  of  the  globe  in  a  way  which  shows  that  he  could  have 
had  no  objection  to  men  turned  opposite  ways.  Probably, 
in  the  eighth  century,  the  roundness  of  the  earth  was  matter 
of  thought  only  to  astronomers.  It  should  always  be  re- 
membered, especially  by  those  who  affirm  persecution  of  a 
true  opinion,  that  but  for  our  knowing  from  Lactantius  that 
the  antipodal  notion  had  been  matter  of  assertion  and  denial 
among  theologians,  we  could  never  have  had  any  great  con- 
fidence in  Virgil  really  having  maintained  the  simple  theory 
of  the  existence  of  antipodes.  And  even  now  we  are  not 
entitled  to  affirm  it  as  having  historical  proof :  the  evidence 

1  An  Irish  antiquary  informs  me  that  Virgil  is  mentioned  in  an- 
nals, at  A.  D.  784,  as  "Verghil,  i.  e.,  the  geometer,  Abbot  of  Achadhbo 
[and  Bishop  of  Saltzburg]  died  in  Germany  in  the  thirteenth  year  of 
his  bishoprick."  No  allusion  is  made  to  his  opinions ;  but  it  seems  he 
was,  by  tradition,  a  mathematician.  The  Abbot  of  Aghabo  (Queen's 
County)  was  canonized  by  Gregory  IX,  in  1233.  The  story  of  the 
second,  or  scapegoat,  Virgil  would  be  much  damaged  by  the  char- 
acter given  to  the  real  bishop,  if  there  were  anything  in  it  to  dilapi- 
date.—A.  De  M. 


34  A  BUDGET  OF   PARADOXES. 

goes  to  Virgil  having  been  charged  with  very  absurd  notions, 
which  it  seems  more  likely  than  not  were  the  absurd  con- 
structions which  ignorant  contemporaries  put  upon  sensible 
opinions  of  his. 

One  curious  part  of  this  discussion  is  that  neither  side 
has  allowed  Pope  Zachary  to  produce  evidence  to  character. 
He  shall  have  been  an  Urban,  say  the  astronomers ;  an  Ur- 
ban he  ought  to  have  been,  say  the  theologians.  What  sort 
of  man  was  Zachary?  He  was  eminently  sensible  and  con- 
ciliatory; he  contrived  to  make  northern  barbarians  hear 
reason  in  a  way  which  puts  him  high  among  that  section  of 
the  early  popes  who  had  the  knack  of  managing  uneducated 
swordsmen.  He  kept  the  peace  in  Italy  to  an  extent  which 
historians  mention  with  admiration.  Even  Bale,  that  Maha- 
rajah of  pope-haters,  allows  himself  to  quote  in  favor  of 
Zachary,  that  "multa  Papalem  dignitatem  decentia,  eadem- 
que  prseclara  (scilicet)  opera  confecit."1  And  this,  though  so 
willing  to  find  fault  that,  speaking  of  Zachary  putting  a 
little  geographical  description  of  the  earth  on  the  portico  of 
the  Lateran  Church,  he  insinuates  that  it  was  intended  to 
affirm  that  the  Pope  was  lord  of  the  whole.  Nor  can  he 
say  how  long  Zachary  held  the  see,  except  by  announcing 
his  death  in  752,  "cum  decem  annis  pestilentiae  sedi  prae- 
fuisset."2 

There  was  another  quarrel  between  Virgil  and  Boni- 
face which  is  -an  illustration.  An  ignorant  priest  had  bap- 
tized "in  nomine  Patria,  et  Filia  et  Spirituo  Sancto."  Boni- 
face declared  the  rite  null  and  void:  Virgil  maintained 
the  contrary;  and  Zachary  decided  in  favor  of  Virgil,  on 
the  ground  that  the  absurd  form  was  only  ignorance  of 
Latin,  and  not  heresy.  It  is  hard  to  believe  that  this  man 
deposed  a  priest  for  asserting  the  whole  globe  to  be  in- 
habited. To  me  the  little  information  that  we  have  seems 

1  "He  performed  many  acts  befitting  the  Papal  dignity,  and  like- 
wise many  excellent  (to  be  sure!)  works." 

2  "After  having  been  on  the  throne  during  ten  years  of  p«6tilence." 


INTRODUCTORY. 


35 


to  indicate — but  not  with  certainty — that  Virgil  maintained 
the  antipodes:  that  his  ignorant  contemporaries  travestied 
his  theory  into  that  of  an  underground  cosmos;  that  the 
Pope  cited  him  to  Rome  to  explain  his  system,  which,  as 
reported,  looked  like  what  all  would  then  have  affirmed  to 
be  heresy;  that  he  gave  satisfactory  explanations,  and  was 
dismissed  with  honor.  It  may  be  that  the  educated  Greek 
monk,  Zachary,  knew  his  Ptolemy  well  enough  to  guess 
what  the  asserted  heretic  would  say ;  we  have  seen  that  he 
seems  to  have  patronized  geography.  The  description  of  the 
earth,  according  to  historians,  was  a  map ;  this  Pope  may 
have  been  more  ready  than  another  to  prick  up  his  ears  at 
any  rumor  of  geographical  heresy,  from  hope  of  informa- 
tion. And  Virgil,  who  may  have  entered  the  sacred  pres- 
ence as  frightened  as  Jacquard,  when  Napoleon  I  sent  for 
him  and  said,  with  a  stern  voice  and  threatening  gesture, 
"You  are  the  man  who  can  tie  a  knot  in  a  stretched  string," 
may  have  departed  as  well  pleased  as  Jacquard  with  the 
riband  and  pension  which  the  interview  was  worth  to  him. 

A  word  more  about  Baronius.  If  he  had  been  pope,  as 
he  would  have  been  but  for  the  opposition  of  the  Spaniards, 
and  if  he  had  lived  ten  years  longer  than  he  did,  and  if 
Clavius,  who  would  have  been  his  astronomical  adviser,  had 
lived  five  years  longer  than  he  did,  it  is  probable,  nay  almost 
certain,  that  the  great  exhibition,  the  proceeding  against 
Galileo,  would  not  have  furnished  a  joke  against  theology 
in  all  time  to  come.  For  Baronius  was  sensible  and  witty 
enough  to  say  that  in  the  Scriptures  the  Holy  Spirit  intended 
to  teach  how  to  go  to  Heaven,  not  how  Heaven  goes ;  and 
Clavius,  in  his  last  years,  confessed  that  the  whole  system 
of  the  heavens  had  broken  down,  and  must  be  mended. 

The  manner  in  which  the  Galileo  case,  a  reality,  and  the 
Virgil  case,  a  fiction,  have  been  hawked  against  the  Roman 
see  are  enough  to  show  that  the  Pope  and  his  adherents 
have  not  cared  much  about  physical  philosophy.  In  truth, 
orthodoxy  has  always  had  other  fish  to  fry.  Physics,  which 


36  A  BUDGET  OF  PARADOXES. 

in  modern  times  has  almost  usurped  the  name  philosophy,  in 
England  at  least,  has  felt  a  little  disposed  to  clothe  herself 
with  all  the  honors  of  persecution  which  belong  to  the  real 
owner  of  the  name.  But  the  bishops,  etc.  of  the  Middle 
Ages  knew  that  the  contest  between  nominalism  and  real- 
ism, for  instance,  had  a  hundred  times  more  bearing  upon 
orthodoxy  than  anything  in  astronomy,  etc.  A  wrong  notion 
about  substance  might  play  the  mischief  with  transubstan- 
tiation. 

The  question  of  the  earth's  motion  was  the  single  point 
in  which  orthodoxy  came  into  real  contact  with  science. 
Many  students  of  physics  were  suspected  of  magic,  many  of 
atheism:  but,  stupid  as  the  mistake  may  have  been,  it  was 
bona  fide  the  magic  or  the  atheism,  not  the  physics,  which 
was  assailed.  In  the  astronomical  case  it  was  the  very  doc- 
trine, as  a  doctrine,  independently  of  consequences,  which 
was  the  corpus  delicti:  and  this  because  it  contradicted  the 
Bible.  And  so  it  did;  for  the  stability  of  the  earth  is  as 
clearly  assumed  from  one  end  of  the  Old  Testament  to 
the  other  as  the  solidity  of  iron.  Those  who  take  the 
Bible  to  be  totidem  verbis  dictated  by  the  God  of  Truth 
can  refuse  to  believe  it;  and  they  make  strange  reasons. 
They  undertake,  a  priori,  to  settle  Divine  intentions.  The 
Holy  Spirit  did  not  mean  to  teach  natural  philosophy:  this 
they  know  beforehand;  or  else  they  infer  it  from  finding 
that  the  earth  does  move,  and  the  Bible  says  it  does  not. 
Of  course,  ignorance  apart,  every  word  is  truth,  or  the 
writer  did  not  mean  truth.  But  this  puts  the  whole  book  on 
its  trial:  for  we  never  can  find  out  what  the  writer  meant, 
until  we  otherwise  find  out  what  is  true.  Those  who  like 
may,  of  course,  declare  for  an  inspiration  over  which  they 
are  to  be  viceroys ;  but  common  sense  will  either  accept 
verbal  meaning  or  deny  verbal  inspiration. 


A  BUDGET  OF  PARADOXES. 

VOLUME  I. 

THE  STORY  OF  BURIDAN'S  ASS. 
Questiones  Morales,  folio,  1489  [Paris].   By  T.  Buridan. 

This  is  the  title  from  the  Hartwell  Catalogue  of  Law 
Books.  I  suppose  it  is  what  is  elsewhere  called  the  "Com- 
mentary on  the  Ethics  of  Aristotle,"  printed  in  1489.1  Buri- 
dan2 (died  about  1358)  is  the  creator  of  the  famous  ass 
which,  as  Burdin's3  ass,  was  current  in  Burgundy,  perhaps 
is,  as  a  vulgar  proverb.  Spinoza4  says  it  was  a  jenny  ass, 
and  that  a  man  would  not  have  been  so  foolish ;  but  whether 
the  compliment  is  paid  to  human  or  to  masculine  character 
does  not  appear — perhaps  to  both  in  one.  The  story  told 
about  the  famous  paradox  is  very  curious.  The  Queen  of 
France,  Joanna  or  Jeanne,  was  in  the  habit  of  sewing  her 
Movers  up  in  sacks,  and  throwing  them  into  the  Seine;  not 
for  blabbing,  but  that  they  might  not  blab — certainly  the 
safer  plan.  Buridan  was  exempted,  and,  in  gratitude,  in- 
vented the  sophism.  What  it  has  to  do  with  the  matter 

JThe  work  is  the  Questiones  foannis  Buridani  super  X  libros  Aris- 
totelis  ad  Nicomachum,  curante  Egidio  Delfo. . .  .Parisiis,  1489,  folio. 
It  also  appeared  at  Paris  in  editions  of  1499,  1513,  and  1518,  and  at 
Oxford  in  1637. 

2  Jean  Buridan  was  born  at  Bethune  about  1298,  and  died  at  Paris 
about  1358.  He  was  professor  of  philosophy  at  the  University  of 
Paris  and  several  times  held  the  office  of  Rector.  As  a  philosopher 
he  was  classed  among  the  nominalists. 

8  So  in  the  original. 

4  Baruch  Spinoza,  or  Benedict  de  Spinoza  as  he  later  called  himself, 
the  pantheistic  philosopher,  excommunicated  from  the  Jewish  faith 
for  heresy,  was  born  at  Amsterdam  in  1632  and  died  there  in  1677. 


38  A    BUDGET   OF    PARADOXES. 

has  never  been  explained.  Assuredly  qui  facit  per  alium 
facit  per  se  will  convict  Buridan  of  prating.  The  argument 
is  as  follows,  and  is  seldom  told  in  full.  Buridan  was  for 
free-will — that  is,  will  which  determines  conduct,  let  mo- 
tives be  ever  so  evenly  balanced.  An  ass  is  equally  pressed 
by  hunger  and  by  thirst ;  a  bundle  of  hay  is  on  one  side,  a 
pail  of  water  on  the  other.  Surely,  you  will  say,  he  will  not 
be  ass  enough  to  die  for  want  of  food  or  drink ;  he  will  then 
make  a  choice — that  is,  will  choose  between  alternatives  of 
equal  force.  The  problem  became  famous  in  the  schools ; 
some  allowed  the  poor  donkey  to  die  of  indecision ;  some 
denied  the  possibility  of  the  balance,  which  was  no  answer 
at  all. 

MICHAEL   SCOTT'S   DEVILS. 

The  following  question  is  more  difficult,  and  involves 
free-will  to  all  who  answer — "Which  you  please."  If  the 
northern  hemisphere  were  land,  and  all  the  southern  hemi- 
sphere water,  ought  we  to  call  the  northern  hemisphere  an 
island,  or  the  southern  hemisphere  a  lake?  Both  the  ques- 
tions would  be  good  exercises  for  paradoxers  who  must  be 
kept  employed,  like  Michael  Scott's1  devils.  The  wizard 

^Michael  Scott,  or  Scot,  was  born  about  1190,  probably  in  Fife- 
shire,  Scotland,  and  died  about  1291.  He  was  one  of  the  best  known 
savants  of  the  court  of  Emperor  Frederick  II,  and  wrote  upon  astrol- 
ogy, alchemy,  and  the  occult  sciences.  He  was  looked  upon  as  a  great 
magician  and  is  mentioned  among  the  wizards  in  Dante's  Inferno. 

"That  other,  round  the  loins 
So  slender  of  his  shape,  was  Michael  Scot, 
Practised  in  every  slight  of  magic  wile."  Inferno,  XX. 

Boccaccio  also  speaks  of  him :  "It  is  not  long  since  there  was  in 
this  city  (Florence)  a  great  master  in  .necromancy,  who  was  called 
Michele  Scotto,  because  he  was  a  Scot."  Decameron,  Dec.  Giorno. 

Scott's  mention  of  him  in  Canto  Second  of  his  Lay  of  the  Last 
Minstrel,  is  well  known : 

"In  these  fair  climes,  it  was  my  lot 
To  meet  the  wondrous  Michael  Scott ; 

A  wizard  of  such  dreaded  fame, 
That  when,  in  Salamanca's  cave, 
Him  listed  his  magic  wand  to  wave, 

The  bells  would  ring  in  Notre  Dame!" 
Sir  Walter's  notes  upon  him  are  of  interest. 


MICHAEL  SCOTT'S  DEVILS.  39 

knew  nothing  about  squaring  the  circle,  etc.,  so  he  set  them 
to  make  ropes  out  of  sea  sand,  which  puzzled  them.  Stupid 
devils ;  much  of  our  glass  is  sea  sand,  and  it  makes  beautiful 
thread.  Had  Michael  set  them  to  square  the  circle  or  to 
find  a  perpetual  motion,  he  would  have  done  his  work  much 
better.  But  all  this  is  conjecture:  who  knows  that  I  have 
not  hit  on  the  very  plan  he  adopted?  Perhaps  the  whole 
race  of  paradoxers  on  hopeless  subjects  are  Michael's  sub- 
ordinates, condemned  to  transmigration  after  transmigra- 
tion, until  their  task  is  done. 

The  above  was  not  a  bad  guess.  A  little  after  the  time 
when  the  famous  Pascal  papers2  were  produced,  I  came  into 
possession  of  a  correspondence  which,  but  for  these  papers, 
I  should  have  held  too  incredible  to  be  put  before  the  world. 
But  when  one  sheep  leaps  the  ditch,  another  will  follow: 
so  I  gave  the  following  account  in  the  Athenceum  of  Oc- 
tober 5,  1867: 

"The  recorded  story  is  that  Michael  Scott,  being  bound  by 
contract  to  produce  perpetual  employment  for  a  number  of 
young  demons,  was  worried  out  of  his  life  in  inventing 
jobs  for  them,  until  at  last  he  set  them  to  make  ropes  out  of 
sea  sand,  which  they  never  could  do.  We  have  obtained  a 
very  curious  correspondence  between  the  wizard  Michael 
and  his  demon-slaves ;  but  we  do  not  feel  at  liberty  to  say 
how  it  came  into  our  hands.  We  much  regret  that  we  did 
not  receive  it  in  time  for  the  British  Association.  It  appears 
that  the  story,  true  as  far  as  it  goes,  was  never  finished. 
The  demons  easily  conquered  the  rope  difficulty,  by  the 
simple  process  of  making  the  sand  into  glass,  and  spinning 
the  glass  into  thread,  which  they  twisted.  Michael,  thor- 
oughly disconcerted,  hit  upon  the  plan  of  setting  some  to 

'These  were  some  of  the  forgeries  which  Michel  Chasles  (1793- 
1880)  was  duped  into  buying.  They  purported  to  be  a  correspondence 
between  Pascal  and  Newton  and  to  show  that  the  former  had  antici- 
pated some  of  the  discoveries  of  the  great  English  physicist  and 
mathematician.  That  they  were  forgeries  was  shown  by  Sir  David 
Brewster  in  1855. 


40  A   BUDGET   OF   PARADOXES. 

square  the  circle,  others  to  find  the  perpetual  motion,  etc. 
He  commanded  each  of  them  to  transmigrate  from  one  hu- 
man body  into  another,  until  their  tasks  were  done.  This 
explains  the  whole  succession  of  cyclometers,  and  all  the 
heroes  of  the  Budget.  Some  of  this  correspondence  is  very 
recent;  it  is  much  blotted,  and  we  are  not  quite  sure  of  its 
meaning:  it  is  full  of  figurative  allusions  to  driving  some- 
thing illegible  down  a  steep  into  the  sea.  It  looks  like  a 
humble  petition  to  be  allowed  some  diversion  in  the  inter- 
vals of  transmigration ;  and  the  answer  is — 
Rumpat  et  serpens  iter  institutum,3 

— a  line  of  Horace,  which  the  demons  interpret  as  a  direction 
to  come  athwart  the  proceedings  of  the  Institute  by  a  sly 
trick.  Until  we  saw  this,  we  were  suspicious  of  M.  Libri.4 
the  unvarying  blunders  of  the  correspondence  look  like 
knowledge.  To  be  always  out  of  the  road  requires  a  map : 
genuine  ignorance  occasionally  lapses  into  truth.  We  thought 
it  possible  M.  Libri  might  have  played  the  trick  to  show  how 
easily  the  French  are  deceived ;  but  with  our  present  in- 
formation, our  minds  are  at  rest  on  the  subject.  We  see  M. 
Chasles  does  not  like  to  avow  the  real  source  of  informa- 
tion: he  will  not  confess  himself  a  spiritualist." 

PHILO  OF  GADARA. 
Philo  of  Gadara1  is  asserted  by  Montucla,2  on  the  author- 

8  "Let  the  serpent  also  break  from  its  appointed  path." 
*Guglielmo  Brutus  Icilius  Timoleon  Libri-Carucci  della  Som- 
maja,  born  at  Florence  in  1803;  died  at  Fiesole  in  1869.  His  His- 
toire  des  Sciences  Mathematiques  appeared  at  Paris  in  1838,  the  en- 
tire first  edition  of  volume  I,  save  some  half  dozen  that  he  had  car- 
ried home,  being  burned  on  the  day  that  the  printing  was  completed. 
He  was  a  great  collector  of  early  printed  works  on  mathematics, 
and  was  accused  of  having  stolen  large  numbers  of  them  from  other 
libraries.  This  accusation  took  him  to  London,  where  he  bitterly 
attacked  his  accusers.  There  were  two  auction  sales  of  his  library, 
and  a  number  of  his  books  found  their  way  into  De  Morgan's  col- 
lection. 

1  Philo  of  Gadara  lived  in  the  second  century  B.  C.     He  was  a 
pupil  of  Sporus,  who  worked  on  the  problem  of  the  two  mean  pro- 
portionals. 

2  In  his  Histoire  des  Mathematiques,  the  first  edition  of  which 


PHILO  OF  GADARA.  41 

ity  of  Eutocitis,3  the  commentator  on  Archimedes,  to  have 
squared  the  circle  within  the  ten-thousandth  part  of  a  unit, 
that  is,  to  four  places  of  decimals.  A  modern  classical  dic- 
tionary represents  it  as  done  by  Philo  to  ten  thousand  places 
of  decimals.  Lacroix  comments  on  Montucla  to  the  effect  that 
myriad  (in  Greek  ten  thousand}  is  here  used  as  we  use  it, 
vaguely,  for  an  immense  number.  On  looking  into  Eutocius, 
I  find  that  not  one  definite  word  is  said  about  the  extent  to 
which  Philo  carried  the  matter.  I  give  a  translation  of  the 
passage : 

"We  ought  to  know  that  Apollonius  Pergseus,  in  his 
Ocytocium  [this  work  is  lost],  demonstrated  the  same  by 
other  numbers,  and  came  nearer,  which  seems  more  accurate, 
but  has  nothing  to  do  with  Archimedes ;  for,  as  before  said, 
he  aimed  only  at  going  near  enough  for  the  wants  of  life. 
Neither  is  Porus  of  Nicaea  fair  when  he  takes  Archimedes 
to  task  for  not  giving  a  line  accurately  equal  to  the  circum- 
ference. He  says  in  his  Cerii  that  his  teacher,  Philo  of 
Gadara,  had  given  a  more  accurate  approximation  (cts  d*/Di- 
jSeo-repov?  api.6fjiov<s  dyayeiv)  than  that  of  Archimedes,  or  than 
7  to  22.  But  all  these  [the  rest  as  well  as  Philo]  miss  the 
intention.  They  multiply  and  divide  by  tens  of  thousands, 
which  no  one  can  easily  do,  unless  he  be  versed  in  the 
logistics  [fractional  computation]  of  Magnus  [now  un- 
known]." 

Montucla,  or  his  source,  ought  not  to  have  made  this 
mistake.  He  had  been  at  the  Greek  to  correct  Philo  Gade- 
tanus,  as  he  had  often  been  called,  and  he  had  brought  away 

appeared  in  1758.  Jean  Etienne  Montucla  was  born  at  Lyons  in 
1725  and  died  at  Versailles  in  1799.  He  was  therefore  only  thirty- 
three  years  old  when  his  great  work  appeared.  The  second  edition, 
with  additions  by  D'Alembert,  appeared  in  1799-1802.  He  also  wrote 
a  work  on  the  quadrature  of  the  circle,  Histoire  des  recherches  sur 
la  Quadrature  du  Cercle,  which  appeared  in  1754. 

8  Eutocius  of  Ascalon  was  born  in  480  A.  D.  He  wrote  com- 
mentaries on  the  first  four  books  of  the  conies  of  Apollonius  of 
Perga  (247-222  B.C.).  He  also  wrote  on  the  Sphere  and  Cylinder 
and  the  Quadrature  of  the  Circle,  and  on  the  two  books  on  Equilib- 
rium of  Archimedes  (287-212  B.  C.) 


42  A   BUDGET   OF    PARADOXES. 

and  quoted  d™  TdSapw.    Had  he  read  two  sentences  further, 
he  would  have  found  the  mistake. 

We  here  detect  a  person  quite  unnoticed  hitherto  by  the 
moderns,  Magnus  the  arithmetician.  The  phrase  is, ironical; 
it  is  as  if  we  should  say,  "To  do  this  a  man  must  be  deep 
in  Cocker."4  Accordingly,  Magnus,  Baveme,5  and  Cocker, 
are  three  personifications  of  arithmetic;  and  there  may  be 
more. 

ON  SQUARING  THE  CIRCLE. 

Aristotle,  treating  of  the  category  of  relation,  denies  that 
the  quadrature  has  been  found,  but  appears  to  assume  that 
it  can  be  done.  Boethius,1  in  his  comment  on  the  passage, 
says  that  it  has  been  done  since  Aristotle,  but  that  the  demon- 
stration is  too  long  for  him  to  give.  Those  who  have  no 
notion  of  the  quadrature  question  may  look  at  the  English 
Cyclopcedia,  art.  "Quadrature  of  the  Circle." 

Tetragonismus.  Id  est  circuli  quadratura  per  Campanum,  Archi- 
medem  Syracusanum,  atque  Boetium  mathematical  perspica- 
cissimos  adinventa. — At  the  end,  Impressum  Venetiis  per  loan. 
Bapti.  Sessa.  Anno  ab  incarnatione  Domini,  1503.  Die  28 
Augusti. 

*  Edward  Cocker  was  born  in  1631  and  died  between  1671  and 
1677.  His  famous  arithmetic  appeared  in  1677  and  went  through 
many  editions.  It  was  written  in  a  style  that  appealed  to  teachers, 
and  was  so  popular  that  the  expression  "According  to  Cocker"  be- 
came a  household  phrase.  Early  in  the  nineteenth  century  there  was 
a  similar  saying  in  America,  "According  to  Daboll,"  whose  arith- 
metic had  some  points  of  analogy  to  that  of  Cocker.  Each  had  a 
well-known  prototype  in  the  ancient  saying,  "He  reckons  like  Nico- 
machus  of  Gerasa." 

8  So  in  the  original,  for  Barreme.  Frangois  Barreme  was  to 
France  what  Cocker  was  to  England.  He  was  born  at  Lyons  in 
1640,  and  died  at  Paris  in  1703.  He  published  several  arithmetics, 
dedicating  them  to  his  patron,  Colbert.  One  of  the  best  known  of 
his  works  is  Uarithmetique,  ou  le  livre  facile  pour  apprendre  farith- 
metique  soi-meme,  1677.  The  French  word  bareme  or  barreme,  a 
ready-reckoner,  is  derived  from  his  name. 

1  Born  at  Rome,  about  480  A.  D. ;  died  at  Pavia,  524.  Gibbon 
speaks  of  him  as  "the  last  of  the  Romans  whom  Cato  or  Tully  could 
have  acknowledged  for  their  countryman."  His  works  on  arithmetic, 
music,  and  geometry  were  classics  in  the  medieval  schools. 


ON   SQUARING  THE   CIRCLE.  43 

This  book  has  never  been  noticed  in  the  history  of  the 
subject,  and  I  cannot  find  any  mention  of  it.  The  quadrature 
of  Campanus2  takes  the  ratio  of  Archimedes,3  7  to  22  to  be 
absolutely  correct;  the  account  given  of  Archimedes  is  not 
a  translation  of  his  book ;  and  that  of  Boetius  has  more  than 
is  in  Boet/nus.  This  book  must  stand,  with  the  next,  as  the 
earliest  in  print  on  the  subject,  until  further  showing:  Mur- 
hard4  and  Kastner5  have  nothing  so  early.  It  is  edited  by 
Lucas  Gauricus,6  who  has  given  a  short  preface.  Luca  Gau- 
rico,  Bishop  of  Civita  Ducale,  an  astrologer  of  astrologers, 
published  this  work  at  about  thirty  years  of  age,  and  lived 
to  eighty-two.  His  works  are  collected  in  folios,  but  I  do 
not  know  whether  they  contain  this  production.  The  poor 
fellow  could  never  tell  his  own  fortune,  because  his  father 
neglected  to  note  the  hour  and  minute  of  his  birth.  But  if 
there  had  been  anything  in  astrology,  he  could  have  worked 
back,  as  Adams7  and  Leverrier8  did  when  they  caught  Nep- 

a  Johannes  Campanus,  of  Novarra,  was  chaplain  to  Pope  Urban 
IV  (1261-1264).  He  was  one  of  the  early  medieval  translators  of 
Euclid  from  the  Arabic  into  Latin,  and  the  first  printed  edition  of 
the  Elements  (Venice,  1482)  was  from  his  translation.  In  this  work 
he  probably  depended  not  a  little  upon  at  least  two  or  three  earlier 
scholars.  He  also  wrote  De  computo  ecclesiastico  Calendarium,  and 
De  quadratura  circuit. 

8  Archimedes  gave  3Vr  and  310Ai  as  the  limits  of  the  ratio  of  the 
circumference  to  the  diameter  of  a  circle. 

*Friedrich  W.  A.  Murhard  was  born  at  Cassel  in  1779  and  died 
there  in  1853.  His  Bibliotheca  Mat  hematic  a,  Leipsic,  1797-1805,  is 
ill  arranged  and  inaccurate,  but  it  is  still  a  helpful  bibliography.  De 
Morgan  speaks  somewhere  of  his  indebtedness  to  it. 

B  Abraham  Gotthelf  Kastner  was  born  at  Leipsic  in  1719,  and 
died  at  Gottingen  in  1800.  He  was  professor  of  mathematics  and 
physics  at  Gottingen.  His  Geschichte  der  Mathematik  (1796-1800) 
was  a  work  of  considerable  merit.  In  the  text  of  the  Budget  of 
Paradoxes  the  name  appears  throughout  as  Kastner  instead  of  Kast- 
ner. 

6  Lucas  Gauricus,  or  Luca  Gaurico,  born  at  Giffoni,  near  Naples, 
in  1476;  died  at  Rome  in  1558.  He  was  an  astrologer  and  mathe- 
matician, and  was  professor  of  mathematics  at  Ferrara  in  I531*  In 
1545  he  became  bishop  of  Civita  Ducale. 

TJohn  Couch  Adams  was  born  at  Lidcot,  Cornwall,  in  1819,  and 
died  in  1892.  He  and  Leverrier  predicted  the  discovery  of  Neptune 
from  the  perturbations  in  Uranus. 

8  Urbain- Jean- Joseph  Leverrier  was  born  at  Saint-L6,  Manche, 


44  A    BUDGET   OF    PARADOXES. 

tune:  at  sixty  he  could  have  examined  every  minute  of  his 
day  of  birth,  by  the  events  of  his  life,  and  so  would  have 
found  the  right  minute.  He  could  then  have  gone  on,  by 
rules  of  prophecy.  Gauricus  was  the  mathematical  teacher 
of  Joseph  Scaliger,9  who  did  him  no  credit,  as  we  shall  see. 

BOVILLUS    ON    THE    QUADRATURE    PROBLEM. 

In  hoc  opere  contenta  Epitome Liber  de  quadratura  Circuli. 

....  Paris,  1503,  folio. 

The  quadrator  is  Charles  Bovillus,1  who  adopted  the  views 
of  Cardinal  Cusa,2  presently  mentioned.  Montucla  is  hard 
on  his  compatriot,  who,  he  says,  was  only  saved  from  the 
laughter  of  geometers  by  his  obscurity.  Persons  must  guard 
against  most  historians  of  mathematics  in  one  point:  they 
frequently  attribute  to  his  own  age  the  obscurity  which  a 
writer  has  in  their  own  time.  This  tract  was  printed  by 
Henry  Stephens,3  at  the  instigation  of  Faber  Stapulensis,4 

in  1811,  and  died  at  Paris  in  1877.  It  was  his  data  respecting  the 
perturbations  of  Uranus  that  were  used  by  Adams  and  himself  in 
locating  Neptune. 

*  Joseph-Juste  Scaliger,  the  celebrated  philologist,  was  born  at 
Agen  in  1540,  and  died  at  Ley  den  in  1609.  His  Cyclometrica  ele- 
menta,  to  which  De  Morgan  refers,  appeared  at  Leyden  in  1594. 

1  The  title  is:  In  hoc  libro  contenta. . .  .Introductio  i  geometria 
. . .  .Liber  de  quadratura  cirfuli.  Liber  de  cubicatione  sphere.  Per- 
spectiva  introductio.  Carolus  Bovillus,  or  Charles  Bouvelles  (Boii- 
elles,  Bouilles,  Bouvel),  was  born  at  Saucourt,  Picardy,  about  1470, 
and  died  at  Noyon  about  1533.  He  was  canon  and  professor  of 
theology  at  Noyon.  His  Introductio  contains  considerable  work  on 
star  polygons,  a  favorite  study  in  the  Middle  Ages  and  early  Re- 
naissance. His  work  Que  hoc  volumine  continetur.  Liber  de  in- 
tellectu.  Liber  de  sensu,  etc.,  appeared  at  Paris  in  1509-10. 

2Nicolaus  Cusanus,  Nicolaus  Chrypffs  or  Krebs,  was  born  at 
Kues  on  the  Mosel  in  1401,  and  died  at  Todi,  Umbria,  August  n, 
1464.  He  held  positions  of  honor  in  the  church,  including  the 
bishopric  of  Brescia.  He  was  made  a  cardinal  in  1448.  He  wrote 
several  works  on  mathematics,  his  Opuscula  varia  appearing  about 
1490,  probably  at  Strasburg,  but  published  without  date  or  place. 
His  Opera  appeared  at  Paris  in  1511  and  again  in  1514,  and  at  Basel 
in  1565. 

"Henry  Stephens  (born  at  Paris  about  1528,  died  at  Lyons  in 
1598)  was  one  of  the  most  successful  printers  of  his  day.  He  was 
known  as  Typographus  Parisiensis,  and  to  his  press  we  owe  some 
of  the  best  works  of  the  period.- 

4  Jacobus  Faber  Stapulensis    (Jacques  le  Fevre  d'Estaples)    was 


BOVILLUS  ON  THE  QUADRATURE  PROBLEM.  45 

and  is  recorded  by  Dechales,5  etc.  It  was  also  introduced  into 
the  Margarita  Philosophica  of  181 5,6  in  the  same  appendix 
with  the  new  perspective  from  Viator.  This  is  not  extreme 
obscurity,  by  any  means.  The  quadrature  deserved  it;  but 
that  is  another  point. 

It  is  stated  by  Montucla  that  Bovillus  makes  TT  =  V 10. 
But  Montucla  cites  a  work  of  1507,  Intro  duct  or  ium  Geo- 
metricum,  which  I  have  never  seen.7  He  finds  in  it  an 
account  which  Bovillus  gives  of  the  quadrature  of  the  peas- 
ant laborer,  and  describes  it  as  agreeing  with  his  own.  But 
the  description  makes  TT  =  3J,  which  it  thus  appears  Bovillus 
could  not  distinguish  from  \/10.  It  seems  also  that  this  3J, 
about  which  we  shall  see  so  much  in  the  sequel,  takes  its  rise 
in  the  thoughtful  head  of  a  poor  laborer.  It  does  him  great 
honor,  being  so  near  the  truth,  and  he  having  no  means  of 
instruction.  In  our  day,  when  an  ignorant  person  chooses 
to  bring  his  fancy  forward  in  opposition  to  demonstration 
which  he  will  not  study,  he  is  deservedly  laughed  at. 

born  at  Estaples,  near  Amiens,  in  1455,  and  died  at  Nerac  in  1536. 
He  was  a  priest,  vicar  of  the  bishop  of  Meaux,  lecturer  on  philos- 
ophy at  the  College  Lemoine  in  Paris,  and  tutor  to  Charles,  son  of 
Francois  I.  He  wrote  on  philosophy,  theology,  and  mathematics. 

8  Claude-Frangois  Milliet  de  Challes  was  born  at  Chambery  in 
1621,  and  died  at  Turin  in  1678.  He  edited  Eudidis  Elementorum 
libri  octo  in  1660,  and  published  a  Cursus  seu  mundus  mathematicus, 
which  included  a  short  history  of  mathematics,  in  1674.  He  also 
wrote  on  mathematical  geography. 

6  This  date  should  be  1503,  if  he  refers  to  the  first  edition.  It  is 
well  known  that  this  is  the  first  encyclopedia  worthy  the  name  to 
appear  in  print.  It  was  written  by  Gregorius  Reisch  (born  at 
Balingen,  and  died  at  Freiburg  in  1487),  prior  of  the  cloister  at 
Freiburg  and  confessor  to  Maximilian  I.  The  first  edition  appeared 
at  Freiburg  in  1503,  and  it  passed  through  many  editions  in  the 
sixteenth  and  seventeenth  centuries.  The  title  of  the  1504  edition 
reads:  Aepitoma  omnis  phylosophiae.  alias  Margarita  phylosophica 
tractans  de  omni  genere  scibili :  Cum  additionibus :  Quae  in  alijs  non 
habentur. 

'This  is  the  Introductio  in  arithmeticam  Divi  S.  Boetii Eft- 
tome  rerum  geometricarum  ex  geometrica  introductio  C.  Bovilli. 
De  quadratura  circuli  demonstratio  ex  Campano,  that  appeared  with- 
out date  about  1507. 


46  A   BUDGET   OF    PARADOXES. 

THE  STORY  OF  LACOMME'S  ATTEMPT  AT  QUADRA- 
TURE. 

Mr.  James  Smith,1  of  Liverpool— hereinafter  notorified— 
attributes  the  first  announcement  of  3J  to  M.  Joseph  La- 
comme,  a  French  well-sinker,  of  whom  he  gives  the  following 
account : 

"In  the  year  1836,  at  which  time  Lacomme  could  neither 
read  nor  write,  he  had  constructed  a  circular  reservoir  and 
wished  to  know  the  quantity  of  stone  that  would  be  re- 
quired to  pave  the  bottom,  and  for  this  purpose  called  on  a 
professor  of  mathematics.  On  putting  his  question  and  giv- 
ing the  diameter,  he  was  surprised  at  getting  the  following 
answer  from  the  Professor :  'Qu'il  lui  etait  impossible  de  le 
lui  dire  au  juste,  attendu  que  personne  n'avait  encore  pit 
trouver  d'une  maniere  exacte  le  rapport  de  la  cir -conference 
au  diametre.'2  From  this  he  was  led  to  attempt  the  solution 
of  the  problem.  His  first  process  was  purely  mechanical, 
and  he  was  so  far  convinced  he  had  made  the  discovery  that 
he  took  to  educating  himself,  and  became  an  expert  arith- 
metician, and  then  found  that  arithmetical  results  agreed 
with  his  mechanical  experiments.  He  appears  to  have  eked 
out  a  bare  existence  for  many  years  by  teaching  arithmetic, 
all  the  time  struggling  to  get  a  hearing  from  some  of  the 
learned  societies,  but  without  success.  In  the  year  1855  he 
found  his  way  to  Paris,  where,  as  if  by  accident,  he  made 
the  acquaintance  of  a  young  gentleman,  son  of  M.  Winter, 
a  commissioner  of  police,  and  taught  him  his  peculiar  meth- 
ods of  calculation.  The  young  man  was  so  enchanted  that 
he  strongly  recommended  Lacomme  to  his  father,  and  sub- 

1  Born  at  Liverpool  in  1805,  and  died  there  about  1872.    He  was 
a  merchant,  and  in  1865  he  published,  at  Liverpool,  a  work  entitled 
The  Quadrature  of  the  Circle,  or  the  True  Ratio  between  the  Diam- 
eter and  Circumference  geometrically  and  mathematically  demon- 
strated.   In  this  he  gives  the  ratio  as  exactly  3Vs. 

2  "That  it  would  be  impossible  to  tell  him  exactly,  since  no  one 
had  yet  been  able  to  find  precisely  the  ratio  of  the  circumference  to 
the  diameter." 


NICOLAUS   OF    CUSA'S   ATTEMPT.  47 

sequently  through  M.  Winter  he  obtained  an  introduction 
to  the  President  of  the  Society  of  Arts  and  Sciences  of  Paris. 
A  committee  of  the  society  was  appointed  to  examine  and 
report  upon  his  discovery,  and  the  society  at  its  seance  of 
March  17,  1856,  awarded  a  silver  medal  of  the  first  class  to 
M.  Joseph  Lacomme  for  his  discovery  of  the  true  ratio  of 
diameter  to  circumference  in  a  circle.  He  subsequently  re- 
ceived three  other  medals  from  other  societies.  While  writ- 
ing this  I  have  his  likeness  before  me,  with  his  medals  on 
his  breast,  which  stands  as  a  frontispiece  to  a  short  biography 
of  this  extraordinary  man,  for  which  I  am  indebted  to  the 
gentleman  who  did  me  the  honor  to  publish  a  French  trans- 
lation of  the  pamphlet  I  distributed  at  the  meeting  of  the 
British  Association  for  the  Advancement  of  Science,  at  Ox- 
ford, in  1860. — Correspondent,  May  3,  1866. 

My  inquiries  show  that  the  story  of  the  medals  is  not 
incredible.  There  are  at  Paris  little  private  societies  which 
have  not  so  much  claim  to  be  exponents  of  scientific  opinion 
as  our  own  Mechanics'  Institutes.  Some  of  them  were  in- 
tended to  give  a  false  lustre:  as  the  "Institut  Historique," 
the  members  of  which  are  "Membre  de  ITnstitut  Historique." 
That  M.  Lacomme  should  have  got  four  medals  from  so- 
cieties of  this  class  is  very  possible :  that  he  should  have  re- 
ceived one  from  any  society  at  Paris  which  has  the  least 
claim  to  give  one  is  as  yet  simply  incredible. 

NICOLAUS  OF  CUSA'S  ATTEMPT. 
Nicolai  de  Cusa  Opera  Omnia.    Venice,  1514.    3  vols.  folio. 

The  real  title  is  "Haec  accurata  recognitio  trium  volu- 
mimmi  operum  clariss.  P.  Nicolai  Cusse . . . .  proxime  se- 
quens  pagina  monstrat."1  Cardinal  Cusa,  who  died  in  1464, 
is  one  of  the  earliest  modern  attempters.  His  quadrature 
is  found  in  the  second  volume,  and  is  now  quite  unreadable. 

1  This  is  the  Paris  edition :  "Parisiis :  ex  officina  Ascensiana  anno 

Christi MDXIIII,"   as   appears   by  the  colophon  of  the   second 

volume  to  which  De  Morgan  refers. 


48  A   BUDGET   OF   PARADOXES. 

In  these  early  days  every  quadrator  found  a  geometrical 
opponent,  who  finished  him.  Regimontanus2  did  this  office 
for  the  Cardinal. 

HENRY  CORNELIUS  AGRIPPA. 

De  Occulta  Philosophia  libri  III.    By  Henry  Cornelius  Agrippa. 

Lyons,  1550,  8vo. 
De  incertitudine  et  vanitate  scientiarum.    By  the  same.   Cologne. 

1531,  8vo. 

The  first  editions  of  these  works  were  of  1530,  as  well 
as  I  can  make  out;  but  the  first  was  in  progress  in  15 10.1 
In  the  second  work  Agrippa  repents  of  having  wasted  time 
on  the  magic  of  the  first;  but  all  those  who  actually  deal 
with  demons  are  destined  to  eternal  fire  with  Jamnes  and 
Mambres  and  Simon  Magus.  This  means,  as  is  the  fact, 
that  his  occult  philosophy  did  not  actually  enter  upon  black 
magic,  but  confined  itself  to  the  power  of  the  stars,  of  num- 
bers, etc.  The  fourth  book,  which  appeared  after  the  death 
of  Agrippa,  and  really  concerns  dealing  with  evil  spirits, 
is  undoubtedly  spurious.  It  is  very  difficult  to  make  out 
what  Agrippa  really  believed  on  the  subject.  I  have  intro- 
duced his  books  as  the  most  marked  specimens  of  treatises 
on  magic,  a  paradox  of  our  day,  though  not  far  from  ortho- 
doxy in  his ;  and  here  I  should  have  ended  my  notice,  if  I 
had  not  casually  found  something  more  interesting  to  the 
reader  of  our  day. 

2  Regiomontanus,  or  Johann  Miiller  of  Konigsberg  (Regiomon- 
tanus),  was  born  at  Konigsberg  in  Franconia,  June  5,  1436,  and  died 
at  Rome  July  6,  1476.  He  studied  at  Vienna  under  the  great  astron- 
omer Peuerbach,  and  was  his  most  famous  pupil.  He  wrote  numer- 
ous works,  chiefly  on  astronomy.  He  is  also  known  by  the  names 
loannes  de  Monte  Regio,  de  Regiomonte,  loannes  Germanus  de 
Regiomonte,  etc. 

1  Henry  Cornelius  Agrippa  was  born  at  Cologne  in  1486  and  died 
either  at  Lyons  in  1534  or  at  Grenoble  in  1535.  He  was  professor  of 
theology  at  Cologne  and  also  at  Turin.  After  the  publication  of  his 
De  Occulta  Philosophia  he  was  imprisoned  for  sorcery.  Both  works 
appeared  at  Antwerp  in  1530,  and  each  passed  through  a  large  num- 
ber of  editions.  A  French  translation  appeared  in  Paris  in  1582, 
and  an  English  one  in  London  in  1651. 


.WHICH   LEADS  TO   WALTER  SCOTT.  49 


WHICH  LEADS  TO  WALTER  SCOTT. 

Walter  Scott,  it  is  well  known,  was  curious  on  all  matters 
connected  with  magic,  and  has  used  them  very  widely.  But 
it  is  hardly  known  how  much  pains  he  has  taken  to  be  cor- 
rect, and  to  give  the  real  thing.  The  most  decided  detail  of 
a  magical  process  which  is  found  in  his  writings  is  that  of 
Dousterswivel  in  The  Antiquary,  and  it  is  obvious,  by  his 
accuracy  of  process,  that  he  does  not  intend  the  adept  for  a 
mere  impostor,  but  for  one  who  had  a  lurking  belief  in  the 
efficacy  of  his  own  processes,  coupled  with  intent  to  make 
a  fraudulent  use  of  them.  The  materials  for  the  process 
are  taken  from  Agrippa.  I  first  quote  Mr.  Dousterswivel: 

". .  .1  take  a  silver  plate  when  she  [the  moon]  is  in  her 
fifteenth  mansion,  which  mansion  is  in  de  head  of  Libra,  and 
I  engrave  upon  one  side  de  worts  Schedbarschemoth  Schar- 
tachan  [ch  should  be  t] — dat  is,  de  Intelligence  of  de  In- 
telligence of  de  moon — and  I  make  his  picture  like  a  flying 
serpent  with  a  turkey-cock's  head — vary  well — Then  upon 
this  side  I  make  de  table  of  de  moon,  which  is  a  square  of 
nine,  multiplied  into  itself,  with  eighty-one  numbers  [nine] 
on  every  side  and  diameter  nine " 

In  the  De  Occulta  Philosophia,  p.  290,  we  find  that  the 
fifteenth  mansion  of  the  moon  incipit  capite  Libra,  and  is 
good  pro  extrahendis  thesauris,  the  object  being  to  discover 
hidden  treasure.  In  p.  246,  we  learn  that  a  silver  plate  must 
be  used  with  the  moon.  In  p.  248,  we  have  the  words  which 
denote  the  Intelligence,  etc.  But,  owing  to  the  falling  of  a 
number  into  a  wrong  line,  or  the  misplacement  of  a  line,  one 
or  other — which  takes  place  in  all  the  editions  I  have  exam- 
ined— Scott  has,  sad  to  say,  got  hold  of  the  wrong  words; 
he  has  written  down  the  demon  of  the  demons  of  the  moon. 
Instead  of  the  gibberish  above,  it  should  have  been  Malcha 
betarsisim  hed  beruah  schenhakim.  In  p.  253,  we  have  the 
magic  square  of  the  moon,  with  eighty-one  numbers,  and  the 
symbol  for  the  Intelligence,  which  Scott  likens  to  a  flying 


50  A   BUDGET   OF   PARADOXES. 

serpent  with  a  turkey-cock's  head.  He  was  obliged  to  say 
something;  but  I  will  stake  my  character — and  so  save  a 
woodcut — on  the  scratches  being  more  like  a  pair  of  legs, 
one  shorter  than  the  other,  without  a  body,  jumping  over  a 
six-barred  gate  placed  side  uppermost.  Those  who  thought 
that  Scott  forged  his  own  nonsense,  will  henceforth  stand 
corrected.  As  to  the  spirit  Peolphan,  etc.,  no  doubt  Scott 
got  it  from  the  authors  he  elsewhere  mentions,  Nicolaus 
Remigius1  and  Petrus  Thyracus;  but  this  last  word  should 
be  Thyrseus. 

The  tendency  of  Scott's  mind  towards  prophecy  is  very 
marked,  and  it  is  always  fulfilled.  Hyder,  in  his  disguise, 
calls  out  to  Tippoo :  "Cursed  is  the  prince  who  barters  jus- 
tice for  lust;  he  shall  die  in  the  gate  by  the  sword  of  the 
stranger."  Tippoo  was  killed  in  a  gateway  at  Seringapatam.2 

FINAEUS  ON  CIRCLE  SQUARING. 
Orontii  Finaei . . .  Quadratura  Circuli.     Paris,  1544,  4to. 

Orontius1  squared  the  circle  out  of  all  comprehension; 
but  he  was  killed  by  a  feather  from  his  own  wing.  His 

1  Nicolaus  Remegius  was  born  in  Lorraine  in  1554,  and  died  at 
Nancy  in  1600.  He  was  a  jurist  and  historian,  and  held  the  office 
of  procurator  general  to  the  Duke  of  Lorraine. 

2  This  was  at  the  storming  of  the  city  by  trie  British  on  May  4, 
1799.  From  his  having  been  born  in  India,  all  this  appealed  strongly 
to  the  interests  of  De  Morgan. 

1  Orontius  Finaeus,  or  Oronce  Fine,  was  born  at  Brianc.on  in  1494 
and  died  at  Paris,  October  6,  1555.  He  was  imprisoned  by  Frangois 
I  for  refusing  to  recognize  the  concordat  (1517).  He  was  made 
professor  of  mathematics  in  the  College  Royal  (later  called  the 
College  de  France)  in  1532.  He  wrote  extensively  on  astronomy 
and  geometry,  but  was  by  no  means  a  great  scholar.  He  was  a 
pretentious  man,  and  his  works  went  through  several  editions.  His 
Protomathesis  appeared  at  Paris  in  1530-32.  The  work  referred  to 
by  De  Morgan  is  the  Quadratura  clrculi  tandem  inventa  &  clarissime 

demonstrata Lutetiae  Parisiorum,  1544,  fol.     In  the  1556  edition 

of  his  De  rebus  mathematicis ,  hactenus  desideratis,  Libri  IIII,  pub- 
lished at  Paris,  the  subtitle  is:  Quibus  inter  catera,  Circuli  quadra- 
tura  Centum  modis,  &  supra,  per  eundem  Orontlum  recenter  ex- 
cogitatis,  demonstrates,  so  that  he  kept  up  his  efforts  until  his 
death. 


FINAEUS  ON   CIRCLE   SQUARING.  51 

former  pupil,  John  Buteo,2  the  same  who — I  believe  for  the 
first  time — calculated  the  question  of  Noah's  ark,  as  to  its 
power  to  hold  all  the  animals  and  stores,  unsquared  him 
completely.  Orontius  was  the  author  of  very  many  works, 
and  died  in  1555.  Among  the  laudatory  verses  which,  as 
was  usual,  precede  this  work,  there  is  one  of  a  rare  charac- 
ter: a  congratulatory  ode  to  the  wife  of  the  author.  The 
French  now  call  this  writer  Oronce  Finee;  but  there  is 
much  difficulty  about  delatinization.  Is  this  more  correct 
than  Oronce  Fine,  which  the  translator  of  De  Thou  uses? 
Or  than  Horonce  Phine,  which  older  writers  give  ?  I  cannot 
understand  why  M.  de  Viette3  should  be  called  Viete,  because 
his  Latin  name  is  Vieta.  It  is  difficult  to  restore  Buteo ;  for 
not  only  now  is  butor  a  blockhead  as  well  as  a  bird,  but  we 
really  cannot  know  what  kind  of  bird  Buteo  stood  for.  We 
may  be  sure  that  Madame  Fine  was  Denise  Blanche;  for 
Dionysia  Candida  can  mean  nothing  else.  Let  her  shade 
rejoice  in  the  fame  which  Hubertus  Sussannaeus  has  given 
her. 

I  ought  to  add  that  the  quadrature  of  Orontius,  and 
solutions  of  all  the  other  difficulties,  were  first  published  in 
De  Rebus  Mathematicis  Hactenus  Desideratis*  of  which  I 
have  not  the  date. 

'Johannes  Buteo  (Boteo,  Buteon,  Bateon)  was  born  in  Dauphine 
c.  1485-1489,  and  died  in  a  cloister  in  1560  or  1564.  Some  writers 
give  Charpey  as  the  place  and  1492  as  the  date  of  his  birth,  and 
state  that  he  died  at  Canar  in  1572.  He  belonged  to  the  order  of 
St.  Anthony,  and  wrote  chiefly  on  geometry,  exposing  the  pretenses 
of  Finaeus.  His  Opera  geometrica  appeared  at  Lyons  in  1554,  and 
his  Logistica  and  De  quadrature,  circuit  libri  duo  at  Lyons  in  1559. 

'This  is  the  great  French  algebraist,  Francois  Viete  (Vieta), 
who  was  born  at  Fontenay-le-Comte  in  1540,  and  died  at  Paris, 
December  13,  1603.  His  well-known  Isagoge  in  artem  analyticam 
appeared  at  Tours  in  1591.  His  Opera  mathematica  was  edited  by 
Van  Schooten  in  1646. 

4  This  is  the  De  Rebus  mathematics  hactenus  desideratis,  Libri 
IIII,  that  appeared  in  Paris  in  1556.  For  the  title  page  see  Smith, 
D.  K,  Kara  Arithmetica,  Boston,  1908,  p.  280. 


52  A  BUDGET  OF  PARADOXES. 

DUCHESNE,  AND  A  DISQUISITION  ON  ETYMOLOGY. 

Nicolai  Raymari  Ursi  Dithmarsi  Fundamentum  Astronomicum, 

id  est,  nova  doctrina  sinuum  et  triangulorum Strasburg, 

1588,  410.1 

People  choose  the  name  of  this  astronomer  for  them- 
selves: I  take  Ursus,  because  he  was  a  bear.  This  book 
gave  the  quadrature  of  Simon  Duchesne,2  or  a  Quercu,  which 
excited  Peter  Metius,3  as  presently  noticed.  It  also  gave  that 
unintelligible  reference  to  Justus  Byrgius  which  has  been 
used  in  the  discussion  about  the  invention  of  logarithms.4 

The  real  name  of  Duchesne  is  Van  der  Eycke.  I  have 
met  with  a  tract  in  Dutch,  Letterkundige  Aanteekeningen, 
upon  Van  Eycke,  Van  Ceulen,5  etc.,  by  J.J.  Dodt  van  Flens- 
burg,6  which  I  make  out  to  be  since  1841  in  date.  I  should 

*The  title  is  correct  except  for  a  colon  after  Astronomicum. 
Nicolaus  Raimarus  Ursus  was  born  in  Henstede  or  Hattstede,  in 
Dithmarschen,  and  died  at  Prague  in  1599  or  1600.  He  was  a  pupil 
of  Tycho  Brahe.  He  also  wrote  De  astronomis  hypothesibus  (1597) 
and  Arithmetica  analytica  vulgo  Cosa  oder  Algebra  (1601).- 

2  Born  at  Dole,  Franche-Comte,  about  1550,  died  in  Holland 
about  1600.  The  work  to  which  reference  is  made  is  the  Quadrature 
du  cercle,  ou  maniere  de  trouver  un  quarre  egal  au  cercle  donne, 
which  appeared  at  Delft  in  1584.  Duchesne  had  the  courage  of  his 
convictions,  not  only  on  circle-squaring  but  on  religion  as  well,  for  he 
was  obliged  to  leave  France  because  of  his  conversion  to  Calvinism. 
De  Morgan's  statement  that  his  real  name  is  Van  der  Eycke  is 
curious,  since  he  was  French  born.  The  Dutch  may  have  translated 
his  name  when  he  became  professor  at  Delft,  but  we  might  equally 
well  say,  that  his  real  name  was  Quercetanus  or  a  Quercu. 

'This  was  the  father  of  Adriaan  Metius  (1571-1635).  He  was  a 
mathematician  and  military  engineer,  and  suggested  the  ratio  "%• 
for  TT,  a  ratio  afterwards  published  by  his  son.  The  ratio,  then  new 
to  Europe,  had  long  been  known  and  used  in  China,  having  been 
found  by  Tsu  Ch'ung-chih  (428-499  A.  D.). 

4  This  was  Jost  Biirgi,  or  Justus  Byrgius,  the  Swiss  mathemati- 
cian of  whom  Kepler  wrote  in  1627:  "Apices  logistici  Justo  Byrgio 
multis  annis  ante  editionem  Neperianam  viam  prseiverunt  ad  hos 
ipsissimos  logarithmos."  He  constructed  a  table  of  antilogarithms 
(Arithmetische  und  geometrische  Progress-Tabulen),  but  it  was  not 
published  until  after  Napier's  work  appeared. 

8  Ludolphus  Van  Ceulen,  born  at  Hildesheim,  and  died  at  Leyden 
in  1610.  It  was  he  who  first  carried  the  computation  of  *  to  35  deci- 
mal places. 

"Jens  Jenssen  Dodt,  van  Flensburg,  a  Dutch  historian,  who  died 
in  1847. 


FALCO'S  RARE  TRACT.  53 

much  like  a  translation  of  this  tract  to  be  printed,  say  in  the 
Phil.  Mag.  Dutch  would  be  clear  English  if  it  were  prop- 
erly spelt.  For  example,  learn-master  would  be  seen  at 
once  to  be  teacher',  but  they  will  spell  it  leermeester.  Of 
these  they  write  as  van  deze\  widow  the  make  weduwe. 
All  this  is  plain  to  me,  who  never  saw  a  Dutch  dictionary  in 
my  life;  but  many  of  their  misspellings  are  quite  uncon- 
querable. 

FALCO'S  RARE  TRACT. 

Jacobus  Falco  Valentinus,  miles  Ordinis  Montesiani,  hanc  circuli 
quadraturam  invenit.     Antwerp,  1589,  4to.1 

The  attempt  is  more  than  commonly  worthless;  but  as 
Montucla  and  others  have  referred  to  the  verses  at  the  end, 
and  as  the  tract  is  of  the  rarest,  I  will  quote  them: 

Circulus  loquitur. 
Vocabar  ante  circulus 
Eramque  curvus  undique 
Ut  alta  sblis  orbita 
Et  arcus  ille  nubium. 
Eram  figura  nobilis 
Carensque  sola  origine 
Carensque  sola  termino. 
Modo  indecora  prodeo 
Novisque  feeder  angulis. 
Nee  hoc  peregit  Archytas2 
Neque  Icari  pater  neque 
Tuus,  lapete,  films. 
Quis  ergo  casus  aut  Deus 
Meam  quadravit  aream? 

Responded  auctor. 
Ad  alta  Turise  ostia 
Lacumque  limpidissimum 
Sita  est  beata  civitas 

*I  do  not  know  this  edition.     There  was  one  "Antverpiae  apud 
Petrum  Bellerum  sub  scuto  Burgundiae,"  4to,  in  1591. 

2 Archytas  of  Tarentum   (430-365  B.C.)   who  wrote  on  propor- 
tion, irrationals,  and  the  duplication  of  the  cube. 


54  A  BUDGET  OF  PARADOXES. 

Parum  Saguntus  abfuit 
Abestque  Sucro  plusculum. 
Hie  est  poeta  quispiam 
Libenter  astra  consulens 
Sibique  semper  arrogans 
Negata  doctioribus, 
Senex  ubique  cogitans 
Sui  frequenter  immemor 
Nee  explicare  circinum 
Nee  exarare  lineas 
Sciens  ut  ipse  prsedicat 
Hie  ergo  bellus  artifex 
Tuam  quadravit  aream.3 

Falco's  verses  are  pretty,  if  the  o  -  mysteries  be  correct ; 
but  of  these  things  I  have  forgotten — what  I  knew.  [One 
mistake  has  been  pointed  out  to  me:  it  is  Archytas]. 

As  a  specimen  of  the  way  in  which  history  is  written,  I 
copy  the  account  which  Montucla — who  is  accurate  when  he 
writes  about  what  he  has  seen — gives  of  these  verses.  He 
gives  the  date  1587;  he  places  the  verses  at  the  beginning 
instead  of  the  end;  he  says  the  circle  thanks  its  quadrator 
affectionately;  and  he  says  the  good  and  modest  chevalier 
gives  all  the  glory  to  the  patron  saint  of  his  order.  All  of 
little  consequence,  as  it  happens ;  but  writing  at  second-hand 
makes  as  complete  mistakes  about  more  important  matters. 

8  The  Circle  Speaks. 

"At  first  a  circle  I  was  called,  But  now  unlovely  do  I  seem 

And  was  a  curve  around  about  Polluted  by  some  angles  new. 

Like  lofty  orbit  of  the  sun  This  thing  Archytas  hath  not  done 

Or  rainbowarch  amongthe clouds.  Nor  noble  sire  of  Icarus 

A  noble  figure  then  was  I —  Nor  son  of  thine,  lapetus. 

And  lacking  nothing  but  a  start,  What  accident  or  god  can  then 

And  lacking  nothing  but  an  end.  Have  quadrated  mine  area?" 

The  Author  Replies. 

"By  deepest  mouth  of  Turia  What  is  denied  to  wiser  men; — 

And  lake  of  limpid  clearness,  lies    An  old  man  musing  here  and  there 
A  happy  state  not  far  removed        And  oft  forgetful  of  himself, 
From  old  Saguntus  ;  farther  yet      Not  knowing  how  to  rightly  place 
A  little  way  from  Sucro  town.         The  compasses,  nor  draw  a  line, 
In  this  place  doth  a  poet  dwell,       As  he  doth  of  himself  relate.  f 
Who  oft  the  stars  will  closely  scan,  This  craftsman  fine,  in  sooth  it  is 
And  always  for  himself  doth  claim  Hath  quadrated  thine  area." 


BUNGUS  ON  THE  MYSTERY  OF  NUMBER.  55 


BUNGUS  ON  THE  MYSTERY  OF  NUMBER. 

Petri  Bungi  Bergomatis  Numerorum  mysteria.     Bergomi  [Ber- 
gamo], 1591,  4to.    Second  Edition. 

The  first  edition  is  said  to  be  of  1585  j1  the  third,  Paris, 
1618.  Bungus  is  not  for  my  purpose  on  his  own  score,  but 
those  who  gave  the  numbers  their  mysterious  characters: 
he  is  but  a  collector.  He  quotes  or  uses  402  authors,  as  we 
are  informed  by  his  list ;  this  just  beats  Warburton,2  whom 
some  eulogist  or  satirist,  I  forget  which,  holds  up  as  having 
used  400  authors  in  some  one  work.  Bungus  goes  through 
1,  2,  3,  etc.,  and  gives  the  account  of  everything  remarkable 
in  which  each  number  occurs ;  his  accounts  not  being  always 
mysterious.  The  numbers  which  have  nothing  to  say  for 
themselves  are  omitted :  thus  there  is  a  gap  between  50  and 
60.  In  treating  666,  Bungus,  a  good  Catholic,  could  not 
compliment  the  Pope  with  it,  but  he  fixes  it  on  Martin 
Luther  with  a  little  forcing.  If  from  A  to  I  represent  1-10, 
from  K  to  S  10-90,  and  from  T  to  Z  100-500,  we  see: 

MARTIN          LUTERA 
30    1    80  100   9   40        20  200  100   5    80    1 
which  gives  666.    Again,  in  Hebrew,  Lulter  does  the  same : 

i    n     5   i  5 

200  400  30  6  30 

And  thus  two  can  play  at  any  game.    The  second  is  better 
than  the  first :  to  Latinize  the  surname  and  not  the  Christian 

*Pietro  Bongo,  or  Petrus  Bungus,  was  born  at  Bergamo,  and 
died  there  in  1601.  His  work  on  the  Mystery  of  Numbers  is  one  of 
the  most  exhaustive  and  erudite  ones  of  the  mystic  writers.  The 
first  edition  appeared  at  Bergamo  in  1583-84;  the  second,  at  Ber- 
gamo in  1584-85;  the  third,  at  yenice  in  1585;  the  fourth,  at  Ber- 
gamo in  1590;  and  the  fifth,  which  De  Morgan  calls  the  second,  in 
1591.  Other  editions,  before  the  Paris  edition  to  which  he  refers, 
appeared  in  1509  and  1614;  and  the  colophon  of  the  Paris  edition  is 
dated  1617.  See  the  editor's  Rara  Arithmetic^  pp.  380-383. 

*  William  Warburton  (1698-1779),  Bishop  of  Gloucester,  whose 
works  got  him  into  numerous  literary  quarrels,  being  the  subject  of 
frequent  satire. 


56  A  BUDGET  OF  PARADOXES. 

name  is  very  unscholarlike.  The  last  number  mentioned  is  a 
thousand  millions ;  all  greater  numbers  are  dismissed  in  half 
a  page.  Then  follows  an  accurate  distinction  between  num- 
ber and  multitude — a  thing  much  wanted  both  in  arithmetic 
and  logic. 

WHICH  LEADS  TO   A   STORY  ABOUT  THE  ROYAL   SO- 
CIETY. 

What  may  be  the  use  of  such  a  book  as  this?  The  last 
occasion  on  which  it  was  used  was  the  following.  Fifteen 
or  sixteen  years  ago  the  Royal  Society  determined  to  restrict 
the  number  of  yearly  admissions  to  fifteen  men  of  science, 
and  noblemen  ad  libitum ;  the  men  of  science  being  selected 
and  recommended  by  the  Council,  with  a  power,  since  prac- 
tically surrendered,  to  the  Society  to  elect  more.  This  plan 
appears  to  me  to  be  directly  against  the  spirit  of  their  char- 
ter, the  true  intent  of  which  is,  that  all  who  are  fit  should  be 
allowed  to  promote  natural  knowledge  in  association,  from 
and  after  the  time  at  which  they  are  both  fit  and  willing. 
It  is  also  working  more  absurdly  from  year  to  year;  the 
tariff  of  fifteen  per  annum  will  soon  amount  to  the  practical 
exlusion  of  many  who  would  be  very  useful.  This  begins 
to  be  felt  already,  I  suspect.  But,  as  appears  above,  the 
body  of  the  Society  has  the  remedy  in  its  own  hands.  When 
the  alteration  was  discussed  by  the  Council,  my  friend  the 
late  Mr.  Galloway,1  then  one  of  the  body,  opposed  it  strongly, 
and  inquired  particularly  into  the  reason  why  -fifteen,  of  all 
numbers,  was  the  one  to  be  selected.  Was  it  because  fifteen 
is  seven  and  eight,  typifying  the  Old  Testament  Sabbath, 
and  the  New  Testament  day  of  the  resurrection  following? 
Was  it  because  Paul  strove  fifteen  days  against  Peter,  prov- 
ing that  he  was  a  doctor  both  of  the  Old  and  New  Testa- 
ment? Was  it  because  the  prophet  Hosea  bought  a  lady 

^Thomas  Galloway  (1796-1851),  who  was  professor  of  mathe- 
matics at  Sandhurst  for  a  time,  and  was  later  the  actuary  of  the 
Amicable  Life  Assurance  Company  of  London.  In  the  latter  capac- 
ity he  naturally  came  to  be  associated  with  De  Morgan. 


A  QUESTION  OF  EVIDENCE.  57 

for  fifteen  pieces  of  silver?  Was  it  because,  according  to 
Micah,  seven  shepherds  and  eight  chiefs  should  waste  the 
Assyrians?  Was  it  because  Ecclesiastes  commands  equal 
reverence  to  be  given  to  both  Testaments — such  was  the 
interpretation — in  the  words  "Give  a  portion  to  seven,  and 
also  to  eight"?  Was  it  because  the  waters  of  the  Deluge 
rose  fifteen  cubits  above  the  mountains? — or  because  they 
lasted  fifteen  decades  of  days?  Was  it  because  Ezekiel's 
temple  had  fifteen  steps?  Was  it  because  Jacob's  ladder 
has  been  supposed  to  have  had  fifteen  steps  ?  Was  it  because 
fifteen  years  were  added  to  the  life  of  Hezekiah?  Was  it 
because  the  feast  of  unleavened  bread  was  on  the  fifteenth 
day  of  the  month  ?  Was  it  because  the  scene  of  the  Ascen- 
sion was  fifteen  stadia  from  Jerusalem?  Was  it  because 
the  stone-masons  and  porters  employed  in  Solomon's  temple 
amounted  to  fifteen  myriads  ?  etc.  The  Council  were  amused 
and  astounded  by  the  volley  of  fifteens  which  was  fired  at 
them ;  they  knowing  nothing  about  Bungus,  of  which  Mr. 
Galloway — who  did  not,  as  the  French  say,  indicate  his 
sources — possessed  the  copy  now  before  me.  In  giving  this 
anecdote  I  give  a  specimen  of  the  book,  which  is  exceedingly 
rare.  Should  another  edition  ever  appear,  which  is  not  very 
probable,  he  would  be  but  a  bungling  Bungus  who  should 
forget  the  fifteen  of  the  Royal  Society. 

AND  ALSO  TO  A  QUESTION  OF  EVIDENCE. 

[I  make  a  remark  on  the  different  colors  which  the  same 
person  gives  to  one  story,  according  to  the  bias  under  which 
he  tells  it.  My  friend  Galloway  told  me  how  he  had  quizzed 
the  Council  of  the  Royal  Society,  to  my  great  amusement. 
Whenever  I  am  struck  by  the  words  of  any  one,  I  carry 
away  a  vivid  recollection  of  position,  gestures,  tones,  etc. 
I  do  not  know  whether  this  be  common  or  uncommon.  I 
never  recall  this  joke  without  seeing  before  me  my  friend, 
leaning  against  his  bookcase,  with  Bungus  open  in  his  hand, 
and  a  certain  half-depreciatory  tone  which  he  often  used 


58  A  BUDGET  OF  PARADOXES. 

when  speaking  of  himself.  Long  after  his  death,  an  F.R.S. 
who  was  present  at  the  discussion,  told  me  the  story.  I  did 
not  say  I  had  heard  it,  but  I  watched  him,  with  Galloway 
at  the  bookcase  before  me.  I  wanted  to  see  whether  the  two 
would  agree  as  to  the  fact  of  an  enormous  budget  of  fifteens 
having  been  fired  at  the  Council,  and  they  did  agree  per- 
fectly. But  when  the  paragraph  of  the  Budget  appeared  in 
the  Athenaum,  my  friend,  who  seemed  rather  to  object  to 
the  showing-up,  assured  me  that  the  thing  was  grossly  ex- 
aggerated; there  was  indeed  a  fifteen  or  two,  but  nothing 
like  the  number  I  had  given.  I  had,  however,  taken  sharp 
note  of  the  previous  narration. 

AND  TO  ANOTHER  QUESTION  OF  EVIDENCE. 

I  will  give  another  instance.  An  Indian  officer  gave  me 
an  account  of  an  elephant,  as  follows.  A  detachment  was 
on  the  march,  and  one  of  the  gun-carriages  got  a  wheel  off 
the  track,  so  that  it  was  also  off  the  ground,  and  hanging 
over  a  precipice.  If  the  bullocks  had  moved  a  step,  carriages, 
bullocks,  and  all  must  have  been  precipitated.  No  one  knew 
what  could  be  done  until  some  one  proposed  to  bring  up  an 
elephant,  and  let  him  manage  it  his  own  way.  The  elephant 
took  a  moment's  survey  of  the  fix,  put  his  trunk  under  the 
axle  of  the  free  wheel,  and  waited.  The  surrounders,  who 
saw  what  he  meant,  moved  the  bullocks  gently  forward,  the 
elephant  followed,  supporting  the  axle,  until  there  was 
ground  under  the  wheel,  when  he  let  it  quietly  down.  From 
all  I  had  heard  of  the  elephant,  this  was  not  too  much  to 
believe.  But  when,  years  afterwards,  I  reminded  my  friend 
of  his  story,  he  assured  me  that  I  had  misunderstood  him, 
that  the  elephant  was  directed  to  put  his  trunk  under  the 
wheel,  and  saw  in  a  moment  why.  This  is  reasonable  sagac- 
ity, and  very  likely  the  correct  account ;  but  I  am  quite  sure 
that,  in  the  fit  of  elephant-worship  under  which  the  story 
was  first  told,  it  was  told  as  I  have  first  stated  it.] 


GIORDANO  BRUNO  AND  HIS  PARADOXES.  59 


GIORDANO  BRUNO  AND  HIS  PARADOXES. 

[Jordani  Bruni  Nolani  de  Monade,  Numero  et  Figura. .  .item  de 
Innumerabilibus,  Immense,  et  Infigurabili..  .Frankfort,  1591, 
Svo.1 

I  cannot  imagine  how  I  came  to  omit  a  writer  whom  I 
have  known  so  many  years,  unless  the  following  story  will 
explain  it.  The  officer  reproved  the  boatswain  for  perpetual 
swearing ;  the  boatswain  answered  that  he  heard  the  officers 
swear.  "Only  in  an  emergency,"  said  the  officer.  "That's 
just  it,"  replied  the  other;  "a  boatswain's  life  is  a  life  of 
'mergency."  Giordano  Bruno  was  all  paradox;  and  my 
mind  was  not  alive  to  his  paradoxes,  just  as  my  ears  might 
have  become  dead  to  the  boatswain's  oaths.  He  was,  as  has 
been  said,  a  vorticist  before  Descartes,2  an  optimist  before 
Leibnitz,  a  Copernican  before  Galileo.  It  would  be  easy 
to  collect  a  hundred  strange  opinions  of  his.  He  was  born 
about  1550,  and  was  roasted  alive  at  Rome,  February  17, 
1600,  for  the  maintenance  and  defence  of  the  holy  Church, 
and  the  rights  and  liberties  of  the  same.  These  last  words 
are  from  the  writ  of  our  own  good  James  I,  under  which 
Leggatt3  was  roasted  at  Smithfield,  in  March  1612;  and  if 
I  had  a  copy  of  the  instrument  under  which  Wightman4  was 
roasted  at  Lichfield,  a  month  afterwards,  I  daresay  I  should 

1  Giordano  Bruno  was  born  near  Naples  about  i55o;    He  left  the 
Dominican  order  to  take  up  Calvinism,  and  among  his  publications 
was  L' expulsion  de  la  bete  triomphante.     He  taught  philosophy  at 
Paris  and  Wittenberg,  and  some  of  his  works  were  published  in 
England  in  1583-86.    Whether  or  not  he  was  roasted  alive  "for  the 
maintenance  and  defence  of  the  holy  Church,"  as  De  Morgan  states, 
depends  upon  one's  religious  point  of  view.     At  any  rate,  he  was 
roasted  as  a  heretic. 

2  Referring  to  part  of  his  Discours  de  la  methode,  Leyden,  1637. 

'^Bartholomew  Legate,  who  was  born  in  Essex  about  1575'  He 
denied  the  divinity  of  Christ  and  was  the  last  heretic  burned  at 
Smithfield. 

*  Edward  Wightman,  born  probably  in  Staffordshire.  He  was 
anti-Trinitarian,  and  claimed  to  be  the  Messiah.  He  was  the  last 
man  burned  for  heresy  in  England. 


6Q  A  BUDGET  OF  PARADOXES. 

find  something  quite  as  edifying.    I  extract  an  account  which 
I  gave  of  Bruno  in  the  Comp.  Aim.  for  1855: 

"He  was  first  a  Dominican  priest,  then  a  Calvinist;  and 
was  roasted  alive  at  Rome,  in  1600,  for  as  many  heresies  of 
opinion,  religious  and  philosophical,  as  ever  lit  one  fire. 
Some  defenders  of  the  papal  cause  have  at  least  worded 
their  accusations  so  to  be  understood  as  imputing  to  him 
villainous  actions.  But  it  is  positively  certain  that  his  death 
was  due  to  opinions  alone,  and  that  retractation,  even  after 
sentence,  would  have  saved  him.  There  exists  a  remarkable 
letter,  written  from  Rome  on  the  very  day  of  the  murder, 
by  Scioppius5  (the  celebrated  scholar,  a  waspish  convert  from 
Lutheranism,  known  by  his  hatred  to  Protestants  and  Jes- 
uits) to  Rittershusius,6  a  well-known  Lutheran  writer  on 
civil  and  canon  law,  whose  works  are  in  the  index  of  pro- 
hibited books.  This  letter  has  been  reprinted  by  Libri  (vol. 
iv.  p.  407).  The  writer  informs  his  friend  (whom  he  wished 
to  convince  that  even  a  Lutheran  would  have  burnt  Bruno) 
that  all  Rome  would  tell  him  that  Bruno  died  for  Lutheran- 
ism  ;  but  this  is  because  the  Italians  do  not  know  the  differ- 
ence between  one  heresy  and  another,  in  which  simplicity 
(says  the  writer)  may  God  preserve  them.  That  is  to  say, 
they  knew  the  difference  between  a  live  heretic  and  a  roasted 
one  by  actual  inspection,  but  had  no  idea  of  the  difference 
between  a  Lutheran  and  a  Calvinist.  The  countrymen  of 
Boccaccio  would  have  smiled  at  the  idea  which  the  German 
scholar  entertained  of  them.  They  said  Bruno  was  burnt 
for  Lutheranism,  a  name  under  which  they  classed  all  Prot- 
estants :  and  they  are  better  witnesses  than  Schopp,  or  Sciop- 
pius. He  then  proceeds  to  describe  to  his  Protestant  friend 
(to  whom  he  would  certainly  not  have  omitted  any  act 
which  both  their  churches  would  have  condemned)  the  mass 
of  opinions  with  which  Bruno  was  charged;  as  that  there 

5  Caspar  ScHopp,  born  at  Neumarck<  in  1576,  died  at  Padua  in 
1649;  grammarian,  philologist,  and  satirist. 

6  Konrad  Ritterhusius,  born  at  Brunswick  in  1560 ;  died  at  Altdorf 
in  1613.    He  was  a  jurist  of  some  power. 


GIORDANO  BRUNO  AND  HIS  PARADOXES.  61 

are  innumerable  worlds,  that  souls  migrate,  that  Moses  was 
a  magician,  that  the  Scriptures  are  a  dream,  that  only  the 
Hebrews  descended  from  Adam  and  Eve,  that  the  devils 
would  be  saved,  that  Christ  was  a  magician  and  deservedly 
put  to  death,  etc.  In  fact,  says  he,  Bruno  has  advanced  all 
that  was  ever  brought  forward  by  all  heathen  philosophers, 
and  by  all  heretics,  ancient  and  modern.  A  time  for  retracta- 
tion was  given,  both  before  sentence  and  after,  which  should 
be  noted,  as  well  for  the  wretched  palliation  which  it  may 
afford,  as  for  the  additional  proof  it  gives  that  opinions,  and 
opinions  only,  brought  him  to  the  stake.  In  this  medley  of 
charges  the  Scriptures  are  a  dream,  while  Adam,  Eve,  devils, 
and  salvation  are  truths,  and  the  Saviour  a  deceiver.  We 
have  examined  no  work  of  Bruno  except  the  De  Monade, 
etc.,  mentioned  in  the  text.  A  strong  though  strange  theism 
runs  through  the  whole,  and  Moses,  Christ,  the  Fathers,  etc., 
are  cited  in  a  manner  which  excites  no  remark  either  way. 
Among  the  versions  of  the  cause  of  Bruno's  death  is  atheism : 
but  this  word  was  very  often  used  to  denote  rejection  of 
revelation,  not  merely  in  the  common  course  of  dispute,  but 
by  such  writers,  for  instance,  as  Brucker7  and  Morhof .8  Thus 
Morhof  says  of  the  De  Monade,  etc.,  that  it  exhibits  no  mani- 
fest signs  of  atheism.  What  he  means  by  the  word  is  clear 
enough,  when  he  thus  speaks  of  a  work  which  acknowledges 
God  in  hundreds  of  places,  and  rejects  opinions  as  blas- 
phemous in  several.  The  work  of  Bruno  in  which  his  astro- 
nomical opinions  are  contained  is  De  Monade,  etc.  (Frank- 
fort, 1591,  8vo).  He  is  the  most  thorough-going  Copernican 
possible,  and  throws  out  almost  every  opinion,  true  or  false, 
which  has  ever  been  discussed  by  astronomers,  from  the 
theory  of  innumerable  inhabited  worlds  and  systems  to  that 

7Johann  Jakob  Brucker,  born  at  Augsburg  in  1696,  died  there  in 
1770.  He  wrote  on  the  history  of  philosophy  (1731-36,  and  1742-44). 

8  Daniel  Georg  Morhof,  born  at  Wismar  in  1639,  died  at  Ltibeck 
in  1691.  He  was  rector  of  the  University  of  Kiel,  and  professor  of 
eloquence,  poetry,  and  history. 


62  A  BUDGET  OF  PARADOXES. 

of  the  planetary  nature  of  comets.  Libri  (vol.  iv)9  has  re- 
printed the  most  striking  part  of  his  expressions  of  Coper- 
nican  opinion." 

THIS  LEADS  TO  THE  CHURCH  QUESTION. 

The  Satanic  doctrine  that  a  church  may  employ  force 
in  aid  of  its  dogma  is  supposed  to  be  obsolete  in  England, 
except  as  an  individual  paradox ;  but  this  is  difficult  to  settle. 
Opinions  are  much  divided  as  to  what  the  Roman  Church 
would  do  in  England,  if  she  could:  any  one  who  doubts 
that  she  claims  the  right  does  not  deserve  an  answer.  When 
the  hopes  of  the  Tractarian  section  of  the  High  Church  were 
in  bloom,  before  the  most  conspicuous  intellects  among  them 
had  transgressed  theif  ministry,  that  they  might  go  to  their 
own  place,  I  had  the  curiosity  to  see  how  far  it  could  be 
ascertained  whether  they  held  the  only  doctrine  which  makes 
me  the  personal  enemy  of  a  sect.  I  found  in  one  of  their 
tracts  the  assumption  of  a  right  to  persecute,  modified  by  an 
asserted  conviction  that  force  was  not  efficient.  I  cannot 
now  say  that  this  tract  was  one  of  the  celebrated  ninety ;  and 
on  looking  at  the  collection  I  find  it  so  poorly  furnished 
with  contents,  etc.,  that  nothing  but  searching  through  three 
thick  volumes  would  decide.  In  these  volumes  I  find,  aug- 
menting as  we  go  on,  declarations  about  the  character  and 
power  of  "the  Church"  which  have  a  suspicious  appearance. 
The  suspicion  is  increased  by  that  curious  piece  of  sophis- 
try, No.  87,  on  religious  reserve.  The  queer  paradoxes  of 
that  tract  leave  us  in  doubt  as  to  everything  but  this,  that  the 
church  (man)  is  not  bound  to  give  his  whole  counsel  in  all 
things,  and  not  bound  to  say  what  the  things  are  in  which 
he  does  not  give  it.  It  is  likely  enough  that  some  of  the 
"rights  and  liberties"  are  but  scantily  described.  There  is 
now  no  fear ;  but  the  time  was  when,  if  not  fear,  there  might 
be  a  looking  for  of  fear  to  come ;  nobody  could  then  be  so 

'In  the  Histoire  des  Sciences  Mathematiques,  vol.  IV,  note  X, 
pp.  416-435  of  the  1841  edition. 


THE   CHURCH   QUESTION.  63 

sure  as  we  now  are  that  the  lion  was  only  asleep.  There  was 
every  appearance  of  a  harder  fight  at  hand  than  was  really 
found  needful. 

Among  other  exquisite  quirks  of  interpretation  in  the 
No.  87  above  mentioned  is  the  following.  God  himself  em- 
ploys reserve;  he  is  said  to  be  decked  with  light  as  with  a 
garment  (the  old  or  prayer-book  version  of  Psalm  civ.  2). 
To  an  ordinary  apprehension  this  would  be  a  strong  image 
of  display,  manifestation,  revelation ;  but  there  is  something 
more.  "Does  not  a  garment  veil  in  some  measure  that  which 
it  clothes?  Is  not  that  very  light  concealment?" 

This  No.  87,  admitted  into  a  series,  fixes  upon  the  man- 
agers of  the  series,  who  permitted  its  introduction,  a  strong 
presumption  of  that  underhand  intent  with  which  they  were 
charged.  At  the  same  time  it  is  honorable  to  our  liberty 
that  this  series  could  be  published:  though  its  promoters 
were  greatly  shocked  when  the  Essayists  and  Bishop  Co- 
lenso1  took  a  swing  on  the  other  side.  When  No.  90  was 
under  discussion,  Dr.  Maitland,2  the  librarian  at  Lambeth, 
asked  Archbishop  Howley3  a  question  about  No.  89.  "I  did 
not  so  much  as  know  there  was  a  No.  89,"  was  the 
answer.  I  am  almost  sure  I  have  seen  this  in  print,  and  quite 
sure  that  Dr.  Maitland  told  it  to  me.  It  is  creditable  that 
there  was  so  much  freedom;  but  No.  90  was  too  bad,  and 
was  stopped. 

The  Tractarian  mania  has  now  (October  1866)  settled 
down  into  a  chronic  vestment  disease,  complicated  with  fits 
of  transubstantiation,  which  has  taken  the  name  of  Ritual- 

1Colenso  (1814-1883),  missionary  bishop  of  Natal,  was  one  of 
the  leaders  of  his  day  in  the  field  of  higher  biblical  criticism.  De 
Morgan  must  have  admired  his  mathematical  works,  which  were  not 
without  merit 

2  Samuel  Roffey  Maitland,  born  at  London  in  1792 ;  died  at  Glou- 
cester in  1866.  He  was  an  excellent  linguist  and  a  critical  student 
of  the  Bible.  He  became  librarian  at  Lambeth  in  1838. 

'Archbishop  Howley  (1766-1848)  was  a  thorough  Tory.  He  was 
one  of  the  opponents  of  the  Roman  Catholic  Relief  bill,  the  Reform 
bill,  and  the  Jewish  Civil  Disabilities  Relief  bill. 


64  A  BUDGET  OF  PARADOXES. 

ism.  The  common  sense  of  our  national  character  will  not 
put  up  with  a  continuance  of  this  grotesque  folly ;  millinery 
in  all  its  branches  will  at  last  be  advertised  only  over  the 
proper  shops.  I  am  told  that  the  Ritualists  give  short  and 
practical  sermons ;  if  so,  they  may  do  good  in  the  end.  The 
English  Establishment  has  always  contained  those  who  want 
an  excitement ;  the  New  Testament,  in  its  plain  meaning,  can 
do  little  for  them.  Since  the  Revolution,  Jacobitism,  Wes- 
leyanism,  Evangelicism,  Puseyism,4  and  Ritualism,  have  come 
on  in  turn,  and  have  furnished  hot  water  for  those  who 
could  not  wash  without  it.  If  the  Ritualists  should  succeed 
in  substituting  short  and  practical  teaching  for  the  high- 
spiced  lectures  of  the  doctrinalists,  they  will  be  remembered 
with  praise.  John  the  Baptist  would  perhaps  not  have 
brought  all  Jerusalem  out  into  the  wilderness  by  his  plain 
and  good  sermons:  it  was  the  camel's  hair  and  the  locusts 
which  got  him  a  congregation,  and  which,  perhaps,  added 
force  to  his  precepts.  When  at  school  I  heard  a  dialogue, 
between  an  usher  and  the  man  who  cleaned  the  shoes,  about 

Mr. ,  a  minister,  a  very  corporate  body  with  due  area  of 

waistcoat.  "He  is  a  man  of  great  erudition,"  said  the  first. 
"Ah,  yes  sir,"  said  Joe;  "any  one  can  see  that  who  looks 
at  that  silk  waistcoat."] 

OF  THOMAS  GEPHYRANDER  SALICETUS. 

[When  I  said  at  the  outset  that  I  had  only  taken  books 
from  my  own  store,  I  should  have  added  that  I  did  not  make 
any  search  for  information  given  as  part  of  a  work.  Had  I 
looked  through  all  my  books,  I  might  have  made  some  curi- 
ous additions.  For  instance,  in  Schott's  Magia  Naturalis1 

*  We  have,  in  America  at  least,  almost  forgotten  the  great  stir 
made  by  Edward  B.  Pusey  (1800-1882)  in  the  great  Oxford  move- 
ment in  the  middle  of  the  nineteenth  century.  He  was  professor  of 
Hebrew  at  Oxford,  and  canon  of  Christ  Church. 

*That  is,  his  Magia  universalis  naturae  et  artis  sive  recondita 
naturalium  et  artificialium  rerum  scientia,  Wiirzburg,  1657,  4to,  with 
editions  at  Bamberg  in  1671,  and  at  Frankfort  in  1677.  Gaspard 
Schott  (Konigshofen  1608,  Wurzburg  1666)  was  a  physicist  and 


OF  THOMAS  GEPHYRANDER  SALICETUS.  65 

(vol.  iii.  pp.  756-778)  is  an  account  of  the  quadrature  of 
Gephyrawder,  as  he  is  misprinted  in  Montucla.  He  was 
Thomas  Gephyrander  Salicetus ;  and  he  published  two  edi- 
tions, in  1608  and  1609.2  I  never  even  heard  of  a  copy  of 
either.  His  work  is  of  the  extreme  of  absurdity :  he  makes  a 
distinction  between  geometrical  and  arithmetical  fractions, 
and  evolves  theorems  from  it.  More  curious  than  his  quad- 
rature is  his  name  ;  what  are  we  to  make  of  it  ?  If  a  German, 
he  is  probably  a  German  form  of  Bridgeman,  and  Salicetus 
refers  him  to  Weiden.  But  Thomas  was  hardly  a  German 
Christian  name  of  his  time;  of  526  German  philosophers, 
physicians,  lawyers,  and  theologians  who  were  biographed 
by  Melchior  Adam,3  only  two  are  of  this  name.  Of  these 
one  is  Thomas  Erastus,4  the  physician  whose  theological 
writings  against  the  Church  as  a  separate  power  have  given 
the  name  of  Erastians  to  those  who  follow  his  doctrine, 
whether  they  have  heard  of  him  or  not.  Erastus  is  little 
known ;  accordingly,  some  have  supposed  that  he  must  be 
Erastus,  the  friend  of  St.  Paul  and  Timothy  (Acts  xix.  22; 
2  Tim.  iv.  20;  Rom.  xvi.  23),  but  what  this  gentleman  did 
to  earn  the  character  is  not  hinted  at.  Few  words  would 
have  done:  Gaius  (Rom.  xvi.  23)  has  an  immortality  which 
many  more  noted  men  have  missed,  given  by  John  Bunyan, 
out  of  seven  words  of  St.  Paul.  I  was  once  told  that  the 
Erastians  got  their  name  from  Blastus,  and  I  could  not 
solve  bl  —  er:  at  last  I  remembered  that  Blastus  was  a 
chamberlain5  as  well  as  Erastus ;  hence  the  association  which 

mathematician,  devoting  most  of  his  attention  to  the  curiosities  of 
his  sciences.  His  type  of  mind  must  have  appealed  to  De  Morgan. 
*  Salic etti  Quadratura  circuit  nova,  perspicua,  expedita,  veraque 
turn  naturalis,  turn  geometrica,  etc.,  1608. — Consideratio  nova  in  opus- 
culum  Archimedis  de  circuli  dimensione,  etc.,  1609. 

3  Melchior  Adam,  who  died  at  Heidelberg  in  1622,  wrote  a  col- 
lection of  biographies  which  was  published  at  Heidelberg  and  Frank- 
fort from  1615  to  1620. 

4  Born  at  Baden  in  1524;  died  at  Basel  in  1583.     The  Erastians 
were  related  to  the  Zwinglians,  and  opposed  all  power  of  excom- 
munication and  the  infliction  of  penalties  by  a  church. 

5  See  Acts  xii.  20. 


66  A  BUDGET  OF  PARADOXES. 

caused  the  mistake.  The  real  heresiarch  was  a  physician 
who  died  in  1583;  his  heresy  was  promulgated  in  a  work, 
published  immediately  after  his  death  by  his  widow,  De  Ex- 
communicatione  Ecclesiastic  a.  He  denied  the  power  of  ex- 
communication on  the  principle  above  stated ;  and  was  an- 
swered by  Besa.8  The  work  was  translated  by  Dr.  R.  Lee7 
(Edinb.  1844, 8vo).  The  other  is  Thomas  Grynseus,8  a  theo- 
logian, nephew  of  Simon,  who  first  printed  Euclid  in  Greek ; 
of  him  Adam  says  that  of  works  he  published  none,  of 
learned  sons  four.  If  Gephyrander  were  a  Frenchman,  his 
name  is  not  so  easily  guessed  at ;  but  he  must  have  been  of 
La  Saussaye.  The  account  given  by  Schott  is  taken  from  a 
certain  Father  Philip  Colbinus,  who  wrote  against  him. 

In  some  manuscripts  lately  given  to  the  Royal  Society, 
David  Gregory,9  who  seems  to  have  seen  Gephyrander's 
work,  calls  him  Salicetus  Westphalus,  which  is  probably  on 
the  title-page.  But  the  only  Weiden  I  can  find  is  in  Bavaria. 
Murhard  has  both  editions  in  his  Catalogue,  but  had  plainly 
never  seen  the  books:  he  gives  the  author  as  Thomas  Gep. 
Hyandrus,  Salicettus  Westphalus.  Murhard  is  a  very  old 
referee  of  mine ;  but  who  the  non  nominandus  was  to  see 
Montucla's  Gephyrauder  in  Murhard's  Gep.  Hyandrus,  both 
writers  being  usually  accurate?] 

NAPIER  ON  REVELATIONS. 

A  plain  discoverie  of  the  whole  Revelation  of  St.  John. . .  .where- 
tmto  are  annexed  certain  oracles  of  Sibylla.  ..  .Set  Foorth  by 
John  Napeir  L.  of  Marchiston.  London,  1611,  4to.1 

'Theodore  de  Bese,  a  French  theologian;  born  at  Vezelay,  in 
Burgundy,  in  1519;  died  at  Geneva,  in  1605. 

7  Dr.  Robert  Lee  (1804-1868)  had  some  celebrity  in  De  Morgan's 
time  through  his  attempt  to  introduce  music  and  written  prayers  into 
the  service  of  the  Scotch  Presbyterian  church. 

8  Born  at  Veringen,  Hohenzollern,   in   1512;   died  at  Roteln  in 
1564. 

9  Born  at  Kinnairdie,  Bannfshire,  in   1661 ;   died  at  London  in 
1708.     His  Astronomiae  Physicae  et  Geometriae  Elementa,  Oxford, 
1702,  was  an  influential  work. 

xThe  title  was  carelessly  copied  by  De  Morgan,  not  an  unusual 


NAPIER  ON   REVELATIONS. 


67 


The  first  edition  was  Edinburgh,  1593,2  4to.  Napier8  al- 
ways believed  that  his  great  mission  was  to  upset  the  Pope, 
and  that  logarithms,  and  such  things,  were  merely  episodes 
and  relaxations.  It  is  a  pity  that  so  many  books  have  been 
written  about  this  matter,  while  Napier,  as  good  as  any, 
is  forgotten  and  unread.  He  is  one  of  the  first  who  gave 
us  the  six  thousand  years.  "There  is  a  sentence  of  the  house 
of  Elias  reserved  in  all  ages,  bearing  these  words :  The  world 
shall  stand  six  thousand  years,  and  then  it  shall  be  con- 
sumed by  fire:  two  thousand  yeares  voide  or  without  lawe, 
two  thousand  yeares  under  the  law,  and  two  thousand  yeares 
shall  be  the  daies  of  the  Messias . . . . " 

I  give  Napier's  parting  salute :  it  is  a  killing  dilemma : 
"In  summar  conclusion,  if  thou  o  Rome  aledges  thy- 
self e  reformed,  and  to  beleeue  true  Christianisme,  then  be- 
leeue  Saint  John  the  Disciple,  whome  Christ  loued,  pub- 
likely  here  in  this  Reuelation  proclaiming  thy  wracke,  but 
if  thou  remain  Ethnick  in  thy  priuate  thoghts,  beleeuing4 
the  old  Oracles  of  the  Sibyls  reuerently  keeped  somtime  in 
thy  Capitol:  then  doth  here  this  Sibyll  proclame  also  thy 
wracke.  Repent  therefore  alwayes,  in  this  thy  latter  breath, 
as  thou  louest  thine  Eternall  salvation.  Amen" 
— Strange  that  Napier  should  not  have  seen  that  this  ap- 
peal could  not  succeed,  unless  the  prophecies  of  the  Apo- 
calypse were  no  true  prophecies  at  all. 

thing  in  his  case.     The  original  reads :  A  Plaine  Discovery,  of  the 

whole   Revelation   of   S.    lohn:    set   downe   in   two   treatises set 

foorth  by  lohn   Napier  L.   of  Marchiston whereunto   are  an- 
nexed, certaine  Oracles  of  Sibylla London 1611. 

3 1  have  not  seen  the  first  edition,  but  it  seems  to  have  appeared 
in  Edinburgh,  in  1593,  with  a  second  edition  there  in  1594.  The  1611 
edition  was  the  third. 

'It  seems  rather  certain  that  Napier  felt  his  theological  work 
of  greater  importance  than  that  in  logarithms.  He  was  born  at 
Merchiston,  near  (now  a  part  of)  Edinburgh,  in  1550,  and  died  there 
in  1617,  three  years  after  the  appearance  of  his  Mirifici  logarith- 
morum  canonis  descriptio. 

'Followed,   in  the  third  edition,   from  which  he  quotes,  by  a 

comma. 


68  A  BUDGET  OF  PARADOXES. 


OF  GILBERT'S  DE  MAGNETK 

De  Magnete  magneticisque  corporibus,  et  de  magno  magnate 
tellure.  By  William  Gilbert  London,  1600,  folio. — There  is 
a  second  edition;  and  a  third,  according  to  Watt.1 

Of  the  great  work  on  the  magnet  there  is  no  need  to 
speak,  though  it  was  a  paradox  in  its  day.  The  posthumous 
work  of  Gilbert,  "De  Mundo  nostro  sublunari  philosophia 
nova"  (Amsterdam,  1651,  4to)2  is,  as  the  title  indicates, 
confined  to  the  physics  of  the  globe  and  its  atmosphere.  It 
has  never  excited  attention:  I  should  hope  it  would  be  ex- 
amined with  our  present  lights. 

OF  GIOVANNI  BATISTA  PORTA. 

Elementorum  Curvilineoriuni  Libri  tres.  By  John  Baptista 
Porta.  Rome,  1610,  ^o.1 

This  is  a  ridiculous  attempt,  which  defies  description, 
except  that  it  is  all  about  lunules.  Porta  was  a  voluminous 
writer.  His  printer  announces  fourteen  works  printed,  and 
four  to  come,  besides  thirteen  plays  printed,  and  eleven 
waiting.  His  name  is,  and  will  be,  current  in  treatises  on 
physics  for  more  reasons  than  one. 

1  There  was  an  edition  published  at  Stettin  in  1633.    An  English 
translation  by  P.  F.  Mottelay  appeared  at  London  in  1893.     Gilbert 
(1540-1603)  was  physician  to  Queen  Elizabeth  and  President  of  the 
College  of  Physicians  at  London.     His  De  Magnete  was  the  first 
noteworthy  treatise  on  physics  printed  in  England.     He  treated  of 
the  earth  as  a  spherical  magnet  and  suggested  the  variation  and 
declination  of  the  needle  as  a  means  of  finding  latitude  at  sea. 

2  The  title  says  "ab  authoris  fratre  collectum,"  although  it  was 
edited  by  J.  Gruterus. 

1  Porta  was  born  at  Naples  in  1550  and  died  there  in  1615.  He 
studied  the  subject  of  lenses  and  the  theory  of  sight,  did  some  work 
in  hydraulics  and  agriculture,  and  was  well  known  as  an  astrologer. 
His  Magiae  naturalis  libri  XX  was  published  at  Naples  in  1589.  The 
above  title  should  read  curvilineorum. 


CATALDI  ON  THE  QUADRATURE.  69 


CATALDI  ON  THE  QUADRATURE. 

Trattato  della  quadratura  del  cerchio.     Di  Pietro  Antonio  Ca- 
taldi.     Bologna,  1612,  folio.1 

Rheticus,2  Vieta,  and  Cataldi  are  the  three  untiring  com- 
puters of  Germany,  France,  and  Italy;  Napier  in  Scotland, 
and  Briggs3  in  England,  come  just  after  them.  This  work 
claims  a  place  as  beginning  with  the  quadrature  of  Pelle- 
grino  Borello4  of  Reggio,  who  will  have  the  circle  to  be 
exactly  3  diameters  and  6%g4  of  a  diameter.  Cataldi,  taking 
Van  Ceulen's  approximation,  works  hard  at  the  rinding  of 
integers  which  nearly  represent  the  ratio.  He  had  not  then 
the  continued  fraction,  a  mode  of  representation  which  he 
gave  the  next  year  in  his  work  on  the  square  root.  He  has 
but  twenty  of  Van  Ceulen's  thirty  places,  which  he  takes 
from  Clavius5 :  and  any  one  might  be  puzzled  to  know  whence 
the  Italians  got  the  result ;  Van  Ceulen,  in  1612,  not  having 
been  translated  from  Dutch.  But  Clavius  names  his  com- 
rade Gruenberger,  and  attributes  the  approximation  to  them 

1  Cataldi  was  born  in  1548  and  died  at  Bologna  in  1626.  He  was 
professor  of  mathematics  at  Perugia,  Florence,  and  Bologna,  and  is 
known  in  mathematics  chiefly  for  his  work  in  continued  fractions. 
He  was  one  of  the  scholarly  men  of  his  day. 

2Georg  Joachim  Rheticus  was  born  at  Feldkirch  in  1514  and  died 
at  Caschau,  Hungary,  in  1576.  He  was  one  of  the  most  prominent 
pupils  of  Copernicus,  his  Narratio  de  libris  revolutionism  Copernici 
(Dantzig,  1540)  having  done  much  to  make  the  theory  of  his  master 
known. 

8  Henry  Briggs,  who  did  so  much  to  make  logarithms  known,  and 
who  used  the  base  10,  was  born  at  Warley  Wood,  in  Yorkshire,  in 
1560,  and  died  at  Oxford  in  1630.  He  was  Savilian  professor  of 
mathematics  at  Oxford,  and  his  grave  may  still  be  seen  there. 

4  He  lived  at  "Reggio  nella  Emilia"  in  the  i6th  and  I7th  centuries. 
His  Regola  e  modo  facilissimo  di  quadrare  il  cerchio  was  published 
at  Reggio  in  1609. 

8  Christoph  Klau  (Clavius)  was  born  at  Bamberg  in  1537,  and 
died  at  Rome  in  1612.  He  was  a  Jesuit  priest  and  taught  mathe- 
matics in  the  Jesuit  College  at  Rome.  He  wrote  a  number  of  works 
on  mathematics,  including  excellent  text-books  on  arithmetic  and 
algebra. 


70  A  BUDGET  OF  PARADOXES. 

jointly;  "Lud. aCollen  et  Chr. Gruenbergerus*  invenerunt," 
which  he  had  no  right  to  do,  unless,  to  his  private  knowl- 
edge, Gruenberger  had  verified  Van  Ceulen.  And  Gruen- 
berger  only  handed  over  twenty  of  the  places.  But  here  is 
one  instance,  out  of  many,  of  the  polyglot  character  of  the 
Jesuit  body,  and  its  advantages  in  literature. 

OF  LANSBERGIUS. 

Philippi  Lausbergii  Cyclometriae  Novae  Libri  Duo.    Middleburg, 
1616,  4U).1 

This  is  one  of  the  legitimate  quadratures,  on  which  I 
shall  here  only  remark  that  by  candlelight  it  is  quadrature 
under  difficulties,  for  all  the  diagrams  are  in  red  ink. 

A   TEXT   LEADING  TO   REMARKS   ON    PRESTER   JOHN. 

Recherches  Curieuses  des  Mesures  du  Monde.    By  S.  C.  de  V. 
Paris,  1626,  8vo  (pp.  48). * 

It  is  written  by  some  Count  for  his  son;  and  if  all  the 
French  nobility  would  have  given  their  sons  the  same  kind 
of  instruction  about  rank,  the  old  French  aristocracy  would 
have  been  as  prosperous  at  this  moment  as  the  English 
peerage  and  squireage.  I  sent  the  tract  to  Capt.  Speke,2 
shortly  after  his  arrival  in  England,  thinking  he  might  like 

"Christopher  Gruenberger,  or  Grienberger,  was  born  at  Halle 
in  Tyrol  in  1561,  and  died  at  Rome  in  1636.  He  was,  like  Clavius, 
a  Jesuit  and  a  mathematician,  and  he  wrote  a  little  upon  the  sub- 
ject of  projections.  His  Prospcctiva  nova  coelestis  appeared  at 
Rome  in  1612. 

1The  name  should,  of  course,  be  Lansbergii  in  the  genitive,  and 
is  so  in  the  original  title.  Philippus  Lansbergius  was  born  at  Ghent 
in  1560,  and  died  at  Middelburg  in  1632.  He  was  a  Protestant 
theologian,  and  was  also  a  physician  and  astronomer.  He  was  a 
well-known  supporter  of  Galileo  and  Copernicus.  His  Commen- 
tationes  in  motum  terrae  diurnum  et  annuum  appeared  at  Middel- 
burg in  1630  and  did  much  to  help  the  new  theory. 

1 1  have  never  seen  the  work.    It  is  rare. 

"The  African  explorer,  born  in  Somersetshire  in  1827,  died  at 
Bath  in  1864.  He  was  the  first  European  to  cross  Central  Africa 
from  north  to  south.  He  investigated  the  sources  of  the  Nile. 


A  TEXT  LEADING  TO  REMARKS  ON   PRESTER  JOHN.        71 

to  see  the  old  names  of  the  Ethiopian  provinces.  But  I 
first  made  a  copy  of  all  that  relates  to  Prester  John,3  himself 
a  paradox.  The  tract  contains,  inter  alia,  an  account  of  the 
four  empires ;  of  the  great  Turk,  the  great  Tartar,  the  great 
Sophy,  and  the  great  Prester  John.  This  word  great 
(grand'),  which  was  long  used  in  the  phrase  "the  great 
Turk,"  is  a  generic  adjunct  to  an  emperor.  Of  the  Tartars 
it  is  said  that  "c'est  vne  nation  prophane  et  barbaresque, 
sale  et  vilaine,  qui  mangent  la  chair  demie  crue,  qui  boiuent 
du  laict  de  jument,  et  qui  n'vsent  de  nappes  et  seruiettes 
que  pour  essuyer  leurs  bouches  et  leurs  mains."4  Many 
persons  have  heard  of  Prester  John,  and  have  a  very  indis- 
tinct idea  of  him.  I  give  all  that  is  said  about  him,  since 
the  recent  discussions  about  the  Nile  may  give  an  interest 
to  the  old  notions  of  geography.5 

"Le  grand  Prestre  Jean  qui  est  le  quatriesme  en  rang, 
est  Empereur  d'Ethiopie,  et  des  Abyssins,  et  se  vante 
d'estre  issu  de  la  race  de  Dauid,  comme  estant  descendu  de 
la  Royne  de  Saba,  Royne  d'Ethiopie,  laquelle  estant  venue 
en  Hierusalem  pour  voir  la  sagesse  de  Salomon,  enuiron 
Tan  du  monde  2952,  s'en  retourna  grosse  d'vn  fils  qu'ils 
nomment  Moylech,  duquel  ils  disent  estre  descendus  en  ligne 
directe.  Et  ainsi  il  se  glorifie  d'estre  le  plus  ancien  Mo- 
narque  de  la  terre,  disant  que  son  Empire  a  dure  plus  de 
trois  mil  ans,  ce  que  nul  autre  Empire  ne  peut  dire.  Aussi 
met-il  en  ses  tiltres  ce  qui  s'ensuit:  Nous,  N.  Souuerain  en 
mes  Royaumes,  vniquement  ayme  de  Dieu,  colomne  de  la 
foy,  sorty  de  la  race  de  luda,  etc.  Les  limites  de  cet  Empire 
touchent  a  la  mer  Rouge,  et  aux  montagnes  d'Azuma  vers 

'Prester  (Presbyter,  priest)  John,  the  legendary  Christian  king 
whose  realm,  in  the  Middle  Ages,  was  placed  both  in  Asia  and  in 
Africa,  is  first  mentioned  in  the  chronicles  of  Otto  of  Freisingen  in 
the  I2th  century.  In  the  I4th  century  his  kingdom  was  supposed  to 
be  Abyssinia. 

*"It  is  a  profane  and  barbarous  nation,  dirty  and  slovenly,  who 
eat  their  meat  half  raw  and  drink  mare's  milk,  and  who  use  table- 
cloths and  napkins  only  to  wipe  their  hands  and  mouths." 

8  For  translation  see  page  73. 


72  A  BUDGET  OF  PARADOXES. 

I'Orient,  et  du  coste  de  1'Occident,  il  est  borne  du  fleuue  du 
Nil,  qui  le  separe  de  la  Nubie,  vers  le  Septentrion  il  a 
I'^igypte,  et  au  Midy  les  Royaumes  de  Congo,  et  de  Mo- 
zambique, sa  longueur  contenant  quarante  degre,  qui  font 
mille  vingt  cinq  lieues,  et  ce  depuis  Congo  ou  Mozambique 
qui  sont  au  Midy,  iusqu'en  yEgypte  qui  est  au  Septentrion,  et 
sa  largeur  contenant  depuis  le  Nil  qui  est  a  1'Occident,  ius- 
qu'aux  montagnes  d'Azuma,  qui  sont  a  I'Orient,  sept  cens 
vingt  cinq  lieues,  qui  font  vingt  neuf  degrez.  Cet  empire 
a  sous  soy  trente  grandes  Prouinces,  sgavoir,  Medra,  Gaga, 
Alchy,  Cedalon,  Mantro,  Finazam,  Barnaquez,  Ambiam, 
Fungy,  Angote,  Cigremaon,  Gorga  Cafatez,  Zastanla,  Zeth, 
Early,  Belangana,  Tygra,  Gorgany,  Barganaza,  d'Ancut, 
Dargaly  Ambiacatina,  Caracogly,  Amara.  Maon  (sic), 
Guegiera,  Bally,  Dobora  et  Macheda.  Toutes  ces  Pro- 
uinces cy  dessus  sont  situees  iustement  sous  la  ligne  equi- 
noxiale,  entres  les  Tropiques  de  Capricorne,  et  de  Cancer. 
Mais  elles  s'approchent  de  nostre  Tropique,  de  deux  cens 
cinquante  lieues  plus  qu'elles  ne  font  de  1'autre  Tropique. 
Ce  mot  de  Prestre  Jean  signifie  grand  Seigneur,  et  n'est  pas 
Prestre  comme  plusieurs  pense,  il  a  este  tousiours  Chrestien, 
mais  souuent  Schismatique :  maintenant  il  est  Catholique,  et 
reconnaist  le  Pape  pour  Souuerain  Pontife.  Fay  veu  quel- 
quVn  des  ses  Euesques,  estant  en  Hierusalem,  auec  lequel 
i'ay  confere  souuent  par  le  moyen  de  nostre  trucheman: 
il  estoit  d'vn  port  graue  et  serieux,  succiur  (sic)  en  son 
parler,  mais  subtil  a  merueilles  en  tout  ce  qu'il  disoit.  II 
prenoit  grand  plaisir  au  recit  que  je  luy  faisais  de  nos  belles 
ceremonies,  et  de  la  grauite  de  nos  Prelats  en  leurs  habits 
Pontificaux,  et  autres  choses  que  je  laisse  pour  dire,  que 
1'Ethiopien  est  ioyoux  et  gaillard,  ne  ressemblant  en  rien 
a  la  salete  du  Tartare,  ny  a  Taffreux  regard  du  miserable 
Arabe,  mais  ils  sont  fins  et  cauteleux,  et  ne  se  fient  en  per- 
sonne,  soupgonneux  a  merueilles,  et  fort  devotieux,  ils  ne 
sont  du  tout  noirs  comme  Ton  croit,  i'entens  parler  de  ceux 
qui  ne  sont  pas  sous  la  ligne  Equinoxiale,  ny  trop  proches 


A  TEXT  LEADING  TO  REMARKS  ON   PRESTER  JOHN.         73 

d'icelle,  car  ceux  qui  sont  dessous  sont  les  Mores  que  nous 
voyons."6 

It  will  be  observed  that  the  author  speaks  of  his  con- 
versation with  an  Ethiopian  bishop,  about  that  bishop's  sov- 
ereign. Something  must  have  passed  between  the  two 
which  satisfied  the  writer  that  the  bishop  acknowledged  his 
own  sovereign  under  some  title  answering  to  Prester  John. 

'  "The  great  Prester  John,  who  is  the  fourth  in  rank,  is  emperor 
of  Ethiopia  and  of  the  Abyssinians,  and  boasts  of  his  descent  from 
the  race  of  David,  as  having  descended  from  the  Queen  of  Sheba, 
Queen  of  Ethiopia.  She,  having  gone  to  Jerusalem  to  see  the  wisdom 
of  Solomon,  about  the  year  of  the  world  2952,  returned  pregnant 
with  a  son  whom  they  called  Moylech,  from  whom  they  claim  descent 
in  a  direct  line.  And  so  he  glories  in  being  the  most  ancient  monarch 
in  the  world,  saying  that  his  empire  has  endured  for  more  than 
three  thousand  years,  which  no  other  empire  is  able  to  assert.  He 
also  puts  into  his  titles  the  following:  'We,  the  sovereign  in  my 
realms,  uniquely  beloved  of  God,  pillar  of  the  faith,  sprung  from  the 
race  of  Judah,  etc.'  The  boundaries  of  this  empire  touch  the  Red 
Sea  and  the  mountains  of  Azuma  on  the  east,  and  on  the  western 
side  it  is  bordered  by  the  River  Nile  which  separates  it  from  Nubia. 
To  the  north  lies  Egypt,  and  to  the  south  the  kingdoms  of  Congo 
and  Mozambique.  It  extends  forty  degrees  in  length,  or  one  thou- 
sand twenty-five  leagues,  from  Congo  or  Mozambique  on  the  south 
to  Egypt  on  the  north ;  and  in  width  it  reaches  from  the  Nile  on  the 
west  to  the  mountains  of  Azuma  on  the  east,  seven  hundred  twenty- 
five  leagues,  or  twenty-nine  degrees.  This  empire  contains  thirty 
large  provinces,  namely  Medra,  Gaga,  Alchy,  Cedalon,  Mantro,  Fina- 
zam,  Barnaquez,  Ambiam,  Fungy,  Angote,  Cigremaon,  Gorga,  Cafa- 
tez,  Zastanla,  Zeth,  Early,  Belangana,  Tygra,  Gorgany,  Barganaza, 
d'Ancut,  Dargaly,  Ambiacatina,  Caracogly,  Amara.  Maon  (sic), 
Guegiera,  Bally,  Dobora,  and  Macheda.  All  of  these  provinces  are  situ- 
ated directly  under  the  equinoctial  line  between  the  tropics  of  Capri- 
corn and  Cancer;  but  they  are  two  hundred  fifty  leagues  nearer  our 
tropic  than  the  other.  The  name  of  Prester  John  signifies  Great 
Lord,  and  is  not  Priest  [Presbyter]  as  many  think.  He  has  always 
been  a  Christian,  but  often  schismatic.  At  the  present  time  he  is  a 
Catholic  and  recognizes  the  Pope  as  sovereign  pontiff.  I  met  one  of 
his  bishops  in  Jerusalem,  and  often  conversed  with  him  through  the 
medium  of  our  guide.  He  was  of  grave  and  serious  bearing,  pleas- 
ant of  speech,  but  wonderfully  subtle  in  everything  he  said.  He  took 
great  delight  in  what  I  had  to  relate  concerning  our  beautiful  cere- 
monies and  the  dignity  of  our  prelates  in  their  pontifical  vestments. 
As  to  other  matters  I  will  only  say  that  the  Ethiopian  is  joyous  and 
merry,  not  at  all  like  the  Tartar  in  the  matter  of  filth,  nor  like  the 
wretched  Arab.  They  are  refined  and  subtle,  trusting  no  one,  wonder- 
fully suspicious,  and  very  devout.  They  are  not  at  all  black  as  is 
commonly  supposed,  by  which  I  refer  to  those  who  do  not  live  under 
the  equator  or  too  near  to  it,  for  these  are  Moors  as  we  shall  see.' 

With  respect  to  this  translation  it  should  be  said  that  the  original 


74  A  BUDGET  OF  PARADOXES. 


CONCERNING  A  TRACT  BY  FIENUS. 

De  Cometa  anni   1618  dissertationes  Thomse  Fieni1   et  Liberti 

Fromondi2 Equidem  Thomae  Fieni  epistolica  qusestio,   An 

verum  sit  Ccelum  moveri  et  Terram  quiescere?   London,  1670, 
8vo. 

This  tract  of  Fienus  against  the  motion  o£  the  earth  is 
a  reprint  of  one  published  in  1619.8  I  have  given  an  account 
of  it  as  a  good  summary  of  arguments  of  the  time,  in  the 
Companion  to  the  Almanac  for  1836. 

forms  of  the  proper  names  have  been  preserved,  although  they  are 
not  those  found  in  modern  works.  It  should  also  be  stated  that 
the  meaning  of  Prester  is  not  the  one  that  was  generally  accepted 
by  scholars  at  the  time  the  work  was  written,  nor  is  it  the  one 
accepted  to-day.  There  seems  to  be  no  doubt  that  the  word  is  de- 
rived from  Presbyter  as  stated  in  note  3  on  page  71,  since  the  above- 
mentioned  chronicles  of  Otto,  bishop  of  Freisingen  about  the  middle 
of  the  twelfth  century,  states  this  fact  clearly.  Otto  received  his  in- 
formation from  the  bishop  of  Gabala  (the  Syrian  Jibal)  who  told 
him  the  story  of  John,  rex  et  sacevdos,  or  Presbyter  John  as  he  liked 
to  be  called.  He  goes  on  to  say:  "Should  it  be  asked  why,  with  all 
this  power  and  splendor,  he  calls  himself  merely  'presbyter/  this  is 
because  of  his  humility,  and  because  it  was  not  fitting  for  one  whose 
server  was  a  primate  and  king,  whose  butler  an  archbishop  and 
king,  whose  chamberlain  a  bishop  and  king,  whose  master  of  the 
horse  an  archimandrite  and  king,  whose  chief  cook  an  abbot  and 
king,  to  be  called  by  such  titles  as  these." 

1  Thomas  Fienus  (Fyens)  was  born  at  Antwerp  in  1567  and  died 
in  1631.  He  was  professor  of  medicine  at  Louvain.  Besides  the 
editions  mentioned  below,  his  De  cometis  anni  1618  appeared  at 
Leipsic  in  1656.  He  also  wrote  a  Disputatio  an  coelum  moveatur 
et  terra  quiescat,  which  appeared  at  Antwerp  in  1619,  and  again  at 
Leipsic  in  1656. 

aLibertus  Fromondus  (1587-^.1653),  a  Belgian  theologian,  dean 
of  the  College  Church  at  Harcourt,  and  professor  at  Louvain.  The 
name  also  appears  as  Froidmont  and  Froimont. 

9  L.  Fromondi. . .  .meteorologicorum  libri  sex.  Cut  accessit  T. 
Fieni  et  L.  Fromondi  dissertationes  de  cometa  anni  1618. . .  .This  is 
from  the  1670  edition.  The  1619  edition  was  published  at  Antwerp. 
The  Meteorologicorum  libri  VI,  appeared  at  Antwerp  in  1627.  He 
also  wrote  Anti-Aristarchus  sive  orbis  terrae  immobilis  liber  unicus 
(Antwerp,  1631)  ;  Labyrrinthus  sive  de  compositione  continui  liber 
unus,  Philosophis,  Mathematicis,  Theologis  utilis  et  jucundus  (Ant- 
werp, 1631)  and  Vesta  sive  Anti-Aristarchi  vindex  adversus  Jac. 
Lansbergium  (Philippi  filium)  et  copernicanos  (Antwerp,  1634). 


ON  BACON'S  NOVUM  ORGANUM.  75 

ON  SNELL'S  WORK. 

Willebrordi  Snellii.    R.  F.  Cyclometricus.    Leyden,  1621,  4to. 

This  is  a  celebrated  work  on  the  approximative  quad- 
rature, which,  having  the  suspicious  word  cyclometricus, 
must  be  noticed  here  for  distinction.1 

ON  BACON'S  NOVUM  ORGANUM. 

1620.  In  this  year,  Francis  Bacon1  published  his  Novum 
Organum,2  which  was  long  held  in  England — but  not  until 
the  last  century — to  be  the  work  which  taught  Newton  and 
all  his  successors  how  to  philosophize.  That  Newton  never 
mentions  Bacon,  nor  alludes  in  any  way  to  his  works,  passed 
for  nothing.  Here  and  there  a  paradoxer  ventured  not  to  find 
all  this  teaching  in  Bacon,  but  he  was  pronounced  blind.  In 
our  day  it  begins  to  be  seen  that,  great  as  Bacon  was,  and 
great  as  his  book  really  is,  he  is  not  the  philosophical  father 
of  modern  discovery. 

But  old  prepossession  will  find  reason  for  anything.  A 
learned  friend  of  mine  wrote  to  me  that  he  had  discovered 
proof  that  Newton  owned  Bacon  for  his  master:  the  proof 
was  that  Newton,  in  some  of  his  earlier  writings,  used  the 

1  Snell  was  born  at  Leyden  in  1591,  and  died  there  in  1626.  He 
studied  under  Tycho  Brahe  and  Kepler,  and  is  known  for  Snell's 
law  of  the  refraction  of  light  He  was  the  first  to  determine  the 
size  of  the  earth  by  measuring  the  arc  of  a  meridian  with  any  fair 
degree  of  accuracy.  The  title  should  read :  Willebrordi  Snellii  R.  F. 
Cyclometricus,  de  circuit  dimensione  secundum  Logistarum  abacos, 
et  ad  Mechanicem  accuratissima. .. . 

1  Bacon  was  born  at  York  House,  London,  in  1561,  and  died  near 
Highgate,  London,  in  1626.  His  Novum  Organum  Scientiarum  or  New 
Method  of  employing  the  reasoning  faculties  in  the  pursuits  of  Truth 
appeared  at  London  in  1620.  He  had  previously  published  a  work 
entitled  Of  the  Proficience  and  Advancement  of  Learning,  divine  and 
humane  ^(London,  1605),  which  again  appeared  in  1621.  His  De 
augmentis  scientiarum  Libri  IX  appeared  at  Paris  in  1624,  and  his 
Historia  naturalis  et  experimental  de  ventis  at  Leyden  in  1638.  He 
was  successively  solicitor  general,  attorney  general,  lord  chancellor 
(1619),  Baron  Verulam  and  Viscount  St.  Albans.  He  was  deprived 
of  office  and  was  imprisoned  in  the  Tower  of  London  in  1621,  but 
was  later  pardoned. 

8  The  Greek  form,  Organon,  is  sometimes  used. 


76  A  BUDGET  OF  PARADOXES. 

phrase  experimentum  crucis,  which  is  Bacon's.  Newton 
may  have  read  some  of  Bacon,  though  no  proof  of  it  ap- 
pears. I  have  a  dim  idea  that  I  once  saw  the  two  words 
attributed  to  the  alchemists :  if  so,  there  is  another  explana- 
tion; for  Newton  was  deeply  read  in  the  alchemists. 

I  subjoin  a  review  which  I  wrote  of  the  splendid  edition 
of  Bacon  by  Spedding,3  Ellis,4  and  Heath.5  All  the  opinions 
therein  expressed  had  been  formed  by  me  long  before :  most 
of  the  materials  were  collected  for  another  purpose. 


The  Works  of  Francis  Bacon.     Edited  by  James  Spedding,  R. 
Leslie  Ellis,  and  Douglas  D.  Heath.   5  vols.1 

No  knowledge  of  nature  without  experiment  and  ob- 
servation: so  said  Aristotle,  so  said  Bacon,  so  acted  Coper- 
nicus, Tycho  Brahe,2  Gilbert,  Kepler,  Galileo,  Harvey,  etc., 
before  Bacon  wrote.3  No  derived  knowledge  until  experi- 
ment and  observation  are  concluded:  so  said  Bacon,  and 
no  one  else.  We  do  not  mean  to  say  that  he  laid  down  his 
principle  in  these  words,  or  that  he  carried  it  to  the  utmost 
extreme:  we  mean  that  Bacon's  ruling  idea  was  the  collec- 

8  James  Spedding  (1808-1881),  fellow  of  Cambridge,  who  devoted 
his  life  to  his  edition  of  Bacon. 

4R.  Leslie  Ellis  (1817-1859),  editor  of  the  Cambridge  Mathemat- 
ical Journal.  He  also  wrote  on  Roman  aqueducts,  on  Boole's  Laws 
of  Thought,  and  on  the  formation  of  a  Chinese  dictionary. 

6  Douglas  Derion  Heath  (1811-1897),  a  classical  and  mathematical 
scholar. 

1  There  have  been  numerous  editions  of  Bacon's  complete  works, 
including  the  following:  Frankfort,  1665;  London,  1730,  1740,  1764, 
1765,  1778,  1893,  1807,  1818,  1819,  1824,  1825-36,  1857-74,  1877.     The 
edition  to  which  De  Morgan  refers  is  that  of  1857-74,  14  vols.,  of 
which  five  were  apparently  out  at  the  time  he  wrote.     There  were 
also  French  editions  in  1800  and  1835. 

2  So  in  the  original  for  Tycho  Brahe. 

8  In  general  these  men  acted  before  Bacon  wrote,  or  at  any  rate 
before  he  wrote  the  Novum  Organum,  but  the  statement  must  not 
be  taken  too  literally.  The  dates  are  as  follows:  Copernicus,  1473- 
1543;  Tycho  Brahe,  1546-1601;  Gilbert,  1540-1603;  Kepler,  1571-1630; 
Galileo,  1564-1642;  Harvey,  1578-1657.  For  example,  Harvey's  Exer- 
citatio  Anatomica  de  Motu  Cordis  et  Sanguinis  did  not  appear  until 
1628,  and  his  Exercitationes  de  Generatione  until  1651. 


ON  BACON'S  NOVUM  ORGANUM.  77 

tion  of  enormous  masses  of  facts,  and  then  digested  pro- 
cesses of  arrangement  and  elimination,  so  artistically  con- 
trived, that  a  man  of  common  intelligence,  without  any  un- 
usual sagacity,  should  be  able  to  announce  the  truth  sought 
for.  Let  Bacon  speak  for  himself,  in  his  editor's  English: 

"But  the  course  I  propose  for  the  discovery  of  sciences 
is  such  as  leaves  but  little  to  the  acuteness  and  strength  of 
wits,  but  places  all  wits  and  understandings  nearly  on  a 
level.  For,  as  in  the  drawing  of  a  straight  line  or  a  per- 
fect circle,  much  depends  on  the  steadiness  and  practice  of 
the  hand,  if  it  be  done  by  aim  of  hand  only,  but  if  with  the 
aid  of  rule  or  compass  little  or  nothing,  so  it  is  exactly 
with  my  plan.  . .  .For  my  way  of  discovering  sciences  goes 
far  to  level  men's  wits,  and  leaves  but  little  to  individual 
excellence ;  because  it  performs  everything  by  the  surest 
rules  and  demonstrations." 

To  show  that  we  do  not  strain  Bacon's  meaning,  we  add 
what  is  said  by  Hooke,4  whom  we  have  already  mentioned 
as  his  professed  disciple,  and,  we  believe,  his  only  disciple 
of  the  day  of  Newton.  We  must,  however,  remind  the 
reader  that  Hooke  was  very  little  of  a  mathematician,  and 
spoke  of  algebra  from  his  own  idea  of  what  others  had 
told  him: 

"The  intellect  is  not  to  be  suffered  to  act  without  its 
helps,  but  is  continually  to  be  assisted  by  some  method  or 
engine,  which  shall  be  as  a  guide  to  regulate  its  actions, 
so  as  that  it  shall  not  be  able  to  act  amiss.  Of  this  engine, 
no  man  except  the  incomparable  Verulam  hath  had  any 
thoughts,  and  he  indeed  hath  promoted  it  to  a  very  good 
pitch ;  but  there  is  yet  somewhat  more  to  be  added,  which 
he  seemed  to  want  time  to  complete.  By  this,  as  by  that 

4  Robert  Hooke  (1635-1703)  studied  under  Robert  Boyle  at  Ox- 
ford. He  was  "Curator  of  Experiments"  to  the  Royal  Society  and 
its  secretary,  and  was  professor  of  geometry  at  Gresham  College, 
London.  It  is  true  that  he  was  "very  little  of  a  mathematician" 
although  he  wrote  on  the  motion  of  the  earth  ( 1674) ,  on  helioscopes 
and  other  instruments  (1675),  on  the  rotation  of  Jupiter  (1666), 
and  on  barometers  and  sails. 


78  A  BUDGET  OF  PARADOXES. 

art  of  algebra  in  geometry,  'twill  be  very  easy  to  proceed 
in  any  natural  inquiry,  regularly  and  certainly ....  For  as 
'tis  very  hard  for  the  most  acute  wit  to  find  out  any  difficult 
problem  in  geometry  without  the  help  of  algebra ....  and 
altogether  as  easy  for  the  meanest  capacity  acting  by  that 
method  to  complete  and  perfect  it,  so  will  it  be  in  the  in- 
quiry after  natural  knowledge." 

Bacon  did  not  live  to  mature  the  whole  of  this  plan.  Are 
we  really  to  believe  that  if  he  had  completed  the  Instauratio 
we  who  write  this — and  who  feel  ourselves  growing  bigger 
as  we  write  it — should  have  been  on  a  level  with  Newton 
in  physical  discovery?  Bacon  asks  this  belief  of  us,  and 
does  not  get  it.  But  it  may  be  said,  Your  business  is  with 
what  he  did  leave,  and  with  its  consequences.  Be  it  so. 
Mr.  Ellis  says:  "That  his  method  is  impracticable  cannot, 
I  think,  be  denied,  if  we  reflect  not  only  that  it  never  has 
produced  any  result,  but  also  that  the  process  by  which 
scientific  truths  have  been  established  cannot  be  so  presented 
as  even  to  appear  to  be  in  accordance  with  it."  That  this 
is  very  true  is  well  known  to  all  who  have  studied  the 
history  of  discovery :  those  who  deny  it  are  bound  to  estab- 
lish either  that  some  great  discovery  has  been  made  by 
Bacon's  method — we  mean  by  the  part  peculiar  to  Bacon — • 
or,  better  still,  to  show  that  some  new  discovery  can  be 
made,  by  actually  making  it.  No  general  talk  about  induc- 
tion: no  reliance  upon  the  mere  fact  that  certain  experi- 
ments or  observations  have  been  made ;  let  us  see  where 
Bacon's  induction  has  been  actually  used  or  can  be  used. 
Mere  induction,  enumeratio  simplex,  is  spoken  of  by  him- 
self with  contempt,  as  utterly  incompetent.  For  Bacon 
knew  well  that  a  thousand  instances  may  be  contradicted 
by  the  thousand  and  first:  so  that  no  enumeration  of  in- 
stances, however  large,  is  "sure  demonstration,"  so  long  as 
any  are  left. 

The  immortal  Harvey,  who  was  inventing — we  use  the 
word  in  its  old  sense — the  circulation  of  the  blood,  while 


ON  BACON'S  NOVUM  ORGANUM.  79 

Bacon  was  in  the  full  flow  of  thought  upon  his  system,  may 
be  trusted  to  say  whether,  when  the  system  appeared,  he 
found  any  likeness  in  it  to  his  own  processes,  or  what  would 
have  been  any  help  to  him,  if  he  had  waited  for  the  Novum 
Organum.  He  said  of  Bacon,  "He  writes  philosophy  like 
a  Lord  Chancellor."  This  has  been  generally  supposed  to 
be  only  a  sneer  at  the  sutor  ultra  crepidam ;  but  we  cannot 
help  suspecting  that  there  was  more  intended  by  it.  To  us, 
Bacon  is  eminently  the  philosopher  of  error  prevented,  not 
of  progress  facilitated.  When  we  throw  off  the  idea  of 
being  led  right,  and  betake  ourselves  to  that  of  being  kept 
from  going  wrong,  we  read  his  writings  with  a  sense  of 
their  usefulness,  his  genius,  and  their  probable  effect  upon 
purely  experimental  science,  which  we  can  be  conscious  of 
upon  no  other  supposition.  It  amuses  us  to  have  to  add 
that  the  part  of  Aristotle's  logic  of  which  he  saw  the  value 
was  the  book  on  refutation  of  fallacies.  Now  is  this  not 
the  notion  of  things  to  which  the  bias  of  a  practised  lawyer 
might  lead  him?  In  the  case  which  is  before  the  Court, 
generally  speaking,  truth  lurks  somewhere  about  the  facts, 
and  the  elimination  of  all  error  will  show  it  in  the  residuum. 
The  two  senses  of  the  word  law  come  in  so  as  to  look  almost 
like  a  play  upon  words.  The  judge  can  apply  the  law  so  soon 
as  the  facts  are  settled:  the  physical  philosopher  has  to  de- 
duce the  law  from  the  facts.  Wait,  says  the  judge,  until 
the  facts  are  determined:  did  the  prisoner  take  the  goods 
with  felonious  intent?  did  the  defendant  give  what  amounts 
to  a  warranty?  or  the  like.  Wait,  says  Bacon,  until  all  the 
facts,  or  all  the  obtainable  facts,  are  brought  in:  apply  my 
rules  of  separation  to  the  facts,  and  the  result  shall  come 
out  as  easily  as  by  ruler  and  compasses.  We  think  it  pos- 
sible that  Harvey  might  allude  to  the  legal  character  of 
Bacon's  notions :  we  can  hardly  conceive  so  acute  a  man, 
after  seeing  what  manner  of  writer  Bacon  was,  meaning 
only  that  he  was  a  lawyer  and  had  better  stick  to  his  busi- 
ness. We  do  ourselves  believe  that  Bacon's  philosophy 


80  A  BUDGET  OF  PARADOXES. 

more  resembles  the  action  of  mind  of  a  common-law  judge 
— not  a  Chancellor — than  that  of  the  physical  inquirers  who 
have  been  supposed  to  follow  in  his  steps.  It  seems  to  us 
that  Bacon's  argument  is,  there  can  be  nothing  of  law  but 
what  must  be  either  perceptible,  or  mechanically  deducible, 
when  all  the  results  of  law,  as  exhibited  in  phenomena, 
are  before  us.  Now  the  truth  is,  that  the  physical  philos- 
opher has  frequently  to  conceive  law  which  never  was  in 
his  previous  thought — to  educe  the  unknown,  not  to  choose 
among  the  known.  Physical  discovery  would  be  very  easy 
work  if  the  inquirer  could  lay  down  his  this,  his  that,  and 
his  t'other,  and  say,  "Now,  one  of  these  it  must  be;  let  us 
proceed  to  try  which."  Often  has  he  done  this,  and  failed ; 
often  has  the  truth  turned  out  to  be  neither  this,  that,  nor 
t'other.  Bacon  seems  to  us  to  think  that  the  philosopher 
is  a  judge  who  has  to  choose,  upon  ascertained  facts,  which 
of  known  statutes  is  to  rule  the  decision :  he  appears  to  us 
more  like  a  person  who  is  to  write  the  statute-book,  with 
no  guide  except  the  cases  and  decisions  presented  in  all  their 
confusion  and  all  their  conflict. 

Let  us  take  the  well-known  first  aphorism  of  the  Novum 
Organum : 

"Man  being  the  servant  and  interpreter  of  nature,  can  do 
and  understand  so  much,  and  so  much  only,  as  he  has  ob- 
served in  fact  or  in  thought  of  the  course  of  nature :  beyond 
this  he  neither  knows  anything  nor  can  do  anything." 

This  aphorism  is  placed  by  Sir  John  Herschel5  at  the 
head  of  his  Discourse  on  the  Study  of  Natural  Philosophy : 
a  book  containing  notions  of  discovery  far  beyond  any  of 
which  Bacon  ever  dreamed ;  and  this  because  it  was  written 

8  The  son  of  the  Sir  William  mentioned  below.  He  was  born  in 
1792  and  died  in  1871.  He  wrote  a  treatise  on  light  (1831)  and  one 
on  astronomy  (1836),  and  established  an  observatory  at  the  Cape 
of  Good  Hope  where  he  made  observations  during  1834-1838,  pub- 
lishing them  in  1847.  On  his  return  to  England  he  was  knighted, 
and  in  1848  was  made  president  of  the  Royal  Society.  The  title  of 
the  work  to  which  reference  is  made  is :  A  preliminary  discourse  on 
the  Study  of  Natural  Philosophy.  It  appeared  at  London  in  1831. 


ON  BACON'S  NOVUM  ORGANUM.  81 

after  discovery,  instead  of  before.  Sir  John  Herschel,  in 
his  version,  has  avoided  the  translation  of  re  vel  mente  ob- 
servaverit,  and  gives  us  only  "by  his  observation  of  the 
order  of  nature."  In  making  this  the  opening  of  an  ex- 
cellent sermon,  he  has  imitated  the  theologians,  who  often 
employ  the  whole  time  of  the  discourse  in  stuffing  matter 
into  the  text,  instead  of  drawing  matter  out  of  it.  'By  ob- 
servation he  (Herschel)  means  the  whole  course  of  dis- 
covery, observation,  hypothesis,  deduction,  comparison,  etc. 
The  type  of  the  Baconian  philosopher  as  it  stood  in  his 
mind,  had  been  derived  from  a  noble  example,  his  own 
father,  William  Herschel,6  an  inquirer  whose  processes  would 
have  been  held  by  Bacon  to  have  been  vague,  insufficient, 
compounded  of  chance  work  and  sagacity,  and  too  meagre 
of  facts  to  deserve  the  name  of  induction.  In  another  work, 
his  treatise  on  Astronomy,7  Sir  John  Herschel,  after  noting 
that  a  popular  account  can  only  place  the  reader  on  the 
threshold,  proceeds  to  speak  as  follows  of  all  the  higher 
departments  of  science.  The  italics  are  his  own: 

"Admission  to  its  sanctuary,  and  to  the  privileges  and 
feelings  of  a  votary,  is  only  to  be  gained  by  one  means — 
sound  and  sufficient  knowledge  of  mathematics,  the  great 
instrument  of  all  exact  inquiry,  without  which  no  man  can 
ever  make  such  advances  in  this  or  any  other  of  the  higher 
departments  of  science  as  can  entitle  him  to  form  an  inde- 
pendent opinion  on  any  subject  of  discussion  within  their 
range" 

How  is  this?  Man  can  know  no  more  than  he  gets 
from  observation,  and  yet  mathematics  is  the  great  instru- 
ment of  all  exact  inquiry.  Are  the  results  of  mathematical 
deduction  results  of  observation?  We  think  it  likely  that 

"Sir  William  was  born  at  Hanover  in  1738  and  died  at  Slough, 
near  Windsor,  in  1822.  He  discovered  the  planet  Uranus  and  six 
satellites,  besides  two  satellites  of  Saturn.  He  was  knighted  by 
George  III. 

7  This  was  the  work  of  1836.  He  also  published  a  work  entitled 
Outlines  of  Astronomy  in  1849. 


82  A  BUDGET  OF  PARADOXES. 

Sir  John  Herschel  would  reply  that  Bacon,  in  coupling 
together  observare  re  and  observare  mente,  has  done  what 
some  wags  said  Newton  afterwards  did  in  his  study-door — 
cut  a  large  hole  of  exit  for  the  large  cat,  and  a  little  hole 
for  the  little  cat.8  But  Bacon  did  no  such  thing:  he  never 
included  any  deduction  under  observation.  To  mathematics 
he  had  a  dislike.  He  averred  that  logic  and  mathematics 
should  be  the  handmaids,  not  the  mistresses,  of  philosophy. 
He  meant  that  they  should  play  a  subordinate  and  subsequent 
part  in  the  dressing  of  the  vast  mass  of  facts  by  which  dis- 
covery was  to  be  rendered  equally  accessible  to  Newton  and 
to  us.  (Bacon  himself  was  very  ignorant  of  all  that  had  been 
done  by  mathematics ;  and,  strange  to  say,  he  especially  ob- 
jected to  astronomy  being  handed  over  to  the  mathemati- 
cians. Leverrier  and  Adams,  calculating  an  unknown  planet 
into  visible  existence  by  enormous  heaps  of  algebra,  furnish 
the  last  comment  of  note  on  this  specimen  of  the  goodness 
of  Bacon's  views.  The  following  account  of  his  knowledge 
of  what  had  been  done  in  his  own  day  or  before  it,  is  Mr. 
Spedding's  collection  of  casual  remarks  in  Mr.  Ellis's  several 
prefaces : 

"Though  he  paid  great  attention  to  astronomy,  dis- 
cussed carefully  the  methods  in  which  it  ought  to  be  studied, 
constructed  for  the  satisfaction  of  his  own  mind  an  elaborate 
theory  of  the  heavens,  and  listened  eagerly  for  the  news 
from  the  stars  brought  by  Galileo's  telescope,  he  appears  to 
have  been  utterly  ignorant  of  the  discoveries  which  had 
just  been  made  by  Kepler's  calculations.  Though  he  com- 
plained in  1623  of  the  want  of  compendious  methods  for 
facilitating  arithmetical  computations,  especially  with  regard 
to  the  doctrine  of  Series,  and  fully  recognized  the  importance 
of  them  as  an  aid  to  physical  inquiries— he  does  not  say  a 
word  about  Napier's  Logarithms,  which  had  been  published 
only  nine,  years  before  and  reprinted  more  than  once  in  the 

"While  Newton  does  not  tell  the  story,  he  refers  in  the  Prindpia 
(1714  edition,  p.  293)  to  the  accident  caused  by  his  cat. 


83 


interval.  He  complained  that  no  considerable  advance  had 
been  made  in  geometry  beyond  Euclid,  without  taking  any 
notice  of  what  had  been  done  by  Archimedes  and  Apollonius. 
He  saw  the  importance  of  determining  accurately  the  spe- 
cific gravity  of  different  substances,  and  himself  attempted 
to  form  a  table  of  them  by  a  rude  process  of  his  own,  with- 
out knowing  of  the  more  scientific  though  still  imperfect 
methods  previously  employed  by  Archimedes,  Ghetaldus,9  and 
Porta.  He  speaks  of  the  evprjKa  of  Archimedes  in  a  manner 
which  implies  that  he  did  not  clearly  apprehend  either  the 
nature  of  the  problem  to  be  solved  or  the  principles  upon 
which  the  solution  depended.  In  reviewing  the  progress 
of  mechanics,  he  makes  no  mention  of  Archimedes  himself, 
or  of  Stevinus,10  Galileo,  Guldinus,11  or  Ghetaldus.  He  makes 
no  allusion  to  the  theory  of  equilibrium.  He  observes  that 
a  ball  of  one  pound  weight  will  fall  nearly  as  fast  through 
the  air  as  a  ball  of  two,  without  alluding  to  the  theory  of 
the  acceleration  of  falling  bodies,  which  had  been  made 
known  by  Galileo  more  than  thirty  years  before.  He  pro- 
poses an  inquiry  with  regard  to  the  lever — namely,  whether 
in  a  balance  with  arms  of  different  length  but  equal  weight 
the  distance  from  the  fulcrum  has  any  effect  upon  the  in- 
clination,— though  the  theory  of  the  lever  was  as  well  under- 
stood in  his  own  time  as  it  is  now.  In  making  an  experiment 

"Marino  Ghetaldi  (1566-1627),  whose  Promotus  'Archimedes  ap- 
peared at  Rome  in  1603,  Nonnullae  propositiones  de  parabola  at 
Rome  in  1603,  and  Apollonius  redivivus  at  Venice  in  1607.  He  was 
a  nobleman  and  was  ambassador  from  Venice  to  Rome. 

10  Simon  Steyin  (born  at  Bruges,  1548;  died  at  the  Hague,  1620). 
He  was  an  engineer  and  a  soldier,  and  his  La  Disme  (1585)  was 
the  first  separate  treatise  on  the  decimal  fraction.  The  contribution 
referred  to  above  is  probably  that  on  the  center  of  gravity  of  three 
bodies  (1586). 

"Habakuk  Guldin  (1577-1643),  who  took  the  name  Paul  on  his 
conversion  to  Catholicism.  He  became  a  Jesuit,  and  was  professor 
of  mathematics  at  Vienna  and  later  at  Gratz.  In  his  Centrobaryca 
sen  de  centra  gravitatis  trium  specierum  quantitatis  continuae  (1635), 
of  the  edition  of  1641,  appears  the  Pappus  rule  for  the  volume  of  a 
solid  formed  by  the  revolution  of  a  plane  figure  about  an  axis,  often 
spoken  of  as  Guldin' s  Theorem. 


84  A  BUDGET  OF  PARADOXES. 

of  his  own  to  ascertain  the  cause  of  the  motion  of  a  wind- 
mill, he  overlooks  an  obvious  circumstance  which  makes  the 
experiment  inconclusive,  and  an  equally  obvious  variation 
of  the  same  experiment  which  would  have  shown  him  that 
his  theory  was  false.  He  speaks  of  the  poles  of  the  earth 
as  fixed,  in  a  manner  which  seems  to  imply  that  he  was  not 
acquainted  with  the  precession  of  the  equinoxes ;  and  in 
another  place,  of  the  north  pole  being  above  and  the  south 
pole  below,  as  a  reason  why  in  our  hemisphere  the  north 
winds  predominate  over  the  south." 

Much  of  this  was  known  before,  but  such  a  summary 
of  Bacon's  want  of  knowledge  of  the  science  of  his  own 
time  was  never  yet  collected  in  one  place.  We  may  add, 
that  Bacon  seems  to  have  been  as  ignorant  of  Wright's12 
memorable  addition  to  the  resources  of  navigation  as  of 
Napier's  addition  to  the  means  of  calculation.  Mathematics 
was  beginning  to  be  the  great  instrument  of  exact  inquiry: 
Bacon  threw  the  science  aside,  from  ignorance,  just  at  the 
time  when  his  enormous  sagacity,  applied  to  knowledge, 
would  have  made  him  see  the  part  it  was  to  play.  If  New- 
ton had  taken  Bacon  for  his  master,  not  he,  but  somebody 
else,  would  have  been  Newton.13 

ON  METEOROLOGICAL  OBSERVATORIES. 

There  is  an  attempt  at  induction  going  on,  which  has 
yielded  little  or  no  fruit,  the  observations  made  in  the 
meteorological  observatories.  This  attempt  is  carried  on 
in  a  manner  which  would  have  caused  Bacon  to  dance  for 
joy;  for  he  lived  in  times  when  Chancellors  did  dance. 

"Edward  Wright  was  born  at  Graveston,  Norfolkshire,  in  1560, 
and  died  at  London  in  1615.  He  was  a  fellow  of  Caius  College, 
Cambridge,  and  in  his  work  entitled  The  correction  of  certain  errors 
in  Navigation  (1599)  he  gives  the  principle  of  Mercator's  projec- 
tion. He  translated  the  Portuum  investigandorum  ratio  of  Stevin  in 
1599- 

18  De  Morgan  never  wrote  a  more  suggestive  sentence.  Its  mes- 
sage is  not  for  his  generation  alone. 


BASIS  OF  MODERN  DISCOVERY.  85 

Russia,  says  M.  Biot,1  is  covered  by  an  army  of  meteoro- 
graphs, with  generals,  high  officers,  subalterns,  and  privates 
with  fixed  and  defined  duties  of  observation.  Other  coun- 
tries have  also  their  systematic  observations.  And  what 
has  come  of  it?  Nothing,  says  M.  Biot,  and  nothing  will 
ever  come  of  it ;  the  veteran  mathematician  and  experimental 
philosopher  declares,  as  does  Mr.  Ellis,  that  no  single  branch 
of  science  has  ever  been  fruitfully  explored  in  this  way. 
There  is  no  special  object,  he  says.  Any  one  would  suppose 
that  M.  Biot's  opinion,  given  to  the  French  Government 
upon  the  proposal  to  construct  meteorological  observatories 
in  Algeria  (Comptes  Rendus,  vol.  xli,  Dec.  31,  1855),  was 
written  to  support  the  mythical  Bacon,  modern  physics, 
against  the  real  Bacon  of  the  Novum  Organum.  There  is 
no  special  object.  In  these  words  lies  the  difference  between 
the  two  methods. 

[In  the  report  to  the  Greenwich  Board  of  Visitors  for 
1867  Mr.  Airy,2  speaking  of  the  increase  of  meteorological 
observatories,  remarks,  "Whether  the  effect  of  this  move- 
ment will  be  that  millions  of  useless  observations  will  be 
added  to  the  millions  that  already  exist,  or  whether  some- 
thing may  be  expected  to  result  which  will  lead  to  a  meteoro- 
logical theory,  I  cannot  hazard  a  conjecture."  This  is  a 
conjecture,  and  a  very  obvious  one:  if  Mr.  Airy  would  have 
given  2%d.  for  the  chance  of  a  meteorological  theory  formed 
by  masses  of  observations,  he  would  never  have  said  what 
I  have  quoted.] 

BASIS  OF  MODERN  DISCOVERY. 

Modern  discoveries  have  not  been  made  by  large  collec- 
tions of  facts,  with  subsequent  discussion,  separation,  and  re- 

1The  eminent  French  physicist,  Jean  Baptiste  Biot  (1779-1862), 
professor  in  the  College  de  France.  His  work  Sur  les  observatoires 
meteor ologiques  appeared  in  1855. 

8  George  Biddell  Airy  (1801-1892),  professor  of  astronomy  and 
physics  at  Cambridge,  and  afterwards  director  of  the  Observatory 
at  Greenwich. 


86  A  BUDGET  OF  PARADOXES. 

suiting  deduction  of  a  truth  thus  rendered  perceptible.  A 
few  facts  have  suggested  an  hypothesis,  which  means  a 
supposition,  proper  to  explain  them.  The  necessary  results 
of  this  supposition  are  worked  out,  and  then,  and  not  till 
then,  other  facts  are  examined  to  see  if  these  ulterior  results 
are  found  in  nature.  The  trial  of  the  hypothesis  is  the 
special  object:  prior  to  which,  hypothesis  must  have  been 
started,  not  by  rule,  but  by  that  sagacity  of  which  no  de- 
scription can  be  given,  precisely  because  the  very  owners 
of  it  do  not  act  under  laws  perceptible  to  themselves.1  The 
inventor  of  hypothesis,  if  pressed  to  explain  his  method, 
must  answer  as  did  Zerah  Colburn,2  when  asked  for  his  mode 
of  instantaneous  calculation.  When  the  poor  boy  had  been 
bothered  for  some  time  in  this  manner,  he  cried  out  in  a 
huff,  "God  put  it  into  my  head,  and  I  can't  put  it  into  yours."3 

1De  Morgan  would  have  rejoiced  in  the  role  played  by  Intuition 
in  the  mathematics  of  to-day,  notably  among  the  followers  of  Pro- 
fessor Klein. 

2  Colburn  was  the  best  known  of  the  calculating  boys  produced 
in  America.  He  was  born  at  Cabot,  Vermont,  in  1804,  and  died  at 
Norwich,  Vermont,  in  1840.  Having  shown  remarkable  skill  in 
numbers  as  early  as  1810,  he  was  taken  to  London  in  1812,  whence 
he  toured  through  Great  Britain  and  to  Paris.  The  Earl  of  Bristol 
placed  him  in  Westminster  School  (1816-1819).  On  his  return  to 
America  he  became  a  preacher,  and  later  a  teacher  of  languages. 

8  The  history  of  calculating  boys  is  interesting.  Mathieu  le  Coc 
(about  1664),  a  boy  of  Lorraine,  could  extract  cube  roots  at  sight 
at  the  age  of  eight.  Tom  Fuller,  a  Virginian  slave  of  the  eighteenth 
century,  although  illiterate,  gave  the  number  of  seconds  in  7  years 
17  days  12  hours  after  only  a  minute  and  a  half  of  thought  Jede- 
diah  Buxton,  an  Englishman  of  the  eighteenth  century,  was  studied 
by  the  Royal  Society  because  of  his  remarkable  powers.  Ampere, 
the  physicist,  made  long  calculations  with  pebbles  at  the  age  of  four. 
Gauss,  one  of  the  few  infant  prodigies  to  become  an  adult  prodigy, 
corrected  his  father's  payroll  at  the  age  of  three.  One  of  the  most 
remarkable  of  the  French  calculating  boys  was  Henri  Mpndeux. 
He  was  investigated  by  Arago,  Sturm,  Cauchy,  and  Liouville,  for 
the  Academic  des  Sciences,  and  a  report  was  written  by  Cauchy. 
His  specialty  was  the  solution  of  algebraic  problems  mentally.  He 
seems  to  have  calculated  squares  and  cubes  by  a  binomial  formula 
of  his  own  invention.  He  died  in  obscurity,  but  was  the  subject 
of  a  Biographie  by  Jacoby  (1846).  George  P.  Bidder,  the  Scotch 
engineer  (1806-1878),  was  exhibited  as  an  arithmetical  prodigy  at 
the  age  of  ten,  and  did  not  attend  school  until  he  was  twelve.  Of 
the  recent  cases  two  deserve  special  mention,  Inaudi  and  Diamandi. 


BASIS  OF  MODERN  DISCOVERY.  87 

Wrong  hypotheses,  rightly  worked  from,  have  produced 
more  useful  results  than  unguided  observation.  But  this  is 
not  the  Baconian  plan.  Charles  the  Second,  when  informed 
of  the  state  of  navigation,  founded  a  Baconian  observatory 
at  Greenwich,  to  observe,  observe,  observe  away  at  the 
moon,  until  her  motions  were  known  sufficiently  well  to 
render  her  useful  in  guiding  the  seaman.  And  no  doubt 
Flamsteed's4  observations,  twenty  or  thirty  of  them  at  least, 
were  of  signal  use.  But  how  ?  A  somewhat  fanciful  thinker, 
one  Kepler,  had  hit  upon  the  approximate  orbits  of  the 
planets  by  trying  one  hypothesis  after  another:  he  found 
the  ellipse,  which  the  Platonists,  well  despised  of  Bacon, 
and  who  would  have  despised  him  as  heartily  if  they  had 
known  him,  had  investigated  and  put  ready  to  hand  nearly 
2000  years  before.5  The  sun  in  the  focus,  the  motions  of 
the  planet  more  and  more  rapid  as  they  approach  the  sun, 
led  Kepler — and  Bacon  would  have  reproved  him  for  his 
rashness — to  imagine  that  a  force  residing  in  the  sun  might 
move  the  planets,  a  force  inversely  as  the  distance.  Bouil- 
laud,6  upon  a  fanciful  analogy,  rejected  the  inverse  distance, 

Jacques  Inaudi  (born  in  1867)  was  investigated  for  the  Academic 
in  1892  by  a  commission  including  Poincare,  Charcot,  and  Binet. 
(See  the  Revue  des  Deux  Mondes,  June  15,  1892,  and  the  laboratory 
bulletins  of  the  Sorbonne).  He  has  frequently  exhibited  his  re- 
markable powers  in  America.  Pericles  Diamandi  was  investigated 
by  the  same  commission  in  1893.  See  Alfred  Binet,  Psychologic  des 
Grands  Calculateurs  et  Joueurs  d'Echecs,  Paris,  1894. 

4  John  Flamsteed's   (1646-1719)   "old  white  house"  was  the  first 
Greenwich  observatory.    He  was  the  Astronomer  Royal  and  first 
head  of  this  observatory. 

5  It  seems  a  pity  that  De  Morgan  should  not  have  lived  to  lash 
those  of  our  time  who  are  demanding  only  the  immediately  prac- 
tical in  mathematics.     His  satire  would  have  been  worth  the  read- 
ing against  those  who  seek  to  stifle  the  science  they  pretend  to  foster. 

'Ismael  Bouillaud,  or  Boulliau,  was  born  in  1605  and  died  at 
Paris  in  1694.  He  was  well  known  as  an  astronomer,  mathemati- 
cian, and  jurist.  He  lived  with  De  Thou  at  Paris,  and  accompanied 
him  to  Holland.  He  traveled  extensively,  and  was  versed  in  the 
astronomical  work  of  the  Persians  and  Arabs.  It  was  in  his 
Astronomia  philolaica,  opus  novum  (Paris,  1645)  that  he  attacked 
Kepler's  laws.  His  tables  were  shown  to  be  erroneous  by  the  fact 
that  the  solar  eclipse  did  not  take  place  as  predicted  by  him  in  1645. 


88  A  BUDGET  OF  PARADOXES. 

and,  rejecting  the  force  altogether,  declared  that  if  such  a 
thing  there  were,  it  would  be  as  the  inverse  square  of  the 
distance.  Newton,  ready  prepared  with  the  mathematics 
of  the  subject,  tried  the  fall  of  the  moon  towards  the  earth, 
away  from  her  tangent,  and  found  that,  as  compared  with 
the  fall  of  a  stone,  the  law  of  the  inverse  square  did  hold 
for  the  moon.  He  deduced  the  ellipse,  he  proceeded  to 
deduce  the  effect  of  the  disturbance  of  the  sun  upon  the 
moon,  upon  the  assumed  theory  of  universal  gravitation. 
He  found  result  after  result  of  his  theory  in  conformity  with 
observed  fact:  and,  by  aid  of  Flamsteed's  observations, 
which  amended  what  mathematicians  call  his  constants,  he 
constructed  his  lunar  theory.  Had  it  not  been  for  Newton, 
the  whole  dynasty  of  Greenwich  astronomers,  from  Flam- 
steed  of  happy  memory,  to  Airy  whom  Heaven  preserve,7 
might  have  worked  away  at  nightly  observation  and  daily 
reduction,  without  any  remarkable  result:  looking  forward, 
as  to  a  millennium,  to  the  time  when  any  man  of  moderate 
intelligence  was  to  see  the  whole  explanation.  What  are 
large  collections  of  facts  for?  To  make  theories  from,  says 
Bacon:  to  try  ready-made  theories  by,  says  the  history  of 
discovery:  it's  all  the  same,  says  the  idolater:  nonsense, 
say  we! 

Time  and  space  run  short:  how  odd  it  is  that  of  the 
three  leading  ideas  of  mechanics,  time,  space,  and  matter, 
the  first  two  should  always  fail  a  reviewer  before  the  third. 
We  might  dwell  upon  many  points,  especially  if  we  at- 
tempted a  more  descriptive  account  of  the  valuable  edition 
before  us.  No  one  need  imagine  that  the  editors,  by  their 
uncompromising  attack  upon  the  notion  of  Bacon's  influence 
common  even  among  mathematicians  and  experimental  phi- 
losophers, have  lowered  the  glory  of  the  great  man  whom 
it  was,  many  will  think,  their  business  to  defend  through 
thick  and  thin.  They  have  given  a  clearer  notion  of  his 

TAs  it  did,  until  1892,  when  Airy  had  reached  the  ripe  age  of 
ninety-one. 


THE  REAL  VALUE  OF  BACON^S  WORKS.  89 

excellencies,  and  a  better  idea  of  the  power  of  his  mind, 
than  ever  we  saw  given  before.  Such  a  correction  as  theirs 
must  have  come,  and  soon,  for  as  Hallam  says — after  noting 
that  the  Novum  Organum  was  never  published  separately 
in  England,  Bacon  has  probably  been  more  read  in  the 
last  thirty  years — now  forty — than  in  the  two  hundred  years 
which  preceded.  He  will  now  be  more  read  than  ever  he 
was.  The  history  of  the  intellectual  world  is  the  history 
of  the  worship  of  one  idol  after  another.  No  sooner  is  it 
clear  that  a  Hercules  has  appeared  among  men,  than  all 
that  imagination  can  conceive  of  strength  is  attributed  to 
him,  and  his  labors  are  recorded  in  the  heavens.  The  time 
arrives  when,  as  in  the  case  of  Aristotle,  a  new  deity  is 
found,  and  the  old  one  is  consigned  to  shame  and  reproach. 
A  reaction  may  afterwards  take  place,  and  this  is  now  hap- 
pening in  the  case  of  the  Greek  philosopher.  The  end  of  the 
process  is,  that  the  opposing  deities  take  their  places,  side 
by  side,  in  a  Pantheon  dedicated  not  to  gods,  but  to  heroes. 

THE  REAL  VALUE  OF  BACON'S  WORKS. 

Passing  over  the  success  of  Bacon's  own  endeavors  to 
improve  the  details  of  physical  science,  which  was  next  to 
nothing,  and  of  his  method  as  a  whole,  which  has  never 
been  practised,  we  might  say  much  of  the  good  influence 
of  his  writings.  Sound  wisdom,  set  in  sparkling  wit,  must 
instruct  and  amuse  to  the  end  of  time:  and,  as  against 
error,  we  repeat  that  Bacon  is  soundly  wise,  so  far  as  he 
goes.  There  is  hardly  a  form  of  human  error  within  his 
scope  which  he  did  not  detect,  expose,  and  attach  to  a  satir- 
ical metaphor  which  never  ceases  to  sting.  He  is  largely 
indebted  to  a  very  extensive  reading;  but  the  thoughts  of 
others  fall  into  his  text  with  such  a  close-fitting  compact- 
ness that  he  can  make  even  the  words  of  the  Sacred  Writers 
pass  for  his  own.  A  saying  of  the  prophet  Daniel,  rather 
a  hackneyed  quotation  in  our  day,  Multi  pertransibunt,  et 
augebitur  scientia,  stands  in  the  title-page  of  the  first  edition 


90  A  BUDGET  OF  PARADOXES. 

of  Montucla's  History  of  Mathematics  as  a  quotation  from 
Bacon — and  it  is  not  the  only  place  in  which  this  mistake 
occurs.  When  the  truth  of  the  matter,  as  to  Bacon's  sys- 
tem, is  fully  recognized,  we  have  little  fear  that  there  will 
be  a  reaction  against  the  man.  First,  because  Bacon  will 
always  live  to  speak  for  himself,  for  he  will  not  cease  to  be 
read:  secondly,  because  those  who  seek  the  truth  will  find 
it  in  the  best  edition  of  his  works,  and  will  be  most  ably  led 
to  know  what  Bacon  was,  in  the  very  books  which  first 
showed  at  large  what  he  was  not. 

THE  CONGREGATION  OF  THE  INDEX,  ON  COPERNICUS. 

In  this  year  ( 1620)  appeared  the  corrections  under  which 
the  Congregation  of  the  Index —  i.  e.,  the  Committee  of 
Cardinals  which  superintended  the  Index  of  forbidden  books 
— proposed  to  allow  the  work  of  Copernicus  to  be  read.  I 
insert  these  conditions  in  full,  because  they  are  often  alluded 
to,  and  I  know  of  no  source  of  reference  accessible  to  a 
twentieth  part  of  those  who  take  interest  in  the  question. 

By  a  decree  of  the  Congregation  of  the  Index,  dated 
March  5,  1616,  the  work  of  Copernicus,  and  another  of 
Didacus  Astunica,1  are  suspended  donee  corrigantur,  as  teach- 
ing: 

"Falsam  illam  doctrinam  Pythagoricam,  divinae  que 
Scripturae  omnino  adversantem,  de  mobilitate  Terrae  et  im- 
mobilitate  Solis."2 

But  a  work  of  the  Carmelite  Foscarini3  is: 

1  Didaci  a  Stunica. ..  .In  7ob  commentaria  appeared  at  Toledo  in 
1584. 

'"The  false  Pythagorean  doctrine,  absolutely  opposed  to  the  Holy 
Scriptures,  concerning  the  mobility  of  the  earth  and  the  immobility 
of  the  sun/' 

8  Paolo  Antonio  Foscarini  (1580-1616),  who  taught  theology  and 
philosophy  at  Naples  and  Messina,  was  one  of  the  first  to  champion 
the  theories  of  Copernicus.  This  was  in  his  Lettera  sopra  f opinion* 
de'  Pittagorici  e  del  Copernico,  della  mobilita  della  Terra  e  stabilita 
del  Sole,  e  il  nuovo  pittagorico  sistema  del  mondo,  4to,^  Naples,  1615. 
The  condemnation  of  the  Congregation  was  published  in  the  follow- 
ing spring,  and  in  the  year  of  Foscarini's  death  at  the  early  age  of 
thirty-six. 


THE  CONGREGATION  OF  THE  INDEX,  ON  COPERNICUS.     91 

"Omnino  prohibendum  atque  damnandum,"  because  "os- 
tendere  conatur  prsef atam  doctrinam ....  consonam  esse  veri- 
tati  et  non  adversari  Sacrae  Scripturse."* 

Works  which  teach  the  false  doctrine  of  the  earth's  mo- 
tion are  to  be  corrected;  those  which  declare  the  doctrine 
conformable  to  Scripture  are  to  be  utterly  prohibited. 

In  a  "Monitum  ad  Nicolai  Copernici  lectorem,  ejusque 
emendatio,  permissio,  et  correctio,"  dated  1620  without  the 
month  or  day,  permission  is  given  to  reprint  the  work  of 
Copernicus  with  certain  alterations ;  and,  by  implication,  to 
read  existing  copies  after  correction  in  writing.  In  the  pre- 
amble the  author  is  called  nobilis  astrologus-,  not  a  compli- 
ment to  his  birth,  which  was  humble,  but  to  his  fame.  The 
suspension  was  because: 

"Sacrse  Scripturae,  ejusque  verse  et  Catholicse  interpre- 
tation! repugnantia  (quod  in  homine  Christiano  minime 
tolerandum)  non  per  hypothesin  tractare,  sed  ut  verissima 
adstruere  non  dubitat!"5 

And  the  corrections  relate: 

"Locis  in  quibus  non  ex  hypothesi,  sed  asserendo  de  situ 
et  motu  Terrae  disputat."6 

That  is,  the  earth's  motion  may  be  an  hypothesis  for 
elucidation  of  the  heavenly  motions,  but  must  not  be  as- 
serted as  a  fact. 

(In  Pref.  circa  finem.)  "Copernicus.  Si  fortasse  erunt 
/AaratoAoyot,  qui  cum  omnium  Mathematum  ignari  sint,  tamen 
de  illis  judicium  sibi  summunt,  propter  aliquem  locum  scrip- 
turse,  male  ad  suum  propositum  detortum,  ausi  fuerint  meum 

"To  be  wholly  prohibited  and  condemned,"  because  "it  seeks  to 
show  that  the  aforesaid  doctrine  is  consonant  with  truth  and  is  not 
opposed  to  the  Holy  Scriptures." 

"  "As  repugnant  to  the  Holy  Scriptures  and  to  its  true  and  Catho- 
lic interpretation  (which  in  a  Christian  man  cannot  be  tolerated  in 
the  least),  he  does  not  hesitate  to  treat  (of  his  subject)  'by  hypoth- 
esis' but  he  even  adds  'as  most  true' I" 

'"To  the  places  in  which  he  discusses  not  by  hypothesis  but  by 
making  assertions  concerning  the  position  and  motion  of  the  earth." 


92  A  BUDGET  OF  PARADOXES. 

hoc  institutum  reprehendere  ac  insectari:  illos  nihil  moror 
adeo  tit  etiam  illorum  judicium  tanquam  temerarium  con- 
temnam.  Non  enim  obscurum  est  Lactantium,  celebrem 
alioqui  scriptorem,  sed  Mathematicum  parum,  admodum 
pueriliter  de  forma  terrse  loqui,  cum  deridet  eos,  qui  terram 
globi  formam  habere  prodiderunt.  Itaque  non  debet  mirum 
videri  studiosis,  si  qui  tales  nos  etiam  videbunt.  Mathemata 
Mathematicis  scribuntur,  quibus  et  hi  nostri  labores,  si  me 
non  fallit  opinio,  videbuntur  etiam  Reipub.  ecclesiastics 
conducere  aUquid ....  Emend.  Ibi  si  fortasse  dele  omnia, 
usque  ad  verbum  hi  nostri  labores  et  sic  accommoda — Ccete- 
rum  hi  nostri  labores."7 

All  the  allusion  to  Lactantius,  who  laughed  at  the  notion 
of  the  earth  being  round,  which  was  afterwards  found  true, 
is  to  be  struck  out. 

(Cap.  5.  lib.  i.  p.  3)  "Copernicus.  Si  tamen  attentius 
rem  consideremus,  videbitur  hsec  qusestio  nondum  absoluta, 
et  idcirco  minime  contemnenda.  Emend.  Si  tamen  atten- 
tius rem  consideremus,  nihil  refert  an  Terram  in  medio 
Mundi,  an  extra  Medium  existere,  quoad  solvendas  cceles- 
tium  motuum  apparentias  existimemus."8 

7  "Copernicus,     If  by  chance  there  shall  be  vain  talkers  who,  al- 
though ignorant  of  all  mathematics,  yet  taking  it  upon  themselves 
to  sit  in  judgment  upon  the  subject  on  account  of  a  certain  passage 
of  Scripture  badly  distorted   for  their  purposes,   shall  have   dared 
to  criticize  and  censure  this  teaching  of  mine,  I  pay  no  attention 
to  them,  even  to  the  extent  of  despising  their  judgment  as  rash. 
For   it  is   not   unknown   that   Lactantius,   a   writer   of   prominence 
in   other    lines    although    but    little   versed    in    mathematics,    spoke 
very   childishly   about   the    form    of   the    earth    when    he    ridiculed 
those  who  declared  that  it  was  spherical.    Hence  it  should  not  seem 
strange  to  the  learned  if  some  shall  look  upon  us  in  the  same  way. 
Mathematics  is  written  for  mathematicians,  to  whom  these  labors 
of  ours  will  seem,  if  I  mistake  not,  to  add  something  even  to  the 

republic  of  the  Church Emend.  Here  strike  out  everything  from 

'if  by  chance'  to  th'e  words  'these  labors  of  ours/  and  adapt  it  thus : 
'But  these  labors  of  ours/" 

8  "Copernicus.    However  if  we  consider  the  matter  more  carefully 
it  will  be  seen  that  the  investigation  is  not  yet  completed,  and  there- 
fore ought  by  no  means  to  be  condemned.    Emend.  However,  if  we 
consider  the  matter  more  carefully  it  is  of  no  consequence  whether 


THE  CONGREGATION  OF  THE  INDEX,  ON   COPERNICUS.      93 

We  must  not  say  the  question  is  not  yet  settled,  but 
only  that  it  may  be  settled  either  way,  so  far  as  mere  ex- 
planation of  the  celestial  motions  is  concerned. 

(Cap.  8.  lib.  i.)  "Totum  hoc  caput  potest  expungi,  quia 
ex  professo  tractat  de  veritate  motus  Terrse,  dum  solvit 
veterum  rationes  probantes  ejus  quietem.  Cum  tamen  prob- 
lematice  videatur  loqui ;  ut  studiosis  satisfiat,  seriesque  et 
ordo  libri  integer  maneat ;  emendetur  ut  infra."9 

A  chapter  which  seems  to  assert  the  motion  should  per- 
haps be  expunged;  but  it  may  perhaps  be  problematical; 
and,  not  to  break  up  the  book,  must  be  amended  as  below. 

(p.  6.)  "Copernicus.  Cur  ergo  hesitamus  adhuc,  mobili- 
tatem  illi  formae  suse  a  natura  congruentem  concedere,  ma- 
gisquam  quod  totus  labatur  mundus,  cujus  finis  ignoratur, 
scirique  nequit,  neque  fateamur  ipsius  cotidianae  revolutio- 
nis  in  coelo  apparentiam  esse,  et  in  terra  veritatem?  Et 
hsec  perinde  se  habere,  ac  si  diceret  Virgilianus  yEneas: 
Provehimur  portu ....  Emend.  Cur  ergo  non  possum  mobi- 
litatem  illi  formse  suse  concedere,  magisque  quod  totus  laba- 
tur mundus,  cujus  finis  ignoratur  scirique  nequit,  et  quse 
apparent  in  ccelo,  perinde  se  habere  ac  si. . .  ."10 

we  regard  the  earth  as  existing  in  the  center  of  the  universe  or 
outside  of  the  center,  so  far  as  the  solution  of  the  phenomena  of 
celestial  movements  is  concerned." 

"The  whole  of  this  chapter  may  be  cut  out,  since  it  avowedly 
treats  of  the  truth  of  the  earth's  motion,  while  it  refutes  the  reasons 
of  the  ancients  proving  its  immobility.  Nevertheless,  since  it  seems 
to  speak  problematically,  in  order  that  it  may  satisfy  the  learned  and 
keep  intact  the  sequence  and  unity  of  the  book  let  it  be  emended 
as  below." 

0  "Copernicus.  Therefore  why  do  we  still  hesitate  to  concede  to 
it  motion  which  is  by  nature  consistent  with  its  form,  the  more  so 
because  the  whole  universe  is  moving,  whose  end  is  not  and  cannot 
be  known,  and  not  confess  that  there  is  in  the  sky  an  appearance  of 
daily  revolution,  while  on  the  earth  there  is  the  truth  of  it  ?  And  in 
like  manner  these  things  are  as  if  Virgil's  ^Eneas  should  say,  'We 
are  borne  from  the  harbor'....  Emend.  Hence  I  cannot  concede 
motion  to  this  form,  the  more  so  because  the  universe  would  fall, 
whose  end  is  not  and  cannot  be  known,  and  what  appears  in  the 
heavens  is  just  as  if. ..." 


94  A  BUDGET  OF  PARADOXES. 

"Why  should  we  hesitate  to  allow  the  earth's  motion," 
must  be  altered  into  "I  cannot  concede  the  earth's  motion." 

(p.  7.)  "Copernicus.  Addo  etiam,  quod  satis  absurdum 
videretur,  continenti  sive  locanti  motum  adscribi,  et  non 
potius  contento  et  locato,  quod  est  terra.  Emend.  Addo  etiam 
difficilius  non  esse  contento  et  locato,  quod  est  Terra,  motum 
adscribere,  quam  continenti."11 

We  must  not  say  it  is  absurd  to  refuse  motion  to  the 
contained  and  located,  and  to  give  it  to  the  containing  and 
locating;  say  that  neither  is  more  difficult  than  the  other. 

(p.  7.)  "Copernicus.  Vides  ergo  quod  ex  his  omnibus 
probabilior  sit  mobilitas  Terrae,  quam  ejus  quies,  prsesertim 
in  cotidiana  revolutione,  tanquam  terrse  maxime  propria. 
Emend.  Fides. . .  .delendus  est  usque  ad  finem  capitis."12 

Strike  out  the  whole  of  the  chapter  from  this  to  the 
end;  it  says  that  the  motion  of  the  earth  is  the  most  prob- 
able hypothesis. 

(Cap.  9.  lib.  i.  p.  7.)  "Copernicus.  Cum  igitur  nihil  pro- 
hibeat  mobilitatem  Terrae,  videndum  nunc  arbitror,  an  etiam 
plures  illi  motus  conveniant,  ut  possit  una  errantium  syde- 
rum  existimari.  Emend.  Cum  igitur  Terram  moveri  as- 
sumpserim,  videndum  nunc  arbitror,  an  etiam  illi  plures 
possint  convenire  motus."13 

^"Copernicus.  I  also  add  that  it  would  seem  very  absurd  that 
motion  should  be  ascribed  to  that  which  contains  and  ^locates,  and 
not  rather  to  that  which  is  contained  and  located,  that  is  the  earth. 
Emend.  I  also  add  that  it  is  not  more  difficult  to  ascribe  motion  to 
the  contained  and  located,  which  is  the  earth,  than  to  that  which 
contains  it." 

" "Copernicus.  You  see,  therefore,  that  from  all  these  things 
the  motion  of  the  earth  is  more  probable  than  its  immobility,  espe- 
cially in  the  daily  revolution  which  is  as  it  were  a  particular  prop- 
erty of  it.  Emend.  Omit  from  'You  see'  to  the  end  of  the  chapter." 

13 "Copernicus.  Therefore,  since  there  is  nothing  to  hinder  the 
motion  of  the  earth,  it  seems  to  me  that  we  should  consider  whether 
it  has  several  motions,  to  the  end  that  it  may  be  looked  upon  as  one 
of  the  moving  stars.  Emend.  Therefore,  since  I  have  assumed  that 
the  earth  moves,  it  seems  to  me  that  we  should  consider  whether  it 
has  several  motions." 


THE  CONGREGATION  OF  THE  INDEX,  ON  COPERNICUS.      95 

We  must  not  say  that  nothing  prohibits  the  motion  of 
the  earth,  only  that  having  assumed  it,  we  may  inquire 
whether  our  explanations  require  several  motions. 

(Cap.  10.  lib.  i.  p.  9.)  "Copernicus.  Non  pudet  nos 
f  ateri ....  hoc  potius  in  mobilitate  terrse  verificari.  Emend. 
Non  pudet  nos  assumere ....  hoc  consequenter  in  mobilitate 
verificari."14 

(Cap.  10.  lib.  i.  p.  10.)  "Copernicus.  Tanta  nimirum  est 
divina  haec.  Opt.  Max.  fabrica.  Emend.  Dele  ilia  verba 
postrema."15 

(Cap.  ii.  lib.  i.16)  "Copernicus.  De  triplici  motu  telluris 
demonstratio.  Emend.  De  hypothesi  triplicis  motus  Terrse, 
ejusque  demonstratione."17 

(Cap.  10.  lib.  iv.  p.  122.18)  "Copernicus.  De  magnitudine 
horum  trium  siderum,  Solis,  Lunse,  et  Terrse.  Emend.  Dele 
verba  horum  trium  siderum,  quia  terra  non  est  sidus,  ut 
facit  earn  Copernicus."19 

We  must  not  say  we  are  not  ashamed  to  acknowledge;  as- 
sume is  the  word.  We  must  not  call  this  assumption  a 
Divine  work.  A  chapter  must  not  be  headed  demonstration, 
but  hypothesis.  The  earth  must  not  be  called  a  star;  the 
word  implies  motion. 

It  will  be  seen  that  it  does  not  take  much  to  reduce 
Copernicus  to  pure  hypothesis.  No  personal  injury  being 
done  to  the  author — who  indeed  had  been  17  years  out  of 

4  "Copernicus.      We    are    not    ashamed   to    acknowledge that 

this  is  preferably  verified  in  the  motion  of  the  earth.     Emend.  We 

are  not  ashamed  to  assume that  this  is  consequently  verified  in 

the  motion." 

5  "Copernicus.     So  divine  is  surely  this  work  of  the  Best  and 
Greatest.    Emend.  Strike  out  these  last  words." 

18  This  should  be  Cap.  u,  lib.  i,  p.  10. 

7  "Copernicus.     Demonstration   of   the   threefold   motion   of   the 
earth.     Emend.   On  the  hypothesis  of  the  threefold  motion  of  the 
earth  and  its  demonstration." 

18  This  should  be  Cap.  20,  lib.  iv,  p.  122. 

8  "Copernicus.    Concerning  the  size  of  these  three  stars,  the  sun, 
the  moon,  and  the  earth.    Emend.  Strike  out  the  words  'these  three 
stars,'  because  the  earth  is  not  a  star  as  Copernicus  would  make  it." 


96  A  BUDGET  OF  PARADOXES. 

reach — the  treatment  of  his  book  is  now  an  excellent  joke. 
It  is  obvious  that  the  Cardinals  of  the  Index  were  a  little 
ashamed  of  their  position,  and  made  a  mere  excuse  of  a 
few  corrections.  Their  mode  of  dealing  with  chap.  8,  this 
problematice  videtur  loqui,  ut  studiosis  satisfiat™  is  an  ex- 
cuse to  avoid  corrections.  But  they  struck  out  the  stinging 
allusion  to  Lactantius21  in  the  preface,  little  thinking,  honest 
men,  for  they  really  believed  what  they  said — that  the  light 
of  Lactantius  would  grow  dark  before  the  brightness  of 
their  own. 

THE  CONVOCATION  AT  OXFORD  EQUALLY  AT  FAULT. 

1622.  I  make  no  reference  to  the  case  of  Galileo,  except 
this.  I  have  pointed  out  (Penny  Cycl.  Suppl.  "Galileo"; 
Engl  Cycl.  "Motion  of  the  Earth")  that  it  is  clear  the  ab- 
surdity was  the  act  of  the  Italian  Inquisition — for  the  private 
and  personal  pleasure  of  the  Pope,  who  knew  that  the  course 
he  took  would  not  commit  him  as  Pope — and  not  of  the 
body  which  calls  itself  the  Church.  Let  the  dirty  proceed- 
ing have  its  right  name.  The  Jesuit  Riccioli,1  the  stoutest 
and  most  learned  Anti-Copernican  in  Europe,  and  the  Puri- 
tan Wilkins,  a  strong  Copernican  and  Pope-hater,  are  equally 
positive  that  the  Roman  Church  never  pronounced  any  de- 
cision :  and  this  in  the  time  immediately  following  the  ridic- 
ulous proceeding  of  the  Inquisition.  In  like  manner  a  deci- 
sion of  the  Convocation  of  Oxford  is  not  a  law  of  the  Eng- 
lish Church;  which  is  fortunate,  for  that  Convocation,  in 
1622,  came  to  a  decision  quite  as  absurd,  and  a  great  deal 

20  He    seems    to    speak   problematically   in    order   to    satisfy    the 
learned. 

21  One  of  the  Church  Fathers,  born  about  250  A.  D.,  and  died  about 
330,  probably  at  Treves.     He  wrote  Divinarum  Institutionum  Libri 
VII,  and  other  controversial  and  didactic  works  against  the  learning 
and  philosophy  of  the  Greeks. 

1  Giovanni  Battista  Riccioli  (1598-1671)  taught  philosophy  and 
theology  at  Parma  and  Bologna,  and  was  later  professor  of  astron- 
omy. His  Almagestum  novum  appeared  in  1651,  and  his  Argomento 
fisico-matematico  contro  il  moto  diurno  della  terra  in  1668. 


THE  CONVOCATION  AT  OXFORD  EQUALLY  AT  FAULT.        97 

more  wicked  than  the  declaration  against  the  motion  of  the 
earth.  The  second  was  a  foolish  mistake;  the  first  was  a 
disgusting  surrender  of  right  feeling.  The  story  is  told 
without  disapprobation  by  Anthony  Wood,  who  never  exag- 
gerated anything  against  the  university  of  which  he  is  wri- 
ting eulogistic  history. 

In  1622,  one  William  Knight2  put  forward  in  a  sermon 
preached  before  the  University  certain  theses  which,  looking 
at  the  state  of  the  times,  may  have  been  improper  and  pos- 
sibly of  seditious  intent.  One  of  them  was  that  the  bishop 
might  excommunicate  the  civil  magistrate:  this  proposition 
the  clerical  body  could  not  approve,  and  designated  it  by  the 
term  erronea*  the  mildest  going.  But  Knight  also  declared 
as  follows: 

"Subditis  mere  privatis,  si  Tyrannus  tanquam  latro  aut 
stuprator  in  ipsos  faciat  impetum,  et  ipsi  nee  potestatem  ordi- 
nariam  implorare,  nee  alia  ratione  effugere  periculum  pos- 
sint,  in  presenti  periculo  se  et  suos  contra  tyrannum,  sicut 
contra  privatum  grassatorem,  defendere  licet."4 

That  is,  a  man  may  defend  his  purse  or  a  woman  her 
honor,  against  the  personal  attack  of  a  king,  as  against  that 
of  a  private  person,  if  no  other  means  of  safety  can  be  found. 
The  Convocation  sent  Knight  to  prison,  declared  the  propo- 
sition "falsa,  periculosa,  et  impia"  and  enacted  that  all  ap- 
plicants for  degrees  should  subscribe  this  censure,  and  make 
oath  that  they  would  neither  hold,  teach,  nor  defend  Knight's 
opinions. 

The  thesis,  in  the  form  given,  was  unnecessary  and  im- 
proper. Though  strong  opinions  of  the  king's  rights  were 
advanced  at  the  time,  yet  no  one  ventured  to  say  that,  min- 

2  He  was  a  native  of  Arlington,  Sussex,  and  a  pensioner  of  Christ's 
College,  Cambridge.  In  1603  he  became  a  master  of  arts  at  Oxford. 

8  Straying,  i.  e.,  from  the  right  way. 

4  "Private  subjects  may,  in  the  presence  of  danger,  defend  them- 
selves or  their  families  against  a  monarch  as  against  any  malefactor, 
if  the  monarch  assaults  them  like  a  bandit  or  a  ravisher,  and  pro- 
vided they  are  unable  to  summon  the  usual  protection  and  cannot  in 
any  way  escape  the  danger." 


98  A  BUDGET  OF  PARADOXES. 

isters  and  advisers  apart,  the  king  might  personally  break 
the  law ;  and  we  know  that  the  first  and  only  attempt  which 
his  successor  made  brought  on  the  crisis  which  cost  him 
his  throne  and  his  head.  But  the  declaration  that  the  propo- 
sition was  false  far  exceeds  in  all  that  is  disreputable  the 
decision  of  the  Inquisition  against  the  earth's  motion.  We 
do  not  mention  this  little  matter  in  England.  Knight  was 
a  Puritan,  and  Neal5  gives  a  short  account  of  his  sermon. 
From  comparison  with  Wood,6  I  judge  that  the  theses,  as 
given,  were  not  Knight's  words,  but  the  digest  which  it  was 
customary  to  make  in  criminal  proceedings  against  opinion. 
This  heightens  the  joke,  for  it  appears  that  the  qualifiers 
of  the  Convocation  took  pains  to  present  their  condemnation 
of  Knight  in  the  terms  which  would  most  unequivocally 
make  their  censure  condemn  themselves.  This  proceeding 
took  place  in  the  interval  between  the  two  proceedings 
against  Galileo:  it  is  left  undetermined  whether  we  must 
say  pot-kettle-pot  or  kettle-pot-kettle. 

Liberti   Fromondi. . .  .Ant-Aristarchus,   sive   orbis   terrae   immo- 
bilis.     Antwerp,  1631,  8vo.T 

This  book  contains  the  evidence  of  an  ardent  opponent 
of  Galileo  to  the  fact,  that  Roman  Catholics  of  the  day  did 
not  consider  the  decree  of  the  Index  or  of  the  Inquisition 
as  a  declaration  of  their  Church.  Fromond  would  have  been 
glad  to  say  as  much,  and  tries  to  come  near  it,  but  con- 
fesses he  must  abstain.  See  Penny  Cyclop.  Suppl.  "Galileo," 
and  Eng.  Cycl  "Motion  of  the  Earth."  The  author  of  a 
celebrated  article  in  the  Dublin  Review,  in  defence  of  the 

"Daniel  Neal  (1678-1743),  an  independent  minister,  wrote  a  His- 
tory of  the  Puritans  that  appeared  in  1732.  The  account  may  be 
found  in  the  New  York  edition  of  1843-44,  vol.  I,  p.  271. 

6  Anthony   Wood    (1632-1695),    whose   Historia    et   Antiquitates 
Universitatis  Oxoniensis  (1674)  and  Athenae  Oxoniensis  (1691)  are 
among  the  classics  on  Oxford. 

7  Part  of  the  title,  not  here  quoted,  shows  the  nature  of  the  work 
more  clearly:  "liber  unicus,  in  quo  decretum  S.  Congregations  S. 
R.  E.  Cardinal,  an.  1616,  adversus  Pythagorico-Copernicanos  editum, 
defenditur." 


THE    METIUS   APPROXIMATION.  99 

Church  of  Rome,  seeing  that  Drinkwater  Bethune8  makes 
use  of  the  authority  of  Fromondus,  but  for  another  purpose, 
sneers  at  him  for  bringing  up  a  "musty  old  Professor." 
If  he  had  known  Fromondus,  and  used  him  he  would  have 
helped  his  own  case,  which  is  very  meagre  for  want  of 
knowledge.9 

Advis  a  Monseigneur  reminentissime  Cardinal  Due  de  Richelieu, 
sur  la  Proposition  faicte  par  le  Sieur  Morin  pour  1'invention 
des  longitudes.  Paris,  1634,  8vo.10 

This  is  the  Official  Report  of  the  Commissioners  ap- 
pointed by  the  Cardinal,  of  whom  Pascal  is  the  one  now 
best  known,  to  consider  Morin's  plan.  See  the  full  account 
in  Delambre,  Hist.  Astr.  Mod.  ii.  236,  etc. 

THE  METIUS  APPROXIMATION. 

Arithmetica  et  Geometria  practica.  By  Adrian  Metius.  Leyden, 
1640,  4to.1 

This  book  contains  the  celebrated  approximation  guessed 
at  by  his  father,  Peter  Metius,2  namely  that  the  diameter  is 

8  This  was  John  Elliot  Drinkwater  Bethune  (1801-1851),  the 
statesman  who  did  so  much  for  legislative  and  educational  reform 
in  India.  His  father,  John  Drinkwater  Bethune,  wrote  a  history  of 
the  siege  of  Gibraltar. 

9 The  article  referred  to  is  about  thirty  years  old;  since  it  ap- 
peared another  has  been  given  (Dubl.  Rev.,  Sept.  1865)  which  is  of 
much  greater  depth.  In  it  will  also  be  found  the  Roman  view  of 
Bishop  Virgil  (ante,  p.  32). — A.  De  M. 

10  Jean  Baptiste  Morin  (1583-1656),  in  his  younger  days  physician 
to  the  Bishop  of  Boulogne  and  the  Duke  of  Luxemburg,  became  in 
1630  professor  of  mathematics  at  the  College  Royale.  His  ^  chief 
contribution  to  the  problem  of  the  determination  of  longitude  is  his 
Longitudinum  terrestrium  et  coelestium  nova  et  hactenus  optata 
scientia  (1634).  He  also  wrote  against  Copernicus  in  his  Famosi 
problematis  de  telluris  motu  vel  quiete  hactenus  optata  solutio  (1631), 
and  against  Lansberg  in  his  Responsio  pro  telluris  quiete  (1634). 

1  The  work  appeared  at  Leyden  in  1626,  at  Amsterdam  in  1634,  at 
Copenhagen  in  1640,  and  again  at  Leyden  in  1650.    The  title  of  the 
1640  edition  is  Arithmeticae  Libri  II  et  Geometriae  Libri  VI.     The 
work  on  which  it  is  based  is  the  Arithmeticae  et  Geometriae  Prac- 
tica, which  appeared  in  1611. 

2  The  father's  name  was  Adriaan,  and  Lalande  says  that  it  was 
Montucla  who  first  made  the  mistake  of  calling  him  Peter,  thinking 


100  A  BUDGET  OF   PARADOXES. 

to  the  circumference  as  113  to  355.  The  error  it  at  the  rate 
'of  about  a  foot  in  2,000  miles.  Peter  Metius,  having  his 
attention  called  to  the  subject  by  the  false  quadrature  of 
Duchesne,  found  that  the  ratio  lay  between  33%oe  and  37%2o- 
He  then  took  the  liberty  of  taking  the  mean  of  both  numera- 
tors and  denominators,  giving  35%is.  He  had  no  right  to  pre- 
sume that  this  mean  was  better  than  either  of  the  extremes ; 
nor  does  it  appear  positively  that  he  did  so.  He  published 
nothing;  but  his  son  Adrian,3  when  Van  Ceulen's  work 
showed  how  near  his  father's  result  came  to  the  truth,  first 
made  it, known  in  the  work  above.  (See  Eng.  Cyclop.,  art. 
"Quadrature.") 

ON  INHABITABLE  PLANETS. 

A  discourse  concerning  a  new  world  and  another  planet,  in  two 

books.     London,  1640,  Svo.1 
Cosmotheoros :  or  conjectures  concerning  the  planetary  worlds 

and  their  inhabitants.    Written  in  Latin,  by  Christianus  Huy- 

ghens.    This  translation  was  first  published  in  1698.    Glasgow 

1757,  8vo.     [The  original  is  also  of  1698.] 2 

The  first  work  is  by  Bishop  Wilkins,  being  the  third 
edition,  [first  in  1638]  of  the  first  book,  "That  the  Moon 
may  be  a  Planet" ;  and  the  first  edition  of  the  second  work, 

that  the  initials  P.  M.  stood  for  Petrus  Metius,  when  in  reality  they 
stood  for  piae  memoriae !  The  ratio  ""/us  was  known  in  China  hun- 
dreds of  years  before  his  time.  See  note  3,  page  52. 

'Adrian  Metius  (1571-1635)  was  professor  of  medicine  at  the 
University  of  Franeker.  His  work  was,  however,  in  the  domain  of 
astronomy,  and  in  this  domain  he  published  several  treatises. 

1  The  first  edition  was  entitled :  The  Discovery  of  a  World  in  the 
Moone.  Or,  a  Discourse  Tending  to  prove  that  'tis  probable  there 
may  be  another  habitable  World  in  that  Planet.  1638,  Svo.  The 
fourth  edition  appeared  in  1684.  John  Wilkins  (1614-1672)  was 
Warden  of  Wadham  College,  Oxford ;  master  of  Trinity,  Cambridge ; 
and,  later,  Bishop  of  Chester.  He  was  influential  in  founding  the 
Royal  Society. 

2 The  first  edition  was  entitled:  C.  Hugenii  Koo-^o^ewpos,  give  de 
Terris  coelestibus,  earumque  ornatu,  conjecturae,  The  Hague,  1698, 
4to.  There  were  several  editions.  It  was  also  translated  into  French 
(1718),  and  there  was  another  English  edition  (1722).  Huyghens 
(1629-1695)  was  one  of  the  best  mathematical  physicists  of  his  time. 


ON    INHABITABLE    PLANETS.  O 

"That  the  Earth  may  be  a  Planet."  [See  more  under  the 
reprint  of  1802.]  Whether  other  planets  be  inhabited  or 
not,  that  is,  crowded  with  organisations  some  of  them  having 
consciousness,  is  not  for  me  to  decide;  but  I  should  be 
much  surprised  if,  on  going  to  one  of  them,  I  should  find 
it  otherwise.  The  whole  dispute  tacitly  assumes  that,  if 
the  stars  and  planets  be  inhabited,  it  must  be  by  things  of 
which  we  can  form  some  idea.  But  for  aught  we  know, 
what  number  of  such  bodies  there  are,  so  many  organisms 
may  there  be,  of  which  we  have  no  way  of  thinking  nor 
of  speaking.  This  is  seldom  remembered.  In  like  manner 
it  is  usually  forgotten  that  the  matter  of  other  planets  may 
be  of  different  chemistry  from  ours.  There  may  be  no 
oxygen  and  hydrogen  in  Jupiter,  which  may  have  gens  of 
its  own.3  But  this  must  not  be  said:  it  would  limit  the 
omniscience  of  the  a  priori  school  of  physical  inquirers,  the 
larger  half  of  the  whole,  and  would  be  very  unphilosophical. 
Nine-tenths  of  my  best  paradoxers  come  out  from  among 
this  larger  half,  because  they  are  just  a  little  more  than  of 
it  at  their  entrance. 

There  was  a  discussion  on  the  subject  some  years  ago, 
which  began  with 

The  plurality  of  worlds :  an  Essay.  London,  1853,  8vo.  [By  Dr. 
Wm.  Whewell,  Master  of  Trinity  College,  Cambridge].  A 
dialogue  on  the  plurality  of  worlds,  being  a  supplement  to  the 
Essay  on  that  subject.  [First  found  in  the  second  edition, 
1854;  removed  to  the  end  in  subsequent  editions,  and  separate 
copies  issued.]4 

A  work  of  skeptical  character,  insisting  on  analogies 
which  prohibit  the  positive  conclusion  that  the  planets,  stars, 
etc.,  are  what  we  should  call  inhabited  worlds.  It  produced 

8  It  is  hardly  necessary  to  say  that  science  has  made  enormous 
advance  in  the  chemistry  of  the  universe  since  these  words  were 
written. 

4  William  Whewell  (1794-1866)  is  best  known  through  his  History 
of  the  Inductive  Sciences  (1837)  and  Philosophy  of  the  Inductive 
Sciences  (1840). 


102  A  BUDGET  OF  PARADOXES. 

several  works  and  a  large  amount  of  controversy  in  reviews. 
The  last  predecessor  of  whom  I  know  was 

Plurality  of  Worlds By  Alexander  Maxwell.   Second  Edition. 

London,  1820,  8vo. 

This  work  is  directed  against  the  plurality  by  an  author 
who  does  not  admit  modern  astronomy.  It  was  occasioned 
by  Dr.  Chalmers's5  celebrated  discourses  on  religion  in  con- 
nection with  astronomy.  The  notes  contain  many  citations 
on  the  gravity  controversy,  from  authors  now  very  little 
read:  and  this  is  its  present  value.  I  find  no  mention  of 
Maxwell,  not  even  in  Watt.6  He  communicated  with  man- 
kind without  the  medium  of  a  publisher;  and,  from  Vieta 
till  now,  this  method  has  always  been  favorable  to  loss  of 
books. 

A  correspondent  informs  me  that  Alex.  Maxwell,  who 
wrote  on  the  plurality  of  worlds,  in  1820,  was  a  law-book- 
seller and  publisher  (probably  his  own  publisher)  in  Bell 
Yard.  He  had  peculiar  notions,  which  he  was  fond  of  dis- 
cussing with  his  customers.  He  was  a  bit  of  a  Sweden- 
borgian. 

INHABITED  PLANETS  IN  FICTION. 
There  is  a  class  of  hypothetical  creations  which  do  not 
belong  to  my  subject,  because  they  are  acknowledged  to  be 
fictions,  as  those  of  Lucian,1  Rabelais,2  Swift,  Francis  God- 

5  Thomas  Chalmers  (1780-1847),  the  celebrated  Scotch  preacher. 
These  discourses  were  delivered  while  he  was  minister  in  a  large 
parish  in  the  poorest  part  of  Glasgow,  and  in  them  he  attempted  to 
bring  science  into  harmony  with  the  Bible.  He  was  afterwards 
professor  of  moral  philosophy  at  St.  Andrew's  (1823-28),  and  pro- 
fessor of  theology  at  Edinburgh  (1828).  He  became  the  leader  of 
a  schism  from  the  Scotch  Presbyterian  Church, — the  Free  Church. 

"That  is,  in  Robert  Watt's  (1774-1819)  Bibliotheca  Britannica 
(posthumous,  1824).  Nor  is  it  given  in  the  Dictionary  of  National 
Biography. 

1  The  late  Greek  satirist  and  poet,  c.  I2O-C.  200  A.  D. 

*  Francois  Rabelais  (c.  1490-1553)  the  humorist  who  created  Pan- 
tagruel  (1533)  and  Gargantua  (1532).  His  work  as  a  physician  and 
as  editor  of  the  works  of  Galen  and  Hippocrates  is  less  popularly 
known. 


INHABITED  PLANETS  IN  FICTION.  103 

win,3  Voltaire,  etc.  All  who  have  more  positive  notions  as  to 
either  the  composition  or  organization  of  other  worlds,  than 
the  reasonable  conclusion  that  our  Architect  must  be  quite 
able  to  construct  millions  of  other  buildings  on  millions  of 
other  plans,  ought  to  rank  with  the  writers  just  mentioned, 
in  all  but  self-knowledge.  Of  every  one  of  their  systems 
I  say,  as  the  Irish  Bishop  said  of  Gulliver's  book, — I  don't 
believe  half  of  it.  Huyghens  had  been  preceded  by  Fon- 
tenelle,4  who  attracted  more  attention.  Huyghens  is  very 
fanciful  and  very  positive ;  but  he  gives  a  true  account  of  his 
method.  "But  since  there's  no  hopes  of  a  Mercury  to  carry 
us  such  a  journey,  we  shall  e'en  be  contented  with  what's 
in  our  power:  we  shall  suppose  ourselves  there. ..."  And 
yet  he  says,  "We  have  proved  that  they  live  in  societies, 
have  hands  and  feet.  ..."  Kircher5  had  gone  to  the  stars 
before  him,  but  would  not  find  any  life  in  them,  either  animal 
or  vegetable. 

The  question  of  the  inhabitants  of  a  particular  planet 
is  one  which  has  truth  on  one  side  or  the  other :  either  there 
are  some  inhabitants,  or  there  are  none.  Fortunately,  it  is 
of  no  consequence  which  is  true.  But  there  are  many 
cases  where  the  balance  is  equally  one  of  truth  and  false- 
hood, in  which  the  choice  is  a  matter  of  importance.  My 
work  selects,  for  the  most  part,  sins  against  demonstration: 
but  the  world  is  full  of  questions  of  fact  or  opinion,  in  which 
a  struggling  minority  will  become  a  majority,  or  else  will 

8  Francis  Godwin  (1562-1633)  bishop  of  Llandaff  and  Hereford. 
Besides  some  valuable  historical  works  he  wrote  The  Man  in  the 
Moone,  or  a  Discourse  of  a  voyage  thither  by  Domingo  Consoles, 
the  Speed  Messenger  of  London,  1638. 

*  Bernard  Le  Bovier  de  Fontenelle  (1657-1757),  historian,  critic, 
mathematician,  Secretary  of  the  Academic  des  Sciences,  and  member 
of  the  Academic  Franchise.  His  Entretien  sur  la  pluralite  des 
mondes  appeared  at  Paris  in  1686. 

"Athanasius  Kircher  (1602-1680),  Jesuit,  professor  of  mathe- 
matics and  philosophy,  and  later  of  Hebrew  and  Syriac,  at  Wurz- 
burg;  still  later  professor  of  mathematics  and  Hebrew  at  Rome. 
He  wrote  several  works  on  physics.  His  collection  of  mathematical 
instruments  and  other  antiquities  became  the  basis  of  the  Kircherian 
Museum  at  Rome. 


104  A  BUDGET  OF   PARADOXES. 

be  gradually  annihilated:  and  each  of  the  cases  subdivides 
into  results  of  good,  and  results  of  evil.  What  is  to  be 
done? 

"Periculosum  est  credere  et  non  credere; 
Hippolitus  obiit  quia  novercae  creditum  est; 
Cassandrse  quia  non  creditum  ruit  Ilium: 
Ergo  exploranda  est  veritas  multum  prius 
Quam  stulta  prove  judicet  sententia."6 

Nova  Demonstratio  immobilitatis  terrse  petita  ex  virtute  mag- 
netica.  By  Jacobus  Grandamicus.  Flexiae  (La  Fleche),  1645, 
4to.7 

No  magnetic  body  can  move  about  its  poles:  the  earth 
is  a  magnetic  body,  therefore,  etc.  The  iron  and  its  mag- 
netism are  typical  of  two  natures  in  one  person;  so  it  is 
said,  "Si  exaltatus  fuero  a  terra,  omnia  traham  ad  me  ip- 
sum."8 

A  VENETIAN  BUDGET  OF  PARADOXES. 

Le  glorie  degli  incogniti,  o  vero  gli  huomini  illustri  dell'  acca- 
demia  de'  signori  incogniti  di  Venetia.  Venice,  1647,  4to. 

This  work  is  somewhat  like  a  part  of  my  own:  it  is  a 
budget  of  Venetian  nobodies  who  wished  to  be  somebodies ; 
but  paradox  is  not  the  only  means  employed.  It  is  of  a 
serio-comic  character,  gives  genuine  portraits  in  copper- 
plate, and  grave  lists  of  works ;  but  satirical  accounts.  The 
astrologer  Andrew  Argoli1  is  there,  and  his  son;  both  of 
whom,  with  some  of  the  others,  have  place  in  modern  works 

'"Both  belief  and  non-belief  are  dangerous.  Hippolitus  died 
because  his  stepmother  was  believed.  Troy  fell  because  Cassandra 
was  not  believed.  Therefore  the  truth  should  be  investigated  long 
before  foolish  opinion  can  properly  judge."  (Proves  probe?). 

7  Jacobus  Grandamicus  (Jacques  Grandami)  was  born  at  Nantes 
in  1588  and  died  at  Paris  in  1672.     He  was  professor  of  theology 
and  philosophy  in  the  Jesuit  colleges  at  Rennes,  Tours,  Rouen,  and 
other  places.     He  wrote  several  works  on  astronomy. 

8  "And  I,  if  I  be  lifted  up  from  the  earth,  will  draw  all  men  unto 
me."    John  xii.  32. 

1  Andrea  Argoli  (1568-1657)  wrote  a  number  of  works  on  astron- 
omy, and  computed  ephemerides  from  1621  to  1700. 


A  VENETIAN   BUDGET  OF  PARADOXES.  105 

on  biography.  Argoli's  discovery  that  logarithms  facilitate 
easy  processes,  but  increase  the  labor  of  difficult  ones,  is 
worth  recording. 

Controversise  de  vera  circuli  mensura inter C.  S.  Longo- 

montanum  et  Jo.  Pellium.2    Amsterdam,  1647,  4to. 

Longomontanus,3  a  Danish  astronomer  of  merit,  squared 
the  circle  in  1644:  he  found  out  that  the  diameter  43  gives 
the  square  root  of  18252  for  the  circumference ;  which  gives 
3.14185...  for  the  ratio.  Pell  answered  him,  and  being 
a  kind  of  circulating  medium,  managed  to  engage  in  the 
controversy  names  known  and  unknown,  as  Roberval, 
Hobbes,  Carcavi,  Lord  Charles  Cavendish,  Pallieur,  Mer- 
senne,  Tassius,  Baron  Wolzogen,  Descartes,  Cavalieri  and 
Golius.4  Among  them,  of  course,  Longomontanus  was  made 

8  So  in  the  original  edition  of  the  Budget.  It  is  Johannem 
Pellum  in  the  original  title.  John  Pell  (1610  or  1611-1685)  studied 
at  Cambridge  and  Oxford,  and  was  professor  of  mathematics  at 
Amsterdam  (1643-46)  and  Breda  (1646-52).  He  left  many  manu- 
scripts but  published  little.  His  name  attaches  by  accident  to  an 
interesting  equation  recently  studied  with  care  by  Dit  E.  E.  Whit- 
ford  (New  York,  1912). 

8Christianus  Longomontanus  (Christen  Longberg  or  Lumborg) 
was  born  in  1569  at  Longberg,  Jutland,  and  died  in  1647  at  Copen- 
hagen. He  was  an  assistant  of  Tycho  Brahe  and  accepted  the 
diurnal  while  denying  the  orbital  motion  of  the  earth.  His  Cyclo- 
metria  e  lunulis  reciproce  demonstrate,  appeared  in  1612  under  the 
name  of  Christen  Severin,  the  latter  being  his  family  name.  He 
wrote  several  other  works  ,pn  the  quadrature  problem,  and  some 
treatises  on  astronomy. 

*The  names  are  really  pretty  well  known.  Giles  Persone  de 
Roberval  was  born  at  Roberval  near  Beauvais  in  1602,  and  died  at 
Paris  in  1675.  He  was  professor  of  philosophy  at  the  College  Ger- 
vais  at  Paris,  and  later  at  the  College  Royal.  He  claimed  to  have 
discovered  the  theory  of  indivisibles  before  Cavalieri,  and  his  work 
is  set  forth  in  his  Traite  des  indivisibles  which  appeared  post- 
humously in  1693. 

Hobbes  (1588-1679),  the  political  and  social  philosopher,  lived 
a  good  part  of  his  time  (1610-41)  in  France  where  he  was  tutor  to 
several  young  noblemen,  including  the  Cavendishes.  His  Leviathan 
(1651)  is  said  to  have  influenced  Spinoza,  Leibnitz,  and  Rousseau. 
His  Quadratura  circuli,  cubatio  sphaerae,  duplicatio  cubi. . .  (London, 
1669),  Rosetum  geometricum. ..  (London,  1671),  and  Lux  Mathe- 
j  censura  doctrinae  Wallisianae  contra  Rosetum  Hobbesii  (Lon- 


106  A  BUDGET  OF   PARADOXES. 

mincemeat :  but  he  is  said  to  have  insisted  on  the  discovery 
in  his  epitaph.5 

don,  1674)  are  entirely  forgotten  to-day.  (See  a  further  note,  in- 
fra.) 

Pierre  de  Carcavi,  a  native  of  Lyons,  died  at  Paris  in  1684.  He 
was  a  member  of  parliament,  royal  librarian,  and  member  of  the 
Academic  des  Sciences.  His  attempt  to  prove  the  impossibility  of 
the  quadrature  appeared  in  1645.  He  was  a  frequent  correspondent 
of  Descartes. 

Cavendish  (1591-1654)  was  Sir  (not  Lord)  Charles.  He  was, 
like  De  Morgan  himself,  a  bibliophile  in  the  domain  of  mathematics. 
His  life  was  one  of  struggle,  his  term  as  member  of  parliament  under 
Charles  I  being  followed  by  gallant  service  in  the  royal  army.  After 
the  war  he  sought  refuge  on  the  continent  where  he  met  most  of  the 
mathematicians  of  his  day.  He  left  a  number  of  manuscripts  on 
mathematics,  which  his  widow  promptly  disposed  of  for  waste  paper. 
If  De  Morgan's  manuscripts  had  been  so  treated  we  should  not  have 
had  his  revision  of  his  Budget  of  Paradoxes. 

Marin  Mersenne  (1588-1648),  a  minorite,  living  in  the  cloisters 
at  Nevers  and  Paris,  was  one  of  the  greatest  Franciscan  scholars. 
He  edited  Euclid,  Apollonius,  Archimedes,  Theodosius,  and  Mene- 
laus  (Paris.  1626),  translated  the  Mechanics  of  Galileo  into  French 
(1634),  wrote  Harmonicorum  Libri  XII  (1636),  and  Cogitata  phy- 
sico-mathematica  (1644),  and  taught  theology  and  philosophy  at 
Nevers. 

Johann  Adolph  Tasse  (Tassius)  was  born  in  1585  and  died  at 
Hamburg  in  1654.  He  was  professor  of  mathematics  in  the  Gym- 
nasium at  Hamburg,  and  wrote  numerous  works  on  astronomy, 
chronology,  statics,  and  elementary  mathematics. 

Johann  Ludwig,  Baron  von  Wolzogen,  seems  to  have  been  one 
of  the  early  Unitarians,  called  Fratres  Polonorum  because  they  took 
refuge  in  Poland.  Some  of  his  works  appear  in  the  Bibliotheca 
Fratrum  Polonorum  (Amsterdam,  1656).  I  find  no  one  by  the  name 
who  was  contributing  to  mathematics  at  this  time. 

Descartes  is  too  well  known  to  need  mention  in  this  connection. 

Bonaventura  Cavalieri  (1598-1647)  was  a  Jesuit,  a  pupil  of  Gali- 
leo, and  professor  of  mathematics  at  Bologna.  His  greatest  work, 
Geometric,  indivisibilibus  continuorum  nova  quadam  ratione  pro- 
mota,  in  which  he  makes  a  noteworthy  step  towards  the  calculus, 
appeared  in  1635. 

Jacob  (Jacques)  Golius  was  born  at  the  Hague  in  1596  and  died 
at  Leyden  in  1667.  His  travels  in  Morocco  and  Asia  Minor  (1622- 
1629)  gave  him  such  knowledge  of  Arabic  that  he  became  professor 
of  that  language  at  Leyden.  After  Snell's  death  he  became  pro- 
fessor of  mathematics  there.  He  translated  Arabic  works  on  mathe- 
matics and  astronomy  into  Latin. 

*  It  would  be  interesting  to  follow  up  these  rumors,  beginning 
perhaps  with  the  tomb  of  Archimedes.  The  Ludolph  van  Ceulen 
story  is  very  likely  a  myth.  The  one  about  Fagnano  may  be  such. 
The  Bernoulli  tomb  does  have  the  spiral,  however  (such  as  it  is), 
as  any  one  may  see  in  the  cloisters  at  Basel  to-day. 


THE  CIRCULATING  MEDIA  OF  MATHEMATICS.  107 

THE  CIRCULATING  MEDIA  OF  MATHEMATICS. 
The  great  circulating  mediums,  who  wrote  to  everybody, 
heard  from  everybody,  and  sent  extracts  to  everybody  else, 
have  been  Father  Mersenne,  John  Collins,  and  the  late 
Professor  Schumacher:  all  "late"  no  doubt,  but  only  the 
last  recent  enough  to  be  so  styled.  If  M.C.S.  should  ever 
again  stand  for  "Member  of  the  Corresponding  Society," 
it  should  raise  an  acrostic  thought  of  the  three.  There  is 
an  allusion  to  Mersenne's  occupation  in  Hobbes's  reply  to 
him.  He  wanted  to  give  Hobbes,  who  was  very  ill  at  Paris, 
the  Roman  Eucharist:  but  Hobbes  said,  "I  have  settled  all 
that  long  ago;  when  did  you  hear  from  Gassendi?"  We 
are  reminded  of  William's  answer  to  Burnet.  John  Collins 
disseminated  Newton,  among  others.  Schumacher  ought 
to  have  been  called  the  postmaster-general  of  astronomy, 
as  Collins  was  called  the  attorney-general  of  mathematics.1 

'Collins  (1625-1683)  was  secretary  of  the  Royal  Society,  and 
was  "a  kind  of  register  of  all  new  improvements  in  mathematics." 
His  office  brought  him  into  correspondence  with  all  of  the  English 
scientists,  and  he  was  influential  in  the  publication  of  various  im- 
portant works,  including  Branker's  translation  of  the  algebra  by 
Rhonius,  with  notes  by  Pell,  which  was  the  first  work  to  contain  the 
present  English-American  symbol  of  division.  He  also  helped  in 
the  publication  of  editions  of  Archimedes  and  Apollonius,  of  Ker- 
sey's Algebra,  and  of  the  works  of  Wallis.  His  profession  was  that 
of  accountant  and  civil  engineer,  and  he  wrote  three  unimportant 
works  on  mathematics  (one  published  posthumously,  and  the  others 
in  1652  and  1658). 

Heinrich  Christian  Schumacher  (1780-1850)  was  professor  of 
astronomy  at  Copenhagen  and  director  of  the  observatory  at  Al- 
tona.  His  translation  of  Carnot's  Geometric  de  position  (1807) 
brought  him  into  personal  relations  with  Gauss,  and  the  friendship 
was  helpful  to  Schumacher.  He  was  a  member  of  many  learned 
societies  and  had  a  large  circle  of  acquaintances.  He  published 
numerous  monographs  and  works  on  astronomy. 

Gassendi  (1592-1655)  might  well  have  been  included  by  De 
Morgan  in  the  group,  since  he  knew  and  was  a  friend  of  most  of 
the  important  mathematicians  of  his  day.  Like  Mersenne,  he  was  a 
minorite,  but  he  was  a  friend  of  Galileo  and  Kepler,  and  wrote  a 
work  under  the  title  Institutio  astronomica,  juxta  hypotheses  Coper- 
nici,  Tychonis-Brahaei  et  Ptolemaei  (1645).  He  taught  philosophy 
at  Aix,  and  was  later  professor  of  mathematics  at  the  College 
Royal  at  Paris. 

Burnet  is  the  Bishop  Gilbert  Burnet  (1643-1715)  who  was  so 
strongly  anti-Romanistic  that  he  left  England  during  the  reign  of 


108  A  BUDGET  OF  PARADOXES. 

THE  SYMPATHETIC  POWDER. 

A  late   discourse by   Sir   Kenelme   Digby Rendered  into 

English  by  R.  White.    London,  1658,  I2mo. 

On  this  work  see  Notes  and  Queries,  2d  series,  vii.  231, 
299,  445,  viii.  190.  It  contains  the  celebrated  sympathetic 
powder.  I  am  still  in  much  doubt  as  to  the  connection  of 
Digby  with  this  tract.1  Without  entering  on  the  subject 
here,  I  observe  that  in  Birch's  History  of  the  Royal  Society,2 
to  which  both  Digby  and  White  belonged,  Digby,  though 
he  brought  many  things  before  the  Society,  never  mentioned 
the  powder,  which  is  connected  only  with  the  names  of 
Evelyn3  and  Sir  Gilbert  Talbot.4  The  sympathetic  powder 
was  that  which  cured  by  anointing  the  weapon  with  its 
salve  instead  of  the  wound.  I  have  long  been  convinced 
that  it  was  efficacious.  The  directions  were  to  keep  the 

James  II  and  joined  the  ranks  of  the  Prince  of  Orange.     William 
made  him  bishop  of  Salisbury. 

1  There  is  some  substantial  basis  for  De  Morgan's  doubts  as  to 
the  connection  of  that  mirandula  of  his  age,  Sir  Kenelm  Digby 
(1603-1665),  with  the  famous  poudre  de  sympathie.  It  is  true  that 
he  was  just  the  one  to  prepare  such  a  powder.  A  dilletante  in 
everything, — learning,  war,  diplomacy,  religion,  letters,  and  science, 
— he  was  the  one  to  exploit  a  fraud  of  this  nature.  He  was  an 
astrologer,  an  alchemist,  and  a  fabricator  of  tales,  and  well  did 
Henry  Stubbes  characterize  him  as  "the  very  Pliny  of  our  age  for 
lying."  He  first  speaks  of  the  powder  in  a  lecture  given  at  Mont- 
pellier  in  1658,  and  in  the  same  year  he  published  the  address  at 
Paris  under  the  title:  Discours  fait  en  une  celebre  assemblee  par  le 
chevalier  Digby ...  .touchant  la  guerison  de  playes  par  la  poudre  de 
sympathie.  The  London  edition  referred  to  by  De  Morgan  also 
came  out  in  1658,  and  several  editions  followed^  it  in  England,  France, 
and  Germany.  But  Nathaniel  Highmore  in  his  History  of  Genera- 
tion (1651)  referred  to  the  concoction  as  "Talbot's  Powder"  some 
years  before  Digby  took  it  up.  The  basis  seems  to  have  been  vitriol, 
and  it  was  claimed  that  it  would  heal  a  wound  by  simply  being 
applied  to  a  bandage  taken  from  it. 

'This  work  by  Thomas  Birch  (1705-1766)  came  out  in  1756-57. 
Birch  was  a  voluminous  writer  on  English  history.  He  was  a  friend 
of  Dr.  Johnson  and  of  Walpole,  and  he  wrote  a  life  of  Robert  Boyle. 

8  We  know  so  much  about  John  Evelyn  (1620-1706)  through  the 
diary  which  he  began  at  the  age  of  eleven,  that  we  forget  his  works 
on  navigation  and  architecture. 

4 1  suppose  this  was  the  seventh  Earl  of  Shrewsbury  (1553-1616). 


HOBBES  AS  A   MATHEMATICIAN.  109 

wound  clean  and  cool,  and  to  take  care  of  diet,  rubbing  the 
salve  on  the  knife  or  sword.5  If  we  remember  the  dreadful 
notions  upon  drugs  which  prevailed,  both  as  to  quantity 
and  quality,  we  shall  readily  see  that  any  way  of  not  dressing 
the  wound  would  have  been  useful.  If  the  physicians  had 
taken  the  hint,  had  been  careful  of  diet  etc.,  and  had  poured 
the  little  barrels  of  medicine  down  the  throat  of  a  practicable 
doll,  they  would  have  had  their  magical  cures  as  well  as  the 
surgeons.8  Matters  are  much  improved  now;  the  quantity 
of  medicine  given,  even  by  orthodox  physicians,  would  have 
been  called  infinitesimal  by  their  professional  ancestors.  Ac- 
cordingly, the  College  of  Physicians  has  a  right  to  abandon 
its  motto,  which  is  Ars  longa,  vita  brevis,  meaning  Practice 
is  long,  so  life  is  short. 

HOBBES  AS  A  MATHEMATICIAN. 

Examinatio  et  emendatio  Mathematicae  Hodiernse.    By  Thomas 
Hobbes.     London,  1666,  4to. 

In  six  dialogues:  the  sixth  contains  a  quadrature  of  the 
circle.1  But  there  is  another  edition  of  this  work,  without 
place  or  date  on  the  title-page,  in  which  the  quadrature  is 
omitted.  This  seems  to  be  connected  with  the  publication 

5  This  is  interesting  in  view  of  the  modern  aseptic  practice  of 
surgery   and   the   antiseptic    treatment    of   wounds   inaugurated   by 
the  late  Lord  Lister. 

6  Perhaps  De  Morgan  had  not  heard  the  ban  mot  of  Dr.  Holmes : 
"I  firmly  believe  that  if  the  whole  materia  medica  could  be  sunk  to 
the  bottom  of  the  sea,  it  would  be  all  the  better  for  mankind  and 
all  the  worse  for  the  fishes." 

1  The  full  title  is  worth  giving,  because  it  shows  the  mathematical 
interests  of  Hobbes,  and  the  nature  of  the  six  dialogues :  Examina- 
tio et  emendatio^  mathematicae  hodiernae  qualis  explicatur  in  libris 
Johannis  Wallisii  geometriae  professoris  Saviliani  in  Academia  Oxo- 
niensi:  distributa  in  sex  dialogos  (i.  De  mathematicae  origine...; 
2.  De  principiis  traditis  ab  Euclide;  3.  De  demonstratione  operationum 
arithmeticarum. . . ;  4.  De  rationibus;  $.De  angula  contactus,  de  sec- 
tionibus  coni,  et  arithmetica  infinitorum;  6.  Dimensio  circuli  tribus 
methodis  demonstrata. .  .item  cycloidis  verae  descriptio  et  proprie- 
tates  aliquot.')  Londini,  1660  (not  1666).  For  a  full  discussion  of 
the  controversy  over  the  circle,  see  George  Croom  Robertson's  biog- 
raphy of  Hobbes  in  the  eleventh  edition  of  the  Encyclopaedia  Britan- 
nica. 


110  A  BUDGET  OF   PARADOXES. 

of  another  quadrature,  without  date,  but  about  1670,  as 
may  be  judged  from  its  professing  to  answer  a  tract  of 
Wallis,  printed  in  1669.2  The  title  is  "Quadrature  circuli 
cubatio  sphserse,  duplicatio  cubi,"  4to.8  Hobbes,  who  began 
in  1655,  was  very  wrong  in  his  quadrature;  but,  though 
not  a  Gregory  St.  Vincent,4  he  was  not  the  ignoramus  in 
geometry  that  he  is  sometimes  supposed.  His  writings, 
erroneous  as  they  are  in  many  things,  contain  acute  remarks 
on  points  of  principle.  He  is  wronged  by  being  coupled 
with  Joseph  Scaliger,  as  the  two  great  instances  of  men  of 
letters  who  have  come  into  geometry  to  help  the  mathemati- 
cians out  of  their  difficulty.  I  have  never  seen  Scaliger's  quad- 
rature,5 except  in  the  answers  of  Adrianus  Romanus,6  Vieta 
and  Clavius,  and  in  the  extracts  of  Kastner.7  Scaliger  had 
no  right  to  such  strong  opponents:  Erasmus  or  Bentley 
might  just  as  well  have  tried  the  problem,  and  either  would 
have  done  much  better  in  any  twenty  minutes  of  his  life.8 

AN  ESTIMATE  OF  SCALIGER. 

Scaliger  inspired  some  mathematicians  with  great  respect 
for  his  geometrical  knowledge.  Vieta,  the  first  man  of  his 
time,  who  answered  him,  had  such  regard  for  his  opponent 

/This  is  his  Animadversions  upon  Mr.  Hobbes*  late  book  De 
principiis  et  ratio  cinatione  geometrarum,  1666,  or  his  Hobbianae 
quadraturae  circuli,  cubationis  sphaerae  et  duplications  cubi  con- 
futatio,  also  of  1669. 

"This  is  the  work  of  1669  referred  to  above. 

4Gregoire  de  St.  Vincent  (1584-1667)  published  his  Opus  geo- 
metricum  quadraturae  circuli  et  sectionum  coni  at  Antwerp  in  1647. 

"This  appears  in  7.  Scaligeri  cyclometrica  elementa  duo,  Lug- 
duni  Batav.,  1594. 

6Adriaen  van  Roomen  (1561-1615)  gave  the  value  of  if  to  sixteen 
decimal  places  in  his  Ideae  mathematicae  pars  prima  (1593),  and 
wrote  his  In  Ar chime dis  circuli  dimensionem  expositio  &  analysis  in 
1597- 

T  Kastner.    See  note  5  on  page  43. 

8  Bentley  (1662-1742)  might  have  done  it,  for  as  the  head  of  Trin- 
ity College,  Cambridge,  and  a  follower  of  Newton,  he  knew  some 
mathematics.  Erasmus  (1466-1536)  lived  a  little  too  early  to  at- 
tempt it,  although  his  brilliant  satire  might  have  been  used  to  good 
advantage  against  those  who  did  try. 


AN    ESTIMATE   OF    SCALIGER.  Ill 

as  made  him  conceal  Scaliger's  name.  Not  that  he  is  very 
respectful  in  his  manner  of  proceeding:  the  following  dry 
quiz  on  his  opponent's  logic  must  have  been  very  cutting, 
being  true.  "In  grammaticis,  dare  navibus  Austros,  et  dare 
naves  Austris,  sunt  seque  significantia.  Sed  in  Geometricis, 
aliud  est  adsumpsisse  circulum  BCD  non  esse  majorem  tri- 
ginta  sex  segmentis  BCDF,  aliud  circulo  BCD  non  esse  majora 
triginta  sex  segmenta  BCDF.  Ilia  adsumptiuncula  vera  est, 
hsec  falsa."1  Isaac  Casaubon,2  in  one  of  his  letters  to  De 
Thou,3  relates  that,  he  and  another  paying  a  visit  to  Vieta, 
the  conversation  fell  upon  Scaliger,  of  whom  the  host  said 
that  he  believed  Scaliger  was  the  only  man  who  perfectly 
understood  mathematical  writers,  especially  the  Greek  ones : 
and  that  he  thought  more  of  Scaliger  when  wrong  than  of 
many  others  when  right ;  "pluris  se  Scaligerum  vel  erran- 
tem  facere  quam  multos KaTopOovvras"*  This  must  have  been 
before  Scaliger's  quadrature  (1594).  There  is  an  old  story 
of  some  one  saying,  "Mallem  cum  Scaligero  errare,  quam 
cum  Clavio  recte  sapere."5  This  I  cannot  help  suspecting 
to  have  been  a  version  of  Vieta's  speech  with  Clavius  satir- 
ically inserted,  on  account  of  the  great  hostility  which  Vieta 
showed  towards  Clavius  in  the  latter  years  of  his  life. 

Montucla  could  not  have  read  with  care  either  Scaliger's 
quadrature  or  Clavius's  refutation.  He  gives  the  first  a 
wrong  date:  he  assures  the  world  that  there  is  no  question 
about  Scaliger's  quadrature  being  wrong,  in  the  eyes  of 
geometers  at  least :  and  he  states  that  Clavius  mortified  him 

1  "In  grammar,  to  give  the  winds  to  the  ships  and  to  give  the  ships 
to  the  winds  mean  the  same  thing.  But  in  geometry  it  is  one  thing 
to  assume  the  circle  BCD  not  greater  than  thirty-six  segments 
BCDF,  and  another  (to  assume)  the  thirty-six  segments  BCDF  not 
greater  than  the  circle.  The  one  assumption  is  true,  the  other  false." 

3  The  Greek  scholar  (1559-1614)  who  edited  a  Greek  and  Latin 
edition  of  Aristotle  in  1590. 

'Jacques  Auguste  de  Thou  (1553-1617),  the  historian  and  states- 
man. 

'  "To  value  Scaliger  higher  even  when  wrong,  than  the  multitude 
when  right." 

5  "I  would  rather  err  with  Scaliger  than  be  right  with  Clavius." 


112  A  BUDGET  OF  PARADOXES. 

extremely  by  showing  that  it  made  the  circle  less  than  its 
inscribed  dodecagon,  which  is,  of  course,  equivalent  to  as- 
serting that  a  straight  line  is  not  always  the  shortest  distance 
between  two  points.  Did  Clavius  show  this?  No,  it  was 
Scaliger  himself  who  showed  it,  boasted  of  it,  and  declared 
it  to  be  a  "noble  paradox"  that  a  theorem  false  in  geometry 
is  true  in  arithmetic;  a  thing,  he  says  with  great  triumph, 
not  noticed  by  Archimedes  himself!  He  says  in  so  many 
words  that  the  periphery  of  the  dodecagon  is  greater  than 
that  of  the  circle;  and  that  the  more  sides  there  are  to  the 
inscribed  figure,  the  more  does  it  exceed  the  circle  in  which 
it  is.  And  here  are  the  words,  on  the  independent  testi- 
monies of  Clavius  and  Kastner: 

"Ambitus  dodecagoni  circulo  inscribendi  plus  potest 
quam  circuli  ambitus.  Et  quanto  deinceps  plurium  laterum 
fuerit  polygonum  circulo  inscribendum,  tanto  plus  poterit 
ambitus  polygoni  quam  ambitus  circuli."6 

There  is  much  resemblance  between  Joseph  Scaliger 
and  William  Hamilton,7  in  a  certain  impetuousity  of  char- 
acter, and  inaptitude  to  think  of  quantity.  Scaliger  main- 
tained that  the  arc  of  a  circle  is  less  than  its  chord  in  arith- 
metic, though  greater  in  geometry;  Hamilton  arrived  at 
two  quantities  which  are  identical,  but  the  greater  the  one 
the  less  the  other.  But,  on  the  whole,  I  liken  Hamilton 
rather  to  Julius  than  to  Joseph.  On  this  last  hero  of  litera- 
ture I  repeat  Thomas  Edwards,8  who  says  that  a  man  is  un- 
learned who,  be  his  other  knowledge  what  it  may,  does  not 

8 "  The  perimeter  of  the  dodecagon  to  be  inscribed  in  a  circle  is 
greater  than  the  perimeter  of  the  circle.  And  the  more  sides  a 
polygon  to  be  inscribed  in  a  circle  successively  has,  so  much  the 
greater  will  the  perimeter  of  the  polygon  be  than  the  perimeter  of 
the  circle." 

7De  Morgan  took,  perhaps,  the  more  delight  in  speaking  thus  of 
Sir  William  Hamilton  (1788-1856)  because  of  a  spirited  controversy 
that  they  had  in  1847  over  the  theory  of  logic.  Possibly,  too,  Sir 
William's  low  opinion  of  mathematics  had  its  influence. 

8  Edwards  (1699-1757)  wrote  The  canons  of  criticism  (1747)  in 
which  he  gave  a  scathing  burlesque  on  Warburton's  Shakespeare. 
It  went  through  six  editions. 


JOHN    GRAUNT    AS    A    PARADOXER.  113 

understand  the  subject  he  writes  about.  And  now  one  of 
many  instances  in  which  literature  gives  to  literature  char- 
acter in  science.  Anthony  Teissier,9  the  learned  annotator 
of  De  Thou's  biographies,  says  of  Finseus,  "II  se  vanta 
sans  raison  avoir  trouve  la  quadrature  du  cercle;  la  gloire 
de  cette  admirable  decouverte  etait  reservee  a  Joseph  Sca- 
liger,  comme  1'a  ecrit  Scevole  de  St.  Marthe."10 

JOHN  GRAUNT  AS  A  PARADOXER. 

Natural  and  Political  Observations upon  the  Bills  of  Mor- 
tality.  By  John  Graunt,  citizen  of  London.   London,  1662,  4to.1 

This  is  a  celebrated  book,  the  first  great  work  upon  mor- 
tality. But  the  author,  going  ultra  crepidam,  has  attributed 
to  the  motion  of  the  moon  in  her  orbit  all  the  tremors  which 
she  gets  from  a  shaky  telescope.2  But  there  is  another  para- 
dox about  this  book :  the  above  absurd  opinion  is  attributed 
to  that  excellent  mechanist,  Sir  William  Petty,  who  passed 
his  days  among  the  astronomers.  Graunt  did  not  write  his 
own  book!  Anthony  Wood3  hints  that  Petty  "assisted,  or 
put  into  a  way"  his  old  benefactor :  no  doubt  the  two  friends 
talked  the  matter  over  many  a  time.  Burnet  and  Pepys4 
state  that  Petty  wrote  the  book.  It  is  enough  for  me  that 

9  Antoine  Teissier  (born  in  1632)  published  his  Eloges  des  hommes 
savants,  tires  de  I'histoire  de  M.  de  Thou  in  1683. 

"  He  boasted  without  reason  of  having  found  the  quadrature  of 
the  circle.  The  glory  of  this  admirable  discovery  was  reserved  for 
Joseph  Scaliger,  as  Scevole  de  St.  Marthe  has  written." 

1  Natural  and  political  observations  mentioned  in  the  following 

Index,  and  made  upon  the  Bills  of  Mortality With  reference  to 

the  government,  religion,  trade,  growth,  ayre,  and  diseases  of  the 
said  city.  London,  1662,  4to.  The  book  went  through  several  editions. 

*Ne  sutor  ultra  crepidam,  "Let  the  cobbler  stick  to  his  last,"  as 
we  now  say. 

8  The  author  (1632-1695)  of  the  Historia  et  Antiquitates  Universi- 
tatis  Oxoniensis  (1674).  See  note  6,  page  98. 

4  The  mathematical  guild  owes  Samuel  Pepys  (1633-1703)  for 
something  besides  his  famous  diary  (1659-1669).  Not  ^only  was  he 
president  of  the  Royal  Society  (1684),  but  he  was  interested  in 
establishing  Sir  William  Boreman's  mathematical  school  at  Green- 
wich. 


114  A  BUDGET  OF  PARADOXES. 

Graunt,  whose  honesty  was  never  impeached,  uses  the  plain- 
est incidental  professions  of  authorship  throughout ;  that  he 
was  elected  into  the  Royal  Society  because  he  was  the 
author;  that  Petty  refers  to  him  as  author  in  scores  of 
places,  and  published  an  edition,  as  editor,  after  Graunt's 
death,  with  Graunt's  name  of  course.  The  note  on  Graunt 
in  the  Biographia  Britannica  may  be  consulted;  it  seems 
to  me  decisive.  Mr.  C.  B.  Hodge,  an  able  actuary,  has  done 
the  best  that  can  be  done  on  the  other  side  in  the  Assurance 
Magazine,  viii.  234.  If  I  may  say  what  is  in  my  mind, 
without  imputation  of  disrespect,  I  suspect  some  actuaries 
have  a  bias:  they  would  rather  have  Petty  the  greater  for 
their  Coryphaeus  than  Graunt  the  less.5 

Pepys  is  an  ordinary  gossip:  but  Burnet's  account  has 
an  animus  which  is  of  a  worse  kind.  He  talks  of  "one 
Graunt,  a  Papist,  under  whose  name  Sir  William  Petty6 
published  his  observations  on  the  bills  of  mortality."  He 
then  gives  the  cock  without  a  bull  story  of  Graunt  being 
a  trustee  of  the  New  River  Company,  and  shutting  up  the 
cocks  and  carrying  off  their  keys,  just  before  the  fire  of 
London,  by  which  a  supply  of  water  was  delayed.7  It  was 
one  of  the  first  objections  made  to  Burnet's  work,  that 
Graunt  was  not  a  trustee  at  the  time;  and  Maitland,  the 
historian  of  London,  ascertained  from  the  books  of  the 
Company  that  he  was  not  admitted  until  twenty-three  days 
after  the  breaking  out  of  the  fire.  Graunt's  first  admission 

"John  Graunt  (1620-1674)  was  a  draper  by  trade,  and  was  a 
member  of  the  Common  Council  of  London  until  he  lost  office  by 
turning  Romanist.  Although  a  shopkeeper,  he  was  elected  to  the 
Royal  Society  on  the  special  recommendation  of  Charles  II.  Petty 
edited  the  fifth  edition  of  his  work,  adding  much  to  its  size  and  value, 
and  this  may  be  the  basis  of  Burnet's  account  of  the  authorship. 

0  Petty  (1623-1687)  was  a  mathematician  and  economist,  and  a 
friend  of  Pell  and  Sir  Charles  Cavendish.  His  survey  of  Ireland, 
made  for  Cromwell,  was  one  of  the  first  to  be  made  on  a  large  scale 
in  a  scientific  manner.  He  was  one  of  the  founders  of  the  Royal 
Society. 

TThe  story  probably  arose  from  Graunt's  recent  conversion  to 
the  Roman  Catholic  faith. 


MANKIND  A  GULLIBLE  LOT.  115 

to  the  Company  took  place  on  the  very  day  on  which  a  com- 
mittee was  appointed  to  inquire  into  the  cause  of  the  fire. 
So  much  for  Burnet.  I  incline  to  the  view  that  Graunt's 
setting  London  on  fire  strongly  corroborates  his  having 
written  on  the  bills  of  mortality:  every  practical  man  takes 
stock  before  he  commences  a  grand  operation  in  business. 

MANKIND  A  GULLIBLE  LOT. 

De  Cometis  :  or  a  discourse  of  the  natures  and  effects  of  Comets, 
as  they  are  philosophically,  historically,  and  astrologically  con- 
sidered. With  a  brief  (yet  full)  account  of  the  III  late  Comets, 
or  blazing  stars,  visible  to  all  Europe.  And  what  (in  a  natural 
way  of  judicature)  they  portend.  Together  with  some  obser- 
vations on  the  nativity  of  the  Grand  Seignior.  By  John  Gad- 
bury,  ^iXo/cta^/AciTi/ciSs.  London,  1665,  4to. 


Gadbury,  though  his  name  descends  only  in  astrology, 
was  a  well-informed  astronomer.1  D'Israeli2  sets  down  Gad- 
bury,  Lilly,  Wharton,  Booker,  etc.,  as  rank  rogues:  I  think 
him  quite  wrong.  The  easy  belief  in  roguery  and  inten- 
tional imposture  which  prevails  in  educated  society  is,  to 
my  mind,  a  greater  presumption  against  the  honesty  of 
mankind  than  all  the  roguery  and  imposture  itself.  Putting 
aside  mere  swindling  for  the  sake  of  gain,  and  looking  at 
speculation  and  paradox,  I  find  very  little  reason  to  suspect 
wilful  deceit.3  My  opinion  of  mankind  is  founded  upon  the 

1He  was  born  in  1627  and  died  in  1704.  He  published  a  series 
of  ephemerides,  beginning  in  1659.-  He  was  imprisoned  in  1679,  at 
the  time  of  the  "Popish  Plot,"  and  again  for  treason  in  1690.  His 
important  astrological  works  are  the  Animal  Cornatum,  or  the  Horn'd 
Beast  (1654)  and  The  Nativity  of  the  late  King  Charls  (1659). 

3  Isaac  DTsraeli  (1766-1848),  in  his  Curiosities  of  Literature 
(1791),  speaking  of  Lilly,  says:  "I  shall  observe  of  this  egregious 
astronomer,  that  there  is  in  this  work,  so  much  artless  narrative, 
and  at  the  same  time  so  much  palpable  imposture,  that  it  is  difficult 
to  know  when  he  is  speaking  what  he  really  believes  to  be  the  truth." 
He  goes  on  to  say  that  Lilly  relates  that  "those  adepts  whose  char- 
acters he  has  drawn  were  the  lowest  miscreants  of  the  town.  Most 
of  them  had  taken  the  air  in  the  pillory,  and  others  had  conjured 
themselves  up  to  the  gallows.  This  seems  a  true  statement  of  facts. 

8  It  is  difficult  to  estimate  William  Lilly  (1602-1681)  fairly.  His 
Merlini  Anglici  ephemeris,  issued  annually  from  1642  to  1681,  brought 


116  A  BUDGET  OF   PARADOXES. 

mournful  fact  that,  so  far  as  I  can  see,  they  find  within 
themselves  the  means  of  believing  in  a  thousand  times  as 
much  as  there  is  to  believe  in,  judging  by  experience.  I  do 
not  say  anything  against  Isaac  D'Israeli  for  talking  his  time. 
We  are  all  in  the  team,  and  we  all  go  the  road,  but  we  do 
not  all  draw. 

A  FORERUNNER  OF  A  WRITTEN  ESPERANTO. 

An  essay  towards  a  real  character  and  a  philosophical  language. 
By  John  Wilkins  [Dean  of  Ripon,  afterwards  Bishop  of  Ches- 
ter].1 London,  1668,  folio. 

This  work  is  celebrated,  but  little  known.  Its  object 
gives  it  a  right  to  a  place  among  paradoxes.  It  proposes  a 
language — if  that  be  the  proper  name — in  which  things 
and  their  relations  shall  be  denoted  by  signs,  not  words: 
so  that  any  person,  whatever  may  be  his  mother  tongue, 
may  read  it  in  his  own  words.  This  is  an  obvious  possi- 
bility, and,  I  am  afraid,  an  obvious  impracticability.  One 
man  may  construct  such  a  system — Bishop  Wilkins  has  done 
it — but  where  is  the  man  who  will  learn  it?  The  second 
tongue  makes  a  language,  as  the  second  blow  makes  a  fray. 
There  has  been  very  little  curiosity  about  his  performance, 
the  work  is  scarce ;  and  I  do  not  know  where  to  refer  the 
reader  for  any  account  of  its  details,  except,  to  the  partial 
reprint  of  Wilkins  presently  mentioned  under  1802,  in  which 
there  is  an  unsatisfactory  abstract.  There  is  nothing  in  the 
Biographia  Britannica,  except  discussion  of  Anthony  Wood's 
statement  that  the  hint  was  derived  from  Dalgarno's  book, 

him  a  great  deal  of  money.  Sir  George  Wharton  (1617-1681)  also 
published  an  almanac  annually  from  1641  to  1666.  He  tried  to  ex- 
pose John  Booker  (1603-1667)  by  a  work  entitled  Mercurio-Coelicio- 
Mastix;  or,  an  Anti-caveat  to  all  such,  as  have  (heretofore}  had  the 
misfortune  to  be  Cheated  and  Deluded  by  that  Grand  and  Traiterous 
Impostor  of  this  Rebellious  Age,  John  Booker,  1644.  Booker  was 
"licenser  of  mathematical  [astrological]  publications,"  and  as  such 
he  had  quarrels  with  Lilly,  Wharton,  and  others. 

JSee  note  i  on  page  100. 


GREGOIRE   DE   ST.   VINCENT.  117 

De  Signis,  1661. 2  Hamilton  (Discussions,  Art.  5,  "Dal- 
garno")  does  not  say  a  word  on  this  point,  beyond  quoting 
Wood;  and  Hamilton,  though  he  did  now  and  then  write 
about  his  countrymen  with  a  rough-nibbed  pen,  knew  per- 
fectly well  how  to  protect  their  priorities. 

GREGOIRE  DE  ST.  VINCENT. 

Problema  Austriacum.  Plus  ultra  Quadratura  Circuli.  Auctore 
P.  Gregorio  a  Sancto  Vincentio  Soc.  Jesu.,  Antwerp,  1647, 
folio. — Opus  Geometricum  posthumum  ad  Mesolabium.  By 
the  same.  Gandavi  [Ghent],  1668,  folio.1 

The  first  book  has  more  than  1200  pages,  on  all  kinds  of 
geometry.  Gregory  St.  Vincent  is  the  greatest  of  circle- 
squarers,  and  his  investigations  led  him  into  many  truths: 
he  found  the  property  of  the  area  of  the  hyperbola2  which  \ 
led  to  Napier's  logarithms  being  called  hyperbolic.  Mon- 
tucla  says  of  him,  with  sly  truth,  that  no  one  has  ever 
squared  the  circle  with  so  much  genius,  or,  excepting  his 
principal  object,  with  so  much  success.3  His  reputation,  and 
the  many  merits  of  his  work,  led  to  a  sharp  controversy  on 
his  quadrature,  which  ended  in  its  complete  exposure  by 
Huyghens  and  others.  He  had  a  small  school  of  followers, 
who  defended  him  in  print. 

2  This  is  the  Ars  Signorum,  vulgo  character  universalis  et  lingua 
philosophica,  that  appeared  at  London  in  1661,  8vo.  George  Dal- 
garno  anticipated  modern  methods  in  the  teaching  of  the  deaf  and 
dumb. 

1  See  note  4  on  page  no. 

2  If  the  hyperbola  is  referred  to  the  asymptotes  as  axes,  the  area 
between  two  ordinates  (x-=a,  x  =  b)  is  the  difference  of  the  loga- 
rithms of  a  and  b  to  the  base  e.    E.  g.,  in  the  case  of  the  hyperbola 
xy  •=.  i,  the  area  between  x  =  a  and  x  =  I  is  log  a. 

"'On  ne  peut  lui  refuser  la  justice  de  remarquer  que  personne 
avant  lui  ne  s'est  porte  dans  cette  recherche  ayec  autant  de  genie, 
&  meme,  si  nous  en  exceptons  son  objet  principal,  avec  autant  de 
succes."  Quadrature  du  Cercle,  p.  66. 


118  A  BUDGET  OF  PARADOXES. 


RENE  DE  SLUSE. 

Renati  Francisci  Slusii  Mesolabum.    Leodii  Eburonum  [Liege], 
1668,  410.1 

The  Mesolabum  is  the  solution  of  the  problem  of  finding 
two  mean  proportionals,  which  Euclid's  geometry  does  not 
attain.  Slusius  is  a  true  geometer,  and  uses  the  ellipse,  etc. : 
but  he  is  sometimes  ranked  with  the  trisecters,  for  which 
reason  I  place  him  here,  with  this  explanation. 

The  finding  of  two  mean  proportionals  is  the  prelim- 
inary to  the  famous  old  problem  of  the  duplication  of  the 
cube,  proposed  by  Apollo  (not  Apollonius)  himself.  D'ls- 
raeli  speaks  of  the  "six  follies  of  science," — the  quadrature, 
the  duplication,  the  perpetual  motion,  the  philosopher's 
stone,  magic,  and  astrology.  He  might  as  well  have  added 
the  trisection,  to  make  the  mystic  number  seven :  but  had  he 
done  so,  he  would  still  have  been  very  lenient;  only  seven 
follies  in  all  science,  from  mathematics  to  chemistry!  Sci- 
ence might  have  said  to  such  a  judge — as  convicts  used  to 
say  who  got  seven  years,  expecting  it  for  life,  "Thank  you, 
my  Lord,  and  may  you  sit  there  till  they  are  over," — may 
the  Curiosities  of  Literature  outlive  the  Follies  of  Science! 

JAMES  GREGORY. 

1668.  In  this  year  James  Gregory,  in  his  Vera  Circuli 
et  Hyperboles  Quadratura*  held  himself  to  have  proved  that 

1The  title  proceeds:  Seu  duae  mediae  proportionates  inter  ex- 
tremas  datas  per  circulum  et  per  infinitas  hyperbolas,  vel  ellipses  et 
per  quamlibet  exhibitae. . .  .Rene  Francois,  Baron  de  Sluse  (1622- 
1685)  was  canon  and  chancellor  of  Liege,  and  a  member  of  the  Royal 
Society.  He  also  published  a  work  on  tangents  (1672).  The  word 
mesolabium  is  from  the  Greek  neffo\dptoi>  or  pecroXapov,  an  instru- 
ment invented  by  Eratosthenes  for  finding  two  mean  proportionals. 

*The  full  title  has  some  interest:  Vera  circuit  et  hyperbolae  quad- 
ratura  cui  accedit  geometriae^  pars  universalis  inserviens  quantita- 
tum  curvarum  transmutationi  et  mensurae.  Authore  Jacobo  Gre- 
gorio  Abredonensi  Scoto Patavii,  1667.  That  is,  James  Greg- 
ory (1638-1675)  of  Aberdeen  (he  was  really  born  near  but  not  in 
the  city),  a  good  Scot,  was  publishing  his  work  down  in  Padua. 
The  reason  was  that  he  had  been  studying  in  Italy,  and  that  this 


BEAULIEU'S  QUADRATURE.  1 19 

the  geometrical  quadrature  of  the  circle  is  impossible.  Few 
mathematicians  read  this  very  abstruse  speculation,  and 
opinion  is  somewhat  divided.  The  regular  circle-squarers 
attempt  the  arithmetical  quadrature,  which  has  long  been 
proved  to  be  impossible.  Very  few  attempt  the  geometrical 
quadrature.  One  of  the  last  is  Malacarne,  an  Italian,  who 
published  his  Solution  Geometrique,  at  Paris,  in  1825.  His 
method  would  make  the  circumference  less  than  three  times 
the  diameter. 

BEAULIEU'S  QUADRATURE. 

La  Geometric  Frangoise,  ou  la  Pratique  aisee La  quadracture 

du  cercle.  Par  le  Sieur  de  Beaulieu,  Ingenieur,  Geographe  du 
Roi Paris,  1676,  8vo.  [not  Pontault  de  Beaulieu,  the  cele- 
brated topographer;  he  died  in  1674] -1 

If  this  book  had  been  a  fair  specimen,  I  might  have 
pointed  to  it  in  connection  with  contemporary  English  works, 
and  made  a  scornful  comparison.  But  it  is  not  a  fair  speci- 
men. Beaulieu  was  attached  to  the  Royal  Household,  and 
throughout  the  century  it  may  be  suspected  that  the  house- 
hold forced  a  royal  road  to  geometry.  Fifty  years  before, 
Beaugrand,  the  king's  secretary,  made  a  fool  of  himself, 
and  [so?]  contrived  to  pass  for  a  geometer.  He  had  inter- 
est enough  to  get  Desargues,  the  most  powerful  geometer 
of  his  time,2  the  teacher  and  friend  of  Pascal,  prohibited  from 

was  a  product  of  his  youth.  He  had  already  (1663)  published  his 
Optica  promota,  and  it  is  not  remarkable  that  his  brilliancy 
brought  him  a  wide  circle  of  friends  on  the  continent  and  the  offer 
of  a  pension  from  Louis  XIV.  He  became  professor  of  mathematics 
at  St.  Andrews  and  later  at  Edinburgh,  and  invented  the  first  suc- 
cessful reflecting  telescope.  The  distinctive  feature  of  his  Vera 
quadrature,  is  his  use  of  an  infinite  converging  series,  a  plan  that 
Archimedes  used  with  the  parabola. 

1  Jean^de  Beaulieu  wrote  several  works  on  mathematics,  including 
La  lumiere  de  I'arithmetique  (n.  d.),  La  lumie're  des  mathematiques 
(1673),  Nouvelle  invention  d'arithmetique  (1677),  and  some  mathe- 
matical tables. 

a  A  just  estimate.  There  were  several  works  published  by  Gerard 
Desargues  (1593-1661),  of  which  the  greatest  was  the  Brouillon 
Prole ct  (Paris,  1639).  There  is  an  excellent  edition  of  the  (Euvres 
de  Desargues  by  M.  Poudra,  Paris,  1864. 


120  A  BUDGET  OF  PARADOXES. 

lecturing.  See  some  letters  on  the  History  of  Perspective, 
which  I  wrote  in  the  Athen&um,  in  October  and  November, 
1861.  Montucla,  who  does  not  seem  to  know  the  true  secret 
of  Beaugrand's  greatness,  describes  him  as  "un  certain  M. 
de  Beaugrand,  mathematicien,  fort  mal  traite  par  Descartes, 
et  a  ce  qu'il  paroit  avec  justice."3 

Beaulieu's  quadrature  amounts  to  a  geometrical  con- 
struction* which  gives  Tr=\/I0.  His  depth  may  be  ascer- 
tained from  the  following  extracts.  First  on  Copernicus: 

"Copernic,  Allemand,  ne  s'est  pas  moins  rendu  illustre 
par  ses  doctes  ecrits;  et  nous  pourrions  dire  de  luy,  qu'il 
seroit  le  seul  et  unique  en  la  force  de  ses  Problemes,  si  sa 
trop  grande  presomption  ne  Tavoit  porte  a  avancer  en  cette 
Science  une  proposition  aussi  absurde,  qu'elle  est  contre  la 
Foy  et  raison,  en  faisant  la  circonference  d'un  Cercle  fixe, 
immobile,  et  le  centre  mobile,  sur  lequel  principe  Geome- 
trique,  il  a  avance  en  son  Traitte  Astrologique  le  Soleil  fixe, 
et  la  Terre  mobile."5 

I  digress  here  to  point  out  that  though  our  quadrators, 
etc.,  very  often,  and  our  historians  sometimes,  assert  that 
men  of  the  character  of  Copernicus,  etc.,  were  treated  with 
contempt  and  abuse  until  their  day  of  ascendancy  came, 
nothing  can  be  more  incorrect.  From  Tycho  Brahe6  to 
Beaulieu,  there  is  but  one  expression  of  admiration  for  the 
genius  of  Copernicus.  There  is  an  exception,  which,  I 

8  "A  certain  M.  de  Beaugrand,  a  mathematician,  very  badly  treated 
by  Descartes,  and,  as  it  appears,  rightly  so." 

*This  is  a  very  old  approximation  for  IT.  One  of  the  latest  pre- 
tended geometric  proofs  resulting  in  this  value  appeared  in  New 
York  in  1910,  entitled  Quadrimetry  (privately  printed). 

5  "Copernicus,  a  German,  made  himself  no  less  illustrious  by  his 
learned  writings ;  and  we  might  say  of  him  that  he  stood  alone  and 
unique  in  the  strength  of  his  problems,  if  his  excessive  presumption 
had  not  led  him  to  set  forth  in  this  science  a  proposition  so  absurd 
that  it  is  contrary  to  faith  and  reason,  namely  that  the  circumference 
of  a  circle  is  fixed  and  immovable  while  the  center  is  movable;  on 
which  geometrical  principle  he  has  declared  in  his  astrological  treat- 
ise that  the  sun  is  fixed  and  the  earth  is  in  motion." 

6  So  in  the  original. 


BEAULIEU'S  QUADRATURE.  121 

believe,  has  been  quite  misunderstood.  Maurolycus,7  in  his 
De  Sphara,  written  many  years  before  its  posthumous  pub- 
lication in  1575,  and  which  it  is  not  certain  he  would  have 
published,  speaking  of  the  safety  with  which  various  authors 
may  be  read  after  his  cautions,  says,  "Toleratur  et  Nicolaus 
Copernicus  qui  Solem  fixum  et  Terram  in  girum  circumverti 
posuit:  et  scutica  potius,  aut  flagello,  quam  reprehensione 
dignus  est."s  Maurolycus  was  a  mild  and  somewhat  con- 
temptuous satirist,  when  expressing  disapproval:  as  we 
should  now  say,  he  pooh-poohed  his  opponents ;  but,  unless 
the  above  be  an  instance,  he  was  never  savage  nor  impetuous. 
I  am  fully  satisfied  that  the  meaning  of  the  sentence  is,  that 
Copernicus,  who  turned  the  earth  like  a  boy's  top,  ought 
rather  to  have  a  whip  given  him  wherewith  to  keep  up  his 
plaything  than  a  serious  refutation.  To  speak  of  tolerating 
a  person  as  being  more  worthy  of  a  flogging  than  an  argu- 
ment, is  almost  a  contradiction. 

I  will  now  extract  Beaulieu's  treatise  on  algebra,  entire. 

"L'Algebre  est  la  science  curieuse  des  Sgavans  et  speciale- 
ment  d'un  General  d'Armee  ou  Capitaine,  pour  promptement 
ranger  une  Armee  en  bataille,  et  nombre  de  Mousquetaires 
et  Piquiers  qui  composent  les  bataillons  d'icelle,  outre  les 
figures  de  1'Arithmetique.  Cette  science  a  5  figures  par- 
ticulieres  en  cette  sorte.  P  signifie  plus  au  commerce,  et 
a  TArmee  Piquiers.  M  signifie  moins,  et  Mousquetaire  en 
1'Art  des  bataillons.  [It  is  quite  true  that  P  and  M  were 
used  for  plus  and  minus  in  a  great  many  old  works.]  R 
signifie  racine  en  la  mesure  du  Cube,  et  en  TArmee  rang.  Q 
signifie  quare  en  1'un  et  Tautre  usage.  C  signifie  cube  en 
la  mesure,  et  Cavallerie  en  la  composition  des  bataillons  et 
escadrons.  Quant  a  Toperation  de  cette  science,  c'est  d'ad- 

7Franciscus  Maurolycus  (1494-1575)  was  really  the  best  mathe- 
matician produced  by  Sicily  for  a  long  period.  He  made  Latin  trans- 
lations of  Theodosius,  Menelaus,  Euclid,  Apollonius,  and  Archi- 
medes, and  wrote  on  cosmography  and  other  mathematical  subjects. 

8  "Nicolaus  Copernicus  is  also  tolerated  who  asserted  that  the  sun 
is  fixed  and  that  the  earth  whirls  about  it ;  and  he  rather  deserves  a 
whip  or  a  lash  than  a  reproof." 


122  A  BUDGET  OF  PARADOXES. 

ditionner  un  plus  d'avec  plus,  la  somme  sera  plus,  et  moins 
d'avec  plus,  on  soustrait  le  moindre  du  plus,  et  la  reste  est 
la  somme  requise  ou  nombre  trouve.  Je  dis  settlement  cecy 
en  passant  pour  ceux  qui  n'en  sgavent  rien  du  tout."9 

This  is  the  algebra  of  the  Royal  Household,  seventy- 
three  years  after  the  death  of  Vieta.  Quaere,  is  it  possible 
that  the  fame  of  Vieta,  who  himself  held  very  high  stations 
in  the  household  all  his  life,  could  have  given  people  the 
notion  that  when  such  an  officer  chose  to  declare  himself 
an  algebraist,  he  must  be  one  indeed?  This  would  explain 
Beaugrand,  Beaulieu,  and  all  the  beaux.  Beaugrand — not 
only  secretary  to  the  king,  but  "mathematician"  to  the  Duke 
of  Orleans — I  wonder  what  his  "fool"  could  have  been  like, 
if  indeed  he  kept  the  offices  separate, — would  have  been  in 
my  list  if  I  had  possessed  his  Geostatique,  published  about 
1638.10  He  makes  bodies  diminish  in  weight  as  they  approach 
the  earth,  because  the  effect  of  a  weight  on  a  lever  is  less 
as  it  approaches  the  fulcrum. 

""Algebra  is  the  curious  science  of  scholars,  and  particularly  for 
a  general  of  an  army,  or  a  captain,  in  order  quickly  to  draw  up  an 
army  in  battle  array  and  to  number  the  musketeers  and  pikemen 
who  compose  it,  without  the  figures  of  arithmetic.  This  science 
has  five  special  figures  of  this  kind:  P  means  plus  in  commerce  and 
pikemen  in  the  army;  M  means  minus,  and  musketeer  in  the  art  of 
war;. . .  .R  signifies  root  in  the  measurement  of  a  cube,  and  rank  in 
the  army,  Q  means  square  (French  quare,  as  then  spelled)  in  both 
cases;  C  means  cube  in  mensuration,  and  cavalry  in  arranging  ba- 
tallions  and  squadrons.  As  for  the  operations  of  this  science,  they 
are  as  follows :  to  add  a  plus  and  a  plus,  the  sum  will  be  plus-,  to  add 
minus  with  plus,  take  the  less  from  the  greater  and  the  remainder 
will  be  the  sum  required  or  the  number  to  be  found.  I  say  this  only  in 
passing,  for  the  benefit  of  those  who  are  wholly  ignorant  of  it." 

10  He  refers  to  the  Joannis  de  Beaugrand Geostatice,  seu  de 

vario  ponder e  graviitm  secundum  varia  a  terrae  (centro)  intervalla 
dissertatio  mathematica,  Paris,  1636.  Pascal  relates  that  de  Beau- 
grand  sent  all  of  Roberval's  theorems  on  the  cycloid  and  Fermat  s 
on  maxima  and  minima  to  Galileo  in  1638,  pretending  that  they  were 
his  own. 


SIR  MATTHEW  HALE.  123 


SIR   MATTHEW   HALE. 

Remarks  upon  two  late  ingenious  discourses By  Dr.  Henry 

More.1    London,  1676,  8vo. 

In  1673  and  1675,  Matthew  Hale,2  then  Chief  Justice, 
published  two  tracts,  an  "Essay  touching  Gravitation,"  and 
"Difficiles  Nugae"  on  the  Torricellian  experiment.  Here 
are  the  answers  by  the  learned  and  voluminous  Henry 
More.  The  whole  would  be  useful  to  any  one  engaged  in 
research  about  ante-Newtonian  notions  of  gravitation. 

Observations  touching  the  principles  of  natural  motions;  and 
especially  touching  rarefaction  and  condensation. ..  .By  the 
author  of  Difficiles  Nuga.  London,  1677,  8vo. 

This  is  another  tract  of  Chief  Justice  Hale,  published 
the  year  after  his  death.  The  reader  will  remember  that 
motion,  in  old  philosophy,  meant  any  change  from  state  to 
state:  what  we  now  describe  as  motion  was  local  motion. 
This  is  a  very  philosophical  book,  about  flux  and  materia 
prima,  virtus  activa  and  essentialis,  and  other  fundamentals. 
I  think  Stephen  Hales,  the  author  of  the  "Vegetable  Statics," 
has  the  writings  of  the  Chief  Justice  sometimes  attributed 
to  him,  which  is  very  puny  justice  indeed.3  Matthew  Hale 
died  in  1676,  and  from  his  devotion  to  science  it  probably 
arose  that  his  famous  Pleas  of  the  Crown*  and  other  law 
works  did  not  appear  until  after  his  death.  One  of  his 

1More  (1614-1687)  was  a  theologian,  a  fellow  of  Christ  College, 
Cambridge,  and  a  Christian  Platonist. 

2  Matthew  Hale   (1609-1676)  the  famous  jurist,  wrote  a  number 
of  tracts  on  scientific,  moral,  and  religious   subjects.     These  were 
collected  and  published  in  1805. 

3  They  might  have  been  attributed  to  many  a  worse  man  than  Dr. 
Hales   (1677-1761),  who  was  a  member  of  the  Royal  Society  and  of 
the  Paris  Academy,  and  whose  scheme  for  the  ventilation  of  prisons 
reduced  the  mortality  at  the  Savoy  prison  from  one  hundred  to  only 
four  a  year.     The  book  to  which   reference  is  made  is   Vegetable 
Staticks  or  an  Account  of  some  statical  experiments  on  the  sap  in 
Vegetables,  1727. 

*  Pleas  of  the  Crown;  or  a  Methodical  Summary  of  the  Principal 
Matters  relating  to  the  subject,  1678. 


124  A  BUDGET  OF  PARADOXES. 

contemporaries  was  the  astronomer  Thomas  Street,  whose 
Caroline  Tables5  were  several  times  printed:  another  con- 
temporary was  his  brother  judge,  Sir  Thomas  Street.6  But 
of  the  astronomer  absolutely  nothing  is  known:  it  is  very 
unlikely  that  he  and  the  judge  were  the  same  person,  but 
there  is  not  a  bit  of  positive  evidence  either  for  or  against, 
so  far  as  can  be  ascertained.  Halley7 — no  less  a  person — 
published  two  editions  of  the  Caroline  Tables,  no  doubt 
after  the  death  of  the  author:  strange  indeed  that  neither 
Halley  nor  any  one  else  should  leave  evidence  that  Street 
was  born  or  died. 

Matthew  Hale  gave  rise  to  an  instance  of  the  lengths 
a  lawyer  will  go  when  before  a  jury  who  cannot  detect  him. 
Sir  Samuel  Shepherd,8  the  Attorney  General,  in  opening 
Hone's9  first  trial,  calls  him  "one  who  was  the  most  learned 
man  that  ever  adorned  the  Bench,  the  most  even  man 
that  ever  blessed  domestic  life,  the  most  eminent  man  that 
ever  advanced  the  progress  of  science,  and  one  of  the 
[very  moderate]  best  and  most  purely  religious  men  that 
ever  lived." 


B  Thomae  Streete  Astronomia  Carolina,  a  new  theory  of  the  celes- 
tial motions,  1661.  It  also  appeared  at  Nuremberg  in  1705,  and  at 
London  in  1710  and  1716  (  Halley' s  editions).  He  wrote  other  works 
on  astronomy. 

8  This  was  the  Sir  Thomas  Street  (1626-1696)  who  passed  sen- 
tence of  death  on  a  Roman  Catholic  priest  for  saying  mass.  The 
priest  was  reprieved  by  the  king,  but  in  the  light  of  the  present  day 
one  would  think  the  justice  more  in  need  of  pardon.  He  took  part 
in  the  trial  of  the  Rye  House  Conspirators  in  1683. 

'Edmund  Halley  (1656-1742),  who  succeeded  Wallis  (1703)  as 
Savilian  professor  of  mathematics  at  Oxford,  and  Flamsteed  (1720) 
as  head  of  the  Greenwich  observatory.  It  is^  of  interest  to  note  that 
he  was  instrumental  in  getting  Newton's  Principia  printed. 

8  Shepherd  (born  in  1760)  was  one  of  the  most  famous  lawyers 
of  his  day.  He  was  knighted  in  1814  and  became  Attorney  General 
in  1817. 

"This  was  William  Hone  (1780-1842),  a  book  publisher,  who 
wrote  satires  against  the  government,  and  who  was  tried  three 
times  because  of  his  parodies  on  the  catechism,  creed,  and  litany 
(illustrated  by  Cruikshank).  He  was  acquitted  on  all  of  the  charges. 


ON   THE  DISCOVERY  OF  ANTIMONY.  125 


ON   THE   DISCOVERY   OF   ANTIMONY. 

Basil  Valentine  his  triumphant  Chariot  of  Antimony,  with  an- 
notations of  Theodore  Kirkringius,  M.D.  With  the  true  book 
of  the  learned  Synesius,  a  Greek  abbot,  taken  out  of  the  Em- 
perour's  library,  concerning  the  Philosopher's  Stone.  Lon- 
don, 1678,  Svo.1 

There  are  said  to  be  three  Hamburg  editions  of  the  col- 
lected works  of  Valentine,  who  discovered  the  common 
antimony,  and  is  said  to  have  given  the  name  antimoine, 
in  a  curious  way.  Finding  that  the  pigs  of  his  convent 
throve  upon  it,  he  gave  it  to  his  brethren,  who  died  of  it.2 
The  impulse  given  to  chemistry  by  R.  Boyle3  seems  to 
have  brought  out  a  vast  number  of  translations,  as  in  the 
following  tract: 

ON  ALCHEMY. 

Collectanea  Chymica :  A  collection  of  ten  several  treatises  in 
chymistry,  concerning  the  liquor  Alkehest,  the  Mercury  of 
Philosophers,  and  other  curiosities  worthy  the  perusal.  Writ- 
ten by  Eir.  Philaletha,1  Anonymus,  J.  B.  Van-Helmont,2  Dr.  Fr. 

1  Valenlinus  was  a  Benedictine  monk  and  was  still  living  at  Erfurt 
in  1413.    His  Currus  triumphalis  antimonii  appeared  in  1624.     Syne- 
sius was  Bishop  of  Ptolemaide,  who  died  about  430.     His  works 
were  printed  at  Paris  in  1605.    Theodor  Kirckring  (1640-1693)  was 
a  fellow-student  of  Spinoza's.     Besides  the  commentary  on  Valen- 
tine he  left  several  works  on  anatomy.    His  commentary  appeared  at 
Amsterdam  in  1671.    There  were  several  editions  of  the  Chariot. 

2  The  chief  difficulty  with  this  curious  "monk-bane"  etymology  is 
its  absurdity.     The  real  origin  of  the  word  has  given  etymologists 
a  good  deal  of  trouble. 

"Robert  Boyle  (1627-1691),  son  of  "the  Great  Earl"  (of  Cork). 
Perhaps  his  best-known  discovery  is  the  law  concerning  the  volume 
of  gases. 

1  The  real  name  of  Eirenaeus  Philalethes  (born  in  1622)  is  un- 
known. It  may  have  been  Childe.  He  claimed  to  have  discovered 
the  philosopher's  stone  in  1645.  His  tract  in  this  work  is  The  Secret 
of  the  Immortal  Liquor  Alkahest  or  Ignis- A  qua.  See  note  7,  infra. 

"Johann  Baptist  van  Helmont,  Herr  von  Merode,  Royenborg 
etc.  (1577-1644).  His  chemical  discoveries  appeared  in  his  Ortus 
medicinae  (1648),  which  went  through  many  editions. 


126  A  BUDGET  OF  PARADOXES. 

Antonie,3  Bernhard  Earl  of  Trevisan,4  Sir  Geo.  Ripley,5  Rog. 
Bacon,6  Geo.  Starkie,7  Sir  Hugh  Platt,8  and  the  Tomb  of  Sem- 
iramis.  See  more  in  the  contents.  London,  1684,  8vo. 

In  the  advertisements  at  the  ends  of  these  tracts  there 
are  upwards  of  a  hundred  English  tracts,  nearly  all  of  the 
period,  and  most  of  them  translations.  Alchemy  looks  up 
since  the  chemists  have  found  perfectly  different  substances 
composed  of  the  same  elements  and  proportions.  It  is  true 
the  chemists  cannot  yet  transmute',  but  they  may  in  time: 
they  poke  about  most  assiduously.  It  seems,  then,  that  the 
conviction  that  alchemy  must  be  impossible  was  a  delusion : 
but  we  do  not  mention  it. 

8  De  Morgan  should  have  written  up  Francis  Anthony  (1550-1623), 
whose  Panacea  aurea  sive  tractatus  duo  de  auro  potabili  (Hamburg, 
1619)  described  a  panacea  that  he  gave  for  every  ill.  He  was  re- 
peatedly imprisoned  for  practicing  medicine  without  a  license  from 
the  Royal  College  of  Physicians. 

4Bernardus  Trevisanus  (1406-1490),  who  traveled  even  through 
Barbary,  Egypt,  Palestine,  and  Persia  in  search  of  the  philosopher's 
stone.  He  wrote  several  works  on  alchemy, — De  Chemica  (1567), 
De  Chemico  Miraculo  (1583),  Trait e  de  la  nature  de  I'oeuf  des  phi- 
losophes  (1659),  etc.,  all  published  long  after  his  death. 

"George  Ripley  (1415-1490)  was  an  Augustinian  monk,  later  a 
chamberlain  of  Innocent  VIII,  and  still  later  a  Carmelite  monk. 
His  Liber  de  mercuris  philosophico  and  other  tracts  first  appeared 
in  Opuscula  quaedam  chymica  (Frankfort,  1614). 

6  Besides  the  Opus  majus,  and  other  of  the  better  known  works 
of  this  celebrated  Franciscan  (1214-1294),  there  are  numerous  tracts 
on  alchemy  that  appeared  in  the  Thesaurus  chymicus    (Frankfort, 
1603). 

7  George   Starkey    (1606-1665   or   1666)   has   special   interest   for 
American  readers.     He  seems  to  have  been  born  in  the  Bermudas 
and  to  have  obtained  the  bachelor's  degree  in  England.     He  then 
went  to  America  and  in  1646  obtained  the  master's  degree  at  Har- 
vard, apparently  under  the  name  of  Stirk.    He  met  Eirenaeus  Phila- 
lethes    (see  note   I  above)    in  America  and  learned  alchemy  from 
him.     Returning  to   England,  he  sold  quack  medicines  there,  and 
died  in   1666  from  the  plague  after  dissecting  a  patient  who  had 
died  of  the  disease.     Among  his  works  was  the  Liquor  Alcahest,  or 
a  Discourse  of  that  Immortal  Dissolvent  of  Paracelsus  and  Helmont, 
which  appeared  (1675)  some  nine  years  after  his  death. 

8  Platt  (1552-1611)  was  the  son  of  a  London  brewer.     Although 
he  left  a  manuscript  on  alchemy,  and  wrote  a  book  entitled  Delights 
for  Ladies   to  adorne   their  Persons   (1607),  he  was  knighted   for 
some  serious  work  on  the  chemistry  of  agriculture,  fertilizing,  brew- 
ing, and  the  preserving  of  foods,  published  in  The  Jewell  House  of 
Art  and  Nature  (1594). 


ON    ALCHEMY.  127 

The  astrologers  and  the  alchemists  caught  it  in  company 
in  the  following,  of  which  I  have  an  unreferenced  note. 

"Mendacem  et  futilem  hominem  nominare  qui  volunt, 
calendariographum  dicunt;  at  qui  sceleratum  simul  ac  im- 
postorem,  chimicum.9 

"Crede  ratem  ventis  corpus  ne  crede  chimistis  ; 
Est  qusevis  chimica  tutior  aura  fide."10 

Among  the  smaller  paradoxes  of  the  day  is  that  of  the 
Times  newspaper,  which  always  spells  it  chymistry:  but  so, 
I  believe,  do  Johnson,  Walker,  and  others.  The  Arabic 
work  is  very  likely  formed  from  the  Greek:  but  it  may  be 
connected  either  with  xrllji*la  or  w^tn 


Lettre  d'un  gentil-homme  de  province  a  une  dame  de  qualite, 
sur  le  sujet  de  la  Comete.  Paris,  1681,  4to. 

An  opponent  of  astrology,  whom  I  strongly  suspect  to 
have  been  one  of  the  members  of  the  Academy  of  Sciences 
under  the  name  of  a  country  gentleman,11  writes  very  good 
sense  on  the  tremors  excited  by  comets. 

The  Petitioning-Comet  :  or  a  brief  Chronology  of  all  the  famous 
Comets  and  their  events,  that  have  happened  from  the  birth  of 
Christ  to  this  very  day.  Together  with  a  modest  enquiry  into 
this  present  comet,  London,  1681,  4to. 

A  satirical  tract  against  the  cometic  prophecy: 
"This  present  comet  (it's  true)  is  of  a  menacing  aspect, 
but  if  the  new  parliament  (for  whose  convention  so  many 
good  men  pray)  continue  long  to  sit,  I  fear  not  but  the  star 
will  lose  its  virulence  and  malignancy,  or  at  least  its  portent 
be  averted  from  this  our  nation  ;  which  being  the  humble 
request  to  God  of  all  good  men,  makes  me  thus  entitle  it, 
a  Petitioning-Comet." 

'  "Those  who  wish  to  call  a  man  a  liar  and  deceiver  speak  of  him 
as  a  writer  of  almanacs;  but  those  who  (would  call  him)  a  scoun- 
drel and  an  imposter  (speak  of  him  as)  a  chemist." 

1  "Trust  your  barque  to  the  winds  but  not  your  body  to  a  chem- 
ist ;  any  breeze  is  safer  than  the  faith  of  a  chemist." 

"Probably  the  Jesuit,  Pere  Claude  Frangois  Menestrier  (1631- 
1705)5  a  well-known  historian. 


128  A  BUDGET  OF  PARADOXES. 

The  following  anecdote  is  new  to  me : 

"Queen  Elizabeth  (1558)  being  then  at  Richmond,  and 
being  disswaded  from  looking  on  a  comet  which  did  then 
appear,  made  answer,  jacta  est  alea,  the  dice  are  thrown; 
thereby  intimating  that  the  pre-order'd  providence  of  God 
was  above  the  influence  of  any  star  or  comet." 

The  argument  was  worth  nothing:  for  the  comet  might 
have  been  on  the  dice  with  the  event;  the  astrologers  said 
no  more,  at  least  the  more  rational  ones,  who  were  about 
half  of  the  whole. 

An  astrological  and  theological  discourse  upon  this  present 
great  conjunction  (the  like  whereof  hath  not  (likely)  been  in 
some  ages)  ushered  in  by  a  great  comet.  London,  1682,  4to. 
By  C.  N.i2 

The  author  foretells  the  approaching  "sabbatical  jubilee," 
but  will  not  fix  the  date:  he  recounts  the  failures  of  his 
predecessors. 

A  judgment  of  the  comet  which  became  first  generally  visible 
to  us  in  Dublin,  December  13,  about  15  minutes  before  5  in 
the  evening,  A.  D.  1680.  By  a  person  of  quality.  Dublin,  1682, 
4to. 

The  author  argues  against  cometic  astrology  with  great 
ability. 

A  prophecy  on  the  conjunction  of  Saturn  and  Jupiter  in  this 
present  year  1682  .  With  some  prophetical  predictions  of  what 
is  likely  to  ensue  therefrom  in  the  year  1684.  By  John  Case, 
Student  in  physic  and  astrology.13  London,  1682,  4to. 

"The  author  was  Christopher  Nesse  (1621-1705),  a  belligerent 
Calvinist,  who  wrote  many  controversial  works  and  succeeded  in 
getting  excommunicated  four  times.  One  of  his  most  virulent  works 
was  A  Protestant  Antidote  against  the  Poison  of  Popery. 

M  John  Case  (c.  1660-1700)  was  a  famous  astrologer  and  physician. 
He  succeeded  to  Lilly's  practice  in  London.  In  a  darkened  room, 
wherein  he  kept  an  array  of  mystical  apparatus,  he  pretended  to 
show  the  credulous  the  ghosts  of  their  departed  relatives.  Besides 
his  astrological  works  he  wrote  one  serious  treatise,  the  Compendium 
Anatomicum  nova  methodo  insiitutum  (1695),  m  which  he  defends 
Harvey^s  theories  of  embryology. 


MATHEMATICAL  THEOLOGY.  129 

According  to  this  writer,  great  conjunctions  of  Jupiter 
and  Saturn  occur  "in  the  fiery  trigon,"  about  once  in  800 
years.  Of  these  there  are  to  be  seven :  six  happened  in  the 
several  times  of  Enoch,  Noah,  Moses,  Solomon,  Christ, 
Charlemagne.  The  seventh,  which  is  to  happen  at  "the 
lamb's  marriage  with  the  bride,"  seems  to  be  that  of  1682 ; 
but  this  is  only  vaguely  hinted. 

De  Quadrature  van  de  Circkel.    By  Jacob  Marcelis.   Amsterdam, 

1698,  4to. 
Ampliatie  en  demonstratie  wegens  de  Quadrature. ..  .By  Jacob 

Marcelis.   Amsterdam,  1699,  4to. 
Eenvoudig  vertoog  briev-wys  geschrevem  am  J.   Marcelis 

Amsterdam,  1702,  4to. 
De  sleutel  en  openinge  van  de  quadrature Amsterdam,  1704, 

4to. 

Who  shall  contradict  Jacob  Marcelis  ?14  He  says  the  cir- 
cumference contains  the  diameter  exactly  times 

~ 1008449087377541679894282184894 
0  6997183637540819440035239271702 

But  he  does  not  come  very  near,  as  the  young  arithmetician 
will  find. 

MATHEMATICAL  THEOLOGY. 

Theologiae  Christianae  Principia  Mathematica.    Auctore  Johanne 
Craig.1    London,  1699,  4to. 

This  is  a  celebrated  speculation,  and  has  been  reprinted 
abroad,  and  seriously  answered.  Craig  is  known  in  the 
early  history  of  fluxions,  and  was  a  good  mathematician. 

"Marcelis  (1636— after  1714)  was  a  soap  maker  of  Amsterdam. 
It  is  to  be  hoped  that  he  made  better  soap  than  values  of  n\ 

*John  Craig  (died  in  1731)  was  a  Scotchman,  but  most  of  his 
life  was  spent  at  Cambridge  reading  and  writing  on  mathematics. 
He  endeavored  to  introduce  the  Leibnitz  differential  calculus  into 
England.  His  mathematical  works  include  the  Methodus  Figurarum 
. . .  Quadraturas  dcterminandi  ( 1685) ,  Tractatus. . .  de  Figurarum  Cur- 
vilincarum  Quadratures  et  locis  Geometricis  (1693),  andDeCalculo 
Flucntium  libri  duo  (1718). 


130  A  BUDGET  OF   PARADOXES. 

He  professed  to  calculate,  on  the  hypothesis  that  the  sus- 
picions against  historical  evidence  increase  with  the  square 
of  the  time,  how  long  it  will  take  the  evidence  of  Chris- 
tianity to  die  out.  He  finds,  by  formulae,  that  had  it  been 
oral  only,  it  would  have  gone  out  A.  D.  800 ;  but,  by  aid  of 
the  written  evidence,  it  will  last  till  A.  D.  3150.  At  this 
period  he  places  the  second  coming,  which  is  deferred  until 
the  extinction  of  evidence,  on  the  authority  of  the  question 
"When  the  Son  of  Man  cometh,  shall  he  find  faith  on  the 
earth?"  It  is  a  pity  that  Craig's  theory  was  not  adopted: 
it  would  have  spared  a  hundred  treatises  on  the  end  of  the 
world,  founded  on  no  better  knowledge  than  his,  and  many 
of  them  falsified  by  the  event.  The  most  recent  (October, 
1863)  is  a  tract  in  proof  of  Louis  Napoleon  being  Anti- 
christ, the  Beast,  the  eighth  Head,  etc. ;  and  the  present  dis- 
pensation is  to  close  soon  after  1864. 

In  order  rightly  to  judge  Craig,  who  added  speculations 
on  the  variations  of  pleasure  and  pain  treated  as  functions 
of  time,  it  is  necessary  to  remember  that  in  Newton's  day 
the  idea  of  force,  as  a  quantity  to  be  measured,  and  as 
following  a  law  of  variation,  was  very  new:  so  likewise 
was  that  of  probability,  or  belief,  as  an  object  of  measure- 
ment.2 The  success  of  the  Principia  of  Newton  put  it  into 
many  heads  to  speculate  about  applying  notions  of  quantity 
to  other  things  not  then  brought  under  measurement.  Craig 
imitated  Newton's  title,  and  evidently  thought  he  was  mak- 
ing a  step  in  advance:  but  it  is  not  every  one  who  can 
plough  with  Samson's  heifer. 

It  is  likely  enough  that  Craig  took  a  hint,  directly  or 
indirectly,  from  Mohammedan  writers,  who  make  a  reply 
to  the  argument  that  the  Koran  has  not  the  evidence  derived 

2  As  is  well  known,  this  subject  owes  much  to  the  Bernoullis. 
Craig's  works  on  the  calculus  brought  him  into  controversy  with 
them.  He  also  wrote  on  other  subjects  in  which  they  were  interested, 
as  in  his  memoir  On  the  Curve  of  the  quickest  descent  (1700),  On  the 
Solid  of  least  resistance  (1700),  and  the  Solution  of  Bernoulli's 
problem  on  Curves  (1704). 


THE  ARISTOCRAT  AS   A   SCIENTIST.  131 

from  miracles.  They  say  that,  as  evidence  of  Christian 
miracles  is  daily  becoming  weaker,  a  time  must  at  last  arrive 
when  it  will  fail  of  affording  assurance  that  they  were  mir- 
acles at  all:  whence  would  arise  the  necessity  of  another 
prophet  and  other  miracles.  Lee,s  the  Cambridge  Orientalist, 
from  whom  the  above  words  are  taken,  almost  certainly 
never  heard  of  Craig  or  his  theory. 

THE  ARISTOCRAT  AS  A   SCIENTIST. 

Copernicans  of  all  sorts  convicted. . .  .to  which  is  added  a  Treat- 
ise of  the  Magnet.  By  the  Hon.  Edw.  Howard,  of  Berks. 
London,  1705,  8vo. 

Not  all  the  blood  of  all  the  Howards  will  gain  respect 
for  a  writer  who  maintains  that  eclipses  admit  no  possible 
explanation  under  the  Copernican  hypothesis,  and  who  asks 
how  a  man  can  "go  200  yards  to  any  place  if  the  moving 
superficies  of  the  earth  does  carry  it  from  him?"  Horace 
Walpole,  at  the  beginning  of  his  Royal  and  Noble  Authors, 
has  mottoed  his  book  with  the  Cardinal's  address  to  Ariosto, 
"Dove  diavolo,  Messer  Ludovico,  avete  pigliato  tante  co- 
glionerie?"1  Walter  Scott  says  you  could  hardly  pick  out, 
on  any  principle  of  selection  —  except  badness  itself,  he 
means  of  course — the  same  number  of  plebeian  authors 
whose  works  are  so  bad.  But  his  implied  satire  on  aristo- 
cratic writing  forgets  two  points.  First,  during  a  large 
period  of  our  history,  when  persons  of  rank  condescended 
to  write,  they  veiled  themselves  under  "a  person  of  honor," 
"a  person  of  quality,"  and  the  like,  when  not  wholly  un- 
described.  Not  one  of  these  has  Walpole  got;  he  omits, 

8  This  is  Samuel  Lee  (1783-1852),  the  young  prodigy  in  lan- 
guages. He  was  apprenticed  to  a  carpenter  at  twelve  and  learned 
Greek  while  working  at  the  trade.  Before  he  was  twenty-five  he 
knew  Hebrew,  Chaldee,  Syriac,  Samaritan,  Persian,  and  Hindustani. 
He  later  became  Regius  professor  of  Hebrew  at  Cambridge. 

1  "Where  the  devil,   Master  Ludovico,  did  you  pick  up  such  a 

collection  ?" 


132  A  BUDGET  OF  PARADOXES. 

for  instance,  Lord  Brounker's2  translation  of  Descartes  on 
Music.  Secondly,  Walpole  only  takes  the  heads  of  houses: 
this  cuts  both  ways;  he  equally  eliminates  the  Hon.  Robert 
Boyle  and  the  precious  Edward  Howard.  The  last  writer  is 
hardly  out  of  the  time  in  which  aristocracy  suppressed  its 
names;  the  avowal  was  then  usually  meant  to  make  the 
author's  greatness  useful  to  the  book.  In  our  day,  literary 
peers  and  honorables  are  very  favorably  known,  and  con- 
tain an  eminent  class.3  They  rough  it  like  others,  and  if 
such  a  specimen  as  Edw.  Howard  were  now  to  appear,  he 
would  be  greeted  with 

"Hereditary  noodle !  knowest  thou  not 
Who  would  be  wise,  himself  must  make  him  so?" 

THE   LONGITUDE   PROBLEM. 

A  new  and  easy  method  to  find  the  longitude  at  land  or  sea. 
London,  1710,  4to. 

This  tract  is  a  little  earlier  than  the  great  epoch  of  such 
publications  (1714),  and  professes  to  find  the  longitude  by 
the  observed  altitudes  of  the  moon  and  two  stars,1 

2  Lord  William  Brounker  (c.  1620-1684),  the  first  president  of 
the  Royal  Society,  is  best  known  in  mathematics  for  his  contribu- 
tions to  continued  fractions. 

"Horace  Walpole  (1717-1797)  published  his  Catalogue  of  the 
Royal  and  Noble  Authors  of  England  in  1758.  Since  his  time  a 
number  of  worthy  names  in  the  domain  of  science  in  general  and  of 
mathematics  in  particular  might  be  added  from  the  peerage  of 
England. 

*It  was  written  by  Charles  Hayes  (1678-1760),  a  mathematician 
and  scholar  of  no  mean  attainments.  He  travelled  extensively,  and 
was  deputy  governor  of  the  Royal  African  Company.  His  Treatise 
on  Fluxions  (London,  1704)  was  the  first  work  in  English  to  ex- 
plain Newton's  calculus.  He  wrote  a  work  entitled  The  Moon 
(1723)  to  prove  that  our  satellite  shines  by  its  own  as  well  as  by 
reflected  light.  His  Chronographia  Asiatica  &  Aegyptica  (1758) 
gives  the  results  of  his  travels. 


THE    LONGITUDE    PROBLEM.  133 

A  new  method  for  discovering  the  longitude  both  at  sea  and 
land,  humbly  proposed  to  the  consideration  of  the  public.2  By 
Wm.  Whiston3  and  Humphry  Ditton.4  London,  1714,  8vo. 

This  is  the  celebrated  tract,  written  by  the  two  Arian 
heretics.  Swift,  whose  orthodoxy  was  as  undoubted  as  his 
meekness,  wrote  upon  it  the  epigram — if,  indeed,  that  be 
epigram  of  which  the  point  is  pious  wish — which  has  been 
so  often  recited  for  the  purity  of  its  style,  a  purity  which 
transcends  modern  printing.  Perhaps  some  readers  may 
think  that  Swift  cared  little  for  Whiston  and  Ditton,  except 
as  a  chance  hearing  of  their  plan  pointed  them  out  as  good 
marks.  But  it  was  not  so:  the  clique  had  their  eye  on  the 
guilty  pair  before  the  publication  of  the  tract.  The  preface 
is  dated  July  7 ;  and  ten  days  afterwards  Arbuthnot5  writes 
as  follows  to  Swift: 

"Whiston  has  at  last  published  his  project  of  the  longi- 
tude; the  most  ridiculous  thing  that  ever  was  thought  on. 
But  a  pox  on  him!  he  has  spoiled  one  of  my  papers  of 
Scriblerus,  which  was  a  proposition  for  the  longitude  not 
very  unlike  his,  to  this  purpose;  that  since  there  was  no 
pole  for  east  and  west,  that  all  the  princes  of  Europe  should 
join  and  build  two  prodigious  poles,  upon  high  mountains, 

"Publick  in  the  original. 

8  Whiston  (1667-1752)  succeeded  Newton  as  Lucasian  professor 
of  mathematics  at  Cambridge.  In  1710  he  turned  Arian  and  was 
expelled  from  the  university.  His  work  on  Primitive  Christianity 
appeared  the  following  year.  He  wrote  many  works  on  astronomy 
and  religion. 

*  Ditton  (1675-1715)  was,  on  Newton's  recommendation,  made 
head  of  the  mathematical  school  at  Christ's  Hospital,  London.  He 
wrote  a  work  on  fluxions  (1706).  His  idea  for  rinding  longitude 
at  sea  was  to  place  stations  in  the  Atlantic  to  fire  off  bombs  at  regu- 
lar intervals,  the  time  between  the  sound  and  the  flash  giving  the 
distance.  He  also  corresponded  with  Huyghens  concerning  the 
use  of  chronometers  for  the  purpose. 

5  This  was  John  Arbuthnot  (c.  1658-1735),  the  mathematician, 
physician  and  wit.  He  was  intimate  with  Pope  and  Swift,  and 
was  Royal  physician  to  Queen  Anne.  Besides  various  satires  he 
published  a  translation  of  Huyghens's  work  on  probabilities  (1692) 
and  a  well-known  treatise  on  ancient  coins,  weights,  and  measures 
(1727). 


134  A  BUDGET  OF  PARADOXES. 

with  a  vast  lighthouse  to  serve  for  a  polestar.  I  was  think- 
ing of  a  calculation  of  the  time,  charges,  and  dimensions. 
Now  you  must  understand  his  project  is  by  lighthouses, 
and  explosion  of  bombs  at  a  certain  hour." 

The  plan  was  certainly  impracticable;  but  Whiston  and 
Ditton  might  have  retorted  that  they  were  nearer  to  the 
longitude  than  their  satirist  to  the  kingdom  of  heaven,  or 
even  to  a  bishopric.  Arbuthnot,  I  think,  here  and  else- 
where, reveals  himself  as  the  calculator  who  kept  Swift 
right  in  his  proportions  in  the  matter  of  the  Lilliputians, 
Brobdingnagians,  etc.  Swift  was  very  ignorant  about  things 
connected  with  number.  He  writes  to  Stella  that  he  has 
discovered  that  leap-year  comes  every  four  years,  and  that 
all  his  life  he  had  thought  it  came  every  three  years.  Did 
he  begin  with  the  mistake  of  Caesar's  priests?  Whether 
or  no,  when  I  find  the  person  who  did  not  understand  leap- 
year  inventing  satellites  of  Mars  in  correct  accordance  with 
Kepler's  third  law,  I  feel  sure  he  must  have  had  help. 

THE  AURORA  BOREALIS. 

An  essay  concerning  the  late  apparition  in  the  heavens  on  the 
6th  of  March.  Proving  by  mathematical,  logical,  and  moral 
arguments,  that  it  cou'd  not  have  been  produced  meerly  by  the 
ordinary  course  of  nature,  but  must  of  necessity  be  a  prodigy. 
Humbly  offered  to  the  consideration  of  the  Royal  Society.  Lon- 
don, 1716,  8vo. 

The  prodigy,  as  described,  was  what  we  should  call  a 
very  decided  and  unusual  aurora  borealis.  The  inference 
was,  that  men's  sins  were  bringing  on  the  end  of  the  world. 
The  author  thinks  that  if  one  of  the  old  "threatening 
prophets"  were  then  alive,  he  would  give  "something  like 
the  following."  I  quote  a  few  sentences  of  the  notion 
which  the  author  had  of  the  way  in  which  Ezekiel,  for  in- 
stance, would  have  addressed  his  Maker  in  the  reign  of 
George  the  First : 

"Begin!  Begin!  O  Sovereign,  for  once,  with  an  effec- 


THE   AURORA   BOREALIS.  135 

tual  clap  of  thunder O  Deity!  either  thunder  to  us  no 

more,  or  when  you  thunder,  do  it  home,  and  strike  with 

vengeance  to  the  mark Tis  not  enough  to  raise  a  storm, 

unless  you  follow  it  with  a  blow,  and  the  thunder  without 

the   bolt,   signifies   just   nothing  at   all Are   then   your 

lightnings  of  so  short  a  sight,  that  they  don't  know  how  to 
hit,  unless  a  mountain  stands  like  a  barrier  in  their  way? 
Or  perhaps  so  many  eyes  open  in  the  firmament  make  you 
lose  your  aim  when  you  shoot  the  arrow?  Is  it  this?  No! 
but,  my  dear  Lord,  it  is  your  custom  never  to  take  hold 
of  your  arms  till  you  have  first  bound  round  your  majestic 
countenance  with  gathered  mists  and  clouds." 

The  principles  of  the  Philosophy  of  the  Expansive  and  Con- 
tractive Forces.... By  Robert  Greene,1  M.A.,  Fellow  of  Clare 
Hall.  Cambridge,  1727,  folio. 

Sanderson2  writes  to  Jones,3  "The  gentleman  has  been 
reputed  mad  for  these  two  years  last  past,  but  never  gave 
the  world  such  ample  testimony  of  it  before."  This  was 
said  of  a  former  work  of  Greene's,  on  solid  geometry,  pub- 
lished in  1712,  in  which  he  gives  a  quadrature.4  He  gives 
the  same  or  another,  I  do  not  know  which,  in  the  present 
work,  in  which  the  circle  is  3%  diameters.  This  volume  is 
of  981  good  folio  pages,  and  treats  of  all  things,  mental  and 
material.  The  author  is  not  at  all  mad,  only  wrong  on 

1  Greene    (1678-1730)    was  a  very  eccentric  individual  and  was 
generally  ridiculed  by  his  contemporaries.     In  his  will  he  directed 
that  his  body  be  dissected  and  his  skeleton  hung  in  the  library  of 
King's  College,  Cambridge.     Unfortunately  for  his  fame,  this  wish 
was  never  carried  out. 

2  This   was   the   historian,    Robert    Sanderson    (1660-1741),   who 
spent  most  of  his  life  at  Cambridge. 

al  presume  this  was  William  Jones  (1675-1749)  the  friend  of 
Newton  and  Halley,  vice-president  of  the  Royal  Society,  in  whose 
Synopsis  Palmariorum  Matheseos  (1706)  the  symbol  v  is  first  used 
for  the  circle  ratio. 

4  This  was  the  Geometrica  solidorum,  sive  materiae,  seu  de  varia 
composition?,  progressione,  rationeque  velo citatum,  Cambridge,  1712. 
The  work  was  parodied  in  A  Taste  of  Philosophical  Fanaticism. .  .by 
a  gentleman  of  the  University  of  Gratz. 


136  A  BUDGET  OF  PARADOXES. 

many  points.  It  is  the  weakness  of  the  orthodox  follower 
of  any  received  system  to  impute  insanity  to  the  solitary 
dissentient:  which  is  voted  (in  due  time)  a  very  wrong 
opinion  about  Copernicus,  Columbus,  or  Galileo,  but  quite 
right  about  Robert  Greene.  If  misconceptions,  acted  on  by 
too  much  self-opinion,  be  sufficient  evidence  of  madness,  it 
would  be  a  curious  inquiry  what  is  the  least  per-centage 
of  the  reigning  school  which  has  been  insane  at  any  one 
time.  Greene  is  one  of  the  sources  for  Newton  being  led 
to  think  of  gravitation  by  the  fall  of  an  apple :  his  authority 
is  the  gossip  of  Martin  Folkes.5  Probably  Folkes  had  it 
from  Newton's  niece,  Mrs.  Conduitt,  whom  Voltaire  ac- 
knowledges as  his  authority.6  It  is  in  the  draft  found  among 
Conduitt's  papers  of  memoranda  to  be  sent  to  Fontenelle. 
But  Fontenelle,  though  a  great  retailer  of  anecdote,  does 
not  mention  it  in  his  eloge  of  Newton ;  whence  it  may  be 
suspected  that  it  was  left  out  in  the  copy  forwarded  to 
France.  D'Israeli  has  got  an  improvement  on  the  story : 
the  apple  "struck  him  a  smart  blow  on  the  head" :  no  doubt 
taking  him  just  on  the  organ  of  causality.  He  was  "sur- 
prised at  the  force  of  the  stroke"  from  so  small  an  apple: 
but  then  the  apple  had  a  mission ;  Homer  would  have  said 

8  The  antiquary  and  scientist  (1690-1754),  president  of  the  Royal 
Society,  member  of  the  Academic,  friend  of  Newton,  and  authority 
on  numismatics. 

6  She  was  Catherine  Barton,  Newton's  step-niece.  She  marrie'd 
John  Conduitt,  master  of  the  mint,  who  collected  materials  for  a 
life  of  Newton. 

A  propos  of  Mrs.  Conduitt's  life  of  her  illustrious  uncle,  Sir 
George  Greenhill  tells  a  very  good  story  on  Poincare\  the  well-known 
French  mathematician.  At  an  address  given  by  the  latter  at  the 
International  Congress  of  Mathematicians  held  in  Rome  in  1908  he 
spoke  of  the  story  of  Newton  and  the  apple  as  a  mere  fable.  After 
the  address  Sir  George  asked  him  why  he  had  done  so,  saying  that 
the  story  was  first  published  by  Voltaire,^  who  had  heard  it  from 
Newton  s  niece,  Mrs.  Conduitt.  Poincare  looked  blank  and  said, 
"Newton,  et  la  niece  de  Newton,  et  Voltaire,— non !  je  ne  vous  com- 
prends  pas !"  He  had  thought  Sir  George  meant  Professor  Volterra 
of  Rome,  whose  name  in  French  is  Voltaire,  and  who  could  not 
possibly  have  known  a  niece  of  Newton  without  bridging  a  century 
or  so. 


THE  AURORA  BOREALIS.  137 

it  was  Minerva  in  the  form  of  an  apple.  "This  led  him  to 
consider  the  accelerating  motion  of  falling  bodies,"  which 
Galileo  had  settled  long  before:  "from  whence  he  deduced 
the  principle  of  gravity,"  which  many  had  considered  be- 
fore him,  but  no  one  had  deduced  anything  from  it.  I  can- 
not imagine  whence  D'Israeli  got  the  rap  on  the  head,  I 
mean  got  it  for  Newton:  this  is  very  unlike  his  usual  ac- 
counts of  things.  The  story  is  pleasant  and  possible:  its 
only  defect  is  that  various  writings,  well  known  to  Newton, 
a  very  learned  mathematician,  had  given  more  suggestion 
than  a  whole  sack  of  apples  could  have  done,  if  they  had 
tumbled  on  that  mighty  head  all  at  once.  And  Pemberton, 
speaking  from  Newton  himself,  says  nothing  more  than  that 
the  idea  of  the  moon  being  retained  by  the  same  force  which 
causes  the  fall  of  bodies  struck  him  for  the  first  time  while 
meditating  in  a  garden.  One  particular  tree  at  Wools- 
thorpe  has  been  selected  as  the  gallows  of  the  appleshaped 
goddess:  it  died  in  1820,  and  Mr.  Turner7  kept  the  wood; 
but  Sir  D.  Brewster8  brought  away  a  bit  of  root  in  1814, 
and  must  have  had  it  on  his  conscience  for  43  years  that 
he  may  have  killed  the  tree.  Kepler's  suggestion  of  gravi- 
tation with  the  inverse  distance,  and  Bouillaud's  proposed 
substitution  of  the  inverse  square  of  the  distance,  are  things 
which  Newton  knew  better  than  his  modern  readers.  I 
discovered  two  anagrams  on  his  name,  which  are  quite*  con- 
clusive :  the  notion  of  gravitation  was  not  new ;  but  Newton 
went  on.  Some  wandering  spirit,  probably  whose  business 
it  was  to  resent  any  liberty  taken  with  Newton's  name,  put 
into  the  head  of  a  friend  of  mine  eighty-one  anagrams  on 
my  own  pair,  some  of  which  hit  harder  than  any  apple. 

7  This  was  the  Edmund  Turner  (1755-1829)  who  wrote  the  Col- 
lections for  the  Town  and  Soke  of  Grantham,  containing  authentic 
Memoirs  of  Sir  Isaac  Newton,  from  Lord  Portsmouth's  Manuscripts, 
London,  1806. 

8  It  may  be  recalled  to  mind  that  Sir  David  (1781-1868)  wrote 
a  life  of  Newton  (1855). 


138  A  BUDGET  OF  PARADOXES. 

DE  MORGAN  ANAGRAMS. 

This  friend,  whom  I  must  not  name,  has  since  made  it 
up  to  about  800  anagrams  on  my  name,  of  which  I  have 
seen  about  650.  Two  of  them  I  have  joined  in  the  title- 
page:  the  reader  may  find  the  sense.  A  few  of  the  others 
are  personal  remarks. 

"Great  gun !  do  us  a  sum !" 
is  a  sneer  at  my  pursuits :  but, 

"Go !  great  sum !  fa*ndu" 
is  more  dignified. 

"Sunt  agro!  gaudemus,"1 
is  happy  as  applied  to  one  of  whom  it  may  be  said : 

"Ne'er  out  of  town ;  'tis  such  a  horrid  life ; 
But  duly  sends  his  family  and  wife." 

"Adsum,  nugator,  suge!"2 

is  addressed  to  a  student  who  continues  talking  after  the 
lecture  has  commenced :  oh !  the  rascal ! 

"Graduatus  sum !  nego"3 

applies  to  one  who  declined  to  subscribe  for  an  M.A.  de- 
gree. 

"Usage  mounts  guard" 
symbolizes  a  person  of  very  fixed  habits. 

"Gus!  Gus!  a  mature  don! 

August  man!  sure,  god! 
And  Gus  must  argue,  O ! 

Snug  as  mud  to  argue, 
Must  argue  on  gauds. 

A  mad  rogue  stung  us. 
Gag  a  numerous  stud. 

Go!  turn  us!  damage  us! 
Tug  us !  O  drag  us !  Amen. 

Grudge  us !  moan  at  us ! 

1  "They  are  in  the  country.    We  rejoice." 

2 "I  am  here,  chatterbox,  suck!" 

8  "I  have  been  graduated !    I  decline !" 


NEWTON'S  DE  MUNDI  SYSTEMATE  LIBER.  139 

Daunt  us !  gag  us  more ! 

Dog-ear  us,  man!  gut  us! 
D —  us !  a  rogue  tugs !" 

are  addressed  to  me  by  the  circle-squarers ;  and, 

"O !  Gus !  tug  a  mean  surd!" 

is  smart  upon  my  preference  of  an  incommensurable  value 
of  TT  to  3%,  or  some  such  simple  substitute.    While, 

"Gus !  Gus !  at  'em  a'  round !" 

ought  to  be  the  backing  of  the  scientific  world  to  the  author 
of  the  Budget  of  Paradoxes. 

The  whole  collection  commenced  existence  in  the  head 
of  a  powerful  mathematician  during  some  sleepless  nights. 
Seeing  how  large  a  number  was  practicable,  he  amused 
himself  by  inventing  a  digested  plan  of  finding  more. 

Is  there  any  one  whose  name  cannot  be  twisted  into 
either  praise  or  satire?  I  have  had  given  to  me, 

"Thomas  Babington  Macaulay 
Mouths  big:  a  Cantab  anomaly." 

NEWTON'S  DE  MUNDI  SYSTEMATE  LIBER. 

A  treatise  of  the  system -of  the  world.     By  Sir  Isaac  Newton. 
Translated  into  English.    London,  1728,  8vo. 

I  think  I  have  a  right  to  one  little  paradox  of  my  own: 
I  greatly  doubt  that  Newton  wrote  this  book.  Castiglione,1 
in  his  Newtoni  Opuscula,2  gives  it  in  the  Latin  which  ap- 
peared in  1731,8  not  for  the  first  time;  he  says  Angli  omnes 
Newtono  tribuunt.4  It  appeared  just  after  Newton's  death, 
without  the  name  of  any  editor,  or  any  allusion  to  Newton's 

^Giovanni  Castiglioni  (Castillon,  Castiglione),  was  born  at  Cas- 
tiglione, in  Tuscany,  in  1708,  and  died  at  Berlin  in  1791.  He  was 
professor  of  mathematics  at  Utrecht  and  at  Berlin.  He  wrote  on 
De  Moivre's  equations  (1762),  Cardan's  rule  (1783),  and  Euclid's 
treatment  of  parallels  (1788-89). 

'This  was  the  Isaaci  Newtoni,  equitis  aurati,  opuscula  mathe- 
matica,  philosophica  et  philologica,  Lausannae  &  Genevae,  1744. 

"At  London,  4to. 

"All  the  English  attribute  it  to  Newton.'" 


140  A  BUDGET  OF  PARADOXES. 

recent  departure,  purporting  to  be  that  popular  treatise 
which  Newton,  at  the  beginning  of  the  third  book  of  the 
Principia,  says  he  wrote,  intending  it  to  be  the  third  book. 
It  is  very  possible  that  some  observant  turnpenny  might 
construct  such  a  treatise  as  this  from  the  third  book,  that 
it  might  be  ready  for  publication  the  moment  Newton  could 
not  disown  it.  It  has  'been  treated  with  singular  silence : 
the  name  of  the  editor  has  never  been  given.  Rigaud5  men- 
tions it  without  a  word :  I  cannot  find  it  in  Brewster's  New- 
ton, nor  in  the  Biographia  Britannica.  There  is  no  copy  in 
the  Catalogue  of  the  Royal  Society's  Library,  either  in  Eng- 
lish or  Latin,  except  in  Castiglione.  I  am  open  to  correc- 
tion; but  I  think  nothing  from  Newton's  acknowledged 
works  will  prove — as  laid  down  in  the  suspected  work — 
that  he  took  Numa's  temple  of  Vesta,  with  a  central  fire,  to 
be  intended  to  symbolize  the  sun  as  the  center  of  our  sys- 
tem, in  the  Copernican  sense.6 

Mr.  Edleston7  gives  an  account  of  the  lectures  "de  motu 
corporum,"  and  gives  the  corresponding  pages  of  the  Latin 
"De  Systemate  Mundi"  of  1731.  But  no  one  mentions  the 
English  of  1728.  This  English  seems  to  agree  with  the 
Latin;  but  there  is  a  mystery  about  it.  The  preface  says, 
"That  this  work  as  here  published  is  genuine  will  so  clearly 
appear  by  the  intrinsic  marks  it  bears,  that  it  will  be  but 
losing  words  and  the  reader's  time  to  take  pains  in  giving 
him  any  other  satisfaction."  Surely  fewer  words  would 
have  been  lost  if  the  prefator  had  said  at  once  that  the  work 
was  from  the  manuscript  preserved  at  Cambridge.  Perhaps 
it  was  a  mangled  copy  clandestinely  taken  and  interpreted. 

6  Stephen  Peter  Rigaud  (1774-1839),  Savilian  professor  of  geom- 
etry at  Oxford  (1810-27)  and  later  professor  of  astronomy  and  head 
of  the  Radcliffe  Observatory.  He  wrote  An  historical  Essay  on  the 
first  publication  of  Sir  Isaac  Newton's  Principia,  Oxford,  1838,  and 
a  two-volume  work  entitled  Correspondence  of  Scientific  Men  of  the 
i^th  Century,  1841. 

6  It  is  no  longer  considered  by  scholars  as  the  work  of  Newton. 

7J.  Edleston,  the  author  of  the  Correspondence  of  Sir  Isaac 
Newton  and  Professor  Cotes,  London,  1850. 


A  BACONIAN  CONTROVERSY.  141 


A  BACONIAN  CONTROVERSY. 

Lord  Bacon  not  the  author  of  "The  Christian  Paradoxes,"  being 
a  reprint  of  "Memorials  of  Godliness  and  Christianity,"  by 
Herbert  Palmer,  B.D.1  With  Introduction,  Memoir,  and  Notes, 
by  the  Rev.  Alexander  B.  Grosart,2  Kenross.  (Private  circula- 
tion, 1864). 

I  insert  the  above  in  this  place  on  account  of  a  slight 
connection  with  the  last.  Bacon's  Paradoxes, — so  attributed 
— were  first  published  as  his  in  some  asserted  "Remains," 
1648.3  They  were  admitted  into  his  works  in  1730,  and  re- 
main there  to  this  day.  The  title  is  "The  Character  of  a 
believing  Christian,  set  forth  in  paradoxes  and  seeming 
contradictions."  The  following  is  a  specimen: 

"He  believes  three  to  be  one  and  one  to  be  three ;  a  father 
not  to  be  older  than  his  son;  a  son  to  be  equal  with  his 
father;  and  one  proceeding  from  both  to  be  equal  with 
both:  he  believes  three  persons  in  one  nature,  and  two 
natures  in  one  person. . .  .He  believes  the  God  of  all  grace 
to  have  been  angry  with  one  that  never  offended  Him ;  and 
that  God  that  hates  sin  to  be  reconciled  to  himself  though 
sinning  continually,  and  never  making  or  being  able  to  make 
Him  any  satisfaction.  He  believes  a  most  just  God  to  have 
punished  a  most  just  person,  and  to  have  justified  himself, 
though  a  most  ungodly  sinner.  He  believes  himself  freely 
pardoned,  and  yet  a  sufficient  satisfaction  was  made  for 
him." 

Who  can  doubt  that  if  Bacon  had  written  this  it  must 
have  been  wrong?  Many  writers,  especially  on  the  Con- 

1  Palmer    (1601-1647)    was   Master   of   Queen's   College,   Cam- 
bridge, a  Puritan  but  not  a  separatist.    His  work,  The  Characters  of 
a  believing  Christian,  in  Paradoxes  and  seeming  contradictions,  ap- 
peared in  1645. 

2  Grosart  (1827-1899)  was  a  Presbyterian  clergyman.    He  was  a 
great  bibliophile,  and  issued  numerous  reprints  of  rare  books. 

8  This  was  the  year  after  Palmer's  death.  The  title  was,  The 
Remaines  of Francis  Lord  Verulam ;  being  Essays  and  sev- 
eral! Letters  to  severall  great  personages,  and  other  pieces  of  various 
and  high  concernment  not  heretofore  published,  London,  1648,  4to. 


142  A  BUDGET  OF  PARADOXES. 

tinent,  have  taken  him  as  sneering  at  (Athanasian)  Chris- 
tianity right  and  left.  Many  Englishmen  have  taken  him 
to  be  quite  in  earnest,  and  to  have  produced  a  body  of  edi- 
fying doctrine.  More  than  a  century  ago  the  Paradoxes  were 
published  as  a  penny  tract;  and,  again,  at  the  same  price, 
in  the  Penny  Sunday  Reader,  vol.  vi,  No.  148,  a  few  pas- 
sages were  omitted,  as  too  strong.  But  all  did  not  agree: 
in  my  copy  of  Peter  Shaw's4  edition  (vol.  ii,  p.  283)  the 
Paradoxes  have  been  cut  out  by  the  binder,  who  has  left 
the  backs  of  the  leaves.  I  never  had  the  curiosity  to  see 
whether  other  copies  of  the  edition  have  been  served  in  the 
same  way.  The  Religious  Tract  Society  republished  them 
recently  in  Selections  from  the  Writings  of  Lord  Bacon,  (no 
date;  bad  plan;  about  1863,  I  suppose).  No  omissions  were 
made,  so  far  as  I  find. 

I  never  believed  that  Bacon  wrote  this  paper ;  it  has 
neither  his  sparkle  nor  his  idiom.  I  stated  my  doubts  even 
before  I  heard  that  Mr.  Spedding,  one  of  Bacon's  editors, 
was  of  the  same  mind.  (Athenceum,  July  16,  1864).  I  was 
little  moved  by  the  wide  consent  of  orthodox  men:  for  I 
knew  how  Bacon,  Milton,  Newton,  Locke,  etc.,  were  always 
claimed  as  orthodox  until  almost  the  present  day.  Of  this 
there  is  a  remarkable  instance. 

LOCKE  AND  SOCINIANISM. 

Among  the  books  which  in  my  younger  day  were  in 
some  orthodox  publication  lists — I  think  in  the  list  of  the 
Christian  Knowledge  Society,  but  I  am  not  sure — was 
Locke's1  "Reasonableness  of  Christianity."  It  seems  to  have 
come  down  from  the  eighteenth  century,  when  the  battle 
was  belief  in  Christ  against  unbelief,  simpliciter,  as  the  logi- 

4  Shaw  (1694-1763)  was  physician  extraordinary  to  George  II. 
He  wrote  on  chemistry  and  medicine,  and  his  edition  of  the  Philo- 
sophical Works  of  Francis  Bacon  appeared  at  London  in  1733. 

1  John  Locke  (1632-1704),  the  philosopher.  This  particular  work 
appeared  in  1695.  There  was  an  edition  in  1834  (vol.  25  of  the 
Sacred  Classics}  and  one  in  1836  (vol.  2  of  the  Christian  Library). 


LOCKE  AND  SOCINIANISM.  143 

cians  say.  Now,  if  ever  there  was  a  Socinian2  book  in  the 
world,  it  is  this  work  of  Locke.  '  These  two,"  says  Locke, 
"faith  and  repentance,  i.  e.,  believing  Jesus  to  be  the  Mes- 
siah, and  a  good  life,  are  the  indispensable  conditions  of 
the  new  covenant,  to  be  performed  by  all  those  who  would 
obtain  eternal  life."  All  the  book  is  amplification  of  this 
doctrine.  Locke,  in  this  and  many  other  things,  followed 
Hobbes,  whose  doctrine,  in  the  Leviathan,  is  fidem,  quanta 
ad  salutem  necessaria  est,  contineri  in  hoc  articulo,  Jesus 
est  Christus.3  For  this  Hobbes  was  called  an  atheist,  which 

3 1  use  the  word  Socinian  because  it  was  so  much  used  in  Locke's 
time;  it  is  used  in  our  own  day  by  the  small  fry,  the  unlearned 
clergy  and  their  immediate  followers,  as  a  term  of  reproach  for  all 
Unitarians.  I  suspect  they  have  a  kind  of  liking  for  the  word;  it 
sounds  like  so  sinful.  The  learned  clergy  and  the  higher  laity  know 
better :  they  know  that  the  bulk  of  the  modern  Unitarians  go  farther 
than  Socinus,  and  are  not  correctly  named  as  his  followers.  The 
Unitarians  themselves  neither  desire  nor  deserve  a  name  which  puts 
them  one  point  nearer  to  orthodoxy  than  they  put  themselves.  That 
point  is  the  doctrine  that  direct  prayer  to  Jesus  Christ  is  lawful  and 
desirable :  this  Socinus  held,  and  the  modern  Unitarians  do  not  hold. 
Socinus,  in  treating  the  subject  in  his  own  Institutio,  an  imperfect  cat- 
echism which  he  left,  lays  much  more  stress  on  John  xiv.  13  than  on  xv. 
16  and  xvi.  23  .  He  is  not  disinclined  to  think  that  Patrem  should  be 
in  the  first  citation,  where  some  put  it;  but  he  says  that  to  ask  the 
Father  in  the  name  of  the  Son  is  nothing  but  praying  to  the  Son  in 
prayer  to  the  Father.  He  labors  the  point  with  obvious  wish  to  secure 
a  conclusive  sanction.  In  the  Racovian  Catechism,  of  which  Faustus 
Socinus  probably  drew  the  first  sketch,  a  clearer  light  is  arrived  at. 
The  translation  says :  "But  wherein  consists  the  divine  honor  due  to 
Christ?  In  adoration  likewise  and  invocation.  For  we  ought  at  all 
times  to  adore  Christ,  and  may  in  our  necessities  address  our  prayers 
to  him  as  often  as  we  please ;  and  there  are  many  reasons  to  induce 
us  to  do  this  freely."  There  are  some  who  like  accuracy,  even  in 
aspersion. — A.  De  M. 

Socinus,  or  Fausto  Paolo  Sozzini  (1539-1604),  was  an  anti- 
trinitarian  who  believed  in  prayer  and  homage  to  Christ.  Leaving 
Italy  after  his  views  became  known,  he  repaired  to  Basel,  but  his 
opinions  were  too  extreme  even  for  the  ^  Calyinists.  He  then  tried 
Transylvania,  attempting  to  convert  to  his  views  the  antitrinitarian 
Bishop  David.  The  only  result  of  his  efforts  was  the  imprisonment 
of  David  and  his  own  flight  to  Poland,  in  which  country  he  spent  the 
rest  of  his  life  (1579-1604).  His  complete  works  appeared  first  at 
Amsterdam  in  1668,  in  the  Bibliotheca  Fratres  Polonorum.  The  Ra- 
covian Catechism  (1605)  appeared  after  his  death,  but  it  seems  to 
have  been  planned  by  him. 

8  "As  much  of  faith  as  is  necessary  to  salvation  is  contained  in 
this  article,  Jesus  is  the  Christ." 


144  A  BUDGET  OF  PARADOXES. 

many  still  believe  him  to  have  been:  some  of  his  contem- 
poraries called  him,  rightly,  a  Socinian.  Locke  was  known 
for  a  Socinian  as  soon  as  his  work  appeared :  Dr.  John  Ed- 
wards,4 his  assailant,  says  he  is  "Socinianized  all  over." 
Locke,  in  his  reply,  says  "there  is  not  one  word  of  Socinian- 
ism  in  it:"  and  he  was  right:  the  positive  Socinian  doctrine 
has  not  one  word  of  Socinianism  in  it ;  Socinianism  consists 
in  omissions.  Locke  and  Hobbes  did  not  dare  deny  the 
Trinity:  for  such  a  thing  Hobbes  might  have  been  roasted, 
and  Locke  might  have  been  strangled.  Accordingly,  the 
well-known  way  of  teaching  Unitarian  doctrine  was  the 
collection  of  the  asserted  essentials  of  Christianity,  without 
naming  the  Trinity,  etc.  This  is  the  plan  Newton  followed, 
in  the  papers  which  have  at  last  been  published.5 

So  I,  for  one,  thought  little  about  the  general  tendency 
of  orthodox  writers  to  claim  Bacon  by  means  of  the  Para- 
doxes. I  knew  that,  in  his  "Confession  of  Faith"8  he  is  a 
Trinitarian  of  a  heterodox  stamp.  His  second  Person  takes 
human  nature  before  he  took  flesh,  not  for  redemption,  but 
as  a  condition  precedent  of  creation.  "God  is  so  holy,  pure, 
and  jealous,  that  it  is  impossible  for  him  to  be  pleased  in 
any  creature,  though  the  work  of  his  own  hands. . . .  [Gen. 
i.  10,  12,  18,  21,  25,  31,  freely  rendered].  But— purposing 
to  become  a  Creator,  and  to  communicate  to  his  creatures, 
he  ordained  in  his  eternal  counsel  that  one  person  of  the 
Godhead  should  be  united  to  one  nature,  and  to  one  par- 
ticular of  his  creatures ;  that  so,  in  the  person  of  the  Media- 
tor, the  true  ladder  might  be  fixed,  whereby  God  might 

'Edwards  (1637-1716)  was  a  Cambridge  fellow,  strongly  Cal- 
vinistic.  He  published  many  theological  works,  attacking  the  Ar- 
minians  and  Socinians.  Locke  and  Whiston  were  special  objects  of 
attack. 

*Sir  I.  Newton's  views  on  points  of  Trinitarian  Doctrine;  his 
Articles  of  Faith,  and  the  General  Coincidence  of  his  Opinions  with 
those  of  J.  Locke;  a  Selection  of  Authorities,  with  Observations, 
London,  1856. 

*  A  Confession  of  the  Faith,  Bristol,  1752,  8vo. 


LOCKE  AND  SOCINIANISM.  145 

descend  to  his  creatures  and  his  creatures  might  ascend  to 
God...." 

This  is  republished  by  the  Religious  Tract  Society,  and 
seems  to  suit  their  theology,  for  they  confess  to  having 
omitted  some  things  of  which  they  disapprove. 

In  1864,  Mr.  Grosart  published  his  discovery  that  the 
Paradoxes  are  by  Herbert  Palmer ;  that  they  were  first  pub- 
lished surreptitiously,  and  immediately  afterwards  by  him- 
self, both  in  1645;  that  the  "Remains"  of  Bacon  did  not 
appear  until  1648 ;  that  from  1645  to  1708,  thirteen  editions 
of  the  "Memorials"  were  published,  all  containing  the  Para- 
doxes. In  spite  of  this,  the  Paradoxes  were  introduced 
into  Bacon's  works  in  1730,  where  they  have  remained. 

Herbert  Palmer  was  of  good  descent,  and  educated  as 
a  Puritan.  He  was  an  accomplished  man,  one  of  the  few 
of  his  day  who  could  speak  French  as  well  as  English.  He 
went  into  the  Church,  and  was  beneficed  by  Laud,7  in  spite 
of  his  puritanism;  he  sat  in  the  Assembly  of  Divines,  and 
was  finally  President  of  Queens'  College,  Cambridge,  in 
which  post  he  died,  August  13,  1647,  in  the  46th  year  of 
his  age. 

Mr.  Grosart  says,  speaking  of  Bacon's  "Remains,"  "All 
who  have  had  occasion  to  examine  our  early  literature  are 
aware  that  it  was  a  common  trick  to  issue  imperfect,  false, 
and  unauthorized  writings  under  any  recently  deceased 
name  that  might  be  expected  to  take.  The  Puritans,  down 
to  John  Bunyan,  were  perpetually  expostulating  and  pro- 
testing against  such  procedure."  I  have  met  with  instances 
of  all  this ;  but  I  did  not  know  that  there  was  so  much  of 
it:  a  good  collection  would  be  very  useful.  The  work  of 
1728,  attributed  to  Newton,  is  likely  enough  to  be  one  of 
the  class. 

TThis  was  really  very  strange,  because  Laud  (1573-1644),  while 
he  was  Archbishop  of  Canterbury,  forced  a  good  deal  of  High 
Church  ritual  on  the  Puritan  clergy,  and  even  wished  to  compel  the 
use  of  a  prayer  book  in  Scotland.  It  was  this  intolerance  that  led 
to  his  impeachment  and  execution. 


146  A  BUDGET  OF   PARADOXES. 

Demonstration  de  I'immobiHtez  de  la  Terre....Par  M.  de  la 
Jonchere,1  Ingenieur  Francois.  Londres,  1728,  8vo. 

A  synopsis  which  is  of  a  line  of  argument  belonging 
to  the  beginning  of  the  preceding  century. 

TWO  FORGOTTEN  CIRCLE  SQUARERS. 

The  Circle  squared;  together  with  the  Ellipsis  and  several  re- 
flections on  it.  The  finding  two  geometrical  mean  propor- 
tionals, or  doubling  the  cube  geometrically.  By  Richard  Locke1 
....London,  no  date,  probably  about  1730,  8vo. 

According  to  Mr.  Locke,  the  circumference  is  three 
diameters,  three-fourths  the  difference  of  the  diameter  and 
the  side  of  the  inscribed  equilateral  triangle,  and  three- 
fourths  the  difference  between  seven-eighths  of  the  diameter 
and  the  side  of  the  same  triangle.  This  gives,  he  says, 
3. 18897.  There  is  an  addition  to  this  tract,  being  an  appen- 
dix to  a  book  on  the  longitude. 

The  Circle  squar'd.  By  Thos.  Baxter,  Crathorn,  Cleaveland, 
Yorkshire.  London,  1732,  8vo. 

Here  7r  =  3.0625.     No  proof  is  offered.2 

The  longitude  discovered  by  the  Eclipses,  Occultations,  and 
Conjunctions  of  Jupiter's  planets.  By  William  Whiston.  Lon- 
don, 1738. 

This  tract  has,  in  some  copies,  the  celebrated  preface 
containing  the  account  of  Newton's  appearance  before  the 
Parliamentary  Committee  on  the  longitude  question,  in  1714 

"The  name  is  Jonchere.  He  was  a  man  of  some  merit^  pro- 
posing (1718)  an  important  canal  in  Burgundy,  and  publishing  a 
work  on  the  Decouverte  des  longitudes  estimees  generalement  im- 
possible a  trouver,  1734  (or  1735). 

1  Locke  invented  a  kind  of  an  instrument  for  finding  longitude, 
and  it  is  described  in  the  appendix,  but  I  can  find  nothing  about  the 
man.  There  was  published  some  years  later  (London,  1751)  another 
work  of  his,  A  new  Problem  to  discover  the  longitude  at  sea, 

*  Baxter,  concerning  whom  I  know  merely  that  he  was  a  school- 
master, starts  with  the  assumption  of  this  value,  and  deduces  from 
it  some  fourteen  properties  relating  to  the  circle. 


THE  STEAMSHIP  SUGGESTED.  147 

(Brewster,  ii.  257-266).  This  "historical  preface,"  is  an 
insertion  and  is  dated  April  28,  1741,  with  four  additional 
pages  dated  August  10,  1741.  The  short  "preface"  is  by  the 
publisher,  John  Whiston,3  the  author's  son. 

THE  STEAMSHIP  SUGGESTED. 

A  description  and  draught  of  a  new-invented  machine  for  carry- 
ing vessels  or  ships  out  of,  or  into  any  harbour,  port,  or  river, 
against  wind  and  tide,  or  in  a  calm.  For  which,  His  Majesty 
has  granted  letters  patent,  for  the  sole  benefit  of  the  author, 
for  the  space  of  fourteen  years.  By  Jonathan  Hulls.1  London : 
printed  for  the  author,  1737.  Price  sixpence  (folding  plate  and 
pp.  48,  beginning  from  title). 

(I  ought  to  have  entered  this  tract  in  its  place.  It  is 
so  rare  that  its  existence  was  once  doubted.  It  is  the  earliest 
description  of  steam-power  applied  to  navigation.  The 
plate  shows  a  barge,  with  smoking  funnel,  and  paddles  at 
the  stem,  towing  a  ship  of  war.  The  engine,  as  described, 
is  Newcomen's.2 

In  1855,  John  Sheepshanks,^  so  well  known  as  a  friend  of 
Art  and  a  public  donor,  reprinted  this  tract,  in  fac-simile, 
from  his  own  copy ;  twenty-seven  copies  of  the  original 
12mo  size,  and  twelve  on  old  paper,  small  4to.  I  have  an 
original  copy,  wanting  the  plate,  and  with  "Price  sixpence" 
carefully  erased,  to  the  honor  of  the  book.* 

8  John,  who  died  in  1780,  was  a  well-known  character  in  his  way. 
He  was  a  bookseller  on  Fleet  Street,  and  his  shop  was  a  general 
rendezvous  for  the  literary  men  of  his  time.  He  wrote  the  Memoirs 
of  the  Life  and  Writings  of  Mr.  William  Whiston  (1749,  with  an- 
other edition  in  1753).  He  was  one  of  the  first  to  issue  regular 
catalogues  of  books  with  prices  affixed. 

1  The  name  appears  both  as  Hulls  and  as  Hull.  He  was  born  in 
Gloucestershire  in  1699.  In  1754  he  published  The  Art  of  Measuring 
made  Easy  by  the  help  of  a  new  Sliding  Scale. 

"Thomas  Newcomen  (1663-1729)  invented  the  first  practical 
steam  engine  about  1710.  It  was  of  about  five  and  a  half  horse 
power,  and  was  used  for  pumping  water  from  coal  mines.  Savery 
had  described  such  an  engine  in  1702,  but  Newcomen  improved  upon 
it  and  made  it  practical. 

"The  well-known  benefactor    of  art  (1787-1863). 

4  The  tract  was  again  reprinted  in  1860. 


148  A  BUDGET  OF   PARADOXES. 

It  is  not  known  whether  Hulls  actually  constructed  a 
boat.5  In  all  probability  his  tract  suggested  to  Symington, 
as  Symington6  did  to  Fulton.) 

THE  NEWTONIANS  ATTACKED. 

Le  vrai  systeme  de  physique  generate  de  M.  Isaac  Newton  ex- 
pose et  analyse  en  parallele  avec  celui  de  Descartes.  By  Louis 
Castel1  [Jesuit  and  F.R.S.]  Paris,  1743,  4to. 

This  is  an  elaborate  correction  of  Newton's  followers, 
and  of  Newton  himself,  who  it  seems  did  not  give  his  own 
views  with  perfect  fidelity.  Father  Castel,  for  instance, 
assures  us  that  Newton  placed  the  sun  at  rest  in  the  center 
of  the  system.  Newton  left  the  sun  to  arrange  that  matter 
with  the  planets  and  the  rest  of  the  universe.  In  this  vol- 
ume of  500  pages  there  is  right  and  wrong,  both  clever. 

A  dissertation  on  the  yEther  of  Sir  Isaac  Newton.  By  Bryan 
Robinson,2  M.D.  Dublin,  1743,  8vo.3 

8  Hulls  made  his  experiment  on  the  Avon,  at  Evesham,  in  1737, 
having  patented  his  machine  in  1736.  He  had  a  Newcomen  engine 
connected  with  six  paddles.  This  was  placed  in  the  front  of  a  small 
tow  boat.  The  experiment  was  a  failure. 

"William  Symington  (1763-1831).  In  1786  he  contructed  a 
working  model  of  a  steam  road  carriage.  The  machinery  was  applied 
to  a  small  boat  in  1788,  and  with  such  success  as  to  be  tried  on  a 
larger  boat  in  1789.  The  machinery  was  clumsy,  however,  and  in 
1801  he  took  out  a  new  patent  for  the  style  of  engine  still  used  on 
paddle  wheel  steamers.  This  engine  was  successfully  used  in  1802, 
on  the  Charlotte  Dundas.  Fulton  (1765-1815)  was  on  board,  and  so 
impressed  Robert  Livingston  with  the  idea  that  the  latter  furnished 
the  money  to  build  the  Clermont  (1807),  the  beginning  of  successful 
river  navigation. 

1  Louis  Bertrand  Castel  (1688-1757),  most  of  whose  life  was 
spent  in  trying  to  perfect  his  Clavecin  oculaire,  an  instrument  on  the 
order  of  the  harpsichord,  intended  to  produce  melodies  and  har- 
monies of  color.  He  also  wrote  L'Optique  des  couleurs  (1740)  and 
Sur  le  fond  de  la  Musique  (1754). 

8  Dr.  Robinson  (1680-1754)  was  professor  of  physic  at  Trinity 
College,  Dublin,  and  three  times  president  of  King  and  Queen's 
College  of  Physicians.  In  his  Treatise  on  the  Animal  Economy 
(1732-3,  with  a  third  edition  in  1738)  he  anticipated  the  discoveries 
of  Lavoisier  and  Priestley  on  the  nature  of  oxygen. 

3  There  was  another  edition,  published  at  London  in  1747,  8vo. 


MATHEMATICAL  THEOLOGY.  149 

A  mathematical  work  professing  to  prove  that  the  as- 
sumed ether  causes  gravitation. 

MATHEMATICAL  THEOLOGY. 

Mathematical  principles  of  theology,  or  the  existence  of  God 
geometrically  demonstrated.  By  Richard  Jack,  teacher  of 
Mathematics.  London,  1747,  Svo.1 

Propositions  arranged  after  the  manner  of  Euclid,  with 
beings  represented  by  circles  and  squares.  But  these  circles 
and  squares  are  logical  symbols,  not  geometrical  ones.  I 
brought  this  book  forward  to  the  Royal  Commission  on  the 
British  Museum  as  an  instance  of  the  absurdity  of  attempt- 
ing a  classed  catalogue  from  the  titles  of  books.  The  title  of 
this  book  sends  it  either  to  theology  or  geometry:  when, 
in  fact,  it  is  a  logical  vagary.  Some  of  the  houses  which 
Jack  built  were  destroyed  by  the  fortune  of  war  in  1745,  at 
Edinburgh:  who  will  say  the  rebels  did  no  good  whatever? 
I  suspect  that  Jack  copied  the  ideas  of  J.  B.  Morinus,  "Quod 
Deus  sit,"  Paris,  1636,2  4to,  containing  an  attempt  of  the 
same  kind,  but  not  stultified  with  diagrams. 

TWO  MODEL  INDORSEMENTS. 

Dissertation,  decouverte,  et  demonstrations  de  la  quadrature 
mathematique  du  cercle.  Par  M.  de  Faure,  geometre.  [s.  I, 
probably  Geneva]  1747,  Svo. 

Analyse  de  la  Quadrature  du  Cercle.  Par  M.  de  Faure,  Gentil- 
homme  Suisse.  Hague,  I749,1  4to. 

According  to  this  octavo  geometer  and  quarto  gentle- 
man, a  diameter  of  81  gives  a  circumference  of  256.  There 
is  an  amusing  circumstance  about  the  quarto  which  has 
been  overlooked,  if  indeed  the  book  has  ever  been  ex- 

*The  author  seems  to  have  shot  his  only  bolt  in  this  work.  I 
can  find  nothing  about  him. 

3  Quod  Deus  sit,  mundusque  ab  ipso  creatus  fuerit  in  tempore, 
ejusque  providentia  gubernetur.  Selecta  aliquot  theoremata  adver- 
sos  atheos,  etc.,  Paris,  1635,  4to. 

*The  British  Museum  Catalogue  mentions  a  copy  of  1740,  but 
this  is  possibly  a  misprint. 


150  A  BUDGET  OF  PARADOXES. 

amined.  John  Bernoulli  (the  one  of  the  day)2  and  Koenig^ 
have  both  given  an  attestation:  my  mathematical  readers 
may  stare  as  they  please,  such  is  the  fact.  But,  on  examina- 
tion, there  will  be  reason  to  think  the  two  sly  Swiss  played 
their  countryman  the  same  trick  as  the  medical  man  played 
Miss  Pickle,  in  the  novel  of  that  name.  The  lady  only 
wanted  to  get  his  authority  against  sousing  her  little  nephew, 
and  said,  "Pray,  doctor,  is  it  not  both  dangerous  and  cruel 
to  be  the  means  of  letting  a  poor  tender  infant  perish  by 
sousing  it  in  water  as  cold  as  ice?" — "Downright  murder, 
I  affirm,"  said  the  doctor;  and  certified  accordingly.  De 
Faure  had  built  a  tremendous  scaffolding  of  equations,  quite 
out  of  place,  and  feeling  cock-sure  that  his  solutions,  if 
correct,  would  square  the  circle,  applied  to  Bernoulli  and 
Koenig — who  after  his  tract  of  two  years  before,  must  have 
known  what  he  was  at — for  their  approbation  of  the  solu- 
tions. And  he  got  it,  as  follows,  well  guarded: 

"Suivant  les  suppositions  posees  dans  ce  Memoire,  il  est 
si  evident  que  /  doit  etre  =  34,  y  =  1,  et  z=  1,  que  cela  n'a 
besoin  ni  de  preuve  ni  d'autorite  pour  etre  reconnu  par  tout 
le  monde.4 

"a  Basle  le  7e  Mai  1749.  JEAN  BERNOULLI." 

"Je  souscris  au  jugement  de  Mr.  Bernoulli,  en  conse- 
quence de  ces  suppositions.5 

"a  la  Haye  le  21  Juin  1749.  S.  KOENIG." 

On  which  de  Faure  remarks  with  triumph — as  I  have 
no  doubt  it  was  intended  he  should  do — "il  conste  clairement 
par  ma  presente  Analyse  et  Demonstration,  qu'ils  y  ont  deja 

'This  was  Johann  II  (1710-1790),  son  of  Johann  I,  who  suc- 
ceeded his  father  as  professor  of  mathematics  at  Basel. 

'Samuel  Koenig  (1712-1757),  who  studied  under  Johann  Ber- 
noulli I.  He  became  professor  of  mathematics  at  Franeker  (1747) 
and  professor  of  philosophy  at  the  Hague  (1749). 

4  "In  accordance  with  the  hypotheses  laid  down  in  this  memoir  it 
is  so  evident  that  /  must  =34,  y  =  I,  and  «  =  i,  that  there  is  no 
need  of  proof  or  authority  for  it  to  be  recognized  by  every  one." 

B"I  subscribe  to  the  judgment  of  Mr.  Bernoulli  as  a  result  of 
these  hypotheses." 


THOMAS  WRIGHT  OF  DURHAM.  151 

reconnu  et  approuve  parfaitement  que  la  quadrature  du 
cercle  est  mathematiquement  demontree."6  It  should  seem 
that  it  is  easier  to  square  the  circle  than  to  get  round  a 
mathematician. 

An  attempt  to  demonstrate  that  all  the  Phenomena  in  Nature 
may  be  explained  by  two  simple  active  principles,  Attraction 
and  Repulsion,  wherein  the  attraction  of  Cohesion,  Gravity 
and  Magnetism  are  shown  to  be  one  and  the  same.  By  Gowin 
Knight.  London,  1748,  4to. 

Dr.  Knight7  was  Mr.  Panizzi's8  archetype,  the  first  Prin- 
cipal Librarian  of  the  British  Museum.  He  was  celebrated 
for  his  magnetical  experiments.  This  work  was  long  neg- 
lected ;  but  is  now  recognized  as  of  remarkable  resemblance 
to  modern  speculations. 

THOMAS  WRIGHT  OF  DURHAM. 

An  original  theory  or  Hypothesis  of  the  Universe.  By  Thomas 
Wright1  of  Durham.  London,  4to,  1750. 

Wright  is  a  speculator  whose  thoughts  are  now  part  of 
our  current  astronomy.  He  took  that  view — or  most  of  it — 
of  the  milky  way  which  afterwards  suggested  itself  to  Wil- 
liam Herschel.  I  have  given  an  account  of  him  and  his 
work  in  the  Philosophical  Magazine  for  April,  1848. 

Wright  was  mathematical  instrument  maker  to  the  King ; 

8  "It  clearly  appears  from  my  present  analysis  and  demonstration 
that  they  have  already  recognized  and  perfectly  agreed  to  the  fact 
that  the  quadrature  of  the  circle  is  mathematically  demonstrated." 

TDr.  Knight  (died  in  1772)  made  some  worthy  contributions  to 
the  literature  of  the  mariner's  compass.  As  De  Morgan  states,  he 
was  librarian  of  the  British  Museum. 

8  Sir  Anthony  Panizzi  (1797-1879)  fled  from  Italy  under  sen- 
tence of  death  (1822).  He  became  assistant  (1831)  and  chief 
(1856)  librarian  of  the  British  Museum,  and  was  knighted  in  1869. 
He  began  the  catalogue  of  printed  books  of  the  Museum. 

1  Wright  (1711-1786)  was  a  physicist.  He  was  offered  the  pro- 
fessorship of  mathematics  at  the  Imperial  Academy  of  St.  Peters- 
burg but  declined  to  accept  it.  This  work  is  devoted  chiefly  to  the 
theory  of  the  Milky  Way,  the  via  lactea  as  he  calls  it  after  the  man- 
ner of  the  older  writers. 


152  A  BUDGET  OF   PARADOXES. 

and  kept  a  shop  in  Fleet  Street.  Is  the  celebrated  business 
of  Troughton  &  Simms,  also  in  Fleet  Street,  a  lineal  des- 
cendant of  that  of  Wright  ?  It  is  likely  enough,  more  likely 
that  that — as  I  find  him  reported  to  have  affirmed — Prester 
John  was  the  descendant  of  Solomon  and  the  Queen  of 
Sheba.  Having  settled  it  thus,  it  struck  me  that  I  might 
apply  to  Mr.  Simms,  and  he  informs  me  that  it  is  as  I 
thought,  the  line  of  descent  being  Wright,  Cole,  John 
Troughton,  Edward  Troughton,2  Troughton  &  Simms.s 

BISHOP  HORNE  ON  NEWTON. 

The  theology  and  philosophy  in  Cicero's  Somnium  Scipionis 
explained.  Or,  a  brief  attempt  to  demonstrate,  that  the  New- 
tonian system  is  perfectly  agreeable  to  the  notions  of  the 
wisest  ancients :  and  that  mathematical  principles  are  the  only 
sure  ones.  [By  Bishop  Home,1  at  the  age  of  nineteen.]  Lon- 
don, 1751,  8vo. 

This  tract,  which  was  not  printed  in  the  collected  works, 
and  is  now  excessively  rare,  is  mentioned  in  Notes  and  Que- 
ries, 1st  S.,  v,  490,  573;  2d  S.,  ix,  15.  The  boyish  satire 
on  Newton  is  amusing.  Speaking  of  old  Benjamin  Martin,2 
he  goes  on  as  follows: 

2  Troughton  (1753-1835)  was  one  of  the  world's  greatest  in- 
strument makers.  He  was  apprenticed  to  his  brother  John,  and  the 
two  succeeded  (1770)  Wright  and  Cole  in  Fleet  Street.  Airy  called 
his  method  of  graduating  circles  the  greatest  improvement  ever 
made  in  instrument  making.  He  constructed  (1800)  the  first  modern 
transit  circle,  and  his  instruments  were  used  in  many  of  the  chief 
observatories  of  the  world. 

'William  Simms  (1793-1860)  was  taken  into  partnership  by 
Troughton  (1826)  after  the  death  of  the  latter's  brother.  The  firm 
manufactured  some  well-known  instruments. 

JThis  was  George  Home  (1730-1792),  fellow  of  Magdalen  Col- 
lege, Oxford,  vice-Chancellor  of  the  University  (1776),  Dean  of 
Canterbury  (1781),  and  Bishop  of  Norwich  (1790).  He  was  a  great 
satirist,  but  most  of  his  pamphlets  against  men  like  Adam  Smith, 
Swedenborg,  and  Hume,  were  anonymous,  as  in  the  case  of  this 
one  against  Newton.  He  was  so  liberal  in  his  attitude  towards  the 
Methodists  that  he  would  not  have  John  Wesley  forbidden  to  preach 
in  his  diocese.  He  was  twenty-one  when  this  tract  appeared. 

a  Martin  (1704-1782)  was  by  no  means  "old  Benjamin  Martin" 
when  Home  wrote  this  pamphlet  in  1749.  In  fact  he  was  then  only 


BISHOP  HORNE  ON   NEWTON.  153 

"But  the  most  elegant  account  of  the  matter  [attraction] 
is  by  that  hominiform  animal,  Mr.  Benjamin  Martin,  who 
having  attended  Dr.  Desaguliers'3  fine,  raree,  gallanty  shew 
for  some  years  [Desaguliers  was  one  of  the  first  who  gave 
public  experimental  lectures,  before  the  saucy  boy  was  born] 
in  the  capacity  of  a  turnspit,  has,  it  seems,  taken  it  into  his 
head  to  set  up  for  a  philosopher." 

Thus  is  preserved  the  fact,  unknown  to  his  biographers, 
that  Benj.  Martin  was  an  assistant  to  Desaguliers  in  his 
lectures.  Hutton*  says  of  him,  that  "he  was  well  skilled  in  the 
whole  circle  of  the  mathematical  and  philosophical  sciences, 
and  wrote  useful  books  on  every  one  of  them" :  this  is  quite 
true ;  and  even  at  this  day  he  is  read  by  twenty  where  Home 
is  read  by  one ;  see  the  stalls,  passim.  All  that  I  say  of  him,  in- 
deed my  knowledge  of  the  tract,  is  due  to  this  contemptuous 
mention  of  a  more  durable  man  than  himself.  My  assistant 
secretary  at  the  Astronomical  Society,  the  late  Mr.  Epps,s 
bought  the  copy  at  a  stall  because  his  eye  was  caught  by  the 
notice  of  "Old  Ben  Martin,"  of  whom  he  was  a  great  reader. 
Old  Ben  could  not  be  a  Fellow  of  the  Royal  Society,  because  he 
kept  a  shop:  even  though  the  shop  sold  nothing  but  philo- 
sophical instruments.  Thomas  Wright,  similarly  situated 
as  to  shop  and  goods,  never  was  a  Fellow.  The  Society 
of  our  day  has  greatly  degenerated :  those  of  the  old  time 
would  be  pleased,  no  doubt,  that  the  glories  of  their  day 

forty-five.  He  was  a  physicist  and  a  well-known  writer  on  scientific 
instruments.  He  also  wrote  Philosophic,  Britannica  or  a  new  and 
comprehensive  system  of  the  Newtonian  Philosophy  (1759). 

3  Jean  Theophile  Desaguliers,  or  Des  Aguliers  (1683-1744)  was 
the  son  of  a  Protestant  who  left  France  after  the  revocation  of  the 
Edict  of  Nantes.     He  became  professor  of  physics  at  Oxford,  and 
afterwards  gave  lectures  in  London.     Later  he  became  chaplain  to 
the  Prince  of  Wales.     He  published  several  works  on  physics. 

4  Charles  Hutton  (1737-1823),  professor  of  mathematics  at  Wool- 
wich (1772-1807).    His  Mathematical  Tables  (1785)  and  Mathemat- 
ical and  Philosophical  Dictionary  (1795-1796)  are  well  known. 

5  James  Epps  (1773-1839)  contributed  a  number  of  memoirs  on 
the  use  and  corrections  of  instruments.     He  was  assistant  secretary 
of  the  Astronomical  Society. 


154  A  BUDGET  OF   PARADOXES. 

should  be  commemorated.  In  the  early  days  of  the  Society, 
there  was  a  similar  difficulty  about  Graunt,  the  author  of 
the  celebrated  work  on  mortality.  But  their  royal  patron, 
"who  never  said  a  foolish  thing,"  sent  them  a  sharp  mes- 
sage, and  charged  them  if  they  found  any  more  such  trades- 
men, they  should  "elect  them  without  more  ado." 

Home's  first  pamphlet  was  published  when  he  was  but 
twenty-one  years  old.  Two  years  afterwards,  being  then 
a  Fellow  of  his  college,  and  having  seen  more  of  the  world, 
he  seems  to  have  felt  that  his  manner  was  a  little  too  pert. 
He  endeavored,  it  is  said,  to  suppress  his  first  tract:  and 
copies  are  certainly  of  extreme  rarity.  He  published  the 
following  as  his  maturer  view: 

A  fair,  candid,  and  impartial  state  of  the  case  between  Sir 
Isaac  Newton  and  Mr.  Hutchinson.6  In  which  is  shown  how 
far  a  system  of  physics  is  capable  of  mathematical  demonstra- 
tion ;  how  far  Sir  Isaac's,  as  such  a  system,  has  that  demon- 
stration; and  consequently,  what  regard  Mr.  Hutchinson' s 
claim  may  deserve  to  have  paid  to  it.  By  George  Home,  M.A. 
Oxford,  1753,  8vo. 

It  must  be  remembered  that  the  successors  of  Newton 
were  very  apt  to  declare  that  Newton  had  demonstrated 
attraction  as  a  physical  cause :  he  had  taken  reasonable  pains 
to  show  that  he  did  not  pretend  to  this.  If  any  one  had 
said  to  Newton,  I  hold  that  every  particle  of  matter  is  a 
responsible  being  of  vast  intellect,  ordered  by  the  Creator 
to  move  as  it  would  do  if  every  other  particle  attracted  it, 
and  gifted  with-  power  to  make  its  way  in  true  accordance 
with  that  law,  as  easily  as  a  lady  picks  her  way  across  the 
street ;  what  have  you  to  say  against  it  ? — Newton  must 
have  replied,  Sir!  if  you  really  undertake  to  maintain  this 
as  demonstrable,  your  soul  had  better  borrow  a  little  power 

'John  Hutchinson  (1674-1737)  was  one  of  the  first  to ^ try  to 
reconcile  the  new  science  of  geology  with  Genesis.  He  denied  the 
Newtonian  hypothesis  as  dangerous  to  religion,  and  because  it  ne- 
cessitated a  vacuum.  He  was  a  mystic  in  his  interpretation  of  the 
Scriptures,  and  created  a  sect  that  went  under  the  name  of  Hutchin- 
sonians. 


BISHOP  HORNE  ON   NEWTON.  155 

from  the  particles  of  which  your  body  is  made:  if  you 
merely  ask  me  to  refute  it,  I  tell  you  that  I  neither  can  nor 
need  do  it ;  for  whether  attraction  comes  in  this  way  or  in 
any  other,  it  comes,  and  that  is  all  I  have  to  do  with  it. 

The  reader  should  remember  that  the  word  attraction, 
as  used  by  Newton  and  the  best  of  his  followers,  only  meant 
a  drawing  towards,  without  any  implication  as  to  the  cause. 
Thus  whether  they  said  that  matter  attracts  .matter,  or  that 
young  lady  attracts  young  gentleman,  they  were  using  one 
word  in  one  sense.  Newton  found  that  the  law  of  the  first 
is  the  inverse  square  of  the  distance:  I  am  not  aware  that 
the  law  of  the  second  has  been  discovered ;  if  there  be  any 
chance,  we  shall  see  it  at  the  year  1856  in  this  list. 

In  this  point  young  Home  made  a  hit.  He  justly  cen- 
sures those  who  fixed  upon  Newton  a  more  positive  knowl- 
edge of  what  attraction  is  than  he  pretended  to  have.  "He 
has  owned  over  and  over  he  did  not  know  what  he  meant 
by  it — it  might  be  this,  or  it  might  be  that,  or  it  might  be 
anything,  or  it  might  be  nothing."  With  the  exception  of 
the  nothing  clause,  this  is  true,  though  Newton  might  have 
answered  Home  by  "Thou  hast  said  it." 

(I  thought  everybody  knew  the  meaning  of  "Thou  hast 
said  it":  but  I  was  mistaken.  In  three  of  the  evangelists 
2v  Aeyeis  is  the  answer  to  "Art  thou  a  king?"  The  force  of 
this  answer,  as  always  understood,  is  "That  is  your  way 
of  putting  it."  The  Puritans,  who  lived  in  Bible  phrases, 
so  understood  it :  and  Walter  Scott,  who  caught  all  peculiar- 
ities of  language  with  great  effect,  makes  a  marked  instance, 
"Were  you  armed? — I  was  not — I  went  in  my  calling,  as 
a  preacher  of  God's  word,  to  encourage  them  that  drew 
the  sword  in  His  cause.  In  other  words,  to  aid  and  abet 
the  rebels,  said  the  Duke.  Thou  hast  spoken  it,  replied  the 
prisoner.") 

Again,  Home  quotes  Rowning7  as  follows: 

7  John  Rowning,  a  Lincolnshire  rector,  died  in  1771.   He  wrote  on 


156  A  BUDGET  OF  PARADOXES. 

"Mr.  Rowning,  pt.  2,  p.  5  in  a  note,  has  a  very  pretty 
conceit  upon  this  same  subject  of  attraction,  about  every 
particle  of  a  fluid  being  intrenched  in  three  spheres  of 
attraction  and  repulsion,  one  within  another,  'the  innermost 
of  which  (he  says)  is  a  sphere  of  repulsion,  which  keeps 
them  from  approaching  into  contact;  the  next,  a  sphere  of 
attraction,  diffused  around  this  of  repulsion,  by  which  the 
particles  are  disposed  to  run  together  into  drops;  and  the 
outermost  of  all,  a  sphere  of  repulsion,  whereby  they  repel 
each  other,  when  removed  out  of  the  attraction.'  So  that 
between  the  urglngs,  and  solicitations,  of  one  and  t'other, 
a  poor  unhappy  particle  must  ever  be  at  his  wit's  end,  not 
knowing  which  way  to  turn,  or  whom  to  obey  first." 

Rowning  has  here  started  the  notion  which  Boscovich8 
afterwards  developed. 

I  may  add  to  what  precedes  that  it  cannot  be  settled  that, 
as  Grange^  says,  Desaguliers  was  the  first  who  gave  ex- 
perimental lectures  in  London.  William  Whiston  gave  some, 
and  Francis  Hauksbee10  made  the  experiments.  The  prospec- 
tus, as  we  should  now  call  it,  is  extant,  a  quarto  tract  of 
plates  and  descriptions,  without  date.  Whiston,  in  his  life, 

physics,  and  published  a  memoir  on  A  machine  for  finding  the  roots 
of  equations  universally  (1770). 

8  It  is  always  difficult  to  sanction  this  spelling  of  the  name  of  this 
Jesuit  father  who  is  so  often  mentioned  in  the  analytic  treatment  of 
conies.  He  was  born  in  Ragusa  in  1711,  and  the  original  spelling  was 
RuSer  Josip  Boskovic.  When  he  went  to  live  in  Italy,  as  professor 
of  mathematics  at  Rome  (1740)  and  at  Pavia,  the  name  was  spelled 
Ruggiero  Giuseppe  Boscovich,  although  Boscovicci  would  seem  to 
a  foreigner  more  natural.  His  astronomical  work  was  notable,  and 
in  his  De  maculis  solaribus  (1736)  there  is  the  first  determination 
of  the  equator  of  a  planet  by  observing  the  motion  of  spots  on  its 
surface.  Boscovich  came  near  having  some  contact  with  America, 
for  he  was  delegated  to  observe  in  California  the  transit  of  Venus 
in  1755,  being  prevented  by  the  dissolution  of  his  order  just  at  that 
time.  He  died  in  1787,  at  Milan. 

*  James  Granger  (1723-1776)  who  wrote  the  Biographical  His- 
tory of  England,  London,  1769.  His  collection  of  prints  was  re- 
markable, numbering  some  fourteen  thousand. 

10  He  was  curator  of  experiments  for  the  Royal  Society.  He 
wrote  a  large  number  of  books  and  monographs  on  physics.  He 
died  about  1713. 


FALLACIES  IN  A  THEORY  OF  ANNUITIES.  157 

gives  1714  as  the  first  date  of  publication,  and  therefore, 
no  doubt,  of  the  lectures.  Desaguliers  removed  to  London 
soon  after  1712,  and  commenced  his  lectures  soon  after  that. 
It  will  be  rather  a  nice  point  to  settle  which  lectured  first; 
probabilities  seem  to  go  in  favor  of  Whiston. 

FALLACIES  IN  A  THEORY  OF  ANNUITIES. 

An  Essay  to  ascertain  the  value  of  leases,  and  annuities  for 
years  and  lives.  By  W[eyman]  L[ee].  London,  1737,  8vo. 

A  valuation  of  Annuities  and  Leases  certain,  for  a  single  life. 
By  Weyman  Lee,  Esq.  of  the  Inner  Temple.  London,  1751, 
8vo.  Third  edition,  1773. 

.  Every  branch  of  exact  science  has  its  paradoxer.  The 
world  at  large  cannot  tell  with  certainty  who  is  right  in 
such  questions  as  squaring  the  circle,  etc.  Mr.  Weyman 
Lee1  was  the  assailant  of  what  all  who  had  studied  called 
demonstration  in  the  question  of  annuities.  He  can  be  ex- 
posed to  the  world :  for  his  error  arose  out  of  his  not  being 
able  to  see  that  the  whole  is  the  sum  of  all  its  parts. 

By  an  annuity,  say  of  £100,  now  bought,  is  meant  that 
the  buyer  is  to  have  for  his  money  £100  in  a  year,  if  he  be 
then  alive,  £100  at  the  end  of  two  years,  if  then  alive,  and  so 
on.  It  is  clear  that  he  would  buy  a  life  annuity  if  he  should 
buy  the  first  £100  in  one  office,  the  second  in  another,  and 
so  on.  All  the  difference  between  buying  the  whole  from 
one  office  and  buying  all  the  separate  contingent  payments 
at  different  offices,  is  immaterial  to  calculation.  Mr.  Lee 
would  have  agreed  with  the  rest  of  the  world  about  the 
payments  to  be  made  to  the  several  different  offices,  in  con- 
sideration of  their  several  contracts:  but  he  differed  from 
every  one  else  about  the  sum  to  be  paid  to  one  office.  He 
contended  that  the  way  to  value  an  annuity  is  to  find  out 
the  term  of  years  which  the  individual  has  an  even  chance 
of  surviving,  and  to  charge  for  the  life  annuity  the  value  of 
an  annuity  certain  for  that  term. 

1Lee  seems  to  have  made  no  impression  on  biographers. 


158  A  BUDGET  OF   PARADOXES. 

It  is  very  common  to  say  that  Lee  took  the  average  life, 
or  expectation,  as  it  is  wrongly  called,  for  his  term:  and 
this  I  have  done  myself,  taking  the  common  story.  Having 
exposed  the  absurdity  of  this  second  supposition,  taking  it 
for  Lee's,  in  my  Formal  Logic,2  I  will  now  do  the  same  with 
the  first. 

A  mathematical  truth  is  true  in  its  extreme  cases.  Lee's 
principle  is  that  an  annuity  on  a  life  is  the  annuity  made 
certain  for  the  term  within  which  it  is  an  even  chance  the 
life  drops.  If,  then,  of  a  thousand  persons,  500  be  sure  to 
die  within  a  year,  and  the  other  500  be  immortal,  Lee's 
price  of  an  annuity  to  any  one  of  these  persons  is  the 
present  value  of  one  payment:  for  one  year  is  the  term 
which  each  one  has  an  even  chance  of  surviving  and  not 
surviving.  But  the  true  value  is  obviously  half  that  of  a 
perpetual  annuity:  so  that  at  5  percent  Lee's  rule  would 
give  less  than  the  tenth  of  the  true  value.  It  must  be  said 
for  the  poor  circle-squarers,  that  they  never  err  so  much 
as  this. 

Lee  would  have  said,  if  alive,  that  I  have  put  an  extreme 
case:  but  any  universal  truth  is  true  in  its  extreme  cases. 
It  is  not  fair  to  bring  forward  an  extreme  case  against  a 
person  who  is  speaking  as  of  usual  occurrences:  but  it  is 
quite  fair  when,  as  frequently  happens,  the  proposer  insists 
upon  a  perfectly  general  acceptance  of  his  assertion.  And 
yet  many  who  go  the  whole  hog  protest  against  being  tickled 
with  the  tail.  Counsel  in  court  are  good  instances :  they  are 
paradoxers  by  trade.  June  13,  1849,  at  Hertford,  there  was 
an  action  about  a  ship,  insured  against  a  total  loss:  some 
planks  were  saved,  and  the  underwriters  refused  to  pay. 
Mr.  Z.  (for  deft.)  "There  can  be  no  degrees  of  totality;  and 
some  timbers  were  saved." — L.  C.  B.  "Then  if  the  vessel 
were  burned  to  the  water's  edge,  and  some  rope  saved  in 
the  boat,  there  would  be  no  total  loss." — Mr.  Z.  "This  is 
putting  a  very  extreme  case." — L.  C.  B.  "The  argument 

2  This  work  appeared  at  London  in  1852. 


MONTUCLA'S  WORK  ON  THE  QUADRATURE.  159 

would  go  that  length."  What  would  Judge  Z. — as  he  now 
is — say  to  the  extreme  case  beginning  somewhere  between 
six  planks  and  a  bit  of  rope? 

MONTUCLA'S   WORK   ON   THE   QUADRATURE. 
Histoire   des   recherches    sur   la   quadrature    du   cercle. . .  .avec 
une  addition  concernant  les  problemes  de  la  duplication  du 
cube  et  de  la  trisection  de  Tangle.     Paris,  1754,  I2mo.     [By 
Montucla.] 

This  is  the  history  of  the  subject.1  It  was  a  little  episode 
to  the  great  history  of  mathematics  by  Montucla,  of  which 
the  first  edition  appeared  in  1758.  There  was  much  addition 
at  the  end  of  the  fourth  volume  of  the  second  edition ;  this 
is  clearly  by  Montucla,  though  the  bulk  of  the  volume  is  put  to- 
gether, with  help  from  Montucla's  papers,  by  Lalande.2  There 
is  also  a  second  edition  of  the  history  of  the  quadrature, 
Paris,  1831,  8vo,  edited,  I  think,  by  Lacroix;  of  which  it 
is  the  great  fault  that  it  makes  hardly  any  use  of  the  addi- 
tional matter  just  mentioned. 

Montucla  is  an  admirable  historian  when  he  is  writing 
from  his  own  direct  knowledge :  it  is  a  sad  pity  that  he  did 
not  tell  us  when  he  was  depending  on  others.  We  are  not 
to  trust  a  quarter  of  his  book,  and  we  must  read  many 
other  books  to  know  which  quarter.  The  fault  is  common 
enough,  but  Montucla's  good  three-quarters  is  so  good  that 
the  fault  is  greater  in  him  than  in  most  others:  I  mean  the 
fault  of  not  acknowledging;  for  an  historian  cannot  read 
everything.  But  it  must  be  said  that  mankind  give  little 
encouragement  to  candor  on  this  point.  Hallam,  in  his 

1  Of  course  this  is  no  longer  true.  The  most  scholarly  work 
to-day  is  that  of  Rudio,  Archimedes,  Huygens,  Lambert,  Legendre, 
vier  Abhandlungen  uber  die  Kreismessung. . .  .mit  einer  Uebersicht 
iibcr  die  Geschichte  des  Problems  von  der  Quadratur  des  Zirkels, 
von  den  'dltesten  Zeiten  bis  auf  unsere  Tage,  Leipsic,  1892. 

2 Joseph  Jerome  le  Francois  de  Lalande  (1732-1807),  professor 
of  astronomy  in  the  College  de  France  (1753)  and  director  of  the 
Paris  Observatory  (1761).  His  writings  on  astronomy  and  his  Bib- 
liographic astronomique,  avec  I'histoire  de  I'astronomie  depuis  1781 
jusqu'en  1802  (Paris,  1803)  are  well  known. 


160  A  BUDGET  OF  PARADOXES. 

History  of  Literature,  states  with  his  own  usual  instinct 
of  honesty  every  case  in  which  he  depends  upon  others : 
Montucla  does  not.  And  what  is  the  consequence? — Mon- 
tucla  is  trusted,  and  believed  in,  and  cried  up  in  the  bulk ; 
while  the  smallest  talker  can  lament  that  Hallam  should 
be  so  unequal  and  apt  to  depend  on  others,  without  remem- 
bering to  mention  that  Hallam  himself  gives  the  informa- 
tion. As  to  a  universal  history  of  any  great  subject  being 
written  entirely  upon  primary  knowledge,  it  is  a  thing  of 
which  the  possibility  is  not  yet  proved  by  an  example.  De- 
lambre  attempted  it  with  astronomy,  and  was  removed  by 
death  before  it  was  finished,3  to  say  nothing  of  the  gaps 
he  left. 

Montucla  was  nothing  of  a  bibliographer,  and  his  de- 
scriptions of  books  in  the  first  edition  were  insufficient.  The 
Abbe  Rive4  fell  foul  of  him,  and  as  the  phrase  is,  gave  it 
him.  Montucla  took  it  with  great  good  humor,  tried  to 
mend,  and,  in  his  second  edition,  wished  his  critic  had  lived 
to  see  the  vernis  de  bibliographe  which  he  had  given  himself. 

I  have  seen  Montucla  set  down  as  an  esprit  fort,  more 
than  once:  wrongly,  I  think.  When  he  mentions  Barrow'ss 
address  to  the  Almighty,  he  adds,  "On  voit,  au  reste,  par  la, 
que  Barrow  etoit  un  pauvre  philosophe;  car  il  croyait  en 
rimmortalite  de  Tame,  et  en  une  Divinite  autre  que  la  nature 


8  De  Morgan  refers  to  his  Histoire  de  I' Astronomic  au  i8e  siccle, 
which  appeared  in  1827,  five  years  after  Delambre's  death.  Jean 
Baptiste  Joseph  Delambre  (1749-1822)  was  a  pupil  of  and  a  collabo- 
rator with  Lalande,  following  his  master  as  professor  of  astronomy 
in  the  College  de  France.  His  work  on  the  measurements  for  the 
metric  system  is  well  known,  and  his  four  histories  of  astronomy, 
ancienne  (1817),  au  moyen  age  (1819),  moderne  (1821),  and  au  i8e 
siecle  (posthumous,  1827)  are  highly  esteemed. 

4  Jean- Joseph  Rive  (1730-1792),  a  priest  who  left  his  cure  under 
grave  charges,  and  a  quarrelsome  character.     His  attack  on  Mon- 
tucla was  a  case  of  the  pot  calling  the  kettle  black ;  for  while  he  was 
a  brilliant  writer  he  was  a  careless  bibliographer. 

5  Isaac  Barrow  (1630-1677)  was  quite  as  well  known  as  a  theo- 
logian as  he  was  from  his  Lucasian  professorship  of  mathematics  at 
Cambridge. 


MONTUCLA'S  WORK  ON  THE  QUADRATURE.  161 

universelle."0  This  is  irony,  not  an  expression  of  opinion. 
In  the  book  of  mathematical  recreations  which  Montucla 
constructed  upon  that  of  Ozanam,7  and  Ozanam  upon  that 
of  Van  Etten,8  now  best  known  in  England  by  Hutton's 
similar  treatment  of  Montucla,  there  is  an  amusing  chapter 
on  the  quadrators.  Montucla  refers  to  his  own  anonymous 
book  of  1754  as  a  curious  book  published  by  Jombert.9  He 
seems  to  have  been  a  little  ashamed  of  writing  about  circle- 
squarers :  what  a  slap  on  the  face  for  an  unborn  Budgeteer ! 
Montucla  says,  speaking  of  France,  that  he  finds  three 
notions  prevalent  among  the  cyclometers:  (1)  that  there 
is  a  large  reward  offered  for  success;  (2)  that  the  longitude 
problem  depends  on  that  success;  (3)  that  the  solution  is 
the  great  end  and  object  of  geometry.  The  same  three 

8  "Besides  we  can  see  by  this  that  Barrow  was  a  poor  philosopher ; 
for  he  believed  in  the  immortality  of  the  soul  and  in  a  Divinity 
other  than  universal  nature." 

TThe  Recreations  mathematiques  et  physiques  (Paris,  1694)  of 
Jacques  Ozanam  (1640-1717)  is  a  work  that  is  still  highly  esteemed. 
Among  various  other  works  he  wrote  a  Dictionnaire  mathematique 
ou  Idee  generate  des  mathematiques  (1690)  that  was  not  without 
merit.  The  Recreations  went  through  numerous  editions  (Paris, 
1694,  1696,  1741,  1750,  1770,  1778,  and  the  Montucla  edition  of  1790; 
London,  1708,  the  Montucla-Hutton  edition  of  1803  and  the  Riddle 
edition  of  1840;  Dublin,  1790). 

8Hendryk  van  Etten,  the  nom  de  plume  of  Jean  Leurechon 
(1591-1670),  rector  of  the  Jesuit  college  at  Bar,  and  professor  of 
philosophy  and  mathematics.  He  wrote  on  astronomy  (1619)  and 
horology  (1616),  and  is  known  for  his  Selecta  Propositipnes  in  tota 
sparsim  mathematica  pulcherrime  propositae  in  solemni  festo  SS. 
Ignatii  et  Francesci  Xaverii,  1622.  The  book  to  which  De  Morgan 
refers  is  his  Recreation  mathematicque,  composee  de  plusieurs  pro- 
blcmes  plaisants  et  facetieux,  Lyons,  1627,  with  an  edition  at  Pont- 
a-Mousson,  1629.  There  were  English  editions  published  at  London 
in  1633,  1653,  and  1674,  and  Dutch  editions  in  1662  and  1672. 

I  do  not  understand  how  De  Morgan  happened  to  miss  own- 
ing the  work  by  Claude  Caspar  Bachet  de  Meziriac  (1581-1638), 
Problcmes  plaisans  et  detectable*,  which  appeared  at  Lyons  in  1612, 
8vo,  with  a  second  edition  in  1624.  There  was  a  fifth  edition  pub- 
lished at  Paris  in  1884. 

9  His  title  page  closes  with  "Paris,  Chez  Ch.  Ant.  Jombert 

M.DCC.LIV." 

This  was  Charles- Antoine  Jombert  (1712-1784),  a  printer  and 
bookseller  with  some  taste  for  painting  and  architecture.  He  wrote 
several  works  and  edited  a  number  of  early  treatises. 


162  A  BUDGET  OF   PARADOXES.- 

notions  are  equally  prevalent  among  the  same  class  in  Eng- 
land. No  reward  has  ever  been  offered  by  the  government 
of  either  country.  The  longitude  problem  in  no  way  de- 
pends upon  perfect  solution;  existing  approximations  are 
sufficient  to  a  point  of  accuracy  far  beyond  what  can  be 
wanted.10  And  geometry,  content  with  what  exists,  has  long 
passed  on  to  other  matters.  Sometimes  a  cyclometer  per- 
suades a  skipper  who  has  made  land  in  the  wrong  place 
that  the  astronomers  are  in  fault,  for  using  a  wrong  measure 
of  the  circle;  and  the  skipper  thinks  it  a  very  comfortable 
solution !  And  this  is  the  utmost  that  the  problem  ever  has 
to  do  with  longitude. 

ANTINEWTONIANISMUS. 

Antinewtonianismus.1     By  Caelestino  Cominale,2  M.D.     Naples, 
1754  and  1756,  2  vols.  4to. 

The  first  volume  upsets  the  theory  of  light;  the  second 
vacuum,  vis  inertise,  gravitation,  and  attraction.  I  confess 
I  never  attempted  these  big  Latin  volumes,  numbering  450 
closely-printed  quarto  pages.  The  man  who  slays  Newton 
in  a  pamphlet  is  the  man  for  me.  But  I  will  lend  them  to 
anybody  who  will  give  security,  himself  in  £500,  and  two 
sureties  in  £250  each,  that  he  will  read  them  through,  and 
give  a  full  abstract;  and  I  will  not  exact  security  for  their 
return.  I  have  never  seen  any  mention  of  this  book :  it  has 
a  printer,  but  not  a  publisher,  as  happens  with  so  many  un- 
recorded books. 

10  The  late  Professor  Newcomb  made  the  matter  plain  even  to 
the  non-mathematical  mind,  when  he  said  that  "ten  decimal  places 
are  sufficient  to  give  the  circumference  of  the  earth  to  the  fraction 
of  an  inch,  and  thirty  decimal  places  would  give  the  circumference 
of  the  whole  visible  universe  to  a  quantity  imperceptible  with  the 
most  powerful  microscope." 

1  Antinewtonianismi  pars  prima,  in  qua  Newtoni  de  coloribus 
systema  ex  propriis  principiis  geometrice  evertitur,  et  nova  de  colori- 
bus theoria  luculentissimis  experiments  demonstrantur . ..  .Naples, 
1754'>  pars  secunda,  Naples,  1756. 

2Celestino  Cominale  (1722-1785)  was  professor  of  medicine  at 
the  University  of  Naples. 


OFFICIAL  BLOW  TO  CIRCLE  SQUARERS.  163 


OFFICIAL  BLOW  TO  CIRCLE  SQUARERS. 

1755.  The  French  Academy  of  Sciences  came  to  the 
determination  not  to  examine  any  more  quadratures  or 
kindred  problems.  This  was  the  consequence,  no  doubt, 
of  the  publication  of  Montucla's  book:  the  time  was  well 
chosen ;  for  that  book  was  a  full  justification  of  the  resolu- 
tion. The  Royal  Society  followed  the  same  course,  I  be- 
lieve, a  few  years  afterwards.  When  our  Board  of  Longi- 
tude was  in  existence,  most  of  its  time  was  consumed  in 
listening  to  schemes,  many  of  which  included  the  quadrature 
of  the  circle.  It  is  certain  that  many  quadrators  have  im- 
agined the  longitude  problem  to  be  connected  with  theirs: 
and  no  doubt  the  notion  of  a  reward  offered  by  Government 
for  a  true  quadrature  is  a  result  of  the  reward  offered  for 
the  longitude.  Let  it  also  be  noted  that  this  longitude  re- 
ward was  not  a  premium  upon  excogitation  of  a  mysterious 
difficulty.  The  legislature  was  made  to  know  that  the 
rational  hopes  of  the  problem  were  centered  in  the  improve- 
ment of  the  lunar  tables  and  the  improvement  of  chronom- 
eters. To  these  objects  alone,  and  by  name,  the  offer  was 
directed:  several  persons  gained  rewards  for  both;  and  the 
offer  was  finally  repealed. 

AN  INTERESTING  HOAX. 

Fundamentalis  Figura  Geometrica,  primas  tantum  lineas  circuli 
quadrature  possibilitatis  ostendens.  By  Niels  Erichsen  (Nico- 
laus  Ericius),  shipbuilder,  of  Copenhagen.  Copenhagen,  1755, 
I2mo. 

This  was  a  gift  from  my  oldest  friend  who  was  not  a 
relative,  Dr.  Samuel  Maitland  of  the  "Dark  Ages."1  He 
found  it  among  his  books,  and  could  not  imagine  how  he 
came  by  it:  I  could  have  told  him.  He  once  collected 
interpretations  of  the  Apocalypse:  and  auction  lots  of  such 

1  The  work  appeared  in  the  years  from  1844  to  1849. 


164  A  BUDGET  OF  PARADOXES. 

books  often  contain  quadratures.  The  wonder  is  he  never 
found  more  than  one. 

The  quadrature  is  not  worth  notice.  Erichsen  is  the  only 
squarer  I  have  met  with  who  has  distinctly  asserted  the  par- 
ticulars of  that  reward  which  has  been  so  frequently  thought 
to  have  been  offered  in  England.  He  says  that  in  1747  the 
Royal  Society  on  the  2d  of  June,  offered  to  give  a  large  re- 
ward for  the  quadrature  of  the  circle  and  a  true  explanation 
of  magnetism,  in  addition  to  £30,000  previously  promised  for 
the  same.  I  need  hardly  say  that  the  Royal  Society  had 
not  £30,000  at  that  time,  and  would  not,  if  it  had  had  such 
a  sum,  have  spent  it  on  the  circle,  nor  on  magnetic  theory; 
nor  would  it  have  coupled  the  two  things.  On  this  book, 
see  Notes  and  Queries,  1st  S.,  xii,  306.  Perhaps  Erichsen 
meant  that  the  £30,000  had  been  promised  by  the  Govern- 
ment, and  the  addition  by  the  Royal  Society. 

October  8,  1866.  I  receive  a  letter  from  a  cyclometer 
who  understands  that  a  reward  is  offered  to  any  one  who 
will  square  the  circle,  and  that  all  competitors  are  to  send 
their  plans  to  me.  The  hoaxers  have  not  yet  failed  out  of 
the  land. 

TWO  JESUIT  CONTRIBUTIONS. 

Theoria  Philosophise  Naturalis  redacta  ad  unicam  legem  virium 
in  natura  existentium.  Editio  Veneta  prima.  By  Roger  Joseph 
Boscovich.  Venice,  1763,  4to. 

The  first  edition  is  said  to  be  of  Vienna,  1758.1  This 
is  a  celebrated  work  on  the  molecular  theory  of  matter, 
grounded  on  the  hypothesis  of  spheres  of  alternate  attrac- 
tion and  repulsion.  Boscovich  was  a  Jesuit  of  varied  pur- 
suit. During  his  measurement  of  a  degree  of  the  meridian, 
while  on  horseback  or  waiting  for  his  observations,  he  com- 
posed a  Latin  poem  of  about  five  thousand  verses  on  eclipses, 

1  There  was  a  Vienna  edition  in  1758,  4to,  and  another  in  1759, 
4to.  This  edition  is  described  on  the  title  page  as  Editio  Veneta 
prima  ipso  auctore  praesente,  et  corrigente. 


TWO   JESUIT   CONTRIBUTIONS.  165 

[with  notes,  which  he  dedicated  to  the  Royal  Society:  De 
\Solis  et  LuncE  defectibus,2  London,   Millar  and  Dodsley, 
1760,  4to. 

Traite  de  paix  entre  Des  Cartes  et  Newton,  precede  des  vies 
litteraires  de  ces  deux  chefs  de  la  physique  moderne. .  .By  Aime 
Henri  Paulian.3  Avignon,  1763,  I2mo. 

I  have  had  these  books  for  many  years  without  feeling 
the  least  desire  to  see  how  a  lettered  Jesuit  would  atone 
Descartes  and  Newton.  On  looking  at  my  two  volumes,  I 
find  that  one  contains  nothing  but  the  literary  life  of  Des- 
cartes; the  other  nothing  but  the  literary  life  of  New- 
ton. The  preface  indicates  more:  and  Watt  mentions  three 
volumes.4  I  dare  say  the  first  two  contain  all  that  is  valu- 
able. On  looking  more  attentively  at  the  two  volumes,  I 
find  them  both  readable  and  instructive;  the  account  of 
Newton  is  far  above  that  of  Voltaire,  but  not  so  popular. 
But  he  should  not  have  said  that  Newton's  family  came  from 
Newton  in  Ireland.  Sir  Rowland  Hill  gives  fourteen  New- 
tons  in  Ireland  :S  twice  the  number  of  the  cities  that  con- 
tended for  the  birth  of  Homer  may  now  contend  for  the 
origin  of  Newton,  on  the  word  of  Father  Paulian. 

Philosophical  Essays,  in  three  parts.    By  R.  Lovett,  Lay  Clerk 

of  the  Cathedral  Church  of  Worcester.    Worcester,  1766,  8vo. 

The  Electrical  Philosopher:  containing  a  new  system  of  physics 

8  The  first  edition  was  entitled  De  solis  ac  lunae  defectibus  libri 
V.  P.  Rogerii  Jose  phi  Boscovich. . . .  cum  ejusdem  auctoris  adnota- 
tionibus,  London,  1760.  It  also  appeared  in  Venice  in  1761,  and  in 
French  translation  by  the  Abbe  de  Baruel  in  1779,  and  was  a  work 
of  considerable  influence. 

Paulian  (1722-1802)  was  professor  of  physics  at  the  Jesuit 
college  at  Avignon.  He  wrote  several  works,  the  most  popular  of 
which,  the  Dictionnaire  de  physique  (Avignon,  1761),  went  through 
nine  editions  by  1789. 

4  This  is  correct. 

5  Probably  referring  to  the  fact  that  Hill  (1795-1879),  who  had 
done  so  much  for  postal  reform,  was  secretary  to  the  postmaster 
general    (1846),  and  his  name  was  a  synonym  for  the  post  office 
directory. 


166  A  BUDGET  OF  PARADOXES. 

founded  upon  the  principle  of  an  universal   Plenum  of  ele- 
mentary fire By  R.  Lovett,  Worcester,  1774,  8vo. 

Mr.  Lovett6  was  one  of  those  ether  philosophers  who 
bring  in  elastic  fluid  as  an  explanation  by  imposition  of 
words,  without  deducing  any  one  phenomenon  from  what 
we  know  of  it.  And  yet  he  says  that  attraction  has  received 
no  support  from  geometry;  though  geometry,  applied  to 
a  particular  law  of  attraction,  had  shown  how  to  predict  the 
motions  of  the  bodies  of  the  solar  system.  He,  and  many 
of  his  stamp,  have  not  the  least  idea  of  the  confirmation 
of  a  theory  by  accordance  of  deduced  results  with  observa- 
tion posterior  to  the  theory. 

BAILLY'S  EXAGGERATED  VIEW  OF  ASTRONOMY. 

Lettres  sur  1'Atlantide  de  Platon,  et  sur  1'ancien  Histoire  de 
1'Asie,  pour  servir  de  suite  aux  lettres  sur  1'origine  des  Sci- 
ences, adressees  a  M.  de  Voltaire,  par  M.  Bailly.1  London  and 
Paris,  1779,  8vo. 

I  might  enter  here  all  Bailly's  histories  of  astronomy.2 
The  paradox  which  runs  through  them  all  more  or  less,  is 
the  doctrine  that  astronomy  is  of  immense  antiquity,  com- 
ing from  some  forgotten  source,  probably  the  drowned  island 
of  Plato,  peopled  by  a  race  whom  Bailly  makes,  as  has 

'Richard  Lovett  (1692-1780)  was  a  good  deal  of  a  charlatan. 
He  claimed  to  have  studied  electrical  phenomena,  and  in  1758  ad- 
vertised that  he  could  effect  marvelous  cures,  especially  of  sore 
throat,  by  means  of  electricity.  Before  publishing  the  works  men- 
tioned by  De  Morgan  he  had  issued  others  of  similar  character, 
including  The  Subtile  Medium  proved  (London,  1756)  and  The 
Reviewers  Reviewed  (London,  1760). 

1Jean  Sylvain  Bailly  (1736-1793),  member  of  the  Academic 
francaise  and  of  the  Academic  des  sciences,  first  deputy  elected  to 
represent  Paris  in  the  Etats-generaux  (1789),  president  of  the  first 
National  Assembly,  and  mayor  of  Paris  (1789-1791).  For  his  vigor 
as  mayor  in  keeping  the  peace,  and  for  his  manly  defence  of  the 
Queen,  he  was  guillotined.  He  was  an  astronomer  of  ability,  but 
is  best  known  for  his  histories  of  the  science. 

'These  were  the  Histoire  de  T  Astronomic  ancienne  (1775),  His- 
toire de  V Astronomic  moderne  (1778-1783),  Histoire  de  I'Astronomie 
indienne  et  orientale  (1787),  and  Lettres  sur  ? origin*  des  peuples  de 
I'Asie  (1775). 


SAINT-MARTIN  ON   ERRORS  AND  TRUTH.  167 

been  said,  to  teach  us  everything  except  their  existence  and 
their  name.  These  books,  the  first  scientific  histories  which 
belong  to  readable  literature,  made  a  great  impression  by 
power  of  style:  Delambre  created  a  strong  reaction,  of  in- 
jurious amount,  in  favor  of  history  founded  on  contemporary 
documents,  which  early  astronomy  cannot  furnish.  These 
letters  are  addressed  to  Voltaire,  and  continue  the  discussion. 
There  is  one  letter  of  Voltaire,  being  the  fourth,  dated  Feb. 
27,  1777,  and  signed  "le  vieux  malade  de  Ferney,  V.  puer 
centum  annorum."3  Then  begin  Bailly's  letters,  from  Jan- 
uary 16  to  May  12,  1778.  From  some  ambiguous  expres- 
sions in  the  Preface,  it  would  seem  that  these  are  fictitious 
letters,  supposed  to  be  addressed  to  Voltaire  at  their  dates. 
Voltaire  went  to  Paris  February  10,  1778,  and  died  there 
May  30.  Nearly  all  this  interval  was  his  closing  scene,  and 
it  is  very  unlikely  that  Bailly  would  have  troubled  him  with 
these  letters.* 

An  inquiry  into  the  cause  of  motion,  or  a  general  theory  of 
physics.  By  S.  Miller.  London,  1781,  4to. 

Newton  all  wrong:  matter  consists  of  two  kinds  of  par- 
ticles, one  inert,  the  other  elastic  and  capable  of  expanding 
themselves  ad  infinitum. 

SAINT-MARTIN   ON   ERRORS   AND   TRUTH. 

Des  Erreurs  et  de  la  Verite,  ou  les  hommes  rappeles  au  prih- 
cipe  universel  de  la  science;  ouvrage  dans  lequel,  en  faisant 
remarquer  aux  observateurs  1'incertitude  de  leurs  recherches, 
et  leurs  meprises  continuelles,  on  leur  indique  la  route  qu'ils 
auroient  du  suivre,  pour  acquerir  1'evidence  physique  sur 
Torigine  du  bien  et  du  mal,  sur  1'homme,  sur  la  nature  mate- 
rielle,  et  la  nature  sacree;  sur  la  base  des  gouvernements 

"The  sick  old  man  of  Ferney,  V.,  a  boy  of  a  hundred  years." 
Voltaire  was  born  in  1694,  and  hence  was  eighty-three  at  this  time. 

4  In  Palmezeaux's  Vie  de  Bailly,  in  Bailly's  Ouvrage  Posthume 
(1810),  M.  de  Sales  is  quoted  as  saying  that  the  Lettres  sur  I'Atlan- 
tide  were  sent  to  Voltaire  and  that  the  latter  did  not  approve  of  the 
theory  set  forth. 


168  A  BUDGET  OF  PARADOXES. 

politiques,  sur  1'autorite  des  souverains,  sur  la  justice  civile 
et  criminelle,  sur  les  sciences,  les  langues,  et  les  arts.  Par 
un  Ph....  Inc A  Edimbourg.  I782.1  Two  vols.  8vo. 

This  is  the  famous  work  of  Louis  Claude  de  Saint- 
Martin2  (1743-1803),  for  whose  other  works,  vagaries  in- 
cluded, the  reader  must  look  elsewhere :  among  other  things, 
he  was  a  translator  of  Jacob  Behmen.3  The  title  promises 
much,  and  the  writer  has  smart  thoughts  now  and  then ; 
but  the  whole  is  the  wearisome  omniscience  of  the  author's 
day  and  country,  which  no  reader  of  our  time  can  tolerate. 
Not  that  we  dislike  omniscience ;  but  we  have  it  of  our  own 
country,  both  home-made  and  imported ;  and  fashions  vary. 
But  surely  there  can  be  but  one  omniscience?  Must  a  man 
have  but  one  wife?  Nay,  may  not  a  man  have  a  new  wife 
while  the  old  one  is  living?  There  was  a  famous  instru- 
mental professor  forty  years  ago,  who  presented  a  friend 

to  Madame .    The  friend  started,  and  looked  surprised ; 

for,  not  many  weeks  before,  he  had  been  presented  to  another 
lady,  with  the  same  title,  at  Paris.  The  musician  observed 
his  surprise,  and  quietly  said,  "Celle-ci  est  Madame  - 
de  Londres."  In  like  manner  we  have  a  London  omniscience 
now  current,  which  would  make  any  one  start  who  only 
knew  the  old  French  article. 

The  book  was  printed  at  Lyons,  but  it  was  a  trick  of 
French  authors  to  pretend  to  be  afraid  of  prosecution:  it 

1The  British  Museum  catalogue  gives  two  editions,  1781  and 
1782. 

a  A  mystic  and  a  spiritualist.  His  chief  work  was  the  one  men- 
tioned here. 

3  Jacob  Behmen,  or  Bohme  (1575-1624),  known  as  "the  German 
theosophist,"  was  founder  of  the  sect  of  Boehmists,  a  cult  allied 
to  the  Swedenborgians.  He  was  given  to  the  study  of  alchemy, 
and  brought  the  vocabulary  of  the  science  into  his  mystic  writings. 
His  sect  was  revived  in  England  in  the  eighteenth  century  through 
the  efforts  of  William  Law.  Saint-Martin  translated  into  French 
two  of  his  Latin  works  under  the  titles  L'Aurore  naissante,  ou  la 
Racine  de  la  philosophie  (1800),  and  Les  trois  principes  de  V essence 
divine  (1802).  The  originals  had  appeared  nearly  two  hundred 
years  earlier,— Aurora  in  1612,  and  De  tribus  principiis  in  1619. 


SAINT-MARTIN  ON  ERRORS  AND  TRUTH.  169 

made  a  book  look  wicked-like  to  have  a  feigned  place  of 
printing,  and  stimulated  readers.  A  Government  which 
had  undergone  Voltaire  would  never  have  drawn  its  sword 
upon  quiet  Saint-Martin.  To  make  himself  look  still  worse, 
he  was  only  ph[ilosophe]  Inc. . . .,  which  is  generally  read 
Inconnu?  but  sometimes  Incredule:*  most  likely  the  am- 
biguity was  intended.  There  is  an  awful  paradox  about  the 
book,  which  explains,  in  part,  its  leaden  sameness.  It  is  all 
about  I'homme,  I'homme,  I'homme,6  except  as  much  as  treats 
of  les  hommes,  les  hommes,  les  hommes  ;7  but  not  one  single 
man  is  mentioned  by  name  in  its  500  pages.  It  reminds 
one  of 

"Water,  water  everywhere, 
And  not  a  drop  to  drink." 

Not  one  opinion  of  any  other  man  is  referred  to,  in  the  way 
of  agreement  or  of  opposition.  Not  even  a  town  is  men- 
tioned: there  is  nothing  which  brings  a  capital  letter  into 
the  middle  of  a  sentence,  except,  by  the  rarest  accident, 
such  a  personification  as  Justice.  A  likely  book  to  want  an 
Edimbourg  godfather ! 

Saint-Martin  is  great  in  mathematics.  The  number  four 
essentially  belongs  to  straight  lines,  and  nine  to  curves. 
The  object  of  a  straight  line  is  to  perpetuate  ad  infinitum 
the  production  of  a  point  from  which  it  emanates.  A  circle 
O  bounds  the  production  of  all  its  radii,  tends  to  destroy 
them,  and  is  in  some  sort  their  enemy.  How  is  it  possible 
that  things  so  distinct  should  not  be  distinguished  in  their 
number  as  well  as  in  their  action?  If  this  important  ob- 
servation had  been  made  earlier,  immense  trouble  would 
have  been  saved  to  the  mathematicians,  who  would  have 
been  prevented  from  searching  for  a  common  measure  to 
lines  which  have  nothing  in  common.  But,  though  all 
straight  lines  have  the  number  four,  it  must  not  be  supposed 
that  they  are  all  equal,  for  a  line  is  the  result  of  its  law  and 

'"Unknown."  ""Skeptical." 

8  "Man,  man,  man."  7  "Men,  men,  men." 


170  A  BUDGET  OF  PARADOXES. 

its  number;  but  though  both  are  the  same  for  all  lines  of 
a  sort,  they  act  differently,  as  to  force,  energy,  and  duration, 
in  different  individuals ;  which  explains  all  differences  of 
length,  etc.  I  congratulate  the  reader  who  understands  this ; 
and  I  do  not  pity  the  one  who  does  not. 

Saint-Martin  and  his  works  are  now  as  completely  for- 
gotten as  if  they  had  never  been  born,  except  so  far  as  this, 
that  some  one  may  take  up  one  of  the  works  as  of  heretical 
character,  and  lay  it  down  in  disappointment,  with  the  re- 
flection that  it  is  as  dull  as  orthodoxy.  For  a  person  who 
was  once  in  some  vogue,  it  would  be  difficult  to  pick  out 
a  more  fossil  writer,  from  Aa  to  Zypoeus,  except, — though 
it  is  unusual  for  (, — )  to  represent  an  interval  of  more 
than  a  year — his  unknown  opponent.  This  opponent,  in  the 
very  year  of  the  Des  Erreurs. . .  .published  a  book  in  two 
parts  with  the  same  fictitious  place  of  printing; 

Tableau  Nature!  des  Rapports  qui  existent  entre  Dieu,  I'Homme, 
et  1'Univers.    A  Edimbourg,  1782,  8vo.8 

There  is  a  motto  from  the  Des  Erreurs  itself,  "Expliquer 
les  choses  par  I'homme,  et  non  1'homme  par  les  choses.  Des 

Erreurs  et  de  la  Verite,  par  un  PH INC ,  p.  9."9 

This  work  is  set  down  in  various  catalogues  and  biographies 

as  written  by  the  PH INC himself.    But  it  is  not 

usual  for  a  writer  to  publish  two  works  in  the  same  year, 
one  of  which  takes  a  motto  from  the  other.  And  the  second 
work  is  profuse  in  capitals  and  italics,  and  uses  Hebrew 
learning:  its  style  differs  much  from  the  first  work.  The 
first  work  sets  out  from  man,  and  has  nothing  to  do  with 
God:  the  second  is  religious  and  raps  the  knuckles  of  the 
first  as  follows:  "Si  nous  voulons  nous  preserver  de  toutes 

8  It  is  interesting  to  read  De  Morgan's  argument  against  Saint- 
Martin's  authorship  of  this  work.  It  is  attributed  to  Saint-Martin 
both  by  the  Biographic  Universelle  and  by  the  British  Museum  Cata- 
logue, and  De  Morgan  says  by  "various  catalogues  and  biographies." 

'  "To  explain  things  by  man  and  not  man  by  things.  On  Errors 
and  Truth,  by  a  Ph.. . .  Inc.. . ." 


A  FORERUNNER  OF  THE   METRIC  SYSTEM.  171 

les  illusions,  et  surtout  des  amorces  de  1'orgueil  par  les- 
quelles  I'homme  est  si  souvent  seduit,  ne  prenons  jamais  les 
hommes,  mais  tou jours  Dieu  pour  notre  terme  de  compa- 
raison."10  The  first  uses  four  and  nine  in  various  ways,  of 
which  I  have  quoted  one:  the  second  says,  "Et  ici  se  trouve 
deja  une  explication  des  nombres  qualre  et  neuf,  qui  ont 
peu  embarrasse  dans  1'ouvrage  deja  cite.  L'homme  s'est 
egare  en  allant  de  quatre  a  neuf .  . .  ."11  The  work  cited  is 
the  Erreurs,  etc.,  and  the  citation  is  in  the  motto,  which  is 
the  text  of  the  opposition  sermon. 

A  FORERUNNER  OF  THE  METRIC  SYSTEM. 

Method   to   discover   the    difference   of  the   earth's    diameters; 
proving  its  true  ratio  to  be  not  less  variable  than  as  45  is  to 

46,   and   shortest   in   its   pole's   axis    174  miles likewise  a 

method  for  fixing  an  universal  standard  for  weights  and  meas- 
ures.    By  Thomas  Williams.1    London,  1788,  8vo. 

Mr.  Williams  was  a  paradoxer  in  his  day,  and  proposed 
what  was,  no  doubt,  laughed  at  by  some.  He  proposed 
the  sort  of  plan  which  the  French — independently  of  course 
— carried  into  effect  a  few  years  after.  He  would  have  the 
52d  degree  of  latitude  divided  into  100,000  parts  and  each 
part  a  geographical  yard.  The  geographical  ton  was  to 
be  the  cube  of  a  geographical  yard  filled  with  sea-water 
taken  some  leagues  from  land.  All  multiples  and  sub- 
divisions were  to  be  decimal. 

I  was  beginning  to  look  up  those  who  had  made  similar 
proposals,  when  a  learned  article  on  the  proposal  of  a 

9  "If  we  would  preserve  ourselves  from  all  illusions,  and  above 
all  from  the  allurements  of  pride,  by  which  man  is  so  often  seduced, 
we  should  never  take  man,  but  always  God,  for  our  term  of  com- 
parison." 

1  "And  here  is  found  already  an  explanation  of  the  numbers  four 
and  nine  which  caused  some  perplexity  in  the  work  cited  above. 
Man  is  lost  in  passing  from  four  to  nine." 

1  Williams  also  took  part  in  the  preparation  of  some  tables  for 
the  government  to  assist  in  the  determination  of  longitude.  He  had 
published  a  work  two  years  before  the  one  here  cited,  on  the  same 
subject, — An  entire  new  work  and  method  to  discover  the  variation 
of  the  Earth's  Diaameters,  London,  1786. 


172  A  BUDGET  OF  PARADOXES. 

metrical  system  came  under  my  eye  in  the  Times  of  Sept. 
15,  1863.  The  author  cites  Mouton,2  who  would  have  the 
minute  of  a  degree  divided  into  10,000  virgulce',  James 
Cassini,3  whose  foot  was  to  be  six  thousandths  of  a  minute ; 
and  Paucton,*  whose  foot  was  the  400,000th  of  a  degree.  I 
have  verified  the  first  and  third  statements ;  surely  the 
second  ought  to  be  the  six-thousandth. 

An  inquiry  into  the  Copernican  system. .. -wherein  it  is  proved, 
in  the  clearest  manner,  that  the  earth  has  only  her  diurnal 

motion with  an  attempt  to  point  out  the  only  true  way 

whereby  mankind  can  receive  any  real  benefit  from  the  study 
of  the  heavenly  bodies.  By  John  Cunningham.5  London, 
1789,  8vo. 

The  "true  way"  appears  to  be  the  treatment  of  heaven 
and  earth  as  emblematical  of  the  Trinity. 

Cosmology.  An  inquiry  into  the  cause  of  what  is  called  gravi- 
tation or  attraction,  in  which  the  motions  of  the  heavenly 
bodies,  and  the  preservation  and  operations  of  all  nature,  are 
deduced  from  an  universal  principle  of  efflux  and  reflux.  By 
T.  Vivian,6  vicar  of  Cornwood,  Devon.  Bath,  1792,  I2mo. 

2  This  is  Gabriel  Mouton    (1618-1694),  a  vicar  at  Lyons,  who 
suggested  as  a  basis  for  a  natural   system  of  measures  the  mille, 
a  minute  of  a  degree  of  the  meridian.     This  appeared  in  his  Ob- 
servationes  diametrorum  soils  et  lunae  apparentium,  meridianarum- 
que  aliquot  altitudinum  cum  tabula  declinationum  solis. . . .    Lyons, 
1670. 

3  Jacques  Cassini  (1677-1756),  one  of  the  celebrated  Cassini  fam- 
ily of  astronomers.    After  the  death  of  his  father  he  became  director 
of  the  observatory  at  Paris.     The  basis  for  a  metric  unit  was  set 
forth  by  him  in  his  Traite  de  la  grandeur  et  de  la  figure  de  la  terre, 
Paris,  1720.    He  was  a  prolific  writer  on  astronomy. 

*  Alexis  Jean  Pierre  Paucton  (1732-1798).  He  was,  for  a  time, 
professor  of  mathematics  at  Strassburg,  but  later  (1796)  held  office 
in  Paris.  His  leading  contribution  to  metrology  was  his  Metrologie 
ou  Traite  des  mesures,  Paris,  1780. 

8  He  was  an  obscure  writer,  born  at  Deptford. 

"He  was  also  a  writer  of  no  scientific  merit,  his  chief  contribu- 
tions being  religious  tracts.  One  of  his  productions,  however,  went 
through  many  editions,  even  being  translated  into  French,  Three 
dialogues  between  a  Minister  and  one  of  his  Parishioners;  on  the 
true  principles  of  Religion  and  salvation  for  sinners  by  Jesus  Christ. 
The  twentieth  edition  appeared  at  Cambridge  in  1786. 


173 


Attraction,  an  influx  of  matter  to  the  sun ;  centrifugal 
force,  the  solar  rays ;  cohesion,  the  pressure  of  the  atmos- 
phere. The  confusion  about  centrifugal  force,  so  called,  as 
demanding  an  external  agent,  is  very  common. 

THOMAS  PAINE'S  RIGHTS  OF  MAN. 

The  rights  of  MAN,  being  an  answer  to  Mr.  Burke's  attack  on 
the  French  Revolution.1  By  Thomas  Paine.2  In  two  parts. 
1791-1792.  8vo.  (Various  editions.)3 

A  vindication  of  the  rights  of  WOMAN,  with  strictures  on  polit- 
ical and  moral  subjects.  By  Mary  Wollstonecraft.4  1792.  Svo. 

A  sketch  of  the  rights  of  BOYS  and  GIRLS.  By  Launcelot  Light, 
of  Westminster  School;  and  Lsetitia  Lookabout,  of  Queen's 
Square,  Bloomsbury.  [By  the  Rev.  Samuel  Parr,5  LL.D.] 
1792.  8vo.  (pp.64). 

When  did  we  three  meet  before?  The  first  work  has 
sunk  into  oblivion:  had  it  merited  its  title,  it  might  have 

1  This  was  the  Reflections  on  the  Revolution  in  France,  and  on 
the  proceedings  in  certain  societies  in  London  relative  to  that  event 
(London,   1790)    by  Edmund   Burke    (1729-1797).     Eleven  editions 
of  the  work  appeared  the  first  year. 

2  Paine   (1736-1809)   was  born  in  Norfolkshire,  of  Quaker  par- 
ents.    He  went  to  America  at  the  beginning  of  the  Revolution  and 
published,  in  January  1776,  a  violent  pamphlet  entitled  Common  Sense. 
He  was  a  private  soldier  under  Washington,  and  on  his  return  to 
England  after  the  war  he  published  The  Rights  of  Man.     He  was 
indicted  for  treason  and  was  outlawed  to  France.     He  was  elected 
to  represent  Calais  at  the  French  convention,  but  his  plea  for  mod- 
eration led  him  perilously  near  the  guillotine.     His  Age  of  Reason 
(1794)  was  dedicated  to  Washington.     He  returned  to  America  in 
1802  and  remained  there  until  his  death. 

8  Part  I  appeared  in  1791  and  was  so  popular  that  eight  editions 
appeared  in  that  year.  It  was  followed  in  1792  by  Part  II,  of  which 
nine  editions  appeared  in  that  year.  Both  parts  were  immediately 
republished  in  Paris,  and  there  have  been  several  subsequent  edi- 
tions. 

*Mary  Wollstonecraft  (i759-i797)  was  only  thirty-three  when 
this  work  came  out  She  had  already  published  An  historical  and 
moral  View  of  the  Origin  and  Progress  of  the  French  Revolution 
(1790),  and  Original  Stories  from  Real  Life  (1791).  She  went  to 
Paris  in  1792  and  remained  during  the  Reign  of  Terror. 

6  Samuel  Parr  (1747-1827)  was  for  a  time  head  assistant  at 
Harrow  (1767-1771),  and  afterwards  headmaster  in  other  schools. 
At  the  time  this  book  was  written  he  was  vicar  of  Hatton,  where  he 
took  private  pupils  (1785-1798)  to  the  strictly  limited  number  of 
seven.  He  was  a  violent  Whig  and  a  caustic  writer. 


174  A  BUDGET  OF  PARADOXES. 

lived.  It  is  what  the  French  call  a  piece  de  circonstance ;  it 
belongs  in  time  to  the  French  Revolution,  and  in  matter  to 
Burke's  opinion  of  that  movement.  Those  who  only  know 
its  name  think  it  was  really  an  attempt  to  write  a  philosoph- 
ical treatise  on  what  we  now  call  socialism.  Silly  govern- 
ment prosecutions  gave  it  what  it  never  could  have  got  for 
itself. 

Mary  Wollstonecraft  seldom  has  her  name  spelled  right. 
I  suppose  the  O !  O !  character  she  got  made  her  Waolstone- 
craft.  Watt  gives  double  insinuation,  for  his  cross-reference 
sends  us  to  Goodwin.6  No  doubt  the  title  of  the  book  was 
an  act  of  discipleship  to  Paine's  Rights  of  Man ;  but  this 
title  is  very  badly  chosen.  The  book  was  marred  by  it, 
especially  when  the  authoress  and  her  husband  assumed  the 
right  of  dispensing  with  legal  sanction  until  the  approach  of 
offspring  brought  them  to  a  sense  of  their  child's  interest.? 
Not  a  hint  of  such  a  claim  is  found  in  the  book,  which  is 
mostly  about  female  education.  The  right  claimed  for  wo- 
man is  to  have  the  education  of  a  rational  human  being, 
and  not  to  be  considered  as  nothing  but  woman  throughout 
youthful  training.  The  maxims  of  Mary  Wollstonecraft  are 
now,  though  not  derived  from  her,  largely  followed  in  the 
education  of  girls,  especially  in  home  education:  just  as 
many  of  the  political  principles  of  Tom  Paine,  again  not 
derived  from  him,  are  the  guides  of  our  actual  legislation. 
I  remember,  forty  years  ago,  an  old  lady  used  to  declare 
that  she  disliked  girls  from  the  age  of  sixteen  to  five-and- 
twenty.  "They  are  full,"  said  she,  "of  femalities."  She 
spoke  of  their  behavior  to  women  as  well  as  to  men.  She 

9  On  Mary  Wollstonecraft's  return  from  France  she  married 
(1797)  William  Godwin  (1756-1836).  He  had  started  as  a  strong 
Calvinistic  Nonconformist  minister,  but  had  become  what  would  now 
be  called  an  anarchist,  at  least  by  conservatives.  He  had  written  an 
Inquiry  concerning  Political  Justice  (1793)  and  a  novel  entitled 
Caleb  Williams,  or  Things  as  they  are  (1794),  both  of  which  were 
of  a  nature  to  attract  his  future  wife. 

TThis  child  was  a  daughter.  She  became  Shelley's  wife,  and 
Godwin's  influence  on  Shelley  was  very  marked. 


THOMAS  PAINE'S  RIGHTS  OF  MAN.  175 

would  have  been  shocked  to  know  that  she  was  a  follower 
of  Mary  Wollstonecraft,  and  had  packed  half  her  book  into 
one  sentence. 

The  third  work  is  a  satirical  attack  on  Mary  Wollstone- 
craft and  Tom  Paine.  The  details  of  the  attack  would  con- 
vince any  one  that  neither  has  anything  which  would  now 
excite  reprobation.  It  is  utterly  unworthy  of  Dr.  Parr,  and 
has  quite  disappeared  from  lists  of  his  works,  if  it  were  ever 
there.  That  it  was  written  by  him  I  take  to  be  evident,  as 
follows.  Nichols,8  who  could  not  fail  to  know,  says  (Anecd., 
vol.  ix,  p.  120)  :  "This  is  a  playful  essay  by  a  first-rate 
scholar,  who  is  elsewhere  noticed  in  this  volume,  but  whose 
name  I  shall  not  bring  forward  on  so  trifling  an  occasion." 
Who  the  scholar  was  is  made  obvious  by  Master  Launcelot 
being  made  to  talk  of  Bellendenus.9  Further,  the  same  boy 
is  made  to  say,  "Let  Dr.  Parr  lay  his  hand  upon  his  heart, 
if  his  conscience  will  let  him,  and  ask  himself  how  many 
thousands  of  wagon-loads  of  this  article  [birch]  he  has 
cruelly  misapplied."  How  could  this  apply  to  Parr,  with  his 
handful  of  private  pupils,10  and  no  reputation  for  severity? 
Any  one  except  himself  would  have  called  on  the  head- 
master of  Westminster  or  Eton.  I  doubt  whether  the  name 
of  Parr  could  be  connected  with  the  rod  by  anything  in 
print,  except  the  above  and  an  anecdote  of  his  pupil,  Tom 
Sheridan.11  The  Doctor  had  dressed  for  a  dinner  visit,  and 

8  This   was   John   Nichols    (1745-1826),  the  publisher  and  anti- 
quary.    He  edited  the   Gentleman's  Magazine    (1792-1826)    and  his 
works   include   the  Literary  Anecdotes   of   the  Eighteenth   Century 
(1812-1815),  to  which  De  Morgan  here  refers. 

9  William  Bellenden,   a   Scotch   professor  at  the  University  of 
Paris,  who  died  about  1633.     His  textbooks  are  now  forgotten,  but 
Parr  edited  an  edition  of  his  works   in   1787.     The  Latin  preface, 
Pracfatio  ad  Bellendum  de  Statu,  was  addressed  to  Burke,  North, 
and  Fox,  and  was  a  satire  on  their  political  opponents. 

10  As  we  have  seen,  he  had  been  head-master  before  he  began 
taking  "his  handful  of  private  pupils." 

11  The  story  has  evidently  got  mixed  up  in  the  telling,  for  Tom 
Sheridan  (1721-1788),  the  great  actor,  was  old  enough  to  have  been 
Dr.  Parr's  father.    It  was  his  son,  Richard  Brinsley  Sheridan  (1751- 
1816),  the  dramatist  and  politician,  who  was  the  pupil  of  Parr.    He 


176  A  BUDGET  OF  PARADOXES. 

was  ready  a  quarter  of  an  hour  too  soon  to  set  off.  "Tom," 
said  he,  "I  think  I  had  better  whip  you  now ;  you  are  sure  to 
do  something  while  I  am  out." — "I  wish  you  would,  sir!" 
said  the  boy ;  "it  would  be  a  letter  of  licence  for  the  whole 
evening."  The  Doctor  saw  the  force  of  the  retort:  my  two 
tutelaries  will  see  it  by  this  time.  They  paid  in  advance; 
and  I  have  given  liberal  interpretation  to  the  order. 

The  following  story  of  Dr.  Parr  was  told  me  and 
others,  about  1829,  by  the  late  Leonard  Horner,12who  knew 
him  intimately.  Parr  was  staying  in  a  house  full  of  com- 
pany, I  think  in  the  north  of  England.  Some  gentlemen 
from  America  were  among  the  guests,  and  after  dinner  they 
disputed  some  of  Parr's  assertions  or  arguments.  So  the 
Doctor  broke  out  with  "Do  you  know  what  country  you 
come  from?  You  come  from  the  place  to  which  we  used 
to  send  our  thieves!"  This  made  the  host  angry,  and  he 
gave  Parr  such  a  severe  rebuke  as  sent  him  from  the  room 
in  ill-humor.  The  rest  walked  on  the  lawn,  amusing  the 
Americans  with  sketches  of  the  Doctor.  There  was  a  dark 
cloud  overhead,  and  from  that  cloud  presently  came  a  voice 
which  called  Tham  (Parr-lisp  for  Sam).  The  company 
were  astonished  for  a  moment,  but  thought  the  Doctor  was 
calling  his  servant  in  the  house,  and  that  the  apparent  direc- 
tion was  an  illusion  arising  out  of  inattention.  But  presently 
the  sound  was  repeated,  certainly  from  the  cloud, 

"And  nearer,  clearer,  deadlier  than  before." 

There  was  now  a  little  alarm :  where  could  the  Doctor  have 
got  to?  They  ran  to  his  bedroom,  and  there  they  discovered 
a  sufficient  rather  than  satisfactory  explanation.  The  Doctor 
had  taken  his  pipe  into  his  bedroom,  and  had  seated  himself, 
in  sulky  mood,  upon  the  higher  bar  of  a  large  and  deep  old- 
fashioned  grate  with  a  high  mantelshelf.  Here  he  had  turn- 
wrote  The  Rivals  (1775)  and  The  School  for  Scandal  (1777)  soon 
after  Parr  left  Harrow. 

"Horner  (1785-1864)  was  a  geologist  and  social  reformer.  He 
was  very  influential  in  improving  the  conditions  of  child  labor. 


ATTACKS  ON    RELIGIOUS   CUSTOMS.  177 

bled  backwards,  and  doubled  himself  up  between  the  bars 
and  the  back  of  the  grate.  He  was  fixed  tight,  and  when 
he  called  for  help,  he  could  only  throw  his  voice  up  the 
chimney.  The  echo  from  the  cloud  was  the  warning  which 
brought  his  friends  to  the  rescue. 

ATTACKS  ON  RELIGIOUS  CUSTOMS. 

Days  of  political  paradox  were  coming,  at  which  we  now 
stare.  Cobbett1  said,  about  1830,  in  earnest,  that  in  the 
country  every  man  who  did  not  take  off  his  hat  to  the 
clergyman  was  suspected,  and  ran  a  fair  chance  of  having 
something  brought  against  him.  I  heard  this  assertion  can- 
vassed, when  it  was  made,  in  a  party  of  elderly  persons. 
The  Radicals  backed  it,  the  old  Tories  rather  denied  it, 
but  in  a  way  which  satisfied  me  they  ought  to  have  denied 
it  less  if  they  could  not  deny  it  more.  But  it  must  be  said 
that  the  Governments  stopped  far  short  of  what  their  parti- 
sans would  have  had  them  do.  All  who  know  Robert  Robin- 
son's2 very  quiet  assault  on  church-made  festivals  in  his 
History  and  Mystery  of  Good  Friday  (1777)3  will  hear  or 
remember  with  surprise  that  the  British  Critic  pronounced 
it  a  direct,  unprovoked,  and  malicious  libel  on  the  most 

1  William  Cobbett  (1762-1835),  the  journalist,  was  a  character 
not  without  interest  to  Americans.  Born  in  Surrey,  he  went  to 
America  at  the  age  of  thirty  and  remained  there  eight  years.  Most 
of  this  time  he  was  occupied  as  a  bookseller  in  Philadelphia,  and 
while  thus  engaged  he  was  fined  for  libel  against  the  celebrated  Dr. 
Rush.  On  his  return  to  England  he  edited  the  Weekly  Political 
Register  (1802-1835),  a  popular  journal  among  the  working  classes. 
He  was  fined  and  imprisoned  for  two  years  because  of  his  attack 
(1810)  on  military  flogging,  and  was  also  (1831)  prosecuted  for 
sedition.  He  further  showed  his  paradox  nature  by  his  History  of 
the  Protestant  Reformation  (1824-1827),  an  attack  on  the  prevail- 
ing Protestant  opinion.  He  also  wrote  a  Life  of  Andrew  Jackson 
(1834).  After  repeated  attempts  he  succeeded  in  entering  parlia- 
ment, a  result  of  the  Reform  Bill. 

'Robinson  (1735-1790)  was  a  Baptist  minister  who  wrote  sev- 
eral theological  works  and  a  number  of  hymns.  His  work  at  Cam- 
bridge so  offended  the  students  that  they  at  one  time  broke  up  the 
services. 

8  This  work  had  passed  through  twelve  editions  by  1823. 


178  A  BUDGET  OF  PARADOXES. 

sacred  institutions  of  the  national  Church.  It  was  reprinted 
again  and  again:  in  1811  it  was  in  a  cheap  form  at  6s.  6d. 
a  hundred.  When  the  Jacobin  day  came,  the  State  was 
really  in  a  fright:  people  thought  twice  before  they  pub- 
lished what  would  now  be  quite  disregarded.  I  examined 
a  quantity  of  letters  addressed  to  George  Dyer4  (Charles 
Lamb's  G.D.)  and  what  between  the  autographs  of  Thel- 
wall,  Hardy,  Home  Tooke,  and  all  the  rebels,*  put  together 
a  packet  which  produced  five  guineas,  or  thereabouts,  for 
the  widow.  Among  them  were  the  following  verses,  sent 
by  the  author — who  would  not  put  his  name,  even  in  a  pri- 
vate letter,  for  fear  of  accidents — for  consultation  whether 
they  could  safely  be  sent  to  an  editor:  and  they  were  not 
sent.  The  occasion  was  the  public  thanksgiving  at  St.  Paul's 
for  the  naval  victories,  December  19,  1797. 

"God  bless  me!  what  a  thing! 
Have  you  heard  that  the  King 
Goes  to  St.  Paul's? 

4  Dyer  (1755-1841),  the  poet  and  reformer,  edited  Robinson's 
Ecclesiastical  Researches  (1790).  He  was  a  life-long  friend  of 
Charles  Lamb,  and  in  their  boyhood  they  were  schoolmates  at 
Christ's  Hospital.  His  Complaints  of  the  Poor  People  of  England 
(1793)  made  him  a  worthy  companion  of  the  paradoxers  above 
mentioned. 

8  These  were  John  Thelwall  (1764-1834)  whose  Politics  for  the 
People  or  Hogswash  (1794)  took  its  title  from  the  fact  that  Burke 
called  the  people  the  "swinish  multitude."  The  book  resulted  in  send- 
ing the  author  to  the  Tower  for  sedition.  In  1798  he  gave  up  poli- 
tics and  start  a  school  of  elocution  which  became  very  famous. 
Thomas  Hardy  (1752-1832),  who  kept  a  bootmaker's  shop  in  Picca- 
dilly, was  a  fellow  prisoner  with  Thelwall,  being  arrested  for  high 
treason.  He  was  founder  (1792)  of  The  London  Corresponding 
Society,  a  kind  of  clearing  house  for  radical  associations  throughout 
the  country.  Home  Tooke  was  really  John  Home  (1736-1812),  he 
having  taken  the  name  of  his  friend  William  Tooke  in  1782.  He 
was  a  radical  of  the  radicals,  and  organized  a  number  of  reform 
societies.  Among  these  was  the  Constitutional  Society  that  voted 
money  (1775)  to  assist  the  American  revolutionists,  appointing  him 
to  give  the  contribution  to  Franklin.  For  this  he  was  imprisoned 
for  a  year.  With  his  fellow  rebels  in  the  Tower  in  1794,  however, 
he  was  acquitted.  As  a  philologist  he  is  known  for  his  early  ad- 
vocacy of  the  study  of  Anglo-Saxon  and  Gothic,  and  his  Diversions 
of  Purley  ( 1786)  is  still  known  to  readers. 


ATTACKS  ON  RELIGIOUS  CUSTOMS.  179 

Good  Lord !  and  when  he's  there, 
He'll  roll  his  eyes  in  prayer, 
To  make  poor  Johnny  stare 
At  this  fine  thing. 

"No  doubt  the  plan  is  wise 
To  blind  poor  Johnny's  eyes 

By  this  grand  show; 
For  should  he  once  suppose 
That  he's  led  by  the  nose, 
Down  the  whole  fabric  goes, 

Church,  lords,  and  king. 

"As  he  shouts  Duncan's6  praise, 
Mind  how  supplies  they'll  raise 

In  wondrous  haste. 
For  while  upon  the  sea 
We  gain  one  victory, 
John  still  a  dupe  will  be 

And  taxes  pay. 

"Till  from  his  little  store 
Three-fourths  or  even  more 

Goes  to  the  Crown. 
Ah,  John!  you  little  think 
How  fast  we  downward  sink 
And  touch  the  fatal  brink 

At  which  we're  slaves." 

I  would  have  indicted  the  author  for  not  making  his 
thirds  and  sevenths  rhyme.  As  to  the  rhythm,  it  is  not 
much  better  than  what  the  French  sang  in  the  Calais  theater 
when  the  Duke  of  Clarence?  took  over  Louis  XVIII  in  1814. 

"God  save  noble  Clarence, 
Who  brings  our  king  to  France ; 

God  save  Clarence ! 
He  maintains  the  glory 
Of  the  British  navy, 
etc.,  etc." 

"This  was  the  admiral,  Adam  Viscount  Duncan  (1731-1804), 
who  defeated  the  Dutch  off  Camperdown  in  1797. 

7  He  was  created  Duke  of  Clarence  and  St.  Andrews  in  1789 
and  was  Admiral  of  the  Fleet  escorting  Louis  XVIII  on  his  return 


180  A  BUDGET  OF  PARADOXES. 

Perhaps  had  this  been  published,  the  Government  would 
have  assailed  it  as  a  libel  on  the  church  service.  They  got 
into  the  way  of  defending  themselves  by  making  libels  on 
the  Church,  of  what  were  libels,  if  on  anything,  on  the 
rulers  of  the  State ;  until  the  celebrated  trials  of  Hone 
settled  the  point  for  ever,  and  established  that  juries  will 
not  convict  for  one  offence,  even  though  it  have  been  com- 
mitted, when  they  know  the  prosecution  is  directed  at  an- 
other offence  and  another  intent. 

HONE'S  FAMOUS  TRIALS. 

The  results  of  Hone's  trials  (William  Hone,  1779-1842) 
are  among  the  important  constitutional  victories  of  our  cen- 
tury. He  published  parodies  on  the  Creeds,  the  Lord's 
Prayer,  the  Catechism,  etc.,  with  intent  to  bring  the  Ministry 
into  contempt:  everybody  knew  that  was  his  purpose.  The 
Government  indicted  him  for  impious,  profane,  blasphemous 
intent,  but  not  for  seditious  intent.  They  hoped  to  wear 
him  out  by  proceeding  day  by  day.  December  18,  1817, 
they  hid  themselves  under  the  Lord's  Prayer,  the  Creed, 
and  the  Commandments ;  December  19,  under  the  Litany ; 
December  20,  under  the  Athanasian  Creed,  an  odd  place  for 
shelter  when  they  could  not  find  it  in  the  previous  places. 
Hone  defended  himself  for  six,  seven,  and  eight  hours  on 
the  several  days:  and  the  jury  acquitted  him  in  15,  105,  and 
20  minutes.  In  the  second  trial  the  offense  was  laid  both 
as  profanity  and  as  sedition,  which  seems  to  have  made  the 
jury  hesitate.  And  they  probably  came  to  think  that  the 
second  count  was  false  pretence :  but  the  length  of  their  de- 
liberation is  a  satisfactory  addition  to  the  value  of  the  whole. 
In  the  first  trial  the  Attorney-General  (Shepherd)  had  the 
impudence  to  say  that  the  libel  had  nothing  of  a  political 
tendency  about  it,  but  was  avowedly  set  off  against  the 
religion  and  worship  of  the  Church  of  England.  The  whole 

to  France  in  1814.  He  became  Lord  High  Admiral  in  1827,  and 
reigned  as  William  IV  from  1830  to  1837. 


HONE'S  FAMOUS  TRIALS.  181 

is  political  in  every  sentence ;  neither  more  nor  less  political 
than  the  following,  which  is  part  of  the  parody  on  the  Cat- 
echism: "What  is  thy  duty  towards  the  Minister?  My  duty 
towards  the  Minister  is,  to  trust  him  as  much  as  I  can;  to 
honor  him  with  all  my  words,  with  all  my  bows,  with  all 
my  scrapes,  and  with  all  my  cringes ;  to  flatter  him ;  to  give 
him  thanks;  to  give  up  my  whole  soul  to  him;  to  idolize 
his  name,  and  obey  his  word,  and  serve  him  blindly  all  the 
days  of  his  political  life."  And  the  parody  on  the  Creed 
begins,  "I  believe  in  George,  the  Regent  almighty,  maker 
of  new  streets  and  Knights  of  the  Bath."  This  is  what  the 
Attorney-General  said  had  nothing  of  a  political  tendency 
about  it.  But  this  was  on  the  first  trial:  Hone  was  not 
known.  The  first  day's  trial  was  under  Justice  Abbott 
(afterwards  C.  J.  Tenterden).1  It  was  perfectly  understood, 
when  Chief  Justice  Ellenborough2  appeared  in  Court  on  the 
second  day,  that  he  was  very  angry  at  the  first  result,  and 
put  his  junior  aside  to  try  his  own  rougher  dealing.  But 
Hone  tamed  the  lion.  An  eye-witness  told  me  that  when 
he  implored  of  Hone  not  to  detail  his  own  father  Bishop 
Law'ss  views  on  the  Athanasian  Creed,  which  humble  peti- 
tion Hone  kindly  granted,  he  held  by  the  desk  for  support. 
And  the  same  when — which  is  not  reported — the  Attorney- 
General  appealed  to  the  Court  for  protection  against  a 

1This  was  Charles  Abbott  (1762-1832)  first  Lord  Tenterden. 
He  succeeded  Lord  Ellenborough  as  Chief  Justice  (1818)  and  was 
raised  to  the  peerage  in  1827.  He  was  a  strong  Tory  and  opposed 
the  Catholic  Relief  Bill,  the  Reform  Bill,  and  the  abolition  of  the 
death  penalty  for  forgery. 

'Edward  Law  (1750-1818),  first  Baron  Ellenborough.  He  was 
chief  counsel  for  Warren  Hastings,  and  his  famous  speech  in  de- 
fense of  his  client  is  well  known.  He  became  Chief  Justice  and  was 
raised  to  the  peerage  in  1802.  He  opposed  all  efforts  to  modernize 
the  criminal  code,  insisting  upon  the  reactionary  principle  of  new 
death  penalties. 

"Edmund  Law  (1703-1787),  Bishop  of  Carlisle  (1768),  was  a 
good  deal  more  liberal  than  his  son.  His  Considerations  on  the 
Propriety  of  requiring  subscription  to  the  Articles  of  Faith  (1774) 
was  published  anonymously.  In  it  he  asserts  that  not  even  the 
clergy  should  be  required  to  subscribe  to  the  thirty-nine  articles. 


182  A  BUDGET  OF  PARADOXES. 

stinging  attack  which  Hone  made  on  the  Bar:  he  held  on, 
and  said,  "Mr.  Attorney,  what  can  I  do!"  I  was  a  boy  of 
twelve  years  old,  but  so  strong  was  the  feeling  of  exultation 
at  the  verdicts  that  boys  at  school  were  not  prohibited  from 
seeing  the  parodies,  which  would  have  been  held  at  any 
other  time  quite  unfit  to  meet  their  eyes.  I  was  not  able 
to  comprehend  all  about  the  Lord  Chief  Justice  until  I  read 
and  heard  again  in  after  years.  In  the  meantime,  Joe  Miller 
had  given  me  the  story  of  the  leopard  which  was  sent  home 
on  board  a  ship  of  war,  and  was  in  two  days  made  as  docile 
as  a  cat  by  the  sailors/  "You  have  got  that  fellow  well 
under,"  said  an  officer.  "Lord  bless  your  Honor!"  said 
Jack,  "if  the  Emperor  of  Marocky  would  send  us  a  cock 
rhinoceros,  we'd  bring  him  to  his  bearings  in  no  time!" 
When  I  came  to  the  subject  again,  it  pleased  me  to  enter- 
tain the  question  whether,  if  the  Emperor  had  sent  a  cock 
rhinoceros  to  preside  on  the  third  day  in  the  King's  Bench, 
Hone  would  have  mastered  him:  I  forget  how  I  settled  it. 
There  grew  up  a  story  that  Hone  caused  Lord  Ellenbor- 
ough's  death,  but  this  could  not  have  been  true.  Lord  Ellen- 
borough  resigned  his  seat  in  a  few  months,  and  died  just 
a  year  after  the  trials ;  but  sixty-eight  years  may  have  had 
more  to  do  with  it  than  his  defeat. 

A  large  subscription  was  raised  for  Hone,  headed  by 
the  Duke  of  Bedford*  for  £105.  Many  of  the  leading  anti- 
ministerialists  joined :  but  there  were  many  of  the  other  side 
who  avowed  their  disapprobation  of  the  false  pretense. 
Many  could  not  venture  their  names.  In  the  list  I  find: 

/Joe  Miller  (1684-1738),  the  famous  Drury  Lane  comedian,  was 
so  illiterate  that  he  could  not  have  written  the  Joe  Miller's  Jests,  or 
the  Wit's  Vade-Mecum  that  appeared  the  year  after  his  death.  It 
was  often  reprinted  and  probably  contained  more  or  less  of  Miller's 
own  jokes. 

6  The  sixth  duke  (1766-1839)  was  much  interested  in  parliamen- 
tary reform.  He  was  a  member  of  the  Society  of  Friends  of  the 
People.  He  was  for  fourteen  years  a  member  of  parliament  (1788- 
1802)  and  was  later  Lord  Lieutenant  of  Ireland  (1806-1807).  He 
afterwards  gave  up  politics  and  became  interested  in  agricultural 
matters. 


HONE'S  FAMOUS  TRIALS.  183 

A  member  of  the  House  of  Lords,  an  enemy  to  persecution, 
and  especially  to  religious  persecution  employed  for  political 
purposes — No  parodist,  but  an  enemy  to  persecution — A 
juryman  on  the  third  day's  trial — Ellen  Borough — My  name 
would  ruin  me — Oh !  minions  of  Pitt — Oil  for  the  Hone — 
The  Ghosts  of  Jeffries6  and  Sir  William  Roy  [Ghosts  of 
Jeffries  in  abundance] — A  conscientious  Jury  and  a  con- 
scientious Attorney,  £1  6s.  8d. — To  Mr.  Hone,  for  defend- 
ing in  his  own  person  the  freedom  of  the  press,  attacked 
for  a  political  object,  under  the  old  pretense  of  supporting 
Religion — A  cut  at  corruption — An  Earldom  for  myself 
and  a  translation  for  my  brother — One  who  disapproves  of 
parodies,  but  abhors  persecution — From  a  schoolboy  who 
wishes  Mr.  Hone  to  have  a  very  grand  subscription — "For 
delicacy's  sake  forbear/5  and  "Felix  trembled"— "I  will  go 
myself  to-morrow" — Judge  Jeffries'  works  rebound  in  calf 
by  Law — Keep  us  from  Law,  and  from  the  Shepherd's 
paw — I  must  not  give  you  my  name,  but  God  bless  you! — 
As  much  like  Judge  Jeffries  as  the  present  times  will  permit 
—May  Jeffries'  fame  and  Jeffries'  fate  on  every  modern 
Jeffries  wait — No  parodist,  but  an  admirer  of  the  man  who 
has  proved  the  fallacy  of  the  Lawyer's  Law,  that  when  a 
man  is  his  own  advocate  he  has  a  fool  for  his  client — A 
Mussulman  who  thinks  it  would  not  be  an  impious  libel  to 
parody  the  Koran — May  the  suspenders  of  the  Habeas 
Corpus  Act  be  speedily  suspended — Three  times  twelve  for 
thrice-tried  Hone,  who  cleared  the  cases  himself  alone, 
and  won  three  heats  by  twelve  to  one,  £1  16s. — A  conscien- 
tious attorney,  i\  6s.  8d. — Rev.  T.  B.  Morris,  rector  of 
Shelf  anger,  who  disapproves  of  the  parodies,  but  abhors 
the  making  an  affected  zeal  for  religion  the  pretext  for 
political  persecution — A  Lawyer  opposed  in  principle  to 

'George  Jeffreys  (c.  1648-1689),  the  favorite  of  James  II,  who 
was  active  in  prosecuting  the  Rye  House  conspirators.  He  was 
raised  to  the  peerage  in  1684  and  held  the  famous  "bloody  assize" 
in  the  following  year,  being  made  Lord  Chancellor  as  a  result.  He 
was  imprisoned  in  the  Tower  by  William  III  and  died  there. 


184  A  BUDGET  OF   PARADOXES. 

Law — For  the  Hone  that  set  the  razor  that  shaved  the  rats 
— Rev.  Dr.  Samuel  Parr,  who  most  seriously  disapproves 
of  all  parodies  upon  the  hallowed  language  of  Scripture 
and  the  contents  of  the  Prayer-book,  but  acquits  Mr.  Hone 
of  intentional  impiety,  admires  his  talents  and  fortitude, 
and  applauds  the  good  sense  and  integrity  of  his  juries — 
Religion  without  hypocrisy,  and  Law  without  impartiality 
— O  Law !  O  Law !  O  Law ! 

These  are  specimens  of  a  great  many  allusive  mottoes. 
The  subscription  was  very  large,  and  would  have  bought 
a  handsome  annuity,  but  Hone  employed  it  in  the  bookselling 
trade,  and  did  not  thrive.  His  Everyday  Book7  and  his  Apoc- 
ryphal New  Testament?  are  useful  books.  On  an  annuity 
he  would  have  thriven  as  an  antiquarian  writer  and  collec- 
tor. It  is  well  that  the  attack  upon  the  right  to  ridicule 
Ministers  roused  a  dormant  power  which  was  equal  to  the 
occasion.  Hone  declared,  on  his  honor,  that  he  had  never 
addressed  a  meeting  in  his  life,  nor  spoken  a  word  before 
more  than  twelve  persons.  Had  he — which  however  could 
not  then  be  done — employed  counsel  and  had  a  guilty  de- 
fense made  for  him,  he  would  very  likely  have  been  con- 
victed, and  the  work  would  have  been  left  to  be  done  by 
another.  No  question  that  the  parodies  disgusted  all  who 
reverenced  Christianity,  and  who  could  not  separate  the 
serious  and  the  ludicrous,  and  prevent  their  existence  in 
combination. 

My  extracts,  etc.,  are  from  the  nineteenth,  seventeenth, 
and  sixteenth  editions  of  the  three  trials,  which  seem  to  have 
been  contemporaneous  (all  in  1818)  as  they  are  made  up 
into  one  book,  with  additional  title  over  all,  and  the  motto 
"Thrice  the  brindled  cat  hath  mew'd."  They  are  published 
by  Hone  himself,  who  I  should  have  said  was  a  publisher 

T  The  Every  Day  Book,  forming  a  Complete  History  of  the  Year, 
Months,  and  Seasons,  and  a  perpetual  Key  to  the  Almanack,  1826- 
1827. 

8  The  first  and  second  editions  appeared  in  1820.  Two  others 
followed  in  1821. 


HONE'S  FAMOUS  TRIALS.  185 

as  well  as  was  to  be.  And  though  the  trials  only  ended 
Dec.  20,  1817,  the  preface  attached  to  this  common  title  is 
dated  Jan.  23,  1818.9 

The  spirit  which  was  roused  against  the  false  dealing  of 
the  Government,  i.  e.,  the  pretense  of  prosecuting  for  im- 
piety when  all  the  world  knew  the  real  offense  was,  if  any- 
thing, sedition — was  not  got  up  at  the  moment:  there  had 
been  previous  exhibitions  of  it.  For  example,  in  the  spring 
of  1818  Mr.  Russell,  a  little  printer  in  Birmingham,  was 
indicted  for  publishing  the  Political  Litany10  on  which  Hone 
was  afterwards  tried.  He  took  his  witnesses  to  the  summer 
Warwick  assizes,  and  was  told  that  the  indictment  had  been 
removed  by  certiorari  into  the  King's  Bench.  He  had  no- 
tice of  trial  for  the  spring  assizes  at  Warwick :  he  took  his 
witnesses  there,  and  the  trial  was  postponed  by  the  Crown. 
He  then  had  notice  for  the  summer  assizes  at  Warwick ; 
and  so  on.  The  policy  seems  to  have  been  to  wear  out  the 
obnoxious  parties,  either  by  delays  or  by  heaping  on  trials. 
The  Government  was  odious,  and  knew  it  could  not  get 
verdicts  against  ridicule,  and  could  get  verdicts  against  im- 
piety. No  difficulty  was  found  in  convicting  the  sellers  of 
Paine's  works,  and  the  like.  When  Hone  was  held  to  bail 
it  was  seen  that  a  crisis  was  at  hand.  All  parties  in  politics 
furnished  him  with  parodies  in  proof  of  religious  persons 
having  made  instruments  of  them.  The  parodies  by  Addi- 
son  and  Luther  were  contributed  by  a  Tory  lawyer,  who  was 
afterwards  a  judge. 

Hone  had  published,  in  1817,  tracts  of  purely  political 
ridicule:  Official  Account  of  the  Noble  Lord's  Bite,™  Trial  of 
the  Dog  for  Biting  the  Noble  Lord,  etc.  These  were  not 
touched.  After  the  trials,  it  is  manifest  that  Hone  was 

8  The  three  trials  of  W.  H.,  for  publishing  three  parodies;  viz. 
the  late  John  Wilkes'  Catechism,  the  Political  Litany,  and  the  Sine- 
curist's  Creed;  on  three  ex-ofhcio  informations,  at  Guildhall,  London, 
Dec.  18,  19,  &  20,  1817, London,  1818. 

10  The  Political  Litany  appeared  in  1817. 
"That  is,  Castlereagh's. 


186  A  BUDGET  OF  PARADOXES. 

to  be  unassailed,  do  what  he  might.  The  Political  House 
that  Jack  built,  in  1819;  The  Man  in  the  Moon,  1820;  The 
Queen's  Matrimonial  Ladder,  Non  mi  ricordo,  The  R — / 
Fowls,  1820;  The  Political  Showman  at  Home,  with  plates 
by  G.  Cruickshank,12  1821  [he  did  all  the  plates]  ;  The  Spirit 
of  Despotism,  1821 — would  have  been  legitimate  marks  for 
prosecution  in  previous  years.  The  biting  caricature  of  sev- 
eral of  these  works  are  remembered  to  this  day.  The  Spirit 
of  Despotism  was  a  tract  of  1795,  of  which  a  few  copies  had 
been  privately  circulated  with  great  secrecy.  Hone  reprinted 
it,  and  prefixed  the  following  address  to  "Robert  Stewart, 
alias  Lord  Castlereagh"^ :  "It  appears  to  me  that  if,  un- 
happily, your  counsels  are  allowed  much  longer  to  prevail 
in  the  Brunswick  Cabinet,  they  will  bring  on  a  crisis,  in 
which  the  king  may  be  dethroned  or  the  people  enslaved. 
Experience  has  shown  that  the  people  will  not  be  enslaved 
— the  alternative  is  the  affair  of  your  employers."  Hone 
might  say  this  without  notice. 

In  1819  Mr.  Murray1*  published  Lord  Byron's  Don  Juan,1* 
and  Hone  followed  it  with  Don  John,  or  Don  Juan  Un- 
masked, a  little  account  of  what  the  publisher  to  the  Ad- 
miralty was  allowed  to  issue  without  prosecution.  The 
parody  on  the  Commandments  was  a  case  very  much  in 
point :  and  Hone  makes  a  stinging  allusion  to  the  use  of  the 
"unutterable  Name,  with  a  profane  levity  unsurpassed  by 

12  The  well-known  caricaturist  (1792-1878),  then  only  twenty-nine 
years  old. 

"Robert  Stewart  (1769-1822)  was  second  Marquis  of  London- 
derry and  Viscount  Castlereagh.  As  Chief  Secretary  for  Ireland 
he  was  largely  instrumental  in  bringing  about  the  union  of  Ireland 
and  Great  Britain.  He  was  at  the  head  of  the  war  department  dur- 
ing most  of  the  Napoleonic  wars,  and  was  to  a  great  extent  respon- 
sible for  the  European  coalition  against  the  Emperor.  He  suicided 
in  1822. 

"John  Murray  (1778-1843),  the  well-known  London  publisher. 
He  refused  to  finish  the  publication  of  Don  Juan,  after  the  first  five 
cantos,  because  of  his  Tory  principles. 

"Only  the  first  two  cantos  appeared  in  1819. 


HONE'S  FAMOUS  TRIALS.  187 

any  other  two  lines  in  the  English  language."  The  lines 
are 

'"Tis  strange — the  Hebrew  noun  which  means  'I  am/ 
The  English  always  use  to  govern  d n." 

Hone  ends  with :  "Lord  Byron's  dedication  of  'Don  Juan'  to 
Lord  Castlereagh  was  suppressed  by  Mr.  Murray  from  deli- 
cacy to  Ministers.  Q.  Why  did  not  Mr.  Murray  suppress  Lord 
Byron's  parody  on  the  Ten  Commandments?  A.  Because 
it  contains  nothing  in  ridicule  of  Ministers,  and  therefore 
nothing  that  they  could  suppose  would  lead  to  the  displeas- 
ure of  Almighty  God." 

The  little  matters  on  which  I  have  dwelt  will  never  ap- 
pear in  history  from  their  political  importance,  except  in  a 
few  words  of  result.  As  a  mode  of  thought,  silly  evasions 
of  all  kinds  belong  to  such  a  work  as  the  present.  Ignorance, 
which  seats  itself  in  the  chair  of  knowledge,  is  a  mother 
of  revolutions  in  politics,  and  of  unread  pamphlets  in  circle- 
squaring.  From  1815  to  1830  the  question  of  revolution  or 
no  revolution  lurked  in  all  our  English  discussions.  The 
high  classes  must  govern ;  the  high  classes  shall  not  govern ; 
and  thereupon  issue  was  to  be  joined.  In  1828-33  the  ques- 
tion came  to  issue;  and  it  was,  Revolution  with  or  without 
civil  war;  choose.  The  choice  was  wisely  made;  and  the 
Reform  Bill  started  a  new  system  so  well  dovetailed  into 
the  old  that  the  joinings  are  hardly  visible.  And  now,  in 
1867,  the  thing  is  repeated  with  a  marked  subsidence  of 
symptoms ;  and  the  party  which  has  taken  the  place  of  the 
extinct  Tories  is  carrying  through  Parliament  a  wider  ex- 
tension of  the  franchise  than  their  opponents  would  have  ven- 
tured. Napoleon  used  to  say  that  a  decided  nose  was  a  sign 
of  power:  on  which  it  has  been  remarked  that  he  had  good 
reason  to  say  so  before  the  play  was  done.  And  so  had 
our  country ;  it  was  saved  from  a  religious  war,  and  from 
a  civil  war,  by  the  power  of  that  nose  over  its  colleagues. 


188  A  BUDGET  OF  PARADOXES. 

THOMAS  TAYLOR,  THE  PLATONIST. 

The  Commentaries  of  Proclus.1   Translated  by  Thomas  Taylor.2 
London,  1792,  2  vols.  4to.3 

The  reputation  of  "the  Platonist"  begins  to  grow,  and 
will  continue  to  grow.  The  most  authentic  account  is  in 
the  Penny  Cyclopaedia,  written  by  one  of  the  few  persons 
who  knew  him  well,  and  one  of  the  fewer  who  possess  all 
his  works.  At  page  Ivi  of  the  Introduction  is  Taylor's  no- 
tion of  the  way  to  find  the  circumference.  It  is  not  geo- 
metrical, for  it  proceeds  on  the  motion  of  a  point :  the  words 
"on  account  of  the  simplicity  of  the  impulsive  motion,  such 
a  line  must  be  either  straight  or  circular"  will  suffice  to 
show  how  Platonic  it  is.  Taylor  certainly  professed  a  kind 
of  heathenism.  D'Israeli  said,  "Mr.  T.  Taylor,  the  Platonic 
philosopher  and  the  modern  Plethon,4  consonant  to  that  phi- 
losophy, professes  polytheism."  Taylor  printed  this  in  large 
type,  in  a  page  by  itself  after  the  dedication,  without  any  dis- 
avowal. I  have  seen  the  following,  Greek  and  translation 
both,  in  his  handwriting:  "lias  dyaflos  fj  ayaObs  c0nKos-  /cat  Tras 
XpicTTiavos  y  ;(/3«mavos  /caicos.  Every  good  man,  so  far  as  he 
is  a  good  man,  is  a  heathen ;  and  every  Christian,  so  far  as 
he  is  a  Christian,  is  a  bad  man."  Whether  Taylor  had  in  his 
head  the  Christian  of  the  New  Testament,  or  whether  he 
drew  from  those  members  of  the  "religious  world"  who 
make  manifest  the  religious  flesh  and  the  religious  devil, 

*  Proclus  (412-485),  one  of  the  greatest  of  the  neo-Platonists, 
studied  at  Alexandria  and  taught  philosophy  at  Athens.  He  left 
commentaries  on  Plato  and  on  part  of  Euclid's  Elements. 

3  Thomas  Taylor  (1758-1835),  called  "the  Platonist,"  had  a  lik- 
ing for  mathematics,  and  was  probably  led  by  his  interest  in  number 
mysticism  to  a  study  of  neo-Platonism.  He  translated  a  number  of 
works  from  the  Latin  and  Greek,  and  wrote  two  works  on  theoretical 
arithmetic  (1816,  1823). 

'There  was  an  earlier  edition,  1788-89. 

*Georgius  Gemistus,  or  Georgius  Pletho  (Plethon),  lived  in 
the  fourteenth  and  fifteenth  centuries.  He  was  a  native  of  Constan- 
tinople, but  spent  most  of  his  time  in  Greece.  He  devoted  much 
time  to  the  propagation  of  the  Platonic  philosophy,  but  also  wrote  on 
divinity,  geography,  and  history. 


A  NEW  ERA  IN  FICTION.  189 

cannot  be  decided  by  us,  and  perhaps  was  not  known  to 
himself.     If  a  heathen,  he  was  a  virtuous  one. 

A  NEW  ERA  IN  FICTION. 

(1795.)  This  is  the  date  of  a  very  remarkable  paradox. 
The  religious  world — to  use  a  name  claimed  by  a  doctrinal 
sect — had  long  set  its  face  against  amusing  literature,  and 
all  works  of  imagination.  Bunyan,  Milton,  and  a  few  others 
were  irresistible ;  but  a  long  face  was  pulled  at  every  at- 
tempt to  produce  something  readable  for  poor  people  and 
poor  children.'  In  1795,  a  benevolent  association  began  to 
circulate  the  works  of  a  lady  who  had  been  herself  a  drama- 
tist, and  had  nourished  a  pleasant  vein  of  satire  in  the  so- 
ciety of  Garrick  and  his  friends ;  all  which  is  carefully  sup- 
pressed in  some  biographies.  r  Hannah  MoreV  Cheap  Re- 
pository Tracts,2  which  were  bought  by  millions  of  copies, 
destroyed  the  vicious  publications  with  which  the  hawkers 
deluged  the  country,  by  the  simple  process  of  furnishing 
the  hawkers  with  something  more  saleable.1 

Dramatic  fiction,  in  which  the  characters  are  drawn  by 
themselves,  was,  at  the  middle  of  the  last  century,  the  mo- 
nopoly of  writers  who  required  indecorum,  such  as  Fielding 
and  Smollett.  All,  or  nearly  all,  which  could  be  permitted 
to  the  young,  was  dry  narrative,  written  by  people  who  could 
not  make  their  personages  talk  character;  they  all  spoke 

1  Hannah  More  (1745-1833),  was,  in  her  younger  days,  a  friend 
of  Burke,  Reynolds,  Dr.  Johnson,  and  Garrick.     At  this  time  she 
wrote  a  number  of  poems  and  aspired  to  become  a  dramatist.    Her 
Percy  (1777),  with  a  prologue  and  epilogue  by  Garrick,  had  a  long 
run  at  Covent  Garden.     Somewhat  later  she  came  to  believe  that 
the  playhouse  was  a  grave  public  evil,  and  refused  to  attend  the 
revival  of  her  own  play  with   Mrs.   Siddons   in  the   leading  part. 
After  1789  she  and  her  sisters  devoted  themselves  to  starting  schools 
for  poor  children,  teaching  them  religion  and  housework,  but  leaving 
them  illiterate. 

2  These  were  issued  at  the  rate  of  three  each  month, — a  story,  a 
ballad,  and  a  Sunday  tract.     They  were  collected  and  published  in 
one  volume  in  1795.     It  is  said  that  two'million  copies  were  sold  the 
first  year.    There  were  also  editions  in  1798,  1819,  1827,  and  1836-37. 


190  A  BUDGET  OF  PARADOXES. 

alike.  The  author  of  the  Rambler^  is  ridiculed,  because  his 
young  ladies  talk  Johnsonese;  but  the  satirists  forget  that 
all  the  presentable  novel-writers  were  equally  incompetent ; 
even  the  author  of  Zeluco  (1789)4  is  the  strongest  possible 
case  in  point. 

Dr.  Moore,s  the  father  of  the  hero  of  Corunna,6  with 
good  narrative  power,  some  sly  humor,  and  much  observa- 
tion of  character,  would  have  been,  in  our  day,  a  writer 
of  the  Peacock7  family.  Nevertheless,  to  one  who  is  accus- 
tomed to  our  style  of  things,  it  is  comic  to  read  the  dialogue 
of  a  jealous  husband,  a  suspected  wife,  a  faithless  maid- 
servant, a  tool  of  a  nurse,  a  wrong-headed  pomposity  of  a 
priest,  and  a  sensible  physician,  all  talking  Dr.  Moore 
through  their  masks.  Certainly  an  Irish  soldier  does  say 
"by  Jasus,"  and  a  cockney  footman  "this  here"  and  "that 
there" ;  and  this  and  the  like  is  all  the  painting  of  characters 
which  is  effected  out  of  the  mouths  of  the  bearers  by  a  nar- 
rator of  great  power.  I  suspect  that  some  novelists  re- 
pressed their  power  under  a  rule  that  a  narrative  should  nar- 
rate, and  that  the  dramatic  should  be  confined  to  the  drama. 

I  make  no  exception  in  favor  of  Miss  Burney;8  though 
she  was  the  forerunner  of  a  new  era.  Suppose  a  country 

8  That  is,  Dr.  Johnson  (1709-1784).  The  Rambler  was  published 
in  1750- 1752>  and  was  an  imitation  of  Addison's  Spectator. 

4  Dr.  Moore,  referred  to  below. 

5  Dr.  John  Moore    (1729-1802),  physician  and  novelist,  is  now 
best  known  for  his  Journal  during  a  Residence  in  France  from  the 
beginning  of  August  to  the  middle  of  December,  1792,  a  work  quoted 
frequently  by  Carlyle  in  his  French  Revolution. 

6  Sir  John  Moore  (1761-1809),  Lieutenant  General  in  the  Napo- 
leonic wars.    He  was  killed  in  the  battle  of  Corunna.    The  poem  by 
Charles  Wolfe  (1791-1823),  The  Burial  of  Sir  John  Moore  (1817), 
is  well  known. 

7  Referring  to  the  novels  of  Thomas  Love  Peacock  (1785-1866), 
who   succeeded  James   Mill   as   chief   examiner   of  the   East   India 
Company,  and  was  in  turn  succeeded  by  John  Stuart  Mill. 

8  Frances  Burney,  Madame  d'Arblay  (1752-1840),  married  Gen- 
eral d'Arblay,  a  French  officer  and  companion  of  Lafayette,  in  1793- 
She  was  only  twenty-five  when  she  acquired  fame  by  her  Evelina, 
or  a  Young  Lady's  Entrance  into  the  World.  Her  Letters  and  Diaries 
appeared  posthumously   (1842-45). 


A  NEW  ERA  IN  FICTION.  191 

in  which  dress  is  always  of  one  color ;  suppose  an  importer 
who  brings  in  cargoes  of  blue  stuff,  red  stuff,  green  stuff, 
etc.,  and  exhibits  dresses  of  these  several  colors,  that  person 
is  the  similitude  of  Miss  Burney.  It  would  be  a  delightful 
change  from  a  universal  dull  brown,  to  see  one  person  all 
red,  another  all  blue,  etc. ;  but  the  real  inventor  of  pleasant 
dress  would  be  the  one  who  could  mix  his  colors  and  keep 
down  the  bright  and  gaudy.  Miss  Burney 's  introduction 
was  so  charming,  by  contrast,  that  she  nailed  such  men  as 
Johnson,  Burke,  Garrick,  etc.,  to  her  books.  But  when  a 
person  who  has  read  them  with  keen  pleasure  in  boyhood,  as 
I  did,  comes  back  to  them  after  a  long  period,  during  which 
he  has  made  acquaintance  with  the  great  novelists  of  our 
century,  three-quarters  of  the  pleasure  is  replaced  by  wonder 
that  he  had  not  seen  he  was  at  a  puppet-show,  not  at  a  drama. 
Take  some  labeled  characters  out  of  our  humorists,  let  them 
be  put  together  into  one  piece,  to  speak  only  as  labeled :  let 
there  be  a  Dominie  with  nothing  but  "Prodigious !"  a  Dick 
Swiveller  with  nothing  but  adapted  quotations;  a  Dr.  Fol- 
liott  with  nothing  but  sneers  at  Lord  Brougham  ;9  and  the 
whole  will  pack  up  into  one  of  Miss  Burney's  novels. 

Maria  Edgeworth,10  Sydney  Owenson  (Lady  Morgan),11 
Jane  Austen,12  Walter  Scott,1^  etc.,  are  all  of  our  century ;  as 

9  Henry  Peter,   Baron  Brougham  and  Vaux    (1778-1868),  well 
known  in  politics,  science,  and  letters.     He  was  one  of  the  founders 
of  the  Edinburgh  Review,  became  Lord  Chancellor  in  1830,  and  took 
part  with  men  like  William  Frend,  De  Morgan's  father-in-law,  in 
the   establishing  of  London   University.     He   was   also   one   of   the 
founders  of  the  Society  for  the  Diffusion  of  Useful  Knowledge.    He 
was   always    friendly   to   De   Morgan,   who    entered   the    faculty   of 
London  University,  whose  work  on  geometry  was  published  by  the 
Society  mentioned,   and  who  was   offered  the  degree  of  doctor  of 
laws  by  the  University  of   Edinburgh   while   Lord   Brougham  was 
Lord  Rector.     The   Edinburgh   honor  was   refused  by  De   Morgan 
who  said  he  "did  not  feel  like  an  LL.D." 

10  Maria  Edgeworth  (1767-1849). 

11  Sydney  Owenson  (c.  1783-1859)  married  Sir  Thomas  Morgan, 
a  well-known  surgeon,  in  1812.    Her  Irish  stories  were  very  popular 
with  the  patriots  but  were  attacked  by  the  Quarterly  Review.     The 
Wild  Irish  Girl  (1806)  went  through  seven  editions  in  two  years. 

18  1775-1817.  13 1771-1832. 


192  A  BUDGET  OF  PARADOXES. 

are,  I  believe,  all  the  Minerva  Press  novels,  as  they  were 
called,  which  show  some  of  the  power  in  question.  Perhaps 
dramatic  talent  found  its  best  encouragement  in  the  drama 
itself.  But  I  cannot  ascertain  that  any  such  power  was  di- 
rected at  the  multitude,  whether  educated  or  uneducated, 
with  natural  mixture  of  character,  under  the  restraints  of 
decorum,  until  the  use  of  it  by  two  religious  writers  of  the 
school  called  "evangelical,"  Hannah  More  and  Rowland 
Hill.14  The  Village  Dialogues,  though  not  equal  to  the  Re- 
pository Tracts,  are  in  many  parts  an  approach,  and  perhaps 
a  copy;  there  is  frequently  humorous  satire,  in  that  most 
effective  form,  self-display.  They  were  published  in  1800, 
and,  partly  at  least,  by  the  Religious  Tract  Society,  the 
lineal  successsor  of  the  Repository  association,  though  know- 
ing nothing  about  its  predecessor.  I  think  it  right  to  add 
that  Rowland  Hill  here  mentioned  is  not  the  regenerator 
of  the  Post  Office.1*  Some  do  not  distinguish  accurately; 
I  have  heard  of  more  than  one  who  took  me  to  have  had 
a  logical  controversy  with  a  diplomatist  who  died  some 
years  before  I  was  born. 

THE  RELIGIOUS  TRACT  SOCIETY. 

A  few  years  ago,  an  attempt  was  made  by  myself  and 
others  to  collect  some  information  about  the  Cheap  Reposi- 
tory (see  Notes  and  Queries,  3d  Series,  vi.  241,  290,  353; 
Christian  Observer,  Dec.  1864,  pp.  944-49).  It  appeared 
that  after  the  Religious  Tract  Society  had  existed  more  than 
fifty  years,  a  friend  presented  it  with  a  copy  of  the  original 
prospectus  of  the  Repository,  a  thing  the  existence  of  which 
was  not  known.  In  this  prospectus  it  is  announced  that 
from  the  plan  "will  be  carefully  excluded  whatever  is  en- 
thusiastic, absurd,  or  superstitious."  The  "evangelical" 

"The  famous  preacher  (1732-1808).  He  was  the  first  chairman 
of  the  Religious  Tract  Society.  He  is  also  known  as  one  of  the 
earliest  advocates  of  vaccination,  in  his  Cow-pock  Inoculation  vindi- 
cated and  recommended  from  matters  of  fact,  1806. 

15  Sir  Rowland  Hill  (1795-1879),  the  father  of  penny  postage. 


THE  RELIGIOUS  TRACT  SOCIETY.  193 

party  had,  from  the  foundation  of  the  Religious  Tract  So- 
ciety, regretted  that  the  Repository  Tracts  "did  not  contain 
a  fuller  statement  of  the  great  evangelical  principles"  ;  while 
in  the  prospectus  it  is  also  stated  that  "no  cause  of  any  par- 
ticular party  is  intended  to  be  served  by  it,  but  general 
Christianity  will  be  promoted  upon  practical  principles." 
This  explains  what  has  often  been  noticed,  that  the  tracts 
contain  a  mild  form  of  "evangelical"  doctrine,  free  from 
that  more  fervid  dogmatism  which  appears  in  the  Village 
Dialogues',  and  such  as  H.  More's  friend,  Bishop  Porteus1 
—  a  great  promoter  of  the  scheme  —  might  approve.  The 
Religious  Tract  Society  (in  1863)  republished  some  of  H. 
More's  tracts,  with  alterations,  additions,  and  omissions  ad 
libitum.  This  is  an  improper  way  of  dealing  with  the  works 
of  the  dead  ;  especially  when  the  reprints  are  of  popular 
works.  A  small  type  addition  to  the  preface  contains: 
"Some  alterations  and  abridgements  have  been  made  to 
adapt  them  to  the  present  times  and  the  aim  of  the  Religious 
Tract  Society."  I  think  every  publicity  ought  to  be  given 
to  the  existence  of  such  a  practice  ;  and  I  reprint  what  I 
said  on  the  subject  in  Notes  and  Queries. 

Alterations  in  works  which  the  Society  fepublishes  are 
a  necessary  part  of  their  plan,  though  such  notes  as  they 
should  judge  to  be  corrective  would  be  the  best  way  of  pro- 
ceeding. But  the  fact  of  alteration  should  be  very  distinctly 
announced  on  the  title  of  the  work  itself,  not  left  to  a  little 
bit  of  small  type  at  the  end  of  the  preface,  in  the  place 
where  trade  advertisements,  or  directions  to  the  binder,  are 
often  found.  And  the  places  in  which  alteration  has  been 
made  should  be  pointed  out,  either  by  marks  of  omission, 
when  omission  is  the  alteration,  or  by  putting  the  altered 
sentences  in  brackets,  when  change  has  been  made.  May 
any  one  alter  the  works  of  the  dead  at  his  own  discretion? 


ilby  Porteus  (1731-1808),  Bishop  of  Chester  (1776)  and 
Bishop  of  London  (1787).  He  encouraged  the  Sunday-school  move- 
ment and  the  dissemination  of  Hannah  More's  tracts.  He  was  an 
active  opponent  of  slavery,  but  also  of  Catholic  emancipation. 


194  A  BUDGET  OF  PARADOXES. 

We  all  know  that  readers  in  general  will  take  each  sentence 
to  be  that  of  the  author  whose  name  is  on  the  title ;  so  that 
a  correcting  republisher  makes  use  of  his  author  s  name  to 
teach  his  own  variation.  The  tortuous  logic  of  "the  trade," 
which  is  content  when  "the  world"  is  satisfied,  is  not  easily 
answered,  any  more  than  an  eel  is  easily  caught;  but  the 
Religious  Tract  Society  may  be  convinced  [in  the  old  sense] 
in  a  sentence.  On  which  course  would  they  feel  most  safe 
in  giving  their  account  to  the  God  of  truth?  "In  your  own 
conscience,  now?" 

1  have  tracked  out  a  good  many  of  the  variations  made 
by  the  Religious  Tract  Society  in  the  recently  published 
volume  of  Repository  Tracts.     Most  of  them  are  doctrinal 
insertions  or  amplifications,  to  the  matter  of  which  Hannah 
More  would  not  have  objected — all  that  can  be  brought 
against  them  is  the  want  of  notice.    But  I  have  found  two 
which  the  respect  I  have  for  the  Religious  Tract  Society, 
in   spite   of  much   difference  on  various  points,   must  not 
prevent  my  designating  as  paltry.     In  the  story  of  Mary 
Wood,  a  kind-hearted  clergyman  converses  with  the  poor 
girl  who  has  ruined  herself  by  lying.     In  the  original,  he 
"assisted  her  in  the  great  work  of  repentance ;"  in  the  re- 
print it  is  to  be  shown  in  some  detail  how  he  did  this.     He 
is  to  begin  by  pointing  out  that  "the  heart  is  deceitful  above 
all  things  and  desperately  wicked."     Now  the  clergyman's 
name  is  Heart-well:  so  to  prevent  his  name  from  contra- 
dicting his  doctrine,  he  is  actually  cut  down  to  Harwell. 
Hannah  Moore  meant  this  good  man  for  one  of  those  de- 
scribed in  Acts  xv.  8,  9,  and  his  name  was  appropriate. 

Again,  Mr.  Flatterwell,  in  persuasion  of  Parley  the  porter 
to  let  him  into  the  castle,  declares  that  the  worst  he  will  do 
is  to  "play  an  innocent  game  of  cards  just  to  keep  you  awake, 
or  sing  a  cheerful  song  writh  the  maids."  Oh  fie!  Miss 
Hannah  More !  and  you  a  single  lady  too,  and  a  contempo- 
rary of  the  virtuous  Bowdler!2  Though  Flatterwell  be  an 

2  Henrietta  Maria  Bowdler  (1754-1830),  generally  known  as  Mrs. 


THE  RELIGIOUS  TRACT  SOCIETY.  195 

allegory  of  the  devil,  this  is  really  too  indecorous,  even  for 
him.     Out  with  the  three  last  words!  and  out  it  is. 

The  Society  cuts  a  poor  figure  before  a  literary  tribunal. 
Nothing  was  wanted  except  an  admission  that  the  remarks 
made  by  me  were  unanswerable,  and  this  was  immediately 
furnished  by  the  Secretary  (N.  and  Q.}  3d  S.,  vi.  290).  In 
a  reply  of  which  six  parts  out  of  seven  are  a  very  amplified 
statement  that  the  Society  did  not  intend  to  reprint  all  Han- 
nah More's  tracts,  the  remaining  seventh  is  as  follows: 

"I  am  not  careful  [perhaps  this  should  be  careful  not}  to 
notice  Professor  De  Morgan's  objections  to  the  changes  in 
'Mary  Wood'  or  'Parley  the  Porter,'  but  would  merely  re- 
iterate that  the  tracts  were  neither  designed  nor  announced 
to  be  'reprints'  of  the  originals  [design  is  only  known  to 
the  designers ;  as  to  announcement,  the  title  is  '  'Tis  all  for 
the  best,  The  Shepherd  of  Salisbury  Plain,  and  other  narra- 
tives by  Hannah  More']  ;  and  much  less  [this  must  be  care- 
ful not\  further  removed  from  answer  than  not  careful} 
can  I  occupy  your  space  by  a  treatise  on  the  Professor's  ques- 
tion :  'May  any  one  alter  the  works  of  the  dead  at  his  own 
discretion  ?'  " 
To  which  I  say:  Thanks  for  help! 

I  predict  that  Hannah  More's  Cheap  Repository  Tracts 
will  somewhat  resemble  the  Pilgrim's  Progress  in  their  fate. 
Written  for  the  cottage,  and  long  remaining  in  their  original 
position,  they  will  become  classical  works  of  their  kind. 
Most  assuredly  this  will  happen  if  my  assertion  cannot  be 
upset,  namely,  that  they  contain  the  first  specimens  of  fiction 
addressed  to  the  world  at  large,  and  widely  circulated,  in 
which  dramatic — as  distinguished  from  puppet — power  is 
shown,  and  without  indecorum. 

Harriet  Bowdler.  She  was  the  author  of  many  religious  tracts  and 
poems.  Her  Poems  and  Essays  (1786)  were  often  reprinted.  The 
story  goes  that  on  the  appearance  of  her  Sermons  on  the  Doctrines 
and  Duties  of  Christianity  (published  anonymously),  Bishop  Por- 
teus  offered  the  author  a  living  under  the  impression  that  it  was 
written  by  a  man. 


196  A  BUDGET  OF  PARADOXES. 

t 

According  to  some  statements  I  have  seen,  but  which 
I  have  riot  verified,  other  publishing  bodies,  such  as  the 
Christian  Knowledge  Society,  have  taken  the  same  liberty 
with  the  names  of  the  dead  as  the  Religious  Tract  Society.3 
If  it  be  so,  the  impropriety  is  the  work  of  the  smaller  spirits 
who  have  not  been  sufficiently  overlooked.  There  must  be 
an  overwhelming  majority  in  the  higher  councils  to  feel 
that,  whenever  altered  works  are  published,  the  fact  of 
alteration  should  be  made  as  prominent  as  the  'name  of  the 
author.  Everything  short  of  this  is  suppression  of  truth, 
and  will  ultimately  destroy  the  credit  of  the  Society.  Equally 
necessary  is  it  that  the  alterations  should  be  noted.  When  it 
comes  to  be  known  that  the  author  before  him  is  altered, 
he  knows  not  where  nor  how  nor  by  whom,  the  lowest 
reader  will  lose  his  interest. 

A  TRIBUTE  TO  WILLIAM  FREND. 

The  principles  of  Algebra.     By  William  Frend.1     London,  1796, 
8vo.    Second  Part,  1799. 

This  Algebra,  says  Dr.  Peacock,2  shows  "great  distrust 

1  William  Frend  (1757-1841),  whose  daughter  Sophia  Elizabeth 
became  De  Morgan's  wife  (1837),  was  at  one  time  a  clergyman  of 
the  Established  Church,  but  was  converted  to  Unitarianism  (1787). 
He  came  under  De  Morgan's  definition  of  a  true  paradoxer,  carry- 
ing on  a  zealous  warfare  for  what  he  thought  right.  As  a  result 
of  his  Address  to  the  Inhabitants  of  Cambridge  (1787),  and  his 
efforts  to  have  abrogated  the  requirement  that  candidates  for  the 
M.A.  must  subscribe  to  the  thirty-nine  articles,  he  was  deprived  of 
his  tutorship  in  1788.  A  little  later  he  was  banished  (see  De  Mor- 
gan's statement  in  the  text)  from  Cambridge  because  of  his  denun- 
ciation of  the  abuses  of  the  Church  and  his  condemnation  of  the 
liturgy.  His  eccentricity  is  seen  in  his  declining  to  use  negative 
quantities  in  the  operations  of  algebra.  He  finally  became  an  actuary 
at  London  and  was  prominent  in  radical  associations.  He  was  a 
mathematician  of  ability,  having  been  second  wrangler  and  having 
nearly  attained  the  first  place,  and  he  was  also  an  excellent  scholar 
in  Latin,  Greek,  and  Hebrew. 

'George  Peacock  (1791-1858),  Fellow  of  Trinity  College,  Cam- 
bridge, Lowndean  professor  of  astronomy,  and  Dean  of  Ely  Cathe- 
dral (1839).  His  tomb  may  be  seen  at  Ely  where  he  spent  the  latter 
part  of  his  life.  He  was  one  of  the  group  that  introduced  the  mod- 
ern continental  notation  of  the  calculus  into  England,  replacing 


A  TRIBUTE  TO  WILLIAM  FREND.  197 

of  the  results  of  algebraical  science  which  were  in  existence 
at  the  time  when  it  was  written/'  Truly  it  does ;  for,  as 
Dr.  Peacock  had  shown  by  full  citation,  it  makes  war  of 
extermination  upon  all  that  distinguishes  algebra  from  arith- 
metic. Robert  Simson3  and  Baron  Maseres4  were  Mr.  Frend's 
predecessors  in  this  opinion. 

The  genuine  respect  which  I  entertained  for  my  father- 
in-law  did  not  prevent  my  canvassing  with  perfect  freedom 
his  anti-algebraical  and  anti-Newtonian  opinions,  in  a  long 
obituary  memoir  read  at  the  Astronomical  Society  in  Feb- 
ruary 1842,  which  was  written  by  me.  It  was  copied  into 
the  Athen&um  of  March  19.  It  must  be  said  that  if  the 
manner  in  which  algebra  was  presented  to  the  learner  had 
been  true  algebra,  he  would  have  been  right :  and  if  he  had 
confined  himself  to  protesting  against  the  imposition  of  at- 
traction as  a  fundamental  part  of  the  existence  of  matter, 
he  would  have  been  in  unity  with  a  great  many,  including 
Newton  himself.  I  wish  he  had  preferred  amendment  to 
rejection  when  he  was  a  college  tutor:  he  wrote  and  spoke 
English  with  a  clearness  which  is  seldom  equaled. 

His  anti-Newtonian  discussions  are  confined  to  the  pre- 
liminary chapters  of  his  Evening  Amusements,5  a  series  of 
astronomical  lessons  in  nineteen  volumes,  following  the 
moon  through  a  period  of  the  golden  numbers. 

There  is  a  mistake  about  him  which  can  never  be  de- 
stroyed. It  is  constantly  said  that,  at  his  celebrated  trial  in 
1792,  for  sedition  and  opposition  to  the  Liturgy,  etc.,  he  was 
expelled  from  the  University.  He  was  banished.  People 
cannot  see  the  difference;  but  it  made  all  the  difference  to 

the   cumbersome    notation    of    Newton,    passing    from   "the    dofage 
of  fluxions  to  the  deism  of  the  calculus." 

'Robert  Simson  (1687-1768),  professor  of  mathematics  at  Glas- 
gow. His  restoration  of  Apollonius  (1749)  and  his  translation  and 
restoration  of  Euclid  (1756,  and  1776— posthumous)  are  well  known. 

4  Francis  Maseres  (1731-1824),  a  prominent  lawyer.   His  mathe- 
matical works  had  some  merit. 

5  These  appeared  annually  from  1804  to  1822. 


198  A  BUDGET  OF  PARADOXES. 

Mr.  Frend.  He  held  his  fellowship  and  its  profits  till  his 
marriage  in  1808,  and  was  a  member  of  the  University  and 
of  its  Senate  till  his  death  in  1841,  as  any  Cambridge  Calen- 
dar up  to  1841  will  show.  That  they  would  have  expelled 
him  if  they  could,  is  perfectly  true;  and  there  is  a  funny 
story — also  perfectly  true — about  their  first  proceedings  be- 
ing under  a  statute  which  would  have  given  the  power,  had 
it  not  been  discovered  during  the  proceedings  that  the  statute 
did  not  exist.  It  had  come  so  near  to  existence  as  to  be  en- 
tered into  the  Vice-Chancellor's  book  for  his  signature, 
which  it  wanted,  as  was  not  seen  till  Mr.  Frend  exposed  it: 
in  fact,  the  statute  had  never  actually  passed. 

There  is  an  absurd  mistake  in  Gunning's6  Reminiscences 
of  Cambridge.  In  quoting  a  passage  of  Mr.  Frend's  pam- 
phlet, which  was  very  obnoxious  to  the  existing  Government, 
it  is  printed  that  the  poor  market-women  complained  that 
they  were  to  be  scotched  a  quarter  of  their  wages  by  taxation ; 
and  attention  is  called  to  the  word  by  its  being  three  times 
printed  in  italics.  In  the  pamphlet  it  is  "sconced" ;  that 
very  common  old  word  for  fined  or  mulcted. 

Lord  Lyndhurst,7  who  has  [1863]  just  passed  away  under 
a  load  of  years  and  honors,  was  Mr.  Frend's  private  pupil 
at  Cambridge.  At  the  time  of  the  celebrated  trial,  he  and 
two  others  amused  themselves,  and  vented  the  feeling  which 
was  very  strong  among  the  undergraduates,  by  chalking  the 
walls  of  Cambridge  with  "Frend  for  ever!"  While  thus 
engaged  in  what,  using  the  term  legally,  we  are  probably 
to  call  his  first  publication,  he  and  his  friends  were  surprised 
by  the  proctors.  Flight  and  chase  followed  of  course :  Cop- 
ley and-  one  of  the  others,  Serjeant  Rough,8  escaped ;  the 

"Henry  Gunning  (1768-1854)  was  senior  esquire  bedell  of  Cam- 
bridge. The  Reminiscences  appeared  in  two  volumes  in  1854. 

7  John  Singleton  Copley,  Baron  Lyndhurst  (1772-1863),  the 
son  of  John  Singleton  Copley  the  portrait  painter,  was  born  in  Bos- 
ton. He  was  educated  at  Trinity  College,  Cambridge,  and  became  a 
lawyer.  He  was  made  Lord  Chancellor  in  1827. 

'Sir  William  Rough  (c.  1772-1838),  a  lawyer  and  poet,  became 
Chief  Justice  of  Ceylon  in  1836.  He  was  knighted  in  1837. 


A  TRIBUTE  TO  WILLIAM  FREND.  199 

third,  whose  name  I  forget,  but  who  afterwards,  I  have  been 
told  was  a  bishop,9  being  lame,  was  captured  and  imposi- 
tioned.  Looking  at  the  Cambridge  Calendar  to  verify  the 
fact  that  Copley  was  an  undergraduate  at  the  time,  I  find 
that  there  are  but  two  other  men  in  the  list  of  honors 
of  his  year  whose  names  are  now  widely  remembered.  And 
they  were  both  celebrated  schoolmasters;  Butler10  of  Har- 
row, and  Tate11  of  Richmond. 

But  Mr.  Frend  had  another  noted  pupil.  I  once  had  a 
conversation  with  a  very  remarkable  man,  who  was  gen- 
erally called  "Place,12  the  tailor,"  but  who  was  politician, 
political  economist,  etc.,  etc.  He  sat  in  the  room  above  his 
shop — he  was  then  a  thriving  master  tailor  at  Charing  Cross 
— surrounded  by  books  enough  for  nine,  to  shame  a  proverb. 
The  blue  books  alone,  cut  up  into  strips,  would  have  measured 
Great  Britain  for  oh-no-we-never-mention-'ems,  the  High- 
lands included.  I  cannot  find  a  biography  of  this  worthy 
and  able  man.  I  happened  to  mention  William  Frend,  and 
he  said,  "Ah!  my  old  master,  as  I  always  call  him.  Many 
and  many  a  time,  and  year  after  year,  did  he  come  in  every 

"Herbert  Marsh,  afterwards  Bishop  of  Peterborough,  a  relation 
of  my  father. — S.  E.  De  M. 

He  was  born  in  1757  and  died  in  1839.  On  the  trial  of  Frend 
he  publicly  protested  against  testifying  against  a  personal  confidant, 
and  was  excused.  He  was  one  of  the  first  of  the  English  clergy  to 
study  modern  higher  criticism  of  the  Bible,  and  amid  much  opposi- 
tion he  wrote  numerous  works  on  the  subject.  He  was  professor  of 
theology  at  Cambridge  (1707),  Bishop  of  Llandaff  (1816),  and 
Bishop  of  Peterborough. 

10  George  Butler  (1774-1853),  Headmaster  of  Harrow  (1805- 
1829),  Chancellor  of  Peterborough  (1836),  and  Dean  of  Peterbor- 
ough (1842). 

"James  Tate  (1771-1843),  Headmaster  of  Richmond  School 
(1796-1833)  and  Canon  of  St.  Paul's  Cathedral  (1833).  He  left 
several  works  on  the  classics. 

"Francis  Place  (1771-1854),  at  first  a  journeyman  breeches 
maker,  and  later  a  master  tailor.  He  was  a  hundred  years  ahead  of 
his  time  as  a  strike  leader,  but  was  not  so  successful  as  an  agitator 
as  he  was  as  a  tailor,  since  his  shop  in  Charing  Cross  made  him 
wealthy.  He  was  a  well-known  radical,  and  it  was  largely  due  to 
his  efforts  that  the  law  against  the  combinations  of  workmen  was 
repealed  in  1824.  His  chief  work  was  The  Principles  of  Population 
(1822). 


200  A  BUDGET  OF  PARADOXES. 

now  and  then  to  give  me  instruction,  while  I  was  sitting 
on  the  board,  working  for  my  living,  you  know." 

Place,  who  really  was  a  sound  economist,  is  joined  with 
Cobbett,  because  they  were  together  at  one  time,  and  because 
he  was,  in  1800,  etc.,  a  great  Radical.  But  for  Cobbett  he 
had  a  great  contempt.  He  told  me  the  following  story.  He 
and  others  were  advising  with  Cobbett  about  the  defense 
he  was  to  make  on  a  trial  for  seditious  libel  which  was  com- 
ing on.  Said  Place,  "You  must  put  in  the  letters  you  have 
received  from  Ministers,  members  of  the  Commons  from  the 
Speaker  downwards,  etc.,  about  your  Register,  and  their 
wish  to  have  subjects  noted.  You  must  then  ask  the  jury 
whether  a  person  so  addressed  must  be  considered  as  a  com- 
mon sower  of  sedition,  etc.  You  will  be  acquitted ;  nay,  if 
your  intention  should  get  about,  very  likely  they  will  man- 
age to  stop  proceedings."  Cobbett  was  too  much  disturbed 

to  listen ;  he  walked  about  the  room  ejaculating  "D the 

prison !"  and  the  like.     He  had  not  the  sense  to  follow  the 
advice,  and  was  convicted. 

Cobbett,  to  go  on  with  the  chain,  was  a  political  acrobat, 
ready  for  any  kind  of  posture.  A  friend  of  mine  gave  me 
several  times  an  account  of  a  mission  to  him.  A  Tory  mem- 
ber— those  who  know  the  old  Tory  world  may  look  for  his 
initials  in  initials  of  two  consecutive  words  of  "Pay  his 
money  with  interest" — who  was,  of  course,  a  political  oppo- 
nent, thought  Cobbett  had  been  hardly  used,  and  deter- 
mined to  subscribe  handsomely  towards  the  expenses  he  was 
incurring  as  a  candidate.  My  friend  was  commissioned  to 
hand  over  the  money — a  bag  of  sovereigns,  that  notes  might 
not  be  traced.  He  went  into  Cobbett's  committee-room, 
told  the  patriot  his  errand,  and  put  the  money  on  the  table. 
"And  to  whom,  sir,  am  I  indebted?"  said  Cobbett.  "The 
donor,"  was  the  answer,  "is  Mr.  Andrew  Theophilus  Smith," 
or  some  such  unlikely  pair  of  baptismals.  "Ah !"  said  Cob- 
bett, "I  have  known  Mr.  A.  T.  S.  a  long  time !  he  was  always 
a  true  friend  of  his  country !" 


A  TRIBUTE  TO  WILLIAM  FREND.  201 

To  return  to  Place.  He  is  a  noted  instance  of  the  ad- 
vantage of  our  jury  system,  which  never  asks  a  man's  poli- 
tics, etc.  The  late  King  of  Hanover,  when  Duke  of  Cumber- 
land, being  unpopular,  was  brought  under  unjust  suspicions 
by  the  suicide  of  his  valet:  he  must  have  seduced  the  wife 
and  murdered  the  husband.  The  charges  were  as  absurd 
as  those  brought  against  the  Englishman  in  the  Frenchman's 
attempt  at  satirical  verses  upon  him: 

"The  Englishman  is  a  very  bad  man; 
He  drink  the  beer  and  he  steal  the  can : 
He  kiss  the  wife  and  he  beat  the  man ; 
And  the  Englishman  is  a  very  G d ." 

The  charges  were  revived  in  a  much  later  day,  and  the 
defense  might  have  given  some  trouble.  But  Place,  who 
had  been  the  foreman  at  the  inquest,  came  forward,  and 
settled  the  question  in  a  few  lines.  Every  one  knew  that 
the  old  Radical  was  quite  free  of  all  disposition  to  suppress 
truth  from  wish  to  curry  favor  with  royalty. 

John  Speed,13  the  author  of  the  English  History,14  1632) 
which  Bishop  Nicolson15  calls  the  best  chronicle  extant,  was 
a  man,  like  Place,  of  no  education,  but  what  he  gave  himself. 
The  bishop  says  he  would  have  done  better  if  he  had  a  better 
training:  but  what,  he  adds,  could  have  been  expected  from 
a  tailor!  This  Speed  was,  as  well  as  Place.  But  he  was 

"Speed  (1552-1629)  was  a  tailor  until  Grevil  (Greville)  made 
him  independent  of  his  trade.  He  was  not  only  an  historian  of 
some  merit,  but  a  skilful  cartographer.  His  maps  of  the  counties 
were  collected  in  the  Theatre  of  the  Empire  of  Great  Britaine,  1611. 
About  this  same  time  he  also  published  Genealogies  recorded  in 
Sacred  Scripture,  a  work  that  had  passed  through  thirty-two  edi- 
tions by  1640. 

14  The  history  of  Great  Britaine  under  the  conquests  of  ye  Ro- 
mans, Saxons,  Danes,  and  Normans London,  1611,  folio.  The 

second  edition  appeared  in  1623 ;  the  third,  to  which  De  Morgan  here 
refers,  posthumously  in  1632;  and  the  fourth  in  1650. 

"William  Nicolson  (1655-1727)  became  Bishop  of  Carlisle  in 
1702,  and  Bishop  of  Derry  in  1718,  His  chief  work  was  the  Histor- 
ical Library  (1696-1724),  in  the  form  of  a  collection  of  documents 
and  chronicles.  It  was  reprinted  in  1736  and  in  1776. 


202  A  BUDGET  OF  PARADOXES. 

released  from  manual  labor  by  Sir  Fulk  Grevil,16  who  en- 
abled him  to  study. 

A  STORY   ON   SIMSON. 

I  have  elsewhere  noticed  that  those  who  oppose  the  mys- 
teries of  algebra  do  not  ridicule  them;  this  I  want  the  cy- 
clometers to  do.  Of  the  three  who  wrote  against  the  great 
point,  the  negative  quantity,  and  the  uses  of  0  which  are 
connected  with  it,  only  one  could  fire  a  squib.  That  Robert 
Simson1  should  do  such  a  thing  will  be  judged  impossible 
by  all  who  admit  tradition.  I  do  not  vouch  for  the  follow- 
ing; I  give  it  as  a  proof  of  the  impression  which  prevailed 
about  him: 

He  used  to  sit  at  his  open  window  on  the  ground  floor, 
as  deep  in  geometry  as  a  Robert  Simson  ought  to  be.  Here 
he  would  be  accosted  by  beggars,  to  whom  he  generally 
gave  a  trifle,  he  roused  himself  to  hear  a  few  words  of  the 
story,  made  his  donation,  and  instantly  dropped  down  into 
his  depths.  Some  wags  one  day  stopped  a  mendicant  who 
was  on  his  way  to  the  window  with  "Now,  my  man,  do  as 
we  tell  you,  and  you  will  get  something  from  that  gentle- 
man, and  a  shilling  from  us  besides.  You  will  go  and  say 
you  are  in  distress,  he  will  ask  you  who  you  are,  and  you 
will  say  you  are  Robert  Simson,  son  of  John  Simson  of 
Kirktonhill."  The  man  did  as  he  was  told ;  Simson  quietly 
gave  him  a  coin,  and  dropped  off.  The  wags  watched  a 
little,  and  saw  him  rouse  himself  again,  and  exclaim  "Robert 
Simson,  son  of  John  Simson  of  Kirktonhill !  why,  that  is  my- 
self. That  man  must  be  an  impostor."  Lord  Brougham 
tells  the  same  story,  with  some  difference  of  details. 

"Sir  Fulk  Grevil,  or  Fulke  Greville  (1554-1628),  was  a  favorite 
of  Queen  Elizabeth,  Chancellor  of  the  Exchequer  under  James  I,  a 
patron  of  literature,  and  a  friend  of  Sir  Philip  Sidney. 

1  See  note  4  on  page  197. 


BARON   MASERES.  203 


BARON  MASERES. 

Baron  Maseres1  was,  as  a  writer,  dry ;  those  who  knew 
his  writings  will  feel  that  he  seldom  could  have  taken  in  a 
joke  or  issued  a  pun.  Maseres  was  the  fourth  wrangler 
of  1752,  and  first  Chancellor's  medallist  (or  highest  in  clas- 
sics) ;  his  second  was  Porteus2  (afterward  Bishop  of  Lon- 
don). Waring3  came  five  years  after  him:  he  could  not 
get  Maseres  through  the  second  page  of  his  first  book  on 
algebra ;  a  negative  quantity  stood  like  a  lion  in  the  way. 
In  1758  he  published  his  Dissertation  on  the  Use  of  the 
Negative  Sign*  4to.  There  are  some  who  care  little  about 
+  and  — ,  who  would  give  it  house-room  for  the  sake  of 
the  four  words  "Printed  by  Samuel  Richardson." 

Maseres  speaks  as  follows :  "A  single  quantity  can  never 
be  marked  with  either  of  those  signs,  or  considered  as 
either  affirmative  or  negative ;  for  if  any  single  quantity,  as 
b,  is  marked  either  with  the  sign  -|-  or  with  the  sign  — 
without  assigning  some  other  quantity,  as  a,  to  which  it  is 
to  be  added,  or  from  which  it  is  to  be  subtracted,  the  mark 
will  have  no  meaning  or  signification:  thus  if  it  be  said 
that  the  square  of  — 5,  or  the  product  of  — 5  into  — 5,  is 
equal  to  +25,  such  an  assertion  must  either  signify  no  more 
than  that  5  times  5  is  equal  to  25  without  any  regard  to  the 
signs,  or  it  must  be  mere  nonsense  and  unintelligible  jargon. 
I  speak  according  to  the  foregoing  definition,  by  which  the 
affirmativeness  or  negativeness  of  any  quantity  implies  a 
relation  to  another  quantity  of  the  same  kind  to  which  it 

1  See  note  5  on  page  197. 

2  See  note  on  page  193. 

8  Edward  Waring  (1736-1796)  was  Lucasian  professor  of  mathe- 
matics at  Cambridge.  He  published  several  works  on  analysis  and 
curves.  The  work  referred  to  was  the  Miscellanea  Analytic?  de 
aequationibus  algebraicis  et  curvarum  proprietatibus,  Cambridge, 
1762. 

*  A  Dissertation  on  the  use  of  the  Negative  Sign  in  Algebra ; 

to  which  is  added,  Machin's  Quadrature  of  the  Circle,  London,  1758. 


204  A  BUDGET  OF  PARADOXES. 

is  added,  or  from  which  it  is  subtracted ;  for  it  may  perhaps 
be  very  clear  and  intelligible  to  those  who  have  formed  to 
themselves  some  other  idea  of  affirmative  and  negative  quan- 
tities different  from  that  above  denned." 

Nothing  can  be  more  correct,  or  more  identically  logical : 
+5  and  — 5,  standing  alone,  are  jargon  if  +5  and  — 5  are 
to  be  understood  as  without  reference  to  another  quantity. 
But  those  who  have  "formed  to  themselves  some  other  idea" 
see  meaning  enough.  The  great  difficulty  of  the  opponents 
of  algebra  lay  in  want  of  power  or  will  to  see  extension  of 
terms.  Maseres  is  right  when  he  implies  that  extension, 
accompanied  by  its  refusal,  makes  jargon.  One  of  my  para- 
doxers  was  present  at  a  meeting  of  the  Royal  Society  (in 
1864,  I  think)  and  asked  permission  to  make  some  remarks 
upon  a  paper.  He  rambled  into  other  things,  and,  naming 
me,  said  that  I  had  written  a  book  in  which  two  sides  of  a 
triangle  are  pronounced  equal  to  the  third. s  So  they  are, 
in  the  sense  in  which  the  word  is  used  in  complete  algebra ; 
in  which  A+B  =  C  makes  A,  B,  C,  three  sides  of  a  triangle, 
and  declares  that  going  over  A  and  B,  one  after  the  other, 
is  equivalent,  in  change  of  place,  to  going  over  C  at  once. 
My  critic,  who  might,  if  he  pleased,  have  objected  to  exten- 
sion, insisted  upon  reading  me  in  unextended  meaning. 

On  the  other  hand,  it  must  be  said  that  those  who  wrote 
on  the  other  idea  wrote  very  obscurely  about  it  and  justified 
Des  Cartes  (De  Methodo)6  when  he  said:  "Algebram  vero, 
ut  solet  doceri,  animadvert!  certis  regulis  et  numerandi  for- 
mulis  ita  esse  contentam,  ut  videatur  potius  ars  quaedam 
confusa,  cujus  usu  ingenium  quodam  modo  turbatur  et  ob- 
scuratur,  quam  scientia  qua  excolatur  et  perspicacius  redda- 

B  The  paper  was  probably  one  on  complex  numbers,  or  possibly 
one  on  quaternions,  in  which  direction  as  well  as  absolute  value  is 
involved. 

8De  Morgan  quotes  from  one  of  the  Latin  editions.  Descartes 
wrote  in  French,  the  title  of  his  first  edition  being:  Discours  de  la 
methode  pour  bien  conduire  sa  raison  et  chercher  la  verite  dans  les 
sciences,  plus  la  dioptrique,  les  meteores  et  la  geometrie  qui  sont  des 
essais  de  cette  methode,  Leyden,  1637,  4to. 


BARON  MASERES.  205 

tur."7  Maseres  wrote  this  sentence  on  the  title  of  his  own 
work,  now  before  me ;  he  would  have  made  it  his  motto  if 
he  had  found  it  earlier. 

There  is,  I  believe,  in  Cobbett's  Annual  Register?  an  ac- 
count of  an  interview  between  Maseres  and  Cobbett  when 
in  prison. 

The  conversation  of  Maseres  was  lively,  and  full  of  se- 
rious anecdote:  but  only  one  attempt  at  humorous  satire  is 
recorded  of  him;  it  is  an  instructive  one.  He  was  born  in 
1731  (Dec.  15),  and  his  father  was  a  refugee.  French  was 
the  language  of  the  house,  with  the  pronunciation  of  the 
time  of  Louis  XIV.  He  lived  until  1824  (May  19),  and  saw 
the  race  of  refugees  who  were  driven  out  by  the  first  Revo- 
lution. Their  pronunciation  differed  greatly  from  his  own ; 
and  he  used  to  amuse  himself  by  mimicking  them.  Those 
who  heard  him  and  them  had  the  two  schools  of  pronuncia- 
tion before  them  at  once ;  a  thing  which  seldom  happens. 
It  might  even  yet  be  worth  while  to  examine  the  Canadian 
pronunciation. 

Maseres  went  as  Attorney-General  to  Quebec;  and  was 
appointed  Cursitor  Baron  of  our  Exchequer  in  1773.  There 
is  a  curious  story  about  his  mission  to  Canada,  which  I  have 
heard  as  good  tradition,  but  have  never  seen  in  print.  The 
reader  shall  have  it  as  cheap  as  I ;  and  I  confess  I  rather 
believe  it.  Maseres  was  inveterately  honest ;  he  could  not, 
at  the  bar,  bear  to  see  his  own  client  victorious,  when  he 
knew  his  cause  was  a  bad  one.  On  a  certain  occasion  he 
was  in  a  cause  which  he  knew  would  go  against  him  if  a 
certain  case  were  quoted.  Neither  the  judge  nor  the  oppo- 
site counsel  seemed  to  remember  this  case,  and  Maseres 
could  not  help  dropping  an  allusion  which  brought  it  out. 

T"I  have  observed  that  algebra  indeed,  as  it  is  usually  taught, 
is  so  restricted  by  definite  rules  and  formulas  of  calculation,  that  it 
seems  rather  a  confused  kind  of  an  art,  by  the  practice  of  which 
the  mind  is  in  a  certain  manner  disturbed  and  obscured,  than  a 
science  by  which  it  is  cultivated  and  made  acute." 

"It  appeared  in  93  volumes,  from  1758  to  1851. 


206  A  BUDGET  OF  PARADOXES. 

His  business  as  a  barrister  fell  off,  of  course.  Some  time 
after,  Mr.  Pitt  (Chatham)  wanted  a  lawyer  to  send  to  Can- 
ada on  a  private  mission,  and  wanted  a  very  honest  man. 
Some  one  mentioned  Maseres,  and  told  the  above  story: 
Pitt  saw  that  he  had  got  the  man  he  wanted.  The  mission 
was  satisfactorily  performed,  and  Maseres  remained  as  At- 
torney-General. 

The  Doctrine  of  Life  Annuities9  (4to,  726  pages,  1783) 
is  a  strange  paradox.  Its  size,  the  heavy  dissertations  on 
the  national  debt,  and  the  depth  of  algebra  supposed  known, 
put  it  out  of  the  question  as  an  elementary  work,  and  it  is 
unfitted  for  the  higher  student  by  its  elaborate  attempt  at 
elementary  character,  shown  in  its  rejection  of  forms  derived 
from  chances  in  favor  of  the  average,  and  its  exhibition  of 
the  separate  values  of  the  years  of  an  annuity,  as  arithmetical 
illustrations.  It  is  a  climax  of  unsaleability,  unreadability, 
and  inutility.  For  intrinsic  nullity  of  interest,  and  dilution 
of  little  matter  with  much  ink,  I  can  compare  this  book  to 
nothing  but  that  of  Claude  de  St.  Martin,  elsewhere  men- 
tioned, or  the  lectures  On  the  Nature  and  Properties  of  Log- 
arithms, by  James  Little,10  Dublin,  1830,  8vo.  (254  heavy 
pages  of  many  words  and  few  symbols),  a  wonderful  weight 
of  weariness. 

The  stock  of  this  work  on  annuities,  very  little  dimin- 
ished, was  given  by  the  author  to  William  Frend,  who  paid 
warehouse  room  for  it  until  about  1835,  when  he  consulted 
me  as  to  its  disposal.  As  no  publisher  could  be  found  who 
would  take  it  as  a  gift,  for  any  purpose  of  sale,  it  was  con- 
signed, all  but  a  few  copies,  to  a  buyer  of  waste  paper. 

Baron  Maseres's  republications  are  well  known:  the 
Scriptores  Logarithmici11  is  a  set  of  valuable  reprints,  mixed 

9  The  principles  of  the  doctrine  of  life -annuities;  explained  in 

a  familiar  manner with  a  variety  of  new  tables  ....,  London, 

1783. 

10 1  suppose  the  one  who  wrote  Conjectures  on  the  physical  causes 
of  Earthquakes  and  Volcanoes,  Dublin,  1820. 

11  Scriptores  Logarithmici;  or,  a  Collection  of  several  curious 


BARON  MASERES.  207 

with  much  which  might  better  have  entered  into  another 
collection.  It  is  not  so  well  known  that  there  is  a  volume 
of  optical  reprints,  Script  ores  Optici,  London,  1823,  4to, 
edited  for  the  veteran  of  ninety-two  by  Mr.  Babbage12  at 
twenty-nine.  This  excellent  volume  contains  James  Greg- 
ory, Des  Cartes,  Halley,  Barrow,  and  the  optical  writings 
of  Huyghens,  the  Principia  of  the  undulatory  theory.  It 
also  contains,  by  the  sort  of  whim  in  which  such  men  as 
Maseres,  myself,  and  some  others  are  apt  to  indulge,  a  reprint 
of  "The  great  new  Art  of  weighing  Vanity,"1^  by  M.  Patrick 
Mathers,  Arch-Bedel  to  the  University  of  St.  Andrews, 
Glasgow,  1672.  Professor  Sinclair, T*  of  Glasgow,  a  good  man 
at  clearing  mines  of  the  water  which  they  did  not  want,  and 
furnishing  cities  with  water  which  they  did  want,  seems  to 
have  written  absurdly  about  hydrostatics,  and  to  have  at- 
tacked a  certain  Sanders,1*  M.A.  So  Sanders,  assisted  by 
James  Gregory,  published  a  heavy  bit  of  jocosity  about  him. 
This  story  of  the  authorship  rested  on  a  note  made  in  his 

tracts  on  the  nature  and  construction  of  Logarithms....  together 
with  same  tracts  on  the  Binomial  Theorem....,  6  vols.,  London, 
1791-1807. 

"Charles  Babbage  (1792-1871),  whose  work  on  the  calculating 
machine  is  well  known.  Maseres  was,  it  is  true,  ninety-two  at  this 
time,  but  Babbage  was  thirty-one  instead  of  twenty-nine.  He  had 
already  translated  Lacroix's  Treatise  on  the  differential  and  integral 
calculus  (1816),  in  collaboration  with  Herschel  and  Peacock.  He 
was  Lucasian  professor  of  mathematics  at  Cambridge  from  1828  to 
1839- 

"  The  great  and  new  Art  of  weighing  Vanity,  or  a  discovery  of 
the  ignorance  of  the  great  and  new  artist  in  his  pseudo-philosophical 
writings.  The  "great  and  new  artist"  was  Sinclair. 

"George  Sinclair,  probably  a  native  of  East  Lothian,  who  died 
in  1696.  He  was  professor  of  philosophy  and  mathematics  at  Glas- 
gow, and  was  one  of  the  first  to  use  the  barometer  in  measuring 
altitudes.  The  work  to  which  De  Morgan  refers  is  his  Hydrostaticks 
(1672).  He  was  a  firm  believer  in  evil  spirits,  his  work  on  the 
subject  going  through  four  editions:  Satan's  Invisible  World  Dis- 
covered; or,  a  choice  collection  of  modern  relations,  proving  evi- 
dently against  the  Saducees  and  Athiests  of  this  present  age,  that 
there  are  Devils,  Spirits,  Witches,  and  Apparitions,  Edinburgh,  1685. 

16  This  was  probably  William  Sanders,  Regent  of  St.  Leonard's 
College,  whose  Theses  philosophicae  appeared  in  1674,  and  whose 
Elementa  geometriae  came  out  a  dozen  years  later. 


208  A  BUDGET  OF  PARADOXES. 

copy  by  Robert  Gray,  M.D. ;  but  it  has  since  been  fully  con- 
firmed by  a  letter  of  James  Gregory  to  Collins,  in  the 
Macclesfield  Correspondence.  "There  is  one  Master  Sin- 
clair, who  did  write  the  Ars  Magna  et  Nova,16  a  pitiful  ig- 
norant fellow,  who  hath  lately  written  horrid  nonsense  in 
the  hydrostatics,  and  hath  abused  a  master  in  the  University, 
one  Mr.  Sanders,  in  print.  This  Mr.  Sanders ....  is  resolved 
to  cause  the  Bedel  of  the  University  to  write  against  him . . . 
We  resolve  to  make  excellent  sport  with  him." 

On  this  I  make  two  remarks :  First,  I  have  learned  from 
experience  that  old  notes,  made  in  books  by  their  possessors, 
are  statements  of  high  authority:  they  are  almost  always 
confirmed.  I  do  not  receive  them  without  hesitation ;  but  I 
believe  that  of  all  the  statements  about  books  which  rest  on 
one  authority,  there  is  a  larger  percentage  of  truth  in  the 
written  word  than  in  the  printed  word.  Secondly,  I  mourn 
to  think  that  when  the  New  Zealander  picks  up  his  old  copy 
of  this  book,  and  reads  it  by  the  associations  of  his  own  day, 
he  may,  in  spite  of  the  many  assurances  I  have  received  that 
my  Athen&um  Bridget  was  amusing,  feel  me  to  be  as  heavy 
as  I  feel  James  Gregory  and  Sanders.  But  he  will  see  that 
I  knew  what  was  coming,  which  Gregory  did  not. 

MR.  TREND'S  BURLESQUE. 

It  was  left  for  Mr.  Frend  to  prove  that  an  impugner  of 
algebra  could  attempt  ridicule.  He  was,  in  1803,  editor  of 
a  periodical  The  Gentleman's  Monthly  Miscellany,  which 
lasted  a  few  months.1  To  this,  among  other  things,  he  con- 
tributed the  following,  in  burlesque  of  the  use  made  of  0, 
to  which  he  objected.2  The  imitation  of  Rabelais,  a  writer 

18  Ars  nova  et  magna  gravitatis  et  levitatis^.  sive  dialogorum  phi- 
losophicorum  libri  sex  de  aeris  vera  ac  reali  gravitate,  Rotterdam, 
1669,  4to. 

1  Volume  I,  Nos.  I  and  2,  appeared  in  1803. 

3  His  daughter,  Mrs.  De  Morgan,  says  in  her  Memoir  of  her 
husband:  "My  father  had  been  second  wrangler  in  a  year  in  which 
the  two  highest  were  close  together,  and  was,  as  his  son-in-law 
afterwards  described  him,  an  exceedingly  clear  thinker.  It  is  pos- 


MR.  TREND'S  BURLESQUE.  209 

in  whom  he  delighted,  is  good:  to  those  who  have  never 
dipped,  it  may  give  such  a  notion  as  they  would  not  easily 
get  elsewhere.  The  point  of  the  satire  is  not  so  good.  But 
in  truth  it  is  not  easy  to  make  pungent  scoffs  upon  what  is 
common  sense  to  all  mankind.  Who  can  laugh  with  effect 
at  six  times  nothing  is  nothing,  as  false  or  unintelligible? 
In  an  article  intended  for  that  undistinguishing  know-0  the 
"general  reader,"  there  would  have  been  no  force  of  satire, 
if  division  by  0  had  been  separated  from  multiplication  by 
the  same. 

I  have  followed  the  above  by  another  squib,  by  the  same 
author,  on  the  English  language.  The  satire  is  covertly 
aimed  at  theological  phraseology ;  and  any  one  who  watches 
this  subject  will  see  that  it  is  a  very  just  observation  that 
the  Greek  words  are  not  boiled  enough. 

PANTAGRUEI/S  DECISION  of  the  QUESTION  about  NOTHING. 

"Pantagruel  determined  to  have  a  snug  afternoon  with 
Epistemon  and  Panurge.  Dinner  was  ordered  to  be  set  in 
a  small  parlor,  and  a  particular  batch  of  Hermitage  with 
some  choice  Burgundy  to  be  drawn  from  a  remote  corner 
of  the  cellar  upon  the  occasion.  By  way  of  lunch,  about 
an  hour  before  dinner,  Pantagruel  was  composing  his  stom- 
ach with  German  sausages,  reindeer's  tongues,  oysters, 
brawn,  and  half  a  dozen  different  sorts  of  English  beer 
just  come  into  fashion,  when  a  most  thundering  knocking 
was  heard  at  the  great  gate,  and  from  the  noise  they  ex- 
pected it  to  announce  the  arrival  at  least  of  the  First  Consul, 
or  king  Gargantua.  Panurge  was  sent  to  reconnoiter,  and 
after  a  quarter  of  an  hour's  absence,  returned  with  the 
news  that  the  University  of  Pontemaca  was  waiting  his  high- 
ness's  leisure  in  the  great  hall,  to  propound  a  question  which 

sible,  as  Mr.  De  Morgan  said,  that  this  mental  clearness  and  direct- 
ness may  have  caused  his  mathematical  heresy,  the  rejection  of  the 
use  of  negative  quantities  in  algebraical  operations;  and  it  is  prob- 
able that  he  thus  deprived  himself  of  an  instrument  of  work,  the  use 
of  which  might  have  led  him  to  greater  eminence  in  the  higher 
branches."  Memoir  of  Augustus  De  Morgan,  London,  1882,  p.  19. 


210  A  BUDGET  OF  PARADOXES. 

had  turned  the  brains  of  thirty-nine  students,  and  had  flung 
twenty-seven  more  into  a  high  fever.  With  all  my  heart, 
says  Pantagruel,  and  swallowed  down  three  quarts  of  Bur- 
ton ale ;  but  remember,  it  wants  but  an  hour  of  dinner  time, 
and  the  question  must  be  asked  in  as  few  words  as  possible ; 
for  I  cannot  deprive  myself  of  the  pleasure  I  expected  to 
enjoy  in  the  company  of  my  good  friends  for  a  set  of  mad- 
headed  masters.  I  wish  brother  John  was  here  to  settle 
these  matters  with  the  black  gentry. 

"Having  said  or  rather  growled  this,  he  proceeded  to  the 
hall  of  ceremony,  and  mounted  his  throne;  Epistemon  and 
Panurge  standing  on  each  side,  but  two  steps  below  him. 
Then  advanced  to  the  throne  the  three  beadles  of  the  Uni- 
versity of  Pontemaca  with  their  silver  staves  on  their  shoul- 
ders, and  velvet  caps  on  their  heads,  and  they  were  followed 
by  three  times  three  doctors,  and  thrice  three  times  three 
masters  of  art ;  for  everything  was  done  in  Pontemaca  by  the 
number  three,  and  on  this  account  the  address  was  written 
on  parchment,  one  foot  in  breadth,  and  thrice  three  times 
thrice  three  feet  in  length.  The  beadles  struck  the  ground 
with  their  heads  and  their  staves  three  times  in  approaching 
the  throne ;  the  doctors  struck  the  ground  with  their  heads 
thrice  three  times,  and  the  masters  did  the  same  thrice  each 
time,  beating  the  ground  with  their  heads  thrice  three  times. 
This  was  the  accustomed  form  of  approaching  the  throne, 
time  out  of  mind,  and  it  was  said  to  be  emblematic  of  the 
usual  prostration  of  science  to  the  throne  of  greatness. 

"The  mathematical  professor,  after  having  spit,  and 
hawked,  and  cleared  his  throat,  and  blown  his  nose  on  a 
handkerchief  lent  to  him,  for  he  had  forgotten  to  bring  his 
own,  began  to  read  the  address.  In  this  he  was  assisted  by 
three  masters  of  arts,  one  of  whom,  with  a  silver  pen, 
pointed  out  the  stops ;  the  second  with  a  small  stick  rapped 
his  knuckles  when  he  was  to  raise  or  lower  his  voice;  and 
a  third  pulled  his  hair  behind  when  he  was  to  look  Pan- 
tagruel in  the  face.  Pantagruel  began  to  chafe  like  a  lion : 


MR.  TREND'S  BURLESQUE.  211 

he  turned  first  on  one  side,  then  on  the  other:  he  listened 
and  groaned,  and  groaned  and  listened,  and  was  in  the  ut- 
most cogitabundity  of  cogitation.  His  countenance  began 
to  brighten,  when,  at  the  end  of  an  hour,  the  reader  stam- 
mered out  these  words : 

"  'It  has  therefore  been  most  clearly  proved  that  as  all 
matter  may  be  divided  into  parts  infinitely  smaller  than  the 
infinitely  smallest  part  of  the  infinitesimal  of  nothing,  so 
nothing  has  all  the  properties  of  something,  and  may  be- 
come, by  just  and  lawful  right,  susceptible  of  addition,  sub- 
traction, multiplication,  division,  squaring,  and  cubing:  that 
it  is  to  all  intents  and  purposes  as  good  as  anything  that 
has  been,  is,  or  can  be  taught  in  the  nine  universities  of  the 
land,  and  to  deprive  it  of  its  rights  is  a  most  cruel  innova- 
tion and  usurpation,  tending  to  destroy  all  just  subordina- 
tion in  the  world,  making  all  universities  superfluous,  level- 
ing vice-chancellors,  doctors,  and  proctors,  masters,  bach- 
elors, and  scholars,  to  the  mean  and  contemptible  state  of 
butchers  and  tallow-chandlers,  bricklayers  and  chimney- 
sweepers, who,  if  it  were  not  for  these  learned  mysteries, 
might  think  that  they  knew  as  much  as  their  betters.  Every 
one  then,  who  has  the  good  of  science  at  heart,  must  pray 
for  the  interference  of  his  highness  to  put  a  stop  to  all  the 
disputes  about  nothing,  and  by  his  decision  to  convince  all 
gainsayers  that  the  science  of  nothing  is  taught  in  the  best 
manner  in  the  universities,  to  the  great  edification  and  im- 
provement of  all  the  youth  in  the  land/ 

"Here  Pantagruel  whispered  in  the  ear  of  Panurge,  who 
nodded  to  Epistemon,  and  they  two  left  the  assembly,  and 
did  not  return  for  an  hour,  till  the  orator  had  finished  his 
task.  The  three  beadles  had  thrice  struck  the  ground  with 
their  heads  and  staves,  the  docters  had  finished  their  com- 
pliments, and  the  masters  were  making  their  twenty-seven 
prostrations.  Epistemon  and  Panurge  went  up  to  Panta- 
gruel, whom  they  found  fast  asleep  and  snoring ;  nor  could 
he  be  roused  but  by  as  many  tugs  as  there  had  been  bow- 


212  A  BUDGET  OF  PARADOXES. 

ings  from  the  corps  of  learning.  At  last  he  opened  his 
eyes,  gave  a  good  stretch,  made  half  a  dozen  yawns,  and 
called  for  a  stoup  of  wine.  I  thank  you,  my  masters,  says 
he;  so  sound  a  nap  I  have  not  had  since  I  came  from  the 
island  of  Priestfolly.  Have  you  dined,  my  masters?  They 
answered  the  question  by  as  many  bows  as  at  entrance ;  but 
his  highness  left  them  to  the  care  of  Panurge,  and  retired 
to  the  little  parlor  with  Epistemon,  where  they  burst  into 
a  fit  of  laughter,  declaring  that  this  learned  Baragouin  about 
nothing  was  just  as  intelligible  as  the  lawyer's  Galimathias. 
Panurge  conducted  the  learned  body  into  a  large  saloon, 
and  each  in  his  way  hearing  a  clattering  of  plates  and  glasses, 
congratulated  himself  on  his  approaching  good  cheer.  There 
they  were  left  by  Panurge,  who  took  his  chair  by  Pantagruel 
just  as  the  soup  was  removed,  but  he  made  up  for  the  want 
of  that  part  of  his  dinner  by  a  pint  of  champagne.  The 
learning  of  the  university  had  whetted  their  appetites ;  what 
they  each  ate  it  is  needless  to  recite ;  good  wine,  good  stories, 
and  hearty  laughs  went  round,  and  three  hours  elapsed  be- 
fore one  soul  of  them  recollected  the  hungry  students  of 
Pontemaca. 

"Epistemon  reminded  them  of  the  business  in  hand,  and 
orders  were  given  for  a  fresh  dozen  of  hermitage  to  be  put 
upon  table,  and  the  royal  attendants  to  get  ready.  As  soon 
as  the  dozen  bottles  were  emptied,  Pantagruel  rose  from 
table,  the  royal  trumpets  sounded,  and  he  was  accompanied 
by  the  great  officers  of  his  court  into  the  large  dining  hall, 
where  was  a  table  with  forty-two  covers.  Pantagruel  sat 
at  the  head,  Epistemon  at  the  bottom,  and  Panurge  in  the 
middle,  opposite  an  immense  silver  tureen,  which  would  hold 
fifty  gallons  of  soup.  The  wise  men  of  Pontemaca  then 
took  their  seats  according  to  seniority.  Every  countenance 
glistened  with  delight ;  the  music  struck  up ;  the  dishes  were 
uncovered.  Panurge  had  enough  to  do  to  handle  the  im- 
mense silver  ladle:  Pantagruel  and  Epistemon  had  no  time 
for  eating,  they  were  fully  employed  in  carving.  The  bill 


MR.  TREND'S  BURLESQUE.  213 

of  fare  announced  the  names  of  a  hundred  different  dishes. 
From  Panurge's  ladle  came  into  the  soup  plate  as  much  as 
he  took  every  time  out  of  the  tureen ;  and  as  it  was  the  rule 
of  the  court  that  every  one  should  appear  to  eat,  as  long  as 
he  sat  at  table,  there  was  the  clattering  of  nine  and  thirty 
spoons  against  the  silver  soup-plates  for  a  quarter  of  an 
hour.  They  were  then  removed,  and  knives  and  forks  were 
in  motion  for  half  an  hour.  Glasses  were  continually  handed 
round  in  the  mean  time,  and  then  everything  was  removed, 
except  the  great  tureen  of  soup.  The  second  course  was 
now  served  up,  in  dispatching  which  half  an  hour  was  con- 
sumed ;  and  at  the  conclusion  the  wise  men  of  Pontemaca 
had  just  as  much  in  their  stomachs  as  Pantagruel  in  his 
head  from  their  address:  for  nothing  was  cooked  up  for 
them  in  every  possible  shape  that  Panurge  could  devise. 

"Wine-glasses,  large  decanters,  fruit  dishes,  and  plates 
were  now  set  on.  Pantagruel  and  Epistemon  alternately 
gave  bumper  toasts:  the  University  of  Pontemaca,  the  eye 
of  the  world,  the  mother  of  taste  and  good  sense  and  uni- 
versal learning,  the  patroness  of  utility,  and  the  second  only 
to  Pantagruel  in  wisdom  and  virtue  (for  these  were  her 
titles),  was  drank  standing  with  thrice  three  times  three, 
and  huzzas  and  clattering  of  glasses ;  but  to  such  wine  the 
wise  men  of  Pontemaca  had  not  been  accustomed;  and 
though  Pantagruel  did  not  suffer  one  to  rise  from  table  till 
the  eighty-first  glass  had  been  emptied,  not  even  the  weak- 
est headed  master  of  arts  felt  his  head  in  the  least  indis- 
posed. The  decanters  indeed  were  often  removed,  but  they 
were  brought  back  replenished,  filled  always  with  nothing. 

"Silence  was  now  proclaimed,  and  in  a  trice  Panurge 
leaped  into  the  large  silver  tureen.  Thence  he  made  his 
bows  to  Pantagruel  and  the  whole  company,  and  commenced 
an  oration  of  signs,  which  lasted  an  hour  and  a  half,  and  in 
which  he  went  over  all  the  matter  contained  in  the  Ponte- 
maca address ;  and  though  the  wise  men  looked  very  serious 
during  the  whole  time,  Pantagruel  himself  and  his  whole 


214  A  BUDGET  OF  PARADOXES. 

court  could  not  help  indulging  in  repeated  bursts  of  laugh- 
ter. It  was  universally  acknowledged  that  he  excelled  him- 
self, and  that  the  arguments  by  which  he  beat  the  English 
masters  of  arts  at  Paris  were  nothing  to  the  exquisite  selec- 
tion of  attitudes  which  he  this  day  assumed.  The  greatest 
shouts  of  applause  were  excited  when  he  was  running  thrice 
round  the  tureen  on  its  rim,  with  his  left  hand  holding  his 
nose,  and  the  other  exercising  itself  nine  and  thirty  times 
on  his  back.  In  this  attitude  he  concluded  with  his  back  to 
the  professor  of  mathematics ;  and  at  the  instant  he  gave  his 
last  flap,  by  a  sudden  jump,  and  turning  heels  over  head  in 
the  air,  he  presented  himself  face  to  face  to  the  professor, 
and  standing  on  his  left  leg,  with  his  left  hand  holding  his 
nose,  he  presented  to  him,  in  a  white  satin  bag,  Pantagruel's 
royal  decree.  Then  advancing  his  right  leg,  he  fixed  it  on 
the  professor's  head,  and  after  three  turns,  in  which  he 
clapped  his  sides  with  both  hands  thrice  three  times,  down 
he  leaped,  and  Pantagruel,  Epistemon,  and  himself  took 
their  leaves  of  the  wise  men  of  Pontemaca. 

"The  wise  men  now  retired,  and  by  royal  orders  were 
accompanied  by  a  guard,  and  according  to  the  etiquette  of 
the  court,  no  one  having  a  royal  order  could  stop  at  any 
public  house  till  it  was  delivered.  The  procession  arrived 
at  Pontemaca  at  nine  o'clock  the  next  morning,  and  the 
sound  of  bells  from  every  church  and  college  announced 
their  arrival.  The  congregation  was  assembled ;  the  royal 
decree  was  saluted  in  the  same  manner  as  if  his  highness 
had  been  there  in  person;  and  after  the  proper  ceremonies 
had  been  performed,  the  satin  bag  was  opened  exactly  at 
twelve  o'clock.  A  finely  emblazoned  roll  was  drawn  forth, 
and  the  public  orator  read  to  the  gaping  assembly  the  fol- 
lowing words: 

"  'They  who  can  make  something  out  of  nothing  shall 
have  nothing  to  eat  at  the  court  of — PANTAGRUEL/  " 


MR.  FREND'S  BURLESQUE.  215 

ORIGIN  of  the  ENGLISH  LANGUAGE,  related  by  a  SWEDE. 

"Some  months  ago  in  a  party  in  Holland,  consisting  of 
natives  of  various  countries,  the  merit  of  their  respective 
languages  became  a  topic  of  conversation.  A  Swede,  who 
had  been  a  great  traveler,  and  could  converse  in  most  of 
the  modern  languages  of  Europe,  laughed  very  heartily  at 
an  Englishman,  who  had  ventured  to  speak  in  praise  of  the 
tongue  of  his  dear  country.  I  never  had  any  trouble,  says  he, 
in  learning  English.  To  my  very  great  surprise,  the  moment 
I  sat  foot  on  shore  at  Gravesend,  I  found  out,  that  I  could 
understand,  with  very  little  trouble,  every  word  that  was 
said.  It  was  a  mere  jargon,  made  up  of  German,  French, 
and  Italian,  with  now  and  then  a  word  from  the  Spanish, 
Latin  or  Greek.  I  had  only  to  bring  my  mouth  to  their 
mode  of  speaking,  which  was  done  with  ease  in  less  than  a 
week,  and  I  was  everywhere  taken  for  a  true-born  English- 
man ;  a  privilege  by  the  way  of  no  small  importance  in  a 
country,  where  each  man,  God  knows  why,  thinks  his  foggy 
island  superior  to  any  other  part  of  the  world :  and  though 
his  door  is  never  free  from  some  dun  or  other  coming  for 
a  tax,  and  if  he  steps  out  of  it  he  is  sure  to  be  knocked  down 
or  to  have  his  pocket  picked,  yet  he  has  the  insolence  to 
think  every  foreigner  a  miserable  slave,  and  his  country  the 
seat  of  everything  wretched.  They  may  talk  of  liberty  as 
they  please,  but  Spain  or  Turkey  for  my  money:  barring 
the  bowstring  and  the  inquisition,  they  are  the  most  com- 
fortable countries  under  heaven,  and  you  need  not  be  afraid 
of  either,  if  you  do  not  talk  of  religion  and  politics.  I  do 
not  see  much  difference  too  in  this  respect  in  England,  for 
when  I  was  there,  one  of  their  most  eminent  men  for  learn- 
ing was  put  in  prison  for  a  couple  of  years,  and  got  his  death 
for  translating  one  of  ^Esop's  fables  into  English,  which 
every  child  in  Spain  and  Turkey  is  taught,  as  soon  as  he 
comes  out  of  his  leading  strings.  Here  all  the  company 
unanimously  cried  out  against  the  Swede,  that  it  was  im- 


216  A  BUDGET  OF  PARADOXES. 

possible :  for  in  England,  the  land  of  liberty,  the  only  thing 
its  worst  enemies  could  say  against  it,  was,  that  they  paid 
for  their  liberty  a  much  greater  price  than  it  was  worth. — 
Every  man  there  had  a  fair  trial  according  to  laws,  which 
everybody  could  understand ;  and  the  judges  were  cool,  pa- 
tient, discerning  men,  who  never  took  the  part  of  the  crown 
against  the  prisoner,  but  gave  him  every  assistance  possible 
for  his  defense. 

"The  Swede  was  borne  down,  but  not  convinced;  and 
he  seemed  determined  to  spit  out  all  his  venom.  Well,  says 
he,  at  any  rate  you  will  not  deny  that  the  English  have  not 
got  a  language  of  their  own,  and  that  they  came  by  it  in  a 
very  odd  way.  Of  this  at  least  I  am  certain,  for  the  whole 
history  was  related  to  me  by  a  witch  in  Lapland,  whilst  I 
was  bargaining  for  a  wind.  Here  the  company  were  all  in 
unison  again  for  the  story. 

"In  ancient  times,  said  the  old  hag,  the  English  occupied 
a  spot  in  Tartary,  where  they  lived  sulkily  by  themselves, 
unknowing  and  unknown.  By  a  great  convulsion  that  took 
place  in  China,  the  inhabitants  of  that  and  the  adjoining 
parts  of  Tartary  were  driven  from  their  seats,  and  after 
various  wanderings  took  up  their  abode  in  Germany.  During 
this  time  nobody  could  understand  the  English,  for  they 
did  not  talk,  but  hissed  like  so  many  snakes.  The  poor 
people  felt  uneasy  under  this  circumstance,  and  in  one  of 
their  parliaments,  or  rather  hissing  meetings,  it  was  deter- 
mined to  seek  a  remedy:  and  an  embassy  was  sent  to  some 
of  our  sisterhood  then  living  on  Mount  Hecla.  They  were 
put  to  a  nonplus,  and  summoned  the  Devil  to  their  relief. 
To  him  the  English  presented  their  petitions,  and  explained 
their  sad  case ;  and  he,  upon  certain  conditions,  promised  to 
befriend  them,  and  to  give  them  a  language.  The  poor 
Devil  was  little  aware  of  what  he  had  promised ;  but  he  is, 
as  all  the  world  knows,  a  man  of  too  much  honor  to  break 
his  word.  Up  and  down  the  world  then  he  went  in  quest 
of  this  new  language:  visited  all  the  universities,  and  all 


MR.  TREND'S  BURLESQUE.  217 

the  schools,  and  all  the  courts  of  law,  and  all  the  play-houses, 
and  all  the  prisons ;  never  was  poor  devil  so  fagged.  It 
would  have  made  your  heart  bleed  to  see  him.  Thrice  did 
he  go  round  the  earth  in  every  parallel  of  latitude ;  and  at 
last,  wearied  and  jaded  out,  back  came  he  to  Hecla  in  de- 
spair, and  would  have  thrown  himself  into  the  volcano,  if 
he  had  been  made  of  combustible  materials.  Luckily  at 
that  time  our  sisters  were  engaged  in  settling  the  balance 
of  Europe;  and  whilst  they  were  looking  over  projects,  and 
counter-projects,  and  ultimatums,  and  post  ultimatums,  the 
poor  Devil,  unable  to  assist  them  was  groaning  in  a  corner 
and  ruminating  over  his  sad  condition. 

"On  a  sudden,  a  hellish  joy  overspread  his  countenance ; 
up  he  jumped,  and,  like  Archimedes  of  old,  ran  like  a  mad- 
man amongst  the  throng,  turning  over  tables,  and  papers, 
and  witches,  roaring  out  for  a  full  hour  together  nothing 
else  but  'tis  found,  'tis  found!  Away  were  sent  the  sister- 
hood in  every  direction,  some  to  traverse  all  the  corners  of 
the  earth,  and  others  to  prepare  a  larger  caldron  than  had 
ever  yet  been  set  upon  Hecla.  The  affairs  of  Europe  were 
at  a  stand :  its  balance  was  thrown  aside ;  prime  ministers 
and  ambassadors  were  everywhere  in  the  utmost  confusion ; 
and,  by  the  way,  they  have  never  been  able  to  find  the 
balance  since  that  time,  and  all  the  fine  speeches  upon  the 
subject,  with  which  your  newspapers  are  every  now  and  then 
filled,  are  all  mere  hocus-pocus  and  rhodomontade.  How- 
ever, the  caldron  was  soon  set  on,  and  the  air  was  darkened 
by  witches  riding  on  broomsticks,  bringing  a  couple  of  folios 
under  each  arm,  and  across  each  shoulder.  I  remember  the 
time  exactly:  it  was  just  as  the  council  of  Nice  had  broken 
up,  so  that  they  got  books  and  papers  there  dog  cheap ;  but 
it  was  a  bad  thing  for  the  poor  English,  as  these  were  the 
worst  materials  that  entered  into  the  caldron.  Besides,  as  the 
Devil  wanted  some  amusement,  and  had  not  seen  an  account 
of  the  transactions  of  this  famous  council,  he  had  all  the  books 
brought  from  it  laid  before  him,  and  split  his  sides  almost 


218  A  BUDGET  OF  PARADOXES. 

with  laughing,  whilst  he  was  reading  the  speeches  and  decrees 
of  so  many  of  his  old  friends  and  acquaintances.  All  this 
while  the  witches  were  depositing  their  loads  in  the  great 
caldron.  There  were  books  from  the  Dalai  Lama,  and  from 
China :  there  were  books  from  the  Hindoos,  and  tallies  from 
the  Caffres:  there  were  paintings  from  Mexico,  and  rocks 
of  hieroglyphics  from  Egypt:  the  last  country  supplied  be- 
sides the  swathings  of  two  thousand  mummies,  and  four- 
fifths  of  the  famed  library  of  Alexandria.  Bubble !  bubble ! 
toil  and  trouble !  never  was  a  day  of  more  labor  and  anxiety ; 
and  if  our  good  master  had  but  flung  in  the  Greek  books  at 
the  proper  time,  they  would  have  made  a  complete  job  of 
it.  He  was  a  little  too  impatient :  as  the  caldron  frothed  up, 
he  skimmed  it  off  with  a  great  ladle,  and  filled  some  thou- 
sands of  our  wind-bags  with  the  froth,  which  the  English 
with  great  joy  carried  back  to  their  own  country.  These 
bags  were  sent  to  every  district:  the  chiefs  first  took  their 
fill,  and  then  the  common  people ;  hence  they  now  speak 
a  language  which  no  foreigner  can  understand,  unless  he 
has  learned  half  a  dozen  other  languages;  and  the  poor 
people,  not  one  in  ten,  understand  a  third  part  of  what  is 
said  to  them.  The  hissing,  however,  they  have  not  entirely 
got  rid  of,  and  every  seven  years,  when  the  Devil,  according 
to  agreement,  pays  them  a  visit,  they  entertain  him  at  their 
common  halls  and  county  meetings  with  their  original  lan- 
guage. 

"The  good-natured  old  hag  told  me  several  other  circum- 
stances, relative  to  this  curious  transaction,  which,  as  there 
is  an  Englishman  in  company,  it  will  be  prudent  to  pass 
over  in  silence:  but  I  cannot  help  mentioning  one  thing 
which  she  told  me  as  a  very  great  secret.  You  know,  says 
she  to  me,  that  the  English  have  more  religions  among  them 
than  any  other  nation  in  Europe,  and  that  there  is  more 
teaching  and  sermonizing  with  them  than  in  any  other  coun- 
try. The  fact  is  this ;  it  matters  not  who  gets  up  to  teach 
them,  the  hard  words  of  the  Greek  were  not  sufficiently 


ON    YOUTHFUL   PRODIGIES.  219 

boiled,  and  whenever  they  get  into  a  sentence,  the  poor 
people's  brains  are  turned,  and  they  know  no  more  what  the 
preacher  is  talking  about,  than  if  he  harangued  them  in 
Arabic.  Take  my  word  for  it  if  you  please ;  but  if  not,  when 
you  get  to  England,  desire  the  bettermost  sort  of  people 
that  you  are  acquainted  with  to  read  to  you  an  act  of  parlia- 
ment, which  of  course  is  written  in  the  clearest  and  plainest 
style  in  which  anything  can  be  written,  and  you  will  find 
that  not  one  in  ten  will  be  able  to  make  tolerable  sense  of  it. 
The  language  would  have  been  an  excellent  language,  if 
it  had  not  been  for  the  council  of  Nice,  and  the  words  had 
been  well  boiled. 

"Here  the  company  burst  out  into  a  fit  of  laughter.  The 
Englishman  got  up  and  shook  hands  with  the  Swede :  si  non 
e  vero,  said  he,  e  ben  trovato.*  But,  however  I  may  laugh  at 
it  here,  I  would  not  advise  you  to  tell  this  story  on  the  other 
side  of  the  water.  So  here's  a  bumper  to  Old  England  for 
ever,  and  God  save  the  king." 

ON  YOUTHFUL  PRODIGIES. 

The  accounts  given  of  extraordinary  children  and  adoles- 
cents frequently  defy  credence.1  I  will  give  two  well-attested 
instances. 

The  celebrated  mathematician  Alexis  Claude  Clairault 
(now  Clairaut)2  was  certainly  born  in  May,  1713.  His  treat- 
ise on  curves  of  double  curvature  (printed  in  1731)3  received 

8  "If  it  is  not  true  it  is  a  good  invention."  A  well-known  Italian 
proverb. 

1  See  page  86,  note  3. 

2  He  was  born  at  Paris  in  1713,  and  died  there  in  1765. 

8  Recherche s  sur  les  courbes  a  double  courbure,  Paris,  1731.  Clai- 
raut was  then  only  eighteen,  and  was  in  the  same  year  made  a  mem- 
ber of  the  Academic  des  sciences.  His  Element  de  geometric  ap- 
peared in  1741.  Meantime  he  had  taken  part  in  the  measurement  of 
a  degree  in  Lapland  (1736-1737).  His  Trait  e  de  la  -figure  de  la 
terre  was  published  in  1741.  The  Academy  of  St.  Petersburg 
awarded  him  a  prize  for  his  Theorie  de  la  lune  (1750).  His  various 
works  on  comets  are  well  known,  particularly  his  Theorie  du  mouve- 
ment  des  cometes  (1760)  in  which  he  applied  the  "problem  of  three 
bodies"  to  Halley's  comet  as  retarded  by  Jupiter  and  Saturn. 


220  A  BUDGET  OF  PARADOXES. 

the  approbation  of  the  Academy  of  Sciences,  August  23, 
1729.  Fontenelle,  in  his  certificate  of  this,  calls  the  author 
sixteen  years  of  age,  and  does  not  strive  to  exaggerate  the 
wonder,  as  he  might  have  done,  by  reminding  his  readers 
that  this  work,  of  original  and  sustained  mathematical  in- 
vestigation, must  have  been  coming  from  the  pen  at  the 
ages  of  fourteen  and  fifteen.  The  truth  was,  as  attested  by 
De  Molieres,4  Clairaut  had  given  public  proofs  of  his  power 
at  twelve  years  old.  His  age  being  thus  publicly  certified, 
all  doubt  is  removed:  say  he  had  been — though  great  won- 
der would  still  have  been  left — twenty-one  instead  of  six- 
teen, his  appearance,  and  the  remembrances  of  his  friends, 
schoolfellows,  etc.,  would  have  made  it  utterly  hopeless  to 
knock  off  five  years  of  that  age  while  he  was  on  view  in 
Paris  as  a  young  lion.  De  Molieres,  who  examined  the 
work  officially  for  the  Garde  des  Sceaux,  is  transported 
beyond  the  bounds  of  official  gravity,  and  says  that  it  "ne 
merite  pas  seulement  d'etre  imprime,  mais  d'etre  admire 
comme  un  prodige  d'imagination,  de  conception,  et  de  ca- 
pacite."5 

That  Blaise  Pascal  was  born  in  June,  1623,  is  per- 
fectly well  established  and  uncontested.6  That  he  wrote  his 
conic  sections  at  the  age  of  sixteen  might  be  difficult  to 
establish,  though  tolerably  well  attested,  if  it  were  not  for 

4  Joseph  Privat,  Abbe  de  Molieres  (1677-1742),  was  a  priest  of 
the  Congregation  of  the  Oratorium.  In  1723  he  became  a  professor 
in  the  College  de  France.  He  was  well  known  as  an  astronomer  and 
a  mathematician,  and  wrote  in  defense  of  Descartes's  theory  of 
vortices  (1728,  1729).  He  also  contributed  to  the  methods  of  find- 
ing prime  numbers  (1705). 

B  "Deserves  not  only  to  be  printed,  but  to  be  admired  as  a  marvel 
of  imagination,  of  understanding,  and  of  ability." 

6  Blaise  Pascal  (1623-1662),  the  well-known  French  philosopher 
and  mathematician.  He  lived  for  some  time  with  the  Port  Royalists, 
and  defended  them  against  the  Jesuits  in  his  Provincial  Letters. 
Among  his  works  are  the  following:  Essai  pour  les  coniques  (1640)  ; 
Recit  de  la  grande  experience  de  I'equilibre  des  liqueurs  (1648),  de- 
scribing his  experiment  in  finding  altitudes  by  barometric  readings ; 
Histoire  de  la  roulette  (1658);  Traite  du  triangle  arithmetique 
(1665)  ;  Aleae  geometria  (1654). 


ON    YOUTHFUL   PRODIGIES.  221 

one  circumstance,  for  the  book  was  not  published.  The 
celebrated  theorem,  "Pascal's  hexagram,"7  makes  all  the 
rest  come  very  easy.  Now  Curabelle,8  in  a  work  published 
in  1644,  sneers  at  Desargues,9  whom  he  quotes,  for  having, 
in  1642,  deferred  a  discussion  until  "cette  grande  proposition 
nommee  le  Pascale  verra  le  jour."10  That  is,  by  the  time 
Pascal  was  nineteen,  the  hexagram  was  circulating  under 
a  name  derived  from  the  author.  The  common  story  about 
Pascal,  given  by  his  sister,11  is  an  absurdity  which  no  doubt 
has  prejudiced  many  against  tales  of  early  proficiency.  He 
is  made,  when  quite  a  boy,  to  invent  geometry  in  the  order 
of  Euclid's  propositions:  as  if  that  order  were  natural  se- 
quence of  investigation.  The  hexagram  at  ten  years  old 
would  be  a  hundred  times  less  unlikely. 

The  instances  named  are  painfully  astonishing:  I  give 
one  which  has  fallen  out  of  sight,  because  it  will  preserve 
an  imperfect  biography.  John  Wilson12  is  Wilson  of  that 

7  This   proposition   shows  that  if  a  hexagon  is  inscribed  in  a 
conic    (in  particular  a  circle)    and  the  opposite  sides  are  produced 
to  meet,  the  three  points  determined  by  their  intersections  will  be  in 
the  same  straight  line. 

8  Jacques  Curabelle,  Examen  des  (Euvres  du  Sr.  Desargues,  Paris, 
1644.     He  also  published  without  date  a  work  entitled:   Foiblesse 
pitoyable  du  Sr.  G.  Desargues  employee  contre  I'examen  fait  de  ses 
ceuvres. 

9  See  page  119,  note  2. 

10  Until   "this   great  proposition  called   Pascal's   should  see  the 
light." 

11  The  story  is  that  his  father,  Etienne  Pascal,  did  not  wish  him 
to  study  geometry  until  he  was  thoroughly  grounded  in  Latin  and 
Greek.     Having  heard  the  nature  of  the  subject,  however,  he  began 
at  the  age  of  twelve  to  construct  figures  by  himself,  drawing  them 
on  the  floor  with  a  piece  of  charcoal.     When  his  father  discovered 
what  he  was  doing  he  was  attempting  to  demonstrate  that  the  sum 
of  the  angles  of  a  triangle  equals  two  right  angles.     The  story  is 
given  by  his  sister,  Mme.  Perier. 

"Sir  John  Wilson  (1741-1793)  was  knighted  in  1786  and  became 
Commissioner  of  the  Great  Seal  in  1792.  He  was  a  lawyer  and  jurist 
of  recognized  merit.  He  stated  his  theorem  without  proof,  the  first 
demonstration  having  been  given  by  Lagrange  in  the  Memoirs  of 
the  Berlin  Academy  for  1771, — Demonstration  d'un  theoreme  nou- 
veau  concernant  les  nombres  premiers.  Euler  also  gave  a  proof  in 
his  Miscellanea  Analytica  (1773).  Fermat's  works  should  be  con- 
sulted in  connection  with  the  early  history  of  this  theorem. 


222  A  BUDGET  OF  PARADOXES. 

Ilk,  that  is,  of  "Wilson's  Theorem."  It  is  this:  if  p  be  a 
prime  number,  the  product  of  all  the  numbers  up  to  p — 1,  in- 
creased by  1,  is  divisible  without  remainder  by  p.  All 
mathematicians  know  this  as  Wilson's  theorem,  but  few 
know  who  Wilson  was.  He  was  born  August  6,  1741,  at 
the  Howe  in  Applethwaite,  and  he  was  heir  to  a  small 
estate  at  Troutbeck  in  Westmoreland.  He  was  sent  to 
Peterhouse,  at  Cambridge,  and  while  an  undergraduate  was 
considered  stronger  in  algebra  than  any  one  in  the  Uni- 
versity, except  Professor  Waring,  one  of  the  most  powerful 
algebraists  of  the  century.13  He  was  the  senior  wrangler  of 
1761,  and  was  then  for  some  time  a  private  tutor.  When 
Paley,14  then  in  his  third  year,  determined  to  make  a  push 
for  the  senior  wranglership,  which  he  got,  Wilson  was 
recommended  to  him  as  a  tutor.  Both  were  ardent  in  their 
work,  except  that  sometimes  Paley,  when  he  came  for  his 
lesson,  would  find  "Gone  a  fishing"  written  on  his  tutor's 
outer  door:  which  was  insult  added  to  injury,  for  Paley 
was  very  fond  of  fishing.  Wilson  soon  left  Cambridge,  and 
went  to  the  bar.  He  practised  on  the  northern  circuit  with 
great  success ;  and,  one  day,  while  passing  his  vacation  on 
his  little  property  at  Troutbeck,  he  received  information,  to 
his  great  surprise,  that  Lord  Thurlow,15  with  whom  he  had 

"He  wrote,  in  1760,  a  tract  in  defense  of  Waring,  a  point  of 
whose  algebra  had  been  assailed  by  a  Dr.  Powell.  Waring  wrote 
another  tract  of  the  same  date.— A.  De  M. 

William  Samuel  Powell  (1717-1775)  was  at  this  time  a  fellow 
of  St.  John's  College,  Cambridge.  In  1765  he  became  Vice  Chan- 
cellor of  the  University.  Waring  was  a  Magdalene  man,  and  while 
candidate  for  the  Lucasian  professorship  he  circulated  privately  his 
Miscellanea  Analytica.  Powell  attacked  this  in  his  Observations  on 
the  First  Chapter  of  a  Book  called  Miscellanea  (1760).  This  attack 
was  probably  in  the  interest  of  another  candidate,  a  man  of  his  own 
college  (St.  John's),  William  Ludlam. 

"William  Paley  (1743-1805)  was  afterwards  a  tutor  at  Christ's 
College,  Cambridge.  He  never  contributed  anything  to  mathematics, 
but  his  Evidences  of  Christianity  (1794)  was  long  considered  some- 
what of  a  classic.  He  also  wrote  Principles  of  Morality  and  Poli- 
tics (1785),  and  Natural  Theology  (1802). 

15  Edward,  first  Baron  Thurlow  (1731-1806)  is  known  to  Ameri- 
cans because  of  his  strong  support  of  the  Royal  prerogative  during 


ON    YOUTHFUL   PRODIGIES.  223 

no  acquaintance,  had  recommended  him  to  be  a  Judge  of 
the  Court  of  Common  Pleas.  He  died,  Oct.  18,  1793,  with 
a  very  high  reputation  as  a  lawyer  and  a  Judge.  These 
facts  are  partly  from  Meadley's  Life  of  Paley™  no  doubt  from 
Paley  himself,  partly  from  the  Gentleman's  Magazine,  and 
fsom  an  epitaph  written  by  Bishop  Watson.17  Wilson  did 
not  publish  anything:  the  theorem  by  which  he  has  cut 
his  name  in  the  theory  of  numbers  was  communicated  to 
Waring,  by  whom  it  was  published.  He  married,  in  1788, 
a  daughter  of  Serjeant  Adair,18  and  left  issue.  Had  a  family, 
many  will  say :  but  a  man  and  his  wife  are  a  family,  even 
without  children.  An  actuary  may  be  allowed  to  be  accurate 
in  this  matter,  of  which  I  was  reminded  by  what  an  actuary 
wrote  of  another  actuary.  William  Morgan,19  in  the  life  of 
his  uncle  Dr.  Richard  Price,20  says  that  the  Doctor  and  his 

the  Revolution.  He  was  a  favorite  of  George  III,  and  became 
Lord  Chancellor  in  1778. 

"George  Wilson  Meadley  (1774-1818)  published  his  Memoirs 
of  ....  Paley  in  1809.  He  also  published  Memoirs  of  Algernon  Sid- 
ney in  1813.  He  was  a  merchant  and  banker,  and  had  traveled  ex- 
tensively in  Europe  and  the  East.  He  was  a  convert  to  unitarianism, 
to  which  sect  Paley  had  a  strong  leaning. 

"Watson  (1737-1816)  was  a  strange  kind  of  man  for  a  bishop- 
ric. He  was  professor  of  chemistry  at  Cambridge  (1764)  at  the  age 
of  twenty-seven.  It  was  his  experiments  that  led  to  the  invention 
of  the  black-bulb  thermometer.  He  is  said  to  have  saved  the  gov- 
ernment £100,000  a  year  by  his  advice  on  the  manufacture  of  gun- 
powder. Even  after  he  became  professor  of  divinity  at  Cambridge 
(1771)  he  published  four  volumes  of  Chemical  Essays  (vol.  I,  1781). 
He  became  Bishop  of  Llandaff  in  1782. 

18  James  Adair   (died  in  1798)   was  counsel  for  the  defense  in 
the  trial  of  the  publishers  of  the  Letters  of  Junius  (1771).    As  King's 
Serjeant  he  assisted  in  prosecuting  Hardy  and  Home  Tooke. 

19  Morgan  (1750-1833)   was  actuary  of  the  Equitable  Assurance 
Society  of  London  (1774-1830),  and  it  was  to  his  great  abilities  that 
the  success  of  that  company  was  due  at  a  time  when  other  corpora- 
tions of  similar  kind  were  meeting  with  disaster.     The  Royal  So- 
ciety awarded  him  a  medal    (1783)    for  a  paper  on  Probability  of 
Survivorship.     He  wrote  several  important  works  on  insurance  and 
finance. 

20  Dr.  Price   (1723-1791)   was  a  non-conformist  minister  and  a 
writer  on  ethics,  economics,  politics,  and  insurance.     He  was  a  de- 
fender of  the  American  Revolution  and  a  personal  friend  of  Frank- 
lin.   In  1778  Congress  invited  him  to  America  to  assist  in  the  finan- 


224  A  BUDGET  OF  PARADOXES. 

wife  were  "never  blessed  with  an  addition  to  their  family." 
I  never  met  with  such  accuracy  elsewhere.  Of  William 
Morgan  I  add  that  my  surname  and  pursuits  have  some- 
times, to  my  credit  be  it  said,  made  a  confusion  between 
him  and  me.  Dates  are  nothing  to  the  mistaken ;  the  last 
three  years  of  Morgan's  life  were  the  first  three  years  of 
my  actuary-life  (1830-33).  The  mistake  was  to  my  advan- 
tage as  well  as  to  my  credit.  I  owe  to  it  the  acquaintance 
of  one  of  the  noblest  of  the  human  race,  I  mean  Elizabeth 
Fry,21  who  came  to  me  for  advice  about  a  philanthropic  de- 
sign, which  involved  life  questions,  under  a  general  im- 
pression that  some  Morgan  had  attended  to  such  things.22 

cial  administration  of  the  new  republic,  but  he  declined.  His  famous 
sermon  on  the  French  Revolution  is  said  to  have  inspired  Burke's 
Reflections  on  the  Revolution  in  France, 

21  Elizabeth  Gurney  (1780-1845),  a  Quaker,  who  married  Joseph 
Fry  (1800),  a  London  merchant.     She  was  the  prime  mover  in  the 
Association  for^  the  Improvement  of  the  Female  Prisoners  in  New- 
gate,  founded  in    1817.     Her  influence   in  prison   reform   extended 
throughout  Europe,  and  she  visited  the  prisons  of  many  countries 
in  her  efforts  to  improve  the  conditions  of  penal  servitude.     The 
friendship  of  Mrs.  Fry  with  the  De  Morgans  began  in   1837.     Her 
scheme    for    a    female    benefit    society    proved    worthless    from    the 
actuarial   standpoint,  and  would  have  been   disastrous  to   all   con- 
cerned if  it  had  been  carried  out,  and  it  was  therefore  fortunate 
that  De  Morgan  ^was  consulted  in  time.    Mrs.  De  Morgan  speaks  of 
the  consultation  in  these  words :  "My  husband,  who  was  very  sensi- 
tive on  such  points,  was  charmed  with  Mrs.  Fry's  voice  and  manner 
as  much  as  by  the  simple  self-forgetfulness  with  which  she  entered 
into  this  business ;  her  own  very  uncomfortable  share  of  it  not  being 
felt  as  an  element  in  the  question,  as  long  as  she  could  be  useful  in 
promoting  good  or  preventing  mischief.     I  can  see  her  now  as  she 
came  into  our  room,  took  off  her  little  round  Quaker  cap,  and  laying 
it  down,  _went  at  once  into  the  matter.    'I  have  followed  thy  advice, 
and  I  think  nothing  further  can  be  done  in  this  case;  but  all  harm 
is  prevented.'    In  the  following  year  I  had  an  opportunity  of  seeing 
the  _  effect  of  her  most  musical  tones.     I  visited  her  at   Stratford, 
taking  my  little  baby  and  nurse  with  me,  to  consult  her  on  some 
articles  on  prison  discipline,  which  I  had  written  for  a  periodical. 
The  baby— three  months  old— was  restless,  and  the  nurse  could  not 
quiet  her,  neither  could  I   entirely,   until  Mrs.   Fry  began  to   read 
something  connected  with  the  subject  of  my  visit,  when  the  infant, 
fixing  her  large  eyes  on  the  reader,  lay  listening  till  she  fell  asleep." 
Memoirs,  p.  91. 

22  Mrs.  Fry  certainly  believed  that  the  writer  was  the  old  actuary 
of  the  Equitable,  when  she  first  consulted  him  upon  the  benevolent 
Assurance  project;  but  we  were  introduced  to  her  by  our  old  and 


NEWTON   AGAIN   OVERTHROWN.  225 


NEWTON  AGAIN  OVERTHROWN. 

A  treatise  on  the  sublime  science  of  heliography,  satisfactorily 
demonstrating  our  great  orb  of  light,  the  sun,  to  be  absolutely 
no  other  than  a  body  of  ice !  Overturning  all  the  received 
systems  of  the  universe  hitherto  extant ;  proving  the  celebrated 
and  indefatigable  Sir  Isaac  Newton,  in  his  theory  of  the  solar 
system,  to  be  as  far  distant  from  the  truth,  as  many  of  the 
heathen  authors  of  Greece  and  Rome.  By  Charles  Palmer,1 
Gent.  London,  1798,  8vo. 

Mr.  Palmer  burned  some  tobacco  with  a  burning  glass, 
saw  that  a  lens  of  ice  would  do  as  well,  and  then  says: 

"If  we  admit  that  the  sun  could  be  removed,  and  a  ter- 
restrial body  of  ice  placed  in  its  stead,  it  would  produce  the 
same  effect.  The  sun  is  a  crystaline  body  receiving  the 
radiance  of  God,  and  operates  on  this  earth  in  a  similar 
manner  as  the  light  of  the  sun  does  when  applied  to  a  con- 
vex mirror  or  glass." 

Nov.  10,  1801.  The  Rev.  Thomas  Cormouls,2  minister 
of  Tettenhall,  addressed  a  letter  to  Sir  Wm.  Herschel,  from 
which  I  extract  the  following: 

"Here  it  may  be  asked,  then,  how  came  the  doctrines  of 
Newton  to  solve  all  astronomic  Phenomina,  and  all  problems 
concerning  the  same,  both  a  parte  ante  and  a  parte  post.3  It 
is  answered  that  he  certainly  wrought  the  principles  he  made 
use  of  into  strickt  analogy  with  the  real  Phenomina  of  the 
heavens,  and  that  the  rules  and  results  arizing  from  them 

dear  friend  Lady  Noel  Byron,  by  whom  she  had  been  long  known 
and  venerated,  and  who  referred  her  to  Mr.  De  Morgan  for  advice. 
An  unusual  degree  of  confidence  in,  and  appreciation  of  each  other, 
arose  on  their  first  meeting  between  the  two,  who  had  so  much  that 
was  externally  different,  and  so  much  that  was  essentially  alike,  in 
their  natures.— S.  E.  De  M. 

Anne  Isabella  Milbanke  (1792-1860)  married  Lord  Byron  in 
1815,  when  both  took  the  additional  name  of  Noel,  her  mother's 
name.  They  were  separated  in  1816. 

1  An  obscure  writer  not  mentioned  in  the  ordinary  biographies. 

2  Not  mentioned  in  the  ordinary  biographies,  and  for  obvious 

reasons. 


3  u 


"Before"  and  "after.' 


226  A  BUDGET  OF  PARADOXES. 

agree  with  them  and  resolve  accurately  all  questions  con- 
cerning them.  Though  they  are  not  fact  and  true,  or  nature, 
but  analogous  to  it,  in  the  manner  of  the  artificial  numbers 
of  logarithms,  sines,  &c.  A  very  important  question  arises 
here,  Did  Newton  mean  to  impose  upon  the  world?  By  no 
means :  he  received  and  used  the  doctrines  reddy  formed ; 
he  did  a  little  extend  and  contract  his  principles  when 
wanted,  and  commit  a  few  oversights  of  consequences.  But 
when  he  was  very  much  advanced  in  life,  he  suspected  the 
fundamental  nullity  of  them:  but  I  have  from  a  certain 
anecdote  strong  ground  to  believe  that  he  knew  it  before 
his  decease  and  intended  to  have  retracted  his  error.  But, 
however,  somebody  did  deceive,  if  not  wilfully,  negligently 
at  least.  That  was  a  man  to  whom  the  world  has  great 
obligations  too.  It  was  no  less  a  philosopher  than  Galileo." 
That  Newton  wanted  to  retract  before  his  death,  is  a 
notion  not  uncommon  among  paradoxers.  Nevertheless, 
there  is  no  retraction  in  the  third  edition  of  the  Principia, 
published  when  Newton  was  eighty-four  years  old!  The 
moral  of  the  above  is,  that  a  gentleman  who  prefers  in- 
structing William  Herschel  to  learning  how  to  spell,  may 
find  a  proper  niche  in  a  proper  place,  for  warning  to  others. 
It  seems  that  gravitation  is  not  truth,  but  only  the  loga- 
rithm of  it. 

BISHOPS  AS  PARADOXERS. 

The  mathematical  and  philosophical  works  of  the  Right  Rev. 
John  Wilkins1....  In  two  volumes.   London,  1802,  8vo. 

This  work,  or  at  least  part  of  the  edition — all  for  aught 
I  know — is  printed  on  wood;  that  is,  on  paper  made  from 
wood-pulp.  It  has  a  rough  surface ;  and  when  held  before 
a  candle  is  of  very  unequal  transparency.  There  is  in  it  a 
reprint  of  the  works  on  the  earth  and  moon.  The  discourse 
on  the  possibility  of  going  to  the  moon,  in  this  and  the 
edition  of  1640,  is  incorporated :  but  from  the  account  in  the 

*On  Bishop  Wilkins  see  note  I  on  page  100. 


BISHOPS    AS    PARADOXERS.  227 

life  prefixed,  and  a  mention  by  D'Israeli,  I  should  suppose 
that  it  had  originally  a  separate  title-page,  and  some  circu- 
lation as  a  separate  tract.  Wilkins  treats  this  subject  half 
seriously,  half  jocosely;  he  has  evidently  not  quite  made 
up  his  mind.  He  is  clear  that  "arts  are  not  yet  come  to 
their  solstice,"  and  that  posterity  will  bring  hidden  things 
to  light.  As  to  the  difficulty  of  carrying  food,  he  thinks, 
scoffing  Puritan  that  he  is,  the  Papists  may  be  trained  to  fast 
the  voyage,  or  may  find  the  bread  of  their  Eucharist  "serve 
well  enough  for  their  viaticum."2  He  also  puts  the  case 
that  the  story  of  Domingo  Gonsales  may  be  realized,  namely, 
that  wild  geese  find  their  way  to  the  moon.  It  will  be  re- 
membered— to  use  the  usual  substitute  for,  It  has  been  for- 
gotten— that  the  posthumous  work  of  Bishop  Francis  God- 
win3 of  Llandaff  was  published  in  1638,  the  very  year  of 
Wilkins's  first  edition,  in  time  for  him  to  mention  it  at  the 
end.  Godwin  makes  Domingo  Gonsales  get  to  the  moon  in 
a  chariot  drawn  by  wild  geese,  and,  as  old  books  would  say, 
discourses  fully  on  that  head.  It  is  not  a  little  amusing  that 
Wilkins  should*  have  been  seriously  accused  of  plagiarizing 
Godwin,  Wilkins  writing  in  earnest,  or  nearly  so,  and  God- 
win writing  fiction.  It  may  serve  to  show  philosophers  how 
very  near  pure  speculation  comes  to  fable.  From  the  sublime 
to  the  ridiculous  is  but  a  step:  which  is  the  sublime,  and 
which  the  ridiculous,  every  one  must  settle  for  himself. 
With  me,  good  fiction  is  the  sublime,  and  bad  speculation 
the  ridiculous.  The  number  of  bishops  in  my  list  is  small. 
I  might,  had  I  possessed  the  book,  have  opened  the  list  of 
quadrators  with  an  Archbishop  of  Canterbury,  or  at  least 
with  a  divine  who  was  not  wholly  not  archbishop.  Thomas 
Bradwardine4  (Bragvardinus,  Bragadinus)  was  elected  in 

2  Pro  vision  for  a  journey. 

3  See  note  3  on  page  103. 

4  Thomas  Bradwardine  (1290-1349),  known  as  Doct or  Profundus, 
proctor  and  professor  of  theology  at  Oxford,  and  afterwards  Chan- 
cellor of   St.   Paul's  and  confessor  to   Edward  III.     The  English 
ascribed  their  success  at  Crecy  to  his  prayers. 


228  A  BUDGET  OF  PARADOXES. 

1348 ;  the  Pope  put  in  another,  who  died  unconsecrated ;  and 
Bradwardine  was  again  elected  in  1349,  and  lived  five  weeks 
longer,  dying,  I  suppose,  unconfirmed  and  unconsecrated.5 
Leland  says  he  held  the  see  a  year,  unus  tantum  annulus* 
which  seems  to  be  a  confusion :  the  whole  business,  from  the 
first  election,  took  about  a  year.  He  squared  the  circle,  and 
his  performance  was  printed  at  Paris  in  1494.  I  have  never 
seen  it,  nor  any  work  of  the  author,  except  a  tract  on  pro- 
portion. 

As  Bradwardine's  works  are  very  scarce  indeed,  I  give 
two  titles  from  one  of  the  Libri  catalogues. 


"ARITHMETIC.  BRAUARDINI  (Thomae)  Arithmetica  speculativa 
revisa  et  correcta  a  Petro  Sanchez  Ciruelo  Aragonesi,  black 
letter,  elegant  woodcut  title-page,  VERY  RARE,  folio.  Parisiis,  per 
Thomam  Anguelast  (prv  Olivier  Senant),  s.a.  circa  I5io.7 

"This  book,  by  Thomas  Bradwardine,  Archbishop  of 
Canterbury  must  be  exceedingly  scarce  as  it  has  escaped 
the  notice  of  Professor  De  Morgan,  who,  in  his  Arithmetical 
Books,  speaks  of  a  treatise  of  the  same  author  on  propor- 
tions,8 printed  at  Vienna  in  1515,  but  does  not  mention  the 
present  work. 

5  He  was  consecrated  Archbishop  of  Canterbury  by  the  Pope  at 
Avignon,  July  13,  1349,  and  died  of  the  plague  at  London  in  the 
same  year. 

6  "One  paltry  little  year." 

7  The  title  is  carelessly  copied,  as  is  so  frequently  the  case  in 
catalogues,  even  of  the  Libri  class.     It  should  read:   Arithmetica 
thome  brauardini.\\Olivier  Senant\\Venum  exponuntur  ab  Oliuiario 
senant  in  vico  diui  Jacobi  sub  signo  beate  Barbare  sedente.    The  colo- 
phon reads:  Explicit  arithmetica  speculatiua  thoe  brauardini  bn  re- 
uisa  et  correcta  a  Petro  sanchez  Ciruelo  aragoncnsi  mathematicas 
legete  Parisius,  ipressa  per  Thoma  anguelart.   There  were  Paris  edi- 
tions of  1495,  1496,  1498,  s.  a.   (c.  1500),  1502,  1504,  1505,  s.a.   (c. 
JSio),  1512,  1530,  a  Valencia  edition  of  1503,  two  Wittenberg  edi- 
tions^ of  1534  and  1536,  and  doubtless  several  others.     The  work  is 
not  "very  rare,"  although  of  course  no  works  of  that  period  are 
common.    See  the  editor's  Rara  Arithmetica,  page  61. 

8  This  is  his  Tractatus  de  proportionibus,  Paris,   1495;  Venice, 
1505;  Vienna,  1515,  with  other  editions. 


THE  QUESTION  OF  PARALLELS.  229 


"Bradwardine  (Archbp.  T.).  Brauardini  (Thomae)  Geometria 
speculativa,  com  Tractatu  de  Quadratura  Circuli  bene  revisa 
a  Petro  Sanchez  Ciruelo,  SCARCE,  folio.  Parisiis,  J.  Petit,  i$n.9 

"In  this  work  we  find  the  polygones  etoiles,10  see  Chasles 
(Apergu,  pp.  480,  487,  521,  523,  &c.)  on  the  merit  of  the 
discoveries  of  this  English  mathematician,  who  was  Arch- 
bishop of  Canterbury  in  the  xivth Century  (tempore  Edward 
III.  A.  D.  1349)  ;  and  who  applied  geometry  to  theology. 
M.  Chasles  says  that  the  present  work  of  Bradwardine  con- 
tains 'Une  theorie  nouvelle  qui  doit  faire  honneur  au  xive 
Siecle.'  mi 

The  titles  do  not  make  it  quite  sure  that  Bradwardine 
is  the  quadrator ;  it  may  be  Peter  Sanchez  after  all.12 

THE  QUESTION  OF  PARALLELS. 

Nouvelle  theorie  des  paralleles.  Par  Adolphe  Kircher1  [so" 
signed  at  the  end  of  the  appendix],  Paris,  1803,  8vo. 

An  alleged  emendation  of  Legendre.2    The  author  refers 

9 The  colophon  of  the  1495  edition  reads:  Et  sic  explicit^  Geo- 
metria Thome  brauardini  cu  tractatulo  de  quadrature,  circuit  bene 
reuisa  a  Petro  sanchez  ciruelo :  operaqz  Guidonis  mercatoris  dili- 
getissime  impresse  parisi0  in  capo  gaillardi.  Anno  dni.  1495.  die. 
20.  maij. 

This  Petro  Ciruelo  was  born  in  Arragon,  and  died  in  1560  at 
Salamanca.  He  studied  mathematics  and  philosophy  at  Paris,  and 
took  the  doctor's  degree  there.  He  taught  at  the  University  of 
Alcala  and  became  canon  of  the  Cathedral  at  Salamanca.  Besides 
his  editions  of  Bradwardine  he  wrote  several  works,  among  them 
the  Liber  arithmeticae  practicae  qui  dicitur  algorithmus  (Paris, 
1495)  and  the  Cursus  quatuor  mathematicarum  artium  liberalium 
(Alcala,  1516). 

10  Star  polygons,  a  subject  of  considerable  study  in  the  later 
Middle  Ages.  See  note  I  on  page  44. 

1  "A  new  theory  that  adds  lustre  to  the  fourteenth  century." 

"There  is  nothing  in  the  edition  of  1495  that  leads  to  this  con- 
clusion. 

1  The  full  title  is :  Nouvelle  theorie  des  paralleles,  avec  un  appen- 
dice  contenant  la  maniere  de  perfectionner  la  theorie  des  paralleles 
de  A.  M.  Legendre.  The  author  had  no  standing  as  a  scientist. 

2Adrien  Marie  Legendre  (1752-1833)  was  one  of  the  great 
mathematicians  of  the  opening  of  the  nineteenth  century.  His  Ele- 
ments de  geometric  (1794)  had  great  influence  on  the  geometry  of 


230  A  BUDGET  OF  PARADOXES. 

to  attempts  by  Hoffman,3  1801,  by  Hauff,4  1799,  and  to  a 
work  of  Karsten,5  or  at  least  a  theory  of  Karsten,  contained 
in  "Tentamen  novae  parallelarum  theoriae  notione  situs  fun- 
datae;  auctore  G.  C.  Schwal,6  Stuttgardae,  1801,  en  8  vo- 
lumes." Surely  this  is  a  misprint;  eight  volumes  on  the 
theory  of  parallels  ?  If  there  be  such  a  work,  I  trust  I  and 
it  may  never  meet,  though  ever  so  far  produced. 

the  United  States.  His  Essai  sur  la  theorie  des  nombres  (1798)  is 
one  of  the  classics  upon  the  subject.  The  work  to  which  Kircher 
refers  is  the  Notcvelle  theorie  des  paralleles  (1803),  in  which  the 
attempt  is  made  to  avoid  using  Euclid's  postulate  of  parallels,  the 
result  being  merely  the  substitution  of  another  assumption  that  was 
even  more  unsatisfactory.  The  best  presentations  of  the  general 
theory  are  W.  B.  Frankland's  Theories  of  Parallelism,  Cambridge, 
1910,  and  Engel  and  Stacker's  Die  Theorie  der  Parallellinien  von 
Euclid  bis  auf  Gauss,  Leipsic,  1895.  Legendre  published  a  second 
work  on  the  theory  the  year  of  his  death,  Reflexions  sur  ....  la 
theorie  des  paralleles  (1833).  His  other  works  include  the  Nou- 
velles  methodes  pour  la  determination  des  orbites  des  cometes  (1805), 
in  which  he  uses  the  method  of  least  squares ;  the  Traite  des  fonc- 
tions  elliptiques  et  des  integrates  (1827-1832),  and  the  Exercises  de 
calcul  integral  (1811,  1816,  1817). 

'Johann  Joseph  Ignatz  von  Hoffmann  (1777-1866),  professor 
of  mathematics  at  Aschaffenburg,  published  his  Theorie  der  Parallel- 
linien in  1801.  He  supplemented  this  by  his  Kritik  der  Parallelen- 
Theorie  in  1807,  and  his  Das  eilfte  Axiom  der  Elemente  des  Euclidis 
neu  bewiesen  in  1859.  He  wrote  other  works  on  mathematics,  but 
none  of  his  contributions  was  of  any  importance. 

4Johann  Karl  Friedrich  Hauff  (1766-1846)  was  successively 
professor  of  mathematics  at  Marburg,  director  of  the  polytechnic 
school  at  Augsburg,  professor  at  the  Gymnasium  at  Cologne,  and 
professor  of  mathematics  and  physics  at  Ghent.  The  work  to  which 
Kircher  refers  is  his  memoirs  on  the  Euclidean  Theorie  der  Paral- 
lelen  in  Hindenburg's  Archiv,  vol.  Ill  (1799),  an  article  of  no  merit 
in  the  general  theory. 

6  Wenceslaus  Johann  Gustav  Karsten  (1732-1787)  was  professor 
of  logic  at  Rostock  (1758)  and  Butzow  (1760),  and  later  became 
professor  of  mathematics  and  physics  at  Halle.  His  work  on  paral- 
lels is  the  Versuch  einer  vollig  berichtigten  Theorie  der  Parallel- 
linien (1779).  He  also  wrote  a  work  entitled  Anfangsgriinde  der 
mathematischen  Wissenschaften  (1780),  but  neither  of  these  works 
was  more  than  mediocre. 

6  Johann  Christoph  Schwab  (not  Schwal)  was  born  in  1743  and 
died  in  1821.  He  was  professor  at  the  Karlsschule  at  Stuttgart. 
De  Morgan's  wish  was  met,  for  the  catalogues  give  "c.  fig.  8,"  so 
that  it  evidently  had  eight  illustrations  instead  of  eight  volumes. 
He  wrote  several  other  works  on  the  principles  of  geometry,  none 
of  any  importance. 


A  PATRIOTIC  PARADOX.  231 

Soluzione  ....  della  quadratura  del  Circolo.  By  Gaetano 
Rossi.7  London,  1804,  8vo. 

The  three  remarkable  points  of  this  book  are,  that  the 
household  of  the  Prince  of  Wales  took  ten  copies,  Signora 
Grassini8  sixteen,  and  that  the  circumference  is  3%  diam- 
eters. That  is,  the  appetite  of  Grassini  for  quadrature  ex- 
ceeded that  of  the  whole  household  (loggia)  of  the  Prince 
of  Wales  in  the  ratio  in  which  the  semi-circumference  ex- 
ceeds the  diameter.  And  these  are  the  first  two  in  the  list 
of  subscribers.  Did  the  author  see  this  theorem? 

A  PATRIOTIC  PARADOX. 

Britain  independent  of  commerce;  or  proofs,  deduced  from  an 
investigation  into  the  true  cause  of  the  wealth  of  nations, 
that  our  riches,  prosperity,  and  power  are  derived  from  sources 
inherent  in  ourselves,  and  would  not  be  affected,  even  though 
our  commerce  were  annihilated.  By  Wm.  Spence.1  4th  edi- 
tion, 1808,  8vo. 

A  patriotic  paradox,  being  in  alleviation  of  the  Com- 
merce panic  which  the  measures  of  Napoleon  I. — who  felt 
our  Commerce,  while  Mr.  Spence  only  saw  it — had  awak- 
ened. In  this  very  month  (August,  1866),  the  Pres.  Brit. 
Assoc.  has  applied  a  similar  salve  to  the  coal  panic ;  it  is  fit 
that  science,  which  rubbed  the  sore,  should  find  a  plaster. 
We  ought  to  have  an  iron  panic  and  a  timber  panic;  and 

'Gaetano  Rossi  of  Catanzaro.  This  was  the  libretto  writer 
(1772-1855),  and  hence  the  imperfections  of  the  work  can  better  be 
condoned.  De  Morgan  should  have  given  a  little  more  of  the  title: 
Soluzione  esatta  e  regolare  ....  del  ....  problema  della  quadratura 
del  circolo.  There  was  a  second  edition,  London,  1805. 

8  This  identifies  Rossi,  for  Josephine  Grassini  (1773-1850)  was 
a  well-known  contralto,  prima  donna  at  Napoleon's  court  opera. 

/William  Spence  (1783-1860)  was  an  entomologist  and  econ- 
omist of  some  standing,  a  fellow  of  the  Royal  Society,  and  one  of 
the  founders  of  the  Entomological  Society  of  London.  The  work 
here  mentioned  was  a  popular  one,  the  first  edition  appearing  in 
1807,  and  four  editions  being  justified  in  a  single  year.  He  also 
wrote  Agriculture  the  Source  of  Britain's  Wealth  (1808)  and  Ob- 
jections against  the  Corn  Bill  refuted  (1815),  besides  a  work  in  four 
volumes  on  entomology  (1815-1826)  in  collaboration  with  William 
Kirby. 


232  A   BUDGET   OF   PARADOXES. 

a  solemn  embassy  to  the  Americans,  to  beg  them  not  to 
whittle,  would  be  desirable.  There  was  a  gold  panic  be- 
ginning, before  the  new  fields  were  discovered.  For  myself, 
I  am  the  unknown  and  unpitied  victim  of  a  chronic  gutta- 
percha  panic :  I  never  could  get  on  without  it ;  to  me,  gutta 
percha  and  Rowland  Hill  are  the  great  discoveries  of  our 
day;  and  not  unconnected  either,  gutta  percha  being  to  the 
submarine  post  what  Rowland  Hill  is  to  the  superterrene. 
I  should  be  sorry  to  lose  cow-choke — I  gave  up  trying  to 
spell  it  many  years  ago — but  if  gutta  percha  go,  I  go  too. 
I  think,  that  perhaps  when,  five  hundred  years  hence,  the 
people  say  to  the  Brit.  Assoc.  (if  it  then  exist)  "Pray  gentle- 
men, is  it  not  time  for  the  coal  to  be  exhausted?"  they  will 
be  answered  out  of  Moliere  (who  will  certainly  then  exist)  : 
"Cela  etait  autrefois  ainsi,  mais  nous  avons  change  tout 
cela."z  A  great  many  people  think  that  if  the  coal  be  used 
up,  it  will  be  announced  some  unexpected  morning  by  all 
the  yards  being  shut  up  and  written  notice  outside,  "Coal 
all  gone !"  just  like  the  "Please,  ma'am,  there  ain't  no  more 
sugar,"  with  which  the  maid  servant  damps  her  mistress 
just  at  breakfast-time.  But  these  persons  should  be  informed 
that  there  is  every  reason  to  think  that  there  will  be  time, 
as  the  city  gentleman  said,  to  venienti  the  occurrite  morbo.3 

SOME  SCIENTIFIC  PARADOXES. 

An  appeal  to  the  republic  of  letters  in  behalf  of  injured  science, 
from  the  opinions  and  proceedings  of  some  modern  authors 
of  elements  of  geometry.  By  George  Douglas.1  Edinburgh, 
1810,  8vo. 

Mr.  Douglas  was  the  author  of  a  very  good  set  of  mathe- 

3  "That  used  to  be  so,  but  we  have  changed  all  that." 
8  "Meet  the  coming  disease." 

1  George  Douglas  (or  Douglass)  was  a  Scotch  writer.  He  got 
out  an  edition  of  the  Elements  of  Euclid  in  1776,  with  an  appendix 
on  trigonometry  and  a  set  of  tables.  His  work  on  Mathematical 
Tables  appeared  in  1809,  and  his  Art  of  Drawing  in  Perspective, 
from  mathematical  principles,  in  1810. 


SOME  SCIENTIFIC  PARADOXES.  233 

matical  tables,  and  of  other  works.  He  criticizes  Simson,2 
Playfair,3  and  others,  —  sometimes,  I  think,  very  justly. 
There  is  a  curious  phrase  which  occurs  more  than  once. 
When  he  wants  to  say  that  something  or  other  was  done 
before  Simson  or  another  was  born,  he  says  "before  he 
existed,  at  least  as  an  author."  He  seems  to  reserve  the 
possibility  of  Simson's  pre-existence,  but  at  the  same  time 
to  assume  that  he  never  wrote  anything  in  his  previous 
state.  Tell  me  that  Simson  pre-existed  in  any  other  way 
than  as  editor  of  some  pre-existent  Euclid?  Tell  Apella!4 
1810.  In  this  year  Jean  Wood,  Professor  of  Mathemat- 
ics in  the  University  of  Virginia  (Richmond),5  addressed 
a  printed  circular  to  "Dr.  Herschel,  Astronomer,  Greenwich 
Observatory."  No  mistake  was  more  common  than  the 
natural  one  of  imagining  that  the  Private  Astronomer  of  the 
king  was  the  Astronomer  Royal  The  letter  was  on  the 

8  See  note  3,  on  page  197. 

'John  Playfair  (1748-1848)  was  professor  of  mathematics  (1785) 
and  natural  philosophy  (1805)  at  the  University  of  Edinburgh.  His 
Elements  of  Geometry  went  through  many  editions. 

'"Tell  Apella"  was  an  expression  current  in  classical  Rome  to 
indicate  incredulity  and  to  show  the  contempt  in  which  the  Jew  was 
held.  Horace  says:  Credat  Judaus  Apella,  "Let  Apella  the  Jew  be- 
lieve it."  Our  "Tell  it  to  the  marines,"  is  a  similar  phrase. 

5  As  De  Morgan  says  two  lines  later,  "No  mistake  is  more  com- 
mon than  the  natural  one  of  imagining  that  the"  — University  of  Vir- 
ginia is  at  Richmond.  The  fact  is  that  it  is  not  there,  and  that  it 
did  not  exist  in  1810.  It  was  not  chartered  until  1819,  and  was  not 
opened  until  1825,  and  then  at  Charlottesville.  The  act  establishing 
the  Central  College,  from  which  the  University  of  Virginia  devel- 
oped, was  passed  in  1816.  The  Jean  Wood  to  whom  De  Morgan 
refers  was  one  John  Wood  who  was  born  about  1775  in  Scotland 
and  who  emigrated  to  the  United  States  in  1800.  He  published  a 
History  of  the  Administration  of  J.  Adams  (New  York,  1802)  that 
was  suppressed  by  Aaron  Burr.  This  act  called  forth  two  works, 
a  Narrative  of  the  Suppression,  by  Col  Burr,  of  the  'History  of  the 
Administration  of  John  Adams'  (1802),  in  which  Wood  was  sus- 
tained; and  the  Antidote  to  John  Wood's  Poison  (1802),  in  which 
he  was  attacked.  The  work  referred  to  in  the  "printed  circular" 
may  have  been  the  New  theory  of  the  diurnal  rotation  of  the  earth 
^Richmond,  Va.,  1809).  Wood  spent  the  last  years  of  his  life  in 
Richmond,  Va.,  making  county  maps.  He  died  there  in  1822.  A 
careful  search  through  works  relating  to  the  University  of  Virginia 
fails  to  show  that  Wood  had  any  connection  with  it. 


234  A   BUDGET   OF   PARADOXES. 

difference  of  velocities  of  the  two  sides  of  the  earth,  arising 
from  the  composition  of  the  rotation  and  the  orbital  motion. 
The  paradox  is  a  fair  one,  and  deserving  of  investigation; 
but,  perhaps  it  would  not  be  easy  to  deduce  from  it  tides, 
trade-winds,  aerolithes,  &c.,  as  Mr.  Wood  thought  he  had 
done  in  a  work  from  which  he  gives  an  extract,  and  which 
he  describes  as  published.  The  composition  of  rotations, 
&c.,  is  not  for  the  world  at  large:  the  paradox  of  the  non- 
rotation  of  the  moon  about  her  axis  is  an  instance.  Ht>w 
many  persons  know  that  when  a  wheel  rolls  on  the  ground, 
the  lowest  point  is  moving  upwards,  the  highest  point  for- 
wards, and  the  intermediate  points  in  all  degrees  of  betwixt 
and  between?  This  is  too  short  an  explanation,  with  some 
good  difficulties. 

The  Elements  of  Geometry.     In  2  vols.     [By  the  Rev.  J.  Dob- 
son,6  B.D.]  Cambridge,  1815.    4to. 

Of  this  unpunctuating  paradoxer  I  shall  give  an  account 
in  his  own  way :  he  would  not  stop  for  any  one ;  why  should 
I  stop  for  him  ?  It  is  worth  while  to  try  how  unpunctuated 
sentences  will  read. 

The  reverend  J  Dobson  BD  late  fellow  of  saint  Johns 
college  Cambridge  was  rector  of  Brandesburton  in  York- 
shire he  was  seventh  wrangler  in  1798  and  died  in  1847  he 
was  of  that  sort  of  eccentricity  which  permits  account  of  his 
private  life  if  we  may  not  rather  say  that  in  such  cases 
private  life  becomes  public  there  is  a  tradition  that  he  was 
called  Death  Dobson  on  account  of  his  head  and  aspect  of 
countenance  being  not  very  unlike  the  ordinary  pictures  of 
a  human  skull  his  mode  of  life  is  reported  to  have  been  very 
singular  whenever  he  visited  Cambridge  he  was  never  known 
to  go  twice  to  the  same  inn  he  never  would  sleep  at  the 
rectory  with  another  person  in  the  house  some  ancient  char- 
woman used  to  attend  to  the  house  but  never  slept  in  it  he 
has  been  known  in  the  time  of  coach  travelling  to  have  de- 

6  There  seems  to  be  nothing  to  add  to  Dobson's  biography  beyond 
what  De  Morgan  has  so  deliciously  set  forth. 


SOME  SCIENTIFIC  PARADOXES.  235 

ferred  his  return  to  Yorkshire  on  account  of  his  disinclina- 
tion to  travel  with  a  lady  in  the  coach  he  continued  his 
mathematical  studies  until  his  death  and  till  his  executors 
sold  the  type  all  his  tracts  to  the  number  of  five  were  kept  in 
type  at  the  university  press  none  of  these  tracts  had  any 
stops  except  full  stops  at  the  end  of  paragraphs  only  neither 
had  they  capitals  except  one  at  the  beginning  of  a  paragraph 
so  that  a  full  stop  was  generally  followed  by  some  white 
as  there  is  not  a  single  proper  name  in  the  whole  of  the 
book  I  have  I  am  not  able  to  say  whether  he  would  have  used 
capitals  before  proper  names  I  have  inserted  them  as  usual 
for  which  I  hope  his  spirit  will  forgive  me  if  I  be  wrong  he 
also  published  the  elements  of  geometry  in  two  volumes 
quarto  Cambridge  1815  this  book  had  also  no  stops  except 
when  a  comma  was  wanted  between  letters  as  in  the  straight 
lines  AB,  BC  I  should  also  say  that  though  the  title  is  un- 
punctuated  in  the  author's  part  it  seems  the  publishers  would 
not  stand  it  in  their  imprint  this  imprint  is  punctuated  as 
usual  and  Deighton  and  Sons  to  prove  the  completeness  of 
their  allegiance  have  managed  that  comma  semicolon  and 
period  shall  all  appear  in  it  why  could  they  not  have  con- 
trived interrogation  and  exclamation  this  is  a  good  precedent 
to  establish  the  separate  right  of  the  publisher  over  the 
imprint  it  is  said  that  only  twenty  of  the  tracts  were  printed 
and  very  few  indeed  of  the  book  on  geometry  it  is  doubtful 
whether  any  were  sold  there  is  a  copy  of  the  geometry  in 
the  university  library  at  Cambridge  and  I  have  one  myself 
the  matter  of  the  geometry  differs  entirely  from  Euclid  and 
is  so  fearfully  prolix  that  I  am  sure  no  mortal  except  the 
author  ever  read  it  the  man  went  on  without  stops  and  with- 
out stop  save  for  a  period  at  the  end  of  a  paragraph  this  is 
the  unpunctuated  account  of  the  unpunctuating  geometer 
suum  cuique  tribuito7  Mrs  Thrale8  would  have  been  amused 

7  "Give  to  each  man  his  due." 

8  Hester  Lynch  Salusbury  (1741-1821),  the  friend  of  Dr.  John- 
son, married   Henry   Thrale    (1763),   a  brewer,  who   died   in    1781. 
She  then  married  Gabriel  Piozzi  (1784),  an  Italian  musician.    Her 


236  A   BUDGET   OF    PARADOXES. 

at  a  Dobson  who  managed  to  come  to  a  full  stop  without 
either  of  the  three  warnings. 

I  do  not  find  any  difficulty  in  reading  Dobson's  geom- 
etry; and  I  have  read  more  of  it  to  try  reading  without 
stops  than  I  should  have  done  had  it  been  printed  in  the 
usual  way.  Those  who  dip  into  the  middle  of  my  paragraph 
may  be  surprised  for  a  moment  to  see  "on  account  of  his 
disinclination  to  travel  with  a  lady  in  the  coach  he  continued 
his  mathematical  studies  until  his  death  and  [further,  of 
course]  until  his  executors  sold  the  type."  But  a  person 
reading  straight  through  would  hardly  take  it  so.  I  should 
add  that,  in  order  to  give  a  fair  trial,  I  did  not  compose  as 
I  wrote,  but  copied  the  words  of  the  correspondent  who  gave 
me  the  facts,  so  far  as  they  went. 

A  RELIGIOUS  PARADOX. 

Philosophia  Sacra,  or  the  principles  of  natural  Philosophy.  Ex- 
tracted from  Divine  Revelation.  By  the  Rev.  Samuel  Pike.1 
Edited  by  the  Rev.  Samuel  Kittle.2  Edinburgh,  1815,  8vo. 

This  is  a  work  of  modified  Hutchinsonianism,  which  I 
have  seen  cited  by  several.  Though  rather  dark  on  the  sub- 
ject, it  seems  not  to  contradict  the  motion  of  the  earth,  or 
the  doctrine  of  gravitation.  Mr.  Kittle  gives  a  list  of  some 
Hutchinsonians, — as  Bishop  Home  ;3  Dr.  Stukeley  ;4  the  Rev. 

Anecdotes  of  the  late  Samuel  Johnson  (1786)  and  Letters  to  and 
from  Samuel  Johnson  (1788)  are  well  known.  She  also  wrote 
numerous  essays  and  poems. 

1  Samuel  Pike  (c.  1717-1773)  was  an  independent  minister,  with 
a  chapel  in  London  and  a  theological  school  in  his  house.  He  later 
became  a  disciple  of  Robert  Sandeman  and  left  the  Independents 
for  the  Sandemanian  church  (1765).  The  Philosophia  Sacra  was 
first  published  at  London  in  1753.  De  Morgan  here  cites  the  second 
edition. 

*  Pike  had  been  dead  over  forty  years  when  Kittle  published  this 
second  edition.  Kittle  had  already  published  a  couple  of  works : 
King  Solomon's  portraiture  of  Old  Age  (Edinburgh,  1813),  and 
Critical  and  Practical  Lectures  on  the  Apocalyptical  Epistles  to  the 
Seven  Churches  of  Asia  Minor  (London,  1814). 

8  See  note  i,  on  page  152. 

4  William  Stukely  (1687-1765)  was  a  fellow  of  the  Royal  Society 
and  of  the  College  of  Physicians  and  Surgeons.  He  afterwards 


A  RELIGIOUS  PARADOX.  237 

W.  Jones,5  author  of  Physiological  Disquisitions ;  Mr.  Spear- 
man,6 author  of  Letters  on  the  Septuagint  and  editor  of 
Hutchinson ;  Mr.  Barker,7  author  of  Reflexions  on  Learn- 
ing ;  Dr.  Catcott,8  author  of  a  work  on  the  creation,  &c. ;  Dr. 
Robertson,9  author  of  a  Treatise  on  the  Hebrew  Language ; 
Dr.  Holloway,10  author  of  Originals,  Physical  and  Theolog- 
ical ;  Dr.  Walter  Hodges,11  author  of  a  work  on  Elohim ; 
Lord  President  Forbes  (ob.  1747). ia 

The  Rev.  William  Jones,  above  mentioned  (1726-1800), 
the  friend  and  biographer  of  Bishop  Home  and  his  stout 

(1729)  entered  the  Church.  He  was  prominent  as  an  antiquary, 
especially  in  the  study  of  the  Roman  and  Druidic  remains  of  Great 
Britain.  He  was  the  author  of  numerous  works,  chiefly  on  paleog- 
raphy. 

5  William  Jones  (1726-1800),  who  should  not  be  confused  with 
his  namesake  who  is  mentioned  in  note  3  on  page  135.  He  was  a 
lifelong  friend  of  Bishop  Horne,  and  his  vicarage  at  Nayland  was 
a  meeting  place  of  an  influential  group  of  High  Churchmen.  Be- 
sides the  Physiological  Disquisitions  (1781)  he  wrote  The  Catholic 
Doctrine  of  the  Trinity  (1756)  and  The  Grand  Analogy  (1793). 

'Robert  Spearman  (1703-1761)  was  a  pupil  of  John  Hutchin- 
son, and  not  only  edited  his  works  but  wrote  his  life.  He  wrote  a 
work  against  the  Newtonian  physics,  entitled  An  Enquiry  after  Phi- 
losophy and  Theology  (Edinburgh,  1755),  besides  the  Letters  to  a 
Friend  concerning  the  Septuagint  Translation  (Edinburgh,  1759)  to 
which  De  Morgan  refers. 

TA  writer  of  no  importance,  at  least  in  the  minds  of  British 
biographers. 

"Alexander  Catcott  (1725-1779),  a  theologian  and  geologist, 
wrote  not  only  a  work  on  the  creation  (1756)  but  a  Treatise  on  the 
Deluge  (1761,  with  a  second  edition  in  1768).  Sir  Charles  Lyell 
considered  the  latter  work  a  valuable  contribution  to  geology. 

8  James  Robertson  (1714-1795),  professor  of  Hebrew  at  the  Uni- 
versity of  Edinburgh.  Probably  De  Morgan  refers  to  his  Grarn- 
matica  Linguae  Hebraa  (Edinburgh,  1758;  with  a  second  edition  in 
1783).  He  also  wrote  Clavis  Pentateuchi  (1770). 

"Benjamin  Holloway  (c.  1691-1759),  a  geologist  and  theologian. 
He  translated  Woodward's  Naturalis  Historia  Telluris,  and  was  in- 
troduced by  Woodward  to  Hutchinson.  The  work  referred  to  by 
De  Morgan  appeared  at  Oxford  in  two  volumes  in  1754. 

"  His  work  was  The  Christian  plan  exhibited  in  the  interpretation 
of  Elohim:  with  observations  upon  a  few  other  matters  relative  to 
the  same  subject,  Oxford,  1752,  with  a  second  edition  in  1755. 

"Duncan  Forbes  (1685-1747)  studied  Oriental  languages  and 
civil  law  at  Leyden.  He  was  Lord  President  of  the  Court  of  Ses- 
sions (i737).  He  wrote  a  number  of  theological  works. 


238  A   BUDGET   OF   PARADOXES. 

defender,  is  best  known  as  William  Jones  of  Nayland,  who 
(1757)13  published  the  Catholic  Doctrine  of  the  Trinity;  he 
was  also  strong  for  the  Hutchinsonian  physical  trinity  of 
fire,  light,  and  spirit.  This  well-known  work  was  generally 
recommended,  as  the  defence  of  the  orthodox  system,  to 
those  who  could  not  go  into  the  learning  of  the  subject. 
There  is  now  a  work  more  suited  to  our  time :  The  Rock  of 
Ages,  by  the  Rev.  E.  H.  Bickersteth,14  now  published  by 
the  Religious  Tract  Society,  without  date,  answered  by  the 
Rev.  Dr.  Sadler,15  in  a  work  (1859)  entitled  Gloria  Patri, 
in  which,  says  Mr.  Bickersteth,  "the  author  has  not  even 
attempted  to  grapple  with  my  main  propositions."  I  have 
read  largely  on  the  controversy,  and  I  think  I  know  what 
this  means.  Moreover,  when  I  see  the  note  "There  are  two 
other  passages  to  which  Unitarians  sometimes  refer,  but  the 
deduction  they  draw  from  them  is,  in  each  case,  refuted  by 
the  context" — I  think  I  see  why  the  two  texts  are  not  named. 
Nevertheless,  the  author  is  a  little  more  disposed  to  yield  to 
criticism  than  his  foregoers ;  he  does  not  insist  on  texts  and 
readings  which  the  greatest  editors  have  rejected.  And  he 
writes  with  courtesy,  both  direct  and  oblique,  towards  his 
antagonists ;  which,  on  his  side  of  this  subject,  is  like  letting 
in  fresh  air.  So  that  I  suspect  the  two  books  will  together 
make  a  tolerably  good  introduction  to  the  subject  for  those 
who  cannot  go  deep.  Mr.  Bickersteth's  book  is  well  arranged 
and  indexed,  which  is  a  point  of  superiority  to  Jones  of 
Nayland.  There  is  a  point  which  I  should  gravely  recom- 
mend to  writers  on  the  orthodox  side.  The  Unitarians  in 

13  Should  be  1756. 

"Edward  Henry  Bickersteth  (1825-1906),  bishop  of  Exeter 
(1885-1900)  ;  published  The  Rock  of  Ages;  or  scripture  testimony  to 
the  one  Eternal  Godhead  of  the  Father,  and  of  the  Son,  and  of  the 
Holy  Ghost  at  Hampstead  in  1859.  A  second  edition  appeared  at 
London  in  1860. 

"Thomas  Sadler  (1822-1891)  took  his  Ph.D.  at  Erlangen  in 
1844,  and  became  a  Unitarian  minister  at  Hampstead,  where  Bicker- 
steth's work  was  published.  Besides  writing  the  Gloria  Patri  (1859), 
he  edited  Crabb  Robinson's  Diaries. 


A  RELIGIOUS  PARADOX.  239 

England  have  frequently  contended  that  the  method  of  prov- 
ing the  divinity  of  Jesus  Christ  from  the  New  Testament 
would  equally  prove  the  divinity  of  Moses.  I  have  not  fallen 
in  the  way  of  any  orthodox  answers  specially  directed  at  the 
repeated  tracts  written  by  Unitarians  in  proof  of  their  asser- 
tion. If  there  be  any,  they  should  be  more  known ;  if  there 
be  none,  some  should  be  written.  Which  ever  side  may 
be  right,  the  treatment  of  this  point  would  be  indeed  com- 
ing to  close  quarters.  The  heterodox  assertion  was  first 
supported,  it  is  said,  by  John  Bidle  or  Biddle  (1615-1662) 
of  Magdalen  College,  Oxford,  the  earliest  of  the  English 
Unitarian  writers,  previously  known  by  a  translation  of 
part  of  Virgil  and  part  of  Juvenal.16  But  I  cannot  find  that 
he  wrote  on  it.17  It  is  the  subject  of  "alptcrew  dvao-rao-ts,  or 
a  new  way  of  deciding  old  controversies.  By  Basanistes. 
Third  edition,  enlarged,"  London,  1815,  8vo.18  It  is  the 
appendix  to  the  amusing,  "Six  more  letters  to  Granville 
Sharp,  Esq.,  ...  By  Gregory  Blunt,  Esq."  London,  8vo., 
1803.19  This  much  I  can  confidently  say,  that  the  study  of 
these  tracts  would  prevent  orthodox  writers  from  some 
curious  slips,  which  are  slips  obvious  to  all  sides  of  opinion. 
The  lower  defenders  of  orthodoxy  frequently  vex  the  spirits 
of  the  higher  ones. 

Since  writing  the  above  I  have  procured  Dr.  Sadler's 
answer.  I  thought  I  knew  what  the  challenger  meant 
when  he  said  the  respondent  had  not  grappled  with  his  main 

"This  was  his  Virgil's  Bucolics  and  the  two  first  Satyrs  of 
Juvenal,  1634. 

17  Possibly  in  his  Twelve  Questions  or  Arguments  drawn  out  of 
Scripture,  wherein  the  commonly  received  Opinion  touching  the 
Deity  of  the  Holy  Spirit  is  clearly  and  fully  refuted,  1647.  This  was 
his  first  heretical  work,  and  it  was  followed  by  a  number  of  others 
that  were  written  during  the  intervals  in  which  the  Puritan  parlia- 
ment allowed  him  out  of  prison.  It  was  burned  by  the  hangman  as 
blasphemous.  Biddle  finally  died  in  prison,  unrepentant  to  the  last. 

"The  first  edition  of  the  anonynous  'Atpeffewv  dvaa-raffts  (by 
Vicars?)  appeared  in  1805. 

"^Possibly  by  Thomas  Pearne  (c.  1753-1827),  a  fellow  of  St. 
Peter's  College,  Cambridge,  and  a  Unitarian  minister. 


240  A   BUDGET   OF   PARADOXES. 

propositions.  I  should  say  that  he  is  clung  on  to  from  be- 
ginning to  end.  But  perhaps  Mr.  B.  has  his  own  meaning 
of  logical  terms,  such  as  "proposition" :  he  certainly  has  his 
own  meaning  of  "cumulative."  He  says  his  evidence  is 
cumulative;  not  a  catena,  the  strength  of  which  is  in  its 
weakest  part,  but  distinct  and  independent  lines,  each  of 
which  corroborates  the  other.  This  is  the  very  opposite  of 
cumulative:  it  is  distributive.  When  different  arguments 
are  each  necessary  to  a  conclusion,  the  evidence  is  cumu- 
lative;  when  any  one  will  do,  even  though  they  strengthen 
each  other,  it  is  distributive.  The  word  "cumulative"  is  a 
synonym  of  the  law  word  "constructive";  a  whole  which 
will  do  made  out  of  parts  which  separately  will  not.  Lord 
Strafford20  opens  his  defence  with  the  use  of  both  words: 
"They  have  invented  a  kind  of  accumulated  or  constructive 
evidence ;  by  which  many  actions,  either  totally  innocent  in 
themselves,  or  criminal  in  a  much  inferior  degree,  shall, 
when  united,  amount  to  treason."  The  conclusion  is,  that 
Mr.  B.  is  a  Cambridge  man;  the  Oxford  men  do  not  con- 
fuse the  elementary  terms  of  logic.  O  dear  old  Cambridge ! 
when  the  New  Zealander  comes  let  him  find  among  the 
relics  of  your  later  sons  some  proof  of  attention  to  the 
elementary  laws  of  thought.  A  little-go  of  logic,  please! 
Mr.  B.,  though  apparently  not  a  Hutchinsonian,  has 
a  nibble  at  a  physical  Trinity.  "If,  as  we  gaze  on  the  sun 
shining  in  the  firmament,  we  see  any  faint  adumbration  of 
the  doctrine  of  the  Trinity  in  the  fontal  orb,  the  light  ever 
generated,  and  the  heat  proceeding  from  the  sun  and  its 
beams — threefold  and  yet  one,  the  sun,  its  light,  and  its 

20  Thomas  Wentworth,  Earl  of  Strafford,  was  borne  in  London 
in  1593,  and  was  executed  there  in  1641.  He  was  privy  councilor  to 
Charles  I,  and  was  Lord  Deputy  of  Ireland.  On  account  of  his 
repressive  measures  to  uphold  the  absolute  power  of  the  king  he 
was  impeached  by  the  Long  Parliament  and  was  executed  for  trea- 
son. The  essence  of  his  defence  is  in  the  sentence  quoted  by  De 
Morgan,  to  which  Pym  replied  that  taken  as  a  whole,  the  acts  tended 
to  show  an  intention  to  change  the  government,  and  this  was  in 
itself  treason. 


A  RELIGIOUS  PARADOX.  241 

heat, — that  luminous  globe,  and  the  radiance  ever  flowing 
from  it,  are  both  evident  to  the  eye;  but  the  vital  warmth 
is  felt,  not  seen,  and  is  only  manifested  in  the  life  it  trans- 
fuses through  creation.  The  proof  of  its  real  existence  is 
self-demonstrating." 

We  shall  see  how  Revilo21  illustrates  orthodoxy  by  mathe- 
matics. It  was  my  duty  to  have  found  one  of  the  many 
illustrations  from  physics;  but  perhaps  I  should  have  for- 
gotten it  if  this  instance  had  not  come  in  my  way.  It  is 
very  bad  physics.  The  sun,  apart  from  its  light,  evident 
to  the  eyel  Heat  more  self-demonstrating  than  light,  be- 
cause felt  I  Heat  only  manifested  by  the  life  it  diffuses! 
Light  implied  not  necessary  to  life!  But  the  theology  is 
worse  than  Sabellianism.22  To  adumbrate — i.  e.,  make  a 
picture  of — the  orthodox  doctrine,  the  sun  must  be  heavenly 
body,  the  light  heavenly  body,  the  heat  heavenly  body ;  and 
yet,  not  three  heavenly  bodies,  but  one  heavenly  body.  The 
truth  is,  that  this  illustration  and  many  others  most  strik- 
ingly illustrate  the  Trinity  of  fundamental  doctrine  held  by 
the  Unitarians,  in  all  its  differences  from  the  Trinity  of 
persons  held  by  the  Orthodox.  Be  right  which  may,  the 
right  or  wrong  of  the  Unitarians  shines  out  in  the  compari- 
son. Dr.  Sadler  confirms  me — by  which  I  mean  that  I  wrote 
the  above  before  I  saw  what  he  says — in  the  following 
words :  "The  sun  is  one  object  with  two  properties,  and  these 
properties  have  a  parallel  not  in  the  second  and  third  per- 
sons of  the  Trinity,  but  in  the  attributes  of  Deity." 

The  letting  light  alone,  as  self-evident,  and  making  heat 
self-demonstrating,  because  felt — i.  e.,  perceptible  now  and 
then — has  the  character  of  the  Irishman's  astronomy: 

81  The  name  assumed  by  a  writer  who  professed  to  give  a  mathe- 
matical explanation  of  the  Trinity,  see  farther  on.— S.  E.  De  M. 

"Sabellius  (fl.  230  A.  D.)  was  an  early  Christian  of  Libyan 
origin.  He  taught  that  Father,  Son,  and  Holy  Spirit  were  different 
names  for  the  same  person. 


242  A   BUDGET   OF   PARADOXES. 

"Long  life  to  the  moon,  for  a  dear  noble  cratur, 
Which  serves  us  for  lamplight  all  night  in  the  dark, 
While  the  sun  only  shines  in  the  day,  which  by  natur, 
Wants  no  light  at  all,  as  ye  all  may  remark." 

SIR  RICHARD  PHILLIPS. 

Sir  Richard  Phillips*  (born  1768)  was  conspicuous  in 
1793,  when  he  was  sentenced  to  a  year's  imprisonment2  for 
selling  Paine's  Rights  of  Man ;  and  again  when,  in  1807,3 
he  was  knighted  as  Sheriff  of  London.  As  a  bookseller, 
he  was  able  to  enforce  his  opinions  in  more  ways  than 
others.  For  instance,  in  James  Mitchell's4  Dictionary  of  the 
Mathematical  and  Physical  Sciences,  1823,  12mo,  which, 
though  he  was  not  technically  a  publisher,  was  printed  for 
him — a  book  I  should  recommend  to  the  collector  of  works 
of  reference — there  is  a  temperate  description  of  his  doc- 
trines, which  one  may  almost  swear  was  one  of  his  condi- 
tions previous  to  undertaking  the  work.  Phillips  himself 
was  not  only  an  anti-Newtonian,  but  carried  to  a  fearful 
excess  the  notion  that  statesmen  and  Newtonians  were  in 
league  to  deceive  the  world.  He  saw  this  plot  in  Mrs. 
Airy's5  pension,  and  in  Mrs.  Somerville's.6  In  1836,  he 

1  Sir  Richard  Phillips  was  born  in  London  in  1767  (not  1768  as 
stated  above),  and  died  there  in  1840.  He  was  a  bookseller  and 
printer  in  Leicester,  where  he  also  edited  a  radical  newspaper.  He 
went  to  London  to  live  in  1795  and  started  the  Monthly  Magazine 
there  in  1796.  Besides  the  works  mentioned  by  De  Morgan  he  wrote 
on  law  and  economics. 

alt  was  really  eighteen  months. 

8  While  he  was  made  sheriff  in  1807  he  was  not  knighted  until 
the  following  year. 

4  James  Mitchell  (c.  1786-1844)  was  a  London  actuary,  or 
rather  a  Scotch  actuary  living  a  good  part  of  his  life  in  London. 
Besides  the  work  mentioned  he  compiled  a  Dictionary  of  Chemistry, 
Mineralogy,  and  Geology  (1823),  and  wrote  On  the  Plurality  of 
Worlds  (1813)  and  The  Elements  of  Astronomy  (1820). 

5Richarda  Smith,  wife  of  Sir  George  Biddell  Airy  (see  note  2, 
page  85)  the  astronomer.  In  1835  Sir  Robert  Peel  offered  a  pension 
of  ^300  a  year  to  Airy,  who  requested  that  it  be  settled  on  his  wife. 

"Mary  Fairfax  (1780-1872)  married  as  her  second  husband  Dr. 
William  Somerville.  In  1826  she  presented  to  the  Royal  Society  a 


SIR  RICHARD   PHILLIPS.  243 

did  me  the  honor  to  attempt  my  conversion.  In  his  first 
letter  he  says: 

"Sir  Richard  Phillips  has  an  inveterate  abhorrence  of 
all  the  pretended  wisdom  of  philosophy  derived  from  the' 
monks  and  doctors  of  the  middle  ages,  and  not  less  of  those 
of  higher  name  who  merely  sought  to  make  the  monkish 
philosophy  more  plausible,  or  so  to  disguise  it  as  to  mystify 
the  mob  of  small  thinkers." 

So  little  did  his  writings  show  any  knowledge  of  an- 
tiquity, that  I  strongly  suspect,  if  required  to  name  one  of 
the  monkish  doctors,  he  would  have  answered — Aristotle. 
These  schoolmen,  and  the  "philosophical  trinity  of  gravi- 
tating force,  projectile  force,  and  void  space,"  were  the 
bogies  of  his  life. 

I  think  he  began  to  publish  speculations  in  the  Monthly 
Magazine  (of  which  he  was  editor)  in  July  1817:  these  he 
republished  separately  in  1818.  In  the  Preface,  perhaps 
judging  the  feelings  of  others  by  his  own,  he  says  that  he 
"fully  expects  to  be  vilified,  reviled,  and  anathematized,  for 
many  years  to  come."  Poor  man!  he  was  let  alone.  He 
appeals  with  confidence  to  the  "impartial  decision  of  pos- 
terity"; but  posterity  does  not  appoint  a  hearing  for  one 
per  cent,  of  the  appeals  which  are  made ;  and  it  is  much  to 
be  feared  that  an  article  in  such  a  work  of  reference  as  this 
will  furnish  nearly  all  her  materials  fifty  years  hence.  The 
following,  addressed  to  M.  Arago,7  in  1835,  will  give  pos- 
terity as  good  a  notion  as  she  will  probably  need: 

"Even  the  present  year  has  afforded  EVER-MEMORABLE 
examples,  paralleled  only  by  that  of  the  Romish  Conclave 
which  persecuted  Galileo.  Policy  has  adopted  that  maxim  of 
Machiavel  which  teaches  that  it  is  more  prudent  to  reward 

paper  on  The  Magnetic  Properties  of  the  Violet  Rays  of  the  Solar 
Spectrum,  which  attracted  much  attention.  It  was  for  her  Mechan- 
ism of  the  Heavens  (1831),  a  popular  translation  of  Laplace's  Meca- 
nique  Celeste,  that  she  was  pensioned. 

7  Dominique  Frangois  Jean  Arago  (1786-1853)  the  celebrated 
French  astronomer  and  physicist. 


244  A    BUDGET    OF    PARADOXES. 

partisans  than  to  persecute  opponents.  Hence,  a  bigotted 
party  had  influence  enough  with  the  late  short-lived  adminis- 
tration [I  think  he  is  wrong  as  to  the  administration]  of 
Wellington,  Peel,  &c.,  to  confer  munificent  royal  pensions  on 
three  writers  whose  sole  distinction  was  their  advocacy  of 
the  Newtonian  philosophy.  A  Cambridge  professor  last  year 
published  an  elaborate  volume  in  illustration  of  Gravitation, 
and  on  him  has  been  conferred  a  pension  of  300/.  per  annum. 
A  lady  has  written  a  light  popular  view  of  the  Newtonian 
Dogmas,  and  she  has  been  complimented  by  a  pension  of 
2001.  per  annum.  And  another  writer,  who  has  recently 
published  a  volume  to  prove  that  the  only  true  philosophy  is 
that  of  Moses,  has  been  endowed  with  a  pension  of  200/. 
per  annum.  Neither  of  them  were  needy  persons,  and  the 
political  and  ecclesiastical  bearing  of  the  whole  was  indicated 
by  another  pension  of  300/.  bestowed  on  a  political  writer, 
the  advocate  of  all  abuses  and  prejudices.  Whether  the  con- 
duct of  the  Romish  Conclave  was  more  base  for  visiting  with 
legal  penalties  the  promulgation  of  the  doctrines  that  the 
Earth  turns  on  its  axis  and  revolves  around  the  Sun ;  or  that 
of  the  British  Court,  for  its  craft  in  conferring  pensions  on 
the  opponents  of  the  plain  corollary,  that  all  the  motions  of 
the  Earth  are  'part  and  parcel'  of  these  great  motions,  and 
those  again  and  all  like  them  consecutive  displays  of  still 
greater  motions  in  equality  of  action  and  reaction,  is  A  QUES- 
TION which  must  be  reserved  for  the  casuists  of  other  genera- 
tions ....  I  cannot  expect  that  on  a  sudden  you  and  your 
friends  will  come  to  my  conclusion,  that  the  present  philos- 
ophy of  the  Schools  and  Universities  of  Europe,  based  on 
faith  in  witchcraft,  magic,  &c.,  is  a  system  of  execrable 
nonsense,  by  which  quacks  live  on  the  faith  of  fools ;  but  I 
desire  a  free  and  fair  examination  of  my  Aphorisms,  and  if 
a  few  are  admitted  to  be  true,  merely  as  courteous  con- 
cessions to  arithmetic,  my  purpose  will  be  effected,  for  men 
will  thus  be  led  to  think ;  and  if  they  think,  then  the  fabric 


SIR   RICHARD    PHILLIPS.  245 

of  false  assumptions,  and  degrading  superstitions  will  soon 
tumble  in  ruins." 

This  for  posterity.  For  the  present  time  I  ground  the 
fame  of  Sir  R.  Phillips  on  his  having  squared  the  circle 
without  knowing  it,  or  intending  to  do  it.  In  the  Protest 
presently  noted  he  discovered  that  "the  force  taken  as  1  is 
equal  to  the  sum  of  all  its  fractions.  .  .thus  1  =  %  +  %  +  %6 
+  %s>  &c->  carried  to  infinity."  This  the  mathematician  in- 
stantly sees  is  equivalent  to  the  theorem  that  the  circum- 
ference of  any  circle  is  double  of  the  diagonal  of  the  cube 
on  its  diameter.8 

I  have  examined  the  following  works  of  Sir  R.  Phillips, 
and  heard  of  many  others  : 

Essays  on  the  proximate  mechanical  causes  of  the  general  phe- 

nomena of  the  Universe,  1818,  I2mo.9 
Protest  against  the  prevailing  principles  of  natural  philosophy, 

with  the  development  of  a  common  sense  system   (no  date, 

8vo,  pp.  i6).10 
Four  dialogues  between  an  Oxford  Tutor  and  a  disciple  of  the 

common-sense  philosophy,  relative  to  the  proximate  causes  of 

material  phenomena.    8vo,  1824. 
A  century  of  original  aphorisms  on  the  proximate  causes  of  the 

phenomena  of  nature,  1835,  I2mo. 

Sir  Richard  Phillips  had  four  valuable  qualities  ;  honesty, 
zeal,  ability,  and  courage.  He  applied  them  all  to  teaching 


8  For  there  is  a  well-known  series 

t-  -22+3*4-  .  .  .  =  -g-. 
If,  therefore,  the  given  series  equals  I,  we  hav« 


or  7rs  =  l2, 
whence  IT  =  2]/37 

But  c  =  itd,  and  twice  the  diagonal  of  a  cube  on  the  diameter 
is  2dV^T 

"There  was  a  second  edition  in  1821. 
"London,  1830. 


246  A   BUDGET   OF   PARADOXES. 

matters  about  which  he  knew  nothing;  and  gained  himself 
an  uncomfortable  life  and  a  ridiculous  memory. 

Astronomy  made  plain;  or  only  way  the  true  perpendicular  dis- 
tance of  the  Sun,  Moon,  or  Stars,  from  this  earth,  can  be  ob- 
tained. By  Wm.  Wood.11  Chatham,  1819,  I2mo. 

If  this  theory  be  true,  it  will  follow,  of  course,  that  this 
earth  is  the  only  one  God  made,  and  that  it  does  not  whirl 
round  the  sun,  but  vice  versa,  the  sun  round  it. 


WHATELY'S  FAMOUS  PARADOX. 

Historic  doubts  relative  to  Napoleon  Buonaparte.    London,  1819, 
8vo. 

This  tract  has  since  been  acknowledged  by  Archbishop 
Whately1  and  reprinted.  It  is  certainly  a  paradox:  but  dif- 
fers from  most  of  those  in  my  list  as  being  a  joke,  and  a 
satire  upon  the  reasoning  of  those  who  cannot  receive  nar- 
rative, no  matter  what  the  evidence,  which  is  to  them  utterly 
improbable  a  priori.  But  had  it  been  serious  earnest,  it 
would  not  have  been  so  absurd  as  many  of  those  which  I 
have  brought  forward.  The  next  on  the  list  is  not  a  joke. 

The  idea  of  the  satire  is  not  new.  Dr.  King,2  in  the 
dispute  on  the  genuineness  of  Phalaris,  proved  with  humor 
that  Bentley  did  not  write  his  own  dissertation.  An  attempt 
has  lately  been  made,  for  the  honor  of  Moses,  to  prove, 

"He  was  a  resident  of  Chatham,  and  seems  to  have  published 
no  other  works. 

^Richard  Whately  (1787-1863)  was,  as  a  child,  a  calculating 
prodigy  (see  note  3,  page  86),  but  lost  the  power  as  is  usually  the 
case  with  well-balanced  minds.  He  was  a  fellow  of  Oriel  College, 
Oxford,  and  in  1825  became  principal  of  St.  Alban  Hall.  He  was 
a  friend  of  Newman,  Keble,  and  others  who  were  interested  in  the 
religious  questions  of  the  day.  He  became  archbishop  of  Dublin  in 
1831.  He  was  for  a  long  time  known  to  students  through  his  Logic 
(1826)  and  Rhetoric  (1828). 

3  William  King,  D.C.L.  (1663-1712),  student  at  Christ  Church, 
Oxford,  and  celebrated  as  a  wit  and  scholar.  His  Dialogues  of  the 
Dead  (1699)  is  a  satirical  attack  on  Bentley. 


WHATELY'S  FAMOUS  PARADOX.  247 

without  humor,  that  Bishop  Colenso  did  not  write  his  own 
book.  This  is  intolerable:  anybody  who  tries  to  use  such  a 
weapon  without  banter,  plenty  and  good,  and  of  form  suited 
to  the  subject,  should  get  the  drubbing  which  the  poor  man 
got  in  the  Oriental  tale  for  striking  the  dervishes  with  the 
wrong  hand. 

The  excellent  and  distinguished  author  of  this  tract  has 
ceased  to  live.  I  call  him  the  Paley  of  our  day :  with  more 
learning  and  more  purpose  than  his  predecessor;  but  per- 
haps they  might  have  changed  places  if  they  had  changed 
centuries.  The  clever  satire  above  named  is  not  the  only 
work  which  he  published  without  his  name.  The  following 
was  attributed  to  him,  I  believe  rightly:  "Considerations 
on  the  Law  of  Libel,  as  relating  to  Publications  on  the 
subject  of  Religion,  by  John  Search."  London,  1833,  8vo. 
This  tract  excited  little  attention:  for  those  who  should 
have  answered,  could  not.  Moreover,  it  wanted  a  prosecu- 
tion to  call  attention  to  it :  the  fear  of  calling  such  attention 
may  have  prevented  prosecutions.  Those  who  have  read 
it  will  have  seen  why. 

The  theological  review  elsewhere  mentioned  attributes 
the  pamphlet  of  John  Search  on  blasphemous  libel  to  Lord 
Brougham.  This  is  quite  absurd:  the  writer  states  points 
of  law  on  credence  where  the  judge  must  have  spoken  with 
authority.  Besides  which,  a  hundred  points  of  style  are 
decisive  between  the  two.  I  think  any  one  who  knows 
Whately's  writing  will  soon  arrive  at  my  conclusion.  Lord 
Brougham  himself  informs  me  that  he  has  no  knowledge 
whatever  of  the  pamphlet. 

It  is  stated  in  Notes  and  Queries  (3  S.  xi.  511)  that 
Search  was  answered  by  the  Bishop  of  Ferns3  as  S.  N.,  with 

8  Thomas  Ebrington  (1760-1835)  was  a  fellow  of  Trinity  College, 
Dublin,  and  taught  divinity,  mathematics,  and  natural  philosophy 
there.  He  became  provost  of  the  college  in  1811,  bishop  of  Lim- 
erick in  1820,  and  bishop  of  Leighlin  and  Ferns  in  1822.  His  edition 
of  Euclid  was  reprinted  a  dozen  times.  The  Reply  to  John  Search's 
Considerations  on  the  Law  of  Libel  appeared  at  Dublin  in  1834. 


248  A   BUDGET   OF   PARADOXES. 

a  rejoinder  by  Blanco  White.4    These  circumstances  increase 
the  probability  that  Whately  was  written  against  and  for. 

VOLTAIRE  A  CHRISTIAN. 

Voltaire  Chretien;  preuves  tirees  de  ses  ouvrages.    Paris,  1820, 
I2mo. 

If  Voltaire  have  not  succeeded  in  proving  himself  a 
strong  theist  and  a  strong  anti-revelationist,  who  is  to  suc- 
ceed in  proving  himself  one  thing  or  the  other  in  any  matter 
whatsoever?  By  occasional  confusion  between  theism  and 
Christianity ;  by  taking  advantage  of  the  formal  phrases  of 
adhesion  to  the  Roman  Church,  which  very  often  occur,  and 
are  often  the  happiest  bits  of  irony  in  an  ironical  produc- 
tion ;  by  citations  of  his  morality,  which  is  decidedly  Chris- 
tian, though  often  attributed  to  Brahmins;  and  so  on — 
the  author  makes  a  fair  case  for  his  paradox,  in  the  eyes 
of  those  who  know  no  more  than  he  tells  them.  If  he  had 
said  that  Voltaire  was  a  better  Christian  than  himself  knew 
of,  towards  all  mankind  except  men  of  letters,  I  for  one 
should  have  agreed  with  him. 

Christian!  the  word  has  degenerated  into  a  synonym  of 
man,  in  what  are  called  Christian  countries.  So  we  have 
the  parrot  who  "swore  for  all  the  world  like  a  Christian," 
and  the  two  dogs  who  "hated  each  other  just  like  Chris- 
tians." When  the  Irish  duellist  of  the  last  century,  whose 
name  may  be  spared  in  consideration  of  its  historic  fame 

*  Joseph  Blanco  White  (1775-1841)  was  the  son  of  an  Irishman 
living  in  Spain.  He  was  born  at  Seville  and  studied  for  orders 
there,  being  ordained  priest  in  1800.  He  lost  his  faith  in  the  Roman 
Catholic  Church,  and  gave  up  the  ministry,  escaping  to  England  at 
the  time  of  the  French  invasion.  At  London  he  edited  Espanol,  a 
patriotic  journal  extensively  circulated  in  Spain,  and  for  this  service 
he  was  pensioned  after  the  expulsion  of  the  French.  He  then  studied 
at  Oriel  College,  Oxford,  and  became  intimate  with  men  like  Whately, 
Newman,  and  Keble.  In  1835  he  became  a  Unitarian.  Among  his 
theological  writings  is  his  Evidences  against  Catholicism  (1825).  The 
"rejoinder"  to  which  De  Morgan  refers  consisted  of  two  letters : 
The  law  of  anti-religious  Libel  reconsidered  (Dublin,  1834)  and  An 
Answer  to  some  Friendly  Remarks  on  "The  Law  of  Anti-Religious 
Libel  Reconsidered"  (Dublin,  1834). 


WRONSKI  ON  THE  LONGITUDE  PROBLEM.  249 

and  the  worthy  people  who  bear  it,  was  (June  12,  1786) 
about  to  take  the  consequence  of  his  last  brutal  murder, 
the  rope  broke,  and  the  criminal  got  up,  and  exclaimed, 
"By  -  -  Mr.  Sheriff,  you  ought  to  be  ashamed  of  your- 
self !  this  rope  is  not  strong  enough  to  hang  a  dog,  far  less 
a  Christian!"  But  such  things  as  this  are  far  from  the 
worst  depravations.  As  to  a  word  so  defiled  by  usage,  it 
is  well  to  know  that  there  is  a  way  of  escape  from  it,  with- 
out renouncing  the  New  Testament.  I  suppose  any  one 
may  assume  for  himself  what  I  have  sometimes  heard  con- 
tended for,  that  no  New  Testament  word  is  to  be  used  in 
religion  in  any  sense  except  that  of  the  New  Testament. 
This  granted,  the  question  is  settled.  The  word  Christian, 
which  occurs  three  times,  is  never  recognized  as  anything 
but  a  term  of  contempt  from  those  without  the  pale  to 
those  within.  Thus,  Herod  Agrippa,  who  was  deep  in 
Jewish  literature,  and  a  correspondent  of  Josephus,  says  to 
Paul  (Acts  xxvi.  28),  "Almost  thou  persuadest  me  to  be 
(what  I  and  other  followers  of  the  state  religion  despise 
under  the  name)  a  Christian."  Again  (Acts  xi.  26),  "The 
disciples  (as  they  called  themselves)  were  called  (by  the 
surrounding  heathens)  Christians  first  in  Antioch."  Thirdly 
(1  Peter  iv.  16),  "Let  none  of  you  suffer  as  a  murderer. . . . 
But  if  as  a  Christian  (as  the  heathen  call  it  by  whom  the 
suffering  conies),  let  him  not  be  ashamed."  That  is  to 
say,  no  disciple  ever  called  himself  a  Christian,  or  applied 
the  name,  as  from  himself,  to  another  disciple,  from  one 
end  of  the  New  Testament  to  the  other;  and  no  disciple 
need  apply  that  name  to  himself  in  our  day,  if  he  dislike 
the  associations  with  which  the  conduct  of  Christians  has 
clothed  it. 

WRONSKI  ON  THE  LONGITUDE  PROBLEM. 

Address  of  M.  Hoene  Wronski  to  the  British  Board  of  Longi- 
tude, upon  the  actual  state  of  the  mathematics,  their  reform, 


250  A   BUDGET   OF   PARADOXES. 

and  upon  the  new  celestial  mechanics,  giving  the  definitive  solu- 
tion of  the  problem  of  longitude.1    London,  1820,  8vo. 

M.  Wronski2  was  the  author  of  seven  quartos  on  mathe- 
matics, showing  very  great  power  of  generalization.  He 
was  also  deep  in  the  transcendental  philosophy,3  and  had 
the  Absolute  at  his  fingers'  ends.  All  this  knowledge  was 
rendered  useless  by  a  persuasion  that  he  had  greatly  ad- 
vanced beyond  the  whole  world,  with  many  hints  that  the 
Absolute  would  not  be  forthcoming,  unless  prepaid.  He 
was  a  man  of  the  widest  extremes.  At  one  time  he  desired 
people  to  see  all  possible  mathematics  in 

Rr  =  A0O0  +  A^  +  A2O2  +  A3O3  +  &c. 

which  he  did  not  explain,  though  there  is  meaning  to  it  in 
the  quartos.  At  another  time  he  was  proposing  the  general 
solution  of  the4  fifth  degree  by  help  of  625  independent 
equations  of  one  form  and  125  of  another.  The  first  sep- 
arate memoir  from  any  Transactions  that  I  ever  possessed 
was  given  to  me  when  at  Cambridge ;  the  refutation  (1819) 
of  this  asserted  solution,  presented  to  the  Academy  of  Lis- 
bon by  Evangelista  Torriano.  I  cannot  say  I  read  it.  The 
tract  above  is  an  attack  on  modern  mathematicians  in  gen- 
eral, and  on  the  Board  of  Longitude,  and  Dr.  Young.5 

aThe  work  was  translated  from  the  French. 

3J.  Hoe'ne  Wronski  (1778-1853)  served,  while  yet  a  mere  boy, 
as  an  artillery  officer  in  Kosciusko's  army  (1791-1794).  He  was 
imprisoned  after  the  battle  of  Maciejowice.  He  afterwards  lived  in 
Germany,  and  (after  1810)  in  Paris.  For  the  bibliography  of  his 
works  see  S.  Dickstein's  article  in  the  Bibliotheca  Mathematics,  vol. 
VI  (2),  page  48. 

3  Perhaps    referring  to   his   Introduction   a   la  philosophic   des 
mathematiques  (1811). 

4  Read  "equation  of  the." 

5  Thomas    Young    (1773-1829),   physician   and   physicist,    some- 
times called  the  founder  of  physiological  optics.     He  seems  to  have 
initiated  the  theory  of  color  blindness  that  was  later  developed  by 
Helmholtz.     The  attack  referred  to  was  because  of  his  connection 
with  the  Board  of  Longitude,  he  having  been  made   (1818)   super- 
intendent of  the  Nautical  Almanac  and  secretary  of  the  Board.     He 
opposed  introducing  into  the  Nautical  Almanac  anything  not  imme- 
diately useful  to  navigation,  and  this  antagonized  many  scientists. 


DR.  MILNER'S  PARADOXES.  251 

DR.  MILNER'S  PARADOXES. 

1820.  In  this  year  died  Dr.  Isaac  Milner,1  President  of 
Queens'  College,  Cambridge,  one  of  the  class  of  rational 
paradoxers.  Under  this  name  I  include  all  who,  in  private 
life,  and  in  matters  which  concern  themselves,  take  their 
own  course,  and  suit  their  own  notions,  no  matter  what 
other  people  may  think  of  them.  These  men  will  put  things 
to  uses  they  were  never  intended  for,  to  the  great  distress 
and  disgust  of  their  gregarious  friends.  I  am  one  of  the 
class,  and  I  could  write  a  little  book  of  cases  in  which  I 
have  incurred  absolute  reproach  for  not  "doing  as  other 
people  do."  I  will  name  two  of  my  atrocities :  I  took  one 
of  those  butter-dishes  which  have  for  a  top  a  dome  with 
holes  in  it,  which  is  turned  inward,  out  of  reach  of  accident, 
when  not  in  use.  Turning  the  dome  inwards,  I  filled  the 
dish  with  water,  and  put  a  sponge  in  the  dome:  the  holes 
let  it  fill  with  water,  and  I  had  a  penwiper,  always  moist, 
and  worth  its  price  five  times  over.  "Why!  what  do  you 
mean  ?  It  was  made  to  hold  butter.  You '  are  always  at 
some  queer  thing  or  other!"  I  bought  a  leaden  comb,  in- 
tended to  dye  the  hair,  it  being  supposed  that  the  applica- 
tion of  lead  will  have  this  effect.  I  did  not  try:  but  I 
divided  the  comb  into  two,  separated  the  part  of  closed 
prongs  from  the  other ;  and  thus  I  had  two  ruling  machines. 
The  lead  marks  paper,  and  by  drawing  the  end  of  one  of  the 
machines  along  a  ruler,  I  could  rule  twenty  lines  at  a  time, 
quite  fit  to  write  on.  I  thought  I  should  have  killed  a  friend 
to  whom  I  explained  it:  he  could  not  for  the  life  of  him 
understand  how  leaden  lines  on  paper  would  dye  the  hair. 

But  Dr.  Milner  went  beyond  me.  He  wanted  a  seat 
suited  to  his  shape,  and  he  defied  opinion  to  a  fearful  point. 

1  Isaac  Milner  (1750-1820)  was  professor  of  natural  philosophy 
at  Cambridge  (1783)  and  later  became,  as  De  Morgan  states,  presi- 
dent of  Queens'  College  (1788).  In  1791  he  became  dean  of  Carlisle, 
and  in  1798  Lucasian  professor  of  mathematics.  His  chief  interest 
was  in  chemistry  and  physics,  but  he  contributed  nothing  of  impor- 
tance to  these  sciences  or  to  mathematics. 


252  A   BUDGET   OF   PARADOXES. 

He  spread  a  thick  block  of  putty  over  a  wooden  chair  and 
sat  in  it  until  it  had  taken  a  ceroplast  copy  of  the  proper 
seat.  This  he  gave  to  a  carpenter  to  be  imitated  in  wood. 
One  of  the  few  now  living  who  knew  him — my  friend, 
General  Perronet  Thompson2 — answers  for  the  wood,  which 
was  shown  him  by  Milner  himself ;  but  he  does  not  vouch 
for  the  material  being  putty,  which  was  in  the  story  told 
me  at  Cambridge ;  William  Frend8  also  remembered  it.  Per- 
haps the  Doctor  took  off  his  great  seal  in  green  wax,  like 
the  Crown;  but  some  soft  material  he  certainly  adopted; 
and  very  comfortable  he  found  the  wooden  copy. 

The  same  gentleman  vouches  for  Milner's  lamp:  but 
this  had  visible  science  in  it;  the  vulgar 
see  no  science  in  the  construction  of  the 
chair.  A  hollow  semi-cylinder,  but  not 
with  a  circular  curve,  revolved  on  pivots. 
The  curve  was  calculated  on  the  law 
that,  whatever  quantity  of  oil  might  be 
in  the  lamp,  the  position  of  equilibrium 
just  brought  the  oil  up  to  the  edge  of 
the  cylinder,  at  which  a  bit  of  wick  was 
placed.  As  the  wick  exhausted  the  oil, 
the  cylinder  slowly  revolved  about  the 
pivots  so  as  to  keep  the  oil  always  touching  the  wick. 

Great  discoveries  are  always  laughed  at;  but  it  is  very 
often  not  the  laugh  of  incredulity;  it  is  a  mode  of  dis- 
torting the  sense  of  inferiority  into  a  sense  of  superiority, 
or  a  mimicry  of  superiority  interposed  between  the  laugher 
and  his  feeling  of  inferiority.  Two  persons  in  conversation 

"Thomas  Perronet  Thompson  (1783-1869),  fellow  of  Queens' 
College,  Cambridge,  saw  service  in  Spain  and  India,  but  after  1822 
lived  in  England.  He  became  major  general  in  1854,  and  general  in 
1868.  Besides  some  works  on  economics  and  politics  he  wrote  a 
Geometry  without  Axioms  (1830)  that  De  Morgan  includes  later  on 
in  his  Budget.  In  it  Thompson  endeavored  to  prove  the  parallel 
postulate. 

8  De  Morgan's  father-in-law.    See  note  i,  page  196. 


DR.  MILNER'S  PARADOXES.  253 

agreed  that  it  was  often  a  nuisance  not  to  be  able  to  lay 
hands  on  a  bit  of  paper  to  mark  the  place  in  a  book,  every 
bit  of  paper  on  the  table  was  sure  to  contain  something  not 
to  be  spared.  I  very  quietly  said  that  I  always  had  a  stock 
of  bookmarkers  ready  cut,  with  a  proper  place  for  them: 
my  readers  owe  many  of  my  anecdotes  to  this  absurd  prac- 
tice. My  two  colloquials  burst  into  a  fit  of  laughter  ;  about 
what  ?  Incredulity  was  out  of  the  question  ;  and  there  could 
be  nothing  foolish  in  my  taking  measures  to  avoid  what  they 
knew  was  an  inconvenience.  I  was  in  this  matter  obviously 
their  superior,  and  so  they  laughed  at  me.  Much  more 
candid  was  the  Royal  Duke  of  the  last  century,  who  was 
noted  for  slow  ideas.  "The  rain  comes  into  my  mouth," 
said  he,  while  riding.  "Had  not  your  Royal  Highness  better 
shut  your  mouth?"  said  the  equerry.  The  Prince  did  so, 
and  ought,  by  rule,  to  have  laughed  heartily  at  his  adviser  ; 
instead  of  this,  he  said  quietly,  "It  doesn't  come  in  now." 

HERBART'S   MATHEMATICAL   PSYCHOLOGY. 

De  Attentionis  mensura  causisque  primariis.     By  J.  F.  Herbart.1 
Koenigsberg,  1822,  4to. 

1Johann  Friedrich  Herbart  (1776-1841),  successor  of  Kant  as 
professor  of  philosophy  at  Konigsberg  (1809-1833),  where  he  estab- 
lished a  school  of  pedagogy.  From  1833  until  ms  death  he  was  pro- 
fessor of  philosophy  at  Gottingen.  The  title  of  the  pamphlet  is  :  De 
Attentionis  mensura  causisque  primariis.  Psychologiae  principia  sta- 
tica  et  mechanica  exemplo  illustraturus  .  .  .  .Regiomonti,.  .  .  .1822.  The 
formulas  in  question  are  given  on  pages  15  and  17,  and  De  Morgan 
has  omitted  the  preliminary  steps,  which  are,  for  the  first  one  : 


unde 


Pro  /=0  etiam  ^  =  0;  hinc  /3/  =  log.  —    -. 


Tt-<*       ' 

These  are,  however,  quite  elementary  as  compared  with  other 
portions  of  the  theory. 


254  A   BUDGET   OF   PARADOXES. 

This  celebrated  philosopher  maintained  that  mathematics 
ought  to  be  applied  to  psychology,  in  a  separate  tract,  pub- 
lished also  in  1822:  the  one  above  seems,  therefore,  to  be 
his  challenge  on  the  subject.  It  is  on  attention,  and  I  think 
it  will  hardly  support  Herbart's  thesis.  As  a  specimen  of 
his  formula,  let  t  be  the  time  elapsed  since  the  consideration 
began,  /?  the  whole  perceptive  intensity  of  the  individual, 
<£  the  whole  of  his  mental  force,  and  z  the  force  given  to  a 
notion  by  attention  during  the  time  t.  Then, 


Now  for  a  test.  There  is  a  jactura,  v,  the  meaning  of  which 
I  do  not  comprehend.  If  there  be  anything  in  it,  my  mathe- 
matical readers  ought  to  interpret  it  from  the  formula 


and  to  this  task  I  leave  them,  wishing  them  better  luck  than 
mine.  The  time  may  come  when  other  manifestations  of 
mind,  besides  belief,  shall  be  submitted  to  calculation:  at 
that  time,  should  it  arrive,  a  final  decision  may  be  passed 
upon  Herbart. 

ON  THE  WHIZGIG. 

The  theory  of  the  Whizgig  considered  ;  in  as  much  as  it  mechan- 
ically exemplifies  the  three  working  properties  of  nature; 
which  are  now  set  forth  under  the  guise  of  this  toy,  for 
children  of  all  ages.  London,  1822,  I2mo  (pp.  24,  B.  McMil- 
lan, Bow  Street,  Covent  Garden). 

The  toy  called  the  whizgig  will  be  remembered  by  many. 
The  writer  is  a  follower  of  Jacob  Behmen,1  William  Law,2 

1  See  note  3,  page  168. 

'William  Law  (1686-1761)  was  a  clergyman,  a  fellow  of  Emanuel 
College,  Cambridge,  and  in  later  life  a  convert  to  Behmen's  philos- 
ophy. He  was  so  free  in  his  charities  that  the  village  in  which  he 
lived  became  so  infested  by  beggars  that  he  was  urged  by  the  citi- 
zens to  leave.  He  wrote  A  serious  call  to  a  devout  and  holy  life 
(1728). 


ON  THE  WHIZGIG.  255 

Richard  Clarke,3  and  Eugenius  Philalethes.4  Jacob  Behmen 
first  announced  the  three  working  properties  of  nature, 
which  Newton  stole,  as  described  in  the  Gentleman's  Maga- 
zine, July,  1782,  p.  329.  These  laws  are  illustrated  in  the 
whizgig.  There  is  the  harsh  astringent,  attractive  com- 
pression ;  the  bitter  compunction,  repulsive  expansion ;  and 
the  stinging  anguish,  duplex  motion.  The  author  hints  that 
he  has  written  other  works,  to  which  he  gives  no  clue.  I 
have  heard  that  Behmen  was  pillaged  by  Newton,  and  Swe- 
denborg5  by  Laplace,6  and  Pythagoras  by  Copernicus,7  and 
Epicurus  by  Dalton,8  &c.  I  do  not  think  this  mention  will 
revive  Behmen ;  but  it  may  the  whizgig,  a  very  pretty  toy, 
and  philosophical  withal,  for  few  of  those  who  used  it  could 
explain  it. 

8  He  was  a  curate  at  Cheshunt,  and  wrote  the  Spiritual  voice 
to  the  Christian  Church  and  to  the  Jews  (London,  1760),  A  second 
warning  to  the  world  by  the  Spirit  of  Prophecy  (London,  1760),  and 
Signs  of  the  Times;  or  a  Voice  to  Babylon  (London,  1773)* 

4  His  real  name  was  Thomas  Vaughan  (1622-1666).  He  was  a 
fellow  of  Jesus  College,  Oxford,  taking  orders,  but  was  deprived 
of  his  living  on  account  of  drunkenness.  He  became  a  mystic  phi- 
losopher and  gave  attention  to  alchemy.  His  works  had  a  large 
circulation,  particularly  on  the  continent.  He  wrote  Magia  Adamica 
(London,  1650),  Euphrates;  or  the  Waters  of  the  East  (London, 
1655),  and  The  Chy  mist's  key  to  shut,  and  to  open;  or  the  True  Doc- 
trine of  Corruption  and  Generation  (London,  1657). 

5Emanuel  Swedenborg,  or  Svedberg  (1688-1772)  the  mystic. 
It  is  not  commonly  known  to  mathematicians  that  he  was  one  of 
their  guild,  but  he  wrote  on  both  mathematics  and  chemistry.  Among 
his  works  are  the  Regelkonst  eller  algebra  (Upsala,  1718)  and  the 
Methodus  nova  inveniendi  longitudines  locorum,  terra  marique,  ope 
lunae  (Amsterdam,  1721,  1727,  and  1766).  After  1747  he  devoted 
his  attention  to  mystic  philosophy. 

6  Pierre  Simon  Laplace   (1749-1827),  whose  Exposition  du  sys- 
teme  du  monde  (1796)  and  Traite  de  mecanique  celeste  (1799)  are 
well  known. 

7  See  note  3,  page  76. 

8  John  Dalton  (1766-1844),  who  taught  mathematics  and  physics 
at  New  College,  Manchester  (1793-1799)  and  was  the  first  to  state 
the  law  of  the  expansion  of  gases  known  by  his  name  and  that  of 
Gay-Lussac.    His  New  system  of  Chemical  Philosophy  (Vol.  I,  pt.  i, 
1808;  pt.  ii,  1810;  vol.  II,  1827)  sets  forth  his  atomic  theory. 


256  A  BUDGET  OF  PARADOXES. 

SOME  MYTHOLOGICAL  PARADOXES. 

A  Grammar  of  infinite  forms;  or  the  mathematical  elements  of 
ancient  philosophy  and  mythology.  By  Wm.  Howison.1  Edin- 
burgh, 1823,  8vo. 

A  curius  combination  of  geometry  and  mythology.  Per- 
seus, for  instance,  is  treated  under  the  head,  "the  evolution 
of  diminishing  hyperbolic  branches." 

The  Mythological  Astronomy  of  the  Ancients;  part  the  second: 

or  the  key  of  Urania,  the  words  of  which  will  unlock  all  the 

mysteries  of  antiquity.     Norwich,  1823,  I2mo. 
A  Companion  to  the  Mythological  Astronomy,  &c.,  containing 

remarks  on  recent  publications Norwich,  1824,  I2mo. 

A  new  Theory  of  the  Earth  and  of  planetary  motion ;  in  which  it 

is  demonstrated  that  the  Sun  is  vicegerent  of  his  own  system. 

Norwich,  1825,  I2mo. 
The  analyzation  of  the  writings  of  the  Jews,  so  far  as  they  are 

found  to  have  any  connection  with  the  sublime   science   of 

astronomy.     [This  is  pp.  97-180  of  some  other  work,  being  all 

I  have  seen.] 

These  works  are  all  by  Sampson  Arnold  Mackey,2  for 
whom  see  Notes  and  Queries,  1st  S.  viii.  468,  565,  ix.  89, 
179.  Had  it  not  been  for  actual  quotations  given  by  one 
correspondent  only  (1st  S.  viii.  565),  that  journal  would 
have  handed  him  down  as  a  man  of  some  real  learning.  An 
extraordinary  man  he  certainly  was:  it  is  not  one  illiterate 
shoemaker  in  a  thousand  who  could  work  upon  such  a  sin- 
gular mass  of  Sanskrit  and  Greek  words,  without  showing 

1  Howison  was  a  poet  and  philosopher.  He  lived  in  Edinburgh 
and  was  a  friend  of  Sir  Walter  Scott.  This  work  appeared  in  1822. 

3  He  was  a  shoemaker,  born  about  1765  at  Haddiscoe,  and  his 
"astro-historical"  lectures  at  Norwich  attracted  a  good  deal  of  atten- 
tion at  one  time.  He  traced  all  geologic  changes  to  differences  in 
the  inclination  of  the  earth's  axis  to  the  plane  of  its  orbit.  Of  the 
works  mentioned  by  De  Morgan  the  first  appeared  at  Norwich  in 
1822-1823,  and  there  was  a  second  edition  in  1824.  The  second 
appeared  in  1824-1825.  The  fourth  was  Urania's  Key  to  the  Reve- 
lation; or  the  analyzation  of  the  writings  of  the  Jews ,  and  was 

first  published  at  Norwich  in  1823,  there  being  a  second  edition  at 
London  in  1833.  His  books  were  evidently  not  a  financial  success, 
for  Mackey  died  in  an  almshouse  at  Norwich. 


SOME  MYTHOLOGICAL  PARADOXES.  257 

evidence  of  being  able  to  read  a  line  in  any  language  but 
his  own,  or  to  spell  that  correctly.  He  was  an  uneducated 
Godfrey  Higgins.3  A  few  extracts  will  put  this  in  a  strong 
light:  one  for  history  of  science,  one  for  astronomy,  and 
one  for  philology: 

"Sir  Isaac  Newton  was  of  opinion  that  'the  atmosphere 
of  the  earth  was  the  sensory  of  God ;  by  which  he  was  en- 
abled to  see  quite  round  the  earth:'  which  proves  that  Sir 
Isaac  had  no  idea  that  God  could  see  through  the  earth. 

"Sir  Richard  [Phillips]  has  given  the  most  rational  ex- 
planation of  the  cause  of  the  earth's  elliptical  orbit  that  I 
have  ever  seen  in  print.  It  is  because  the  earth  presents  its 
watery  hemisphere  to  the  sun  at  one  time  and  that  of  solid 
land  the  other ;  but  why  has  he  made  his  Oxonian  astonished 
at  the  coincidence?  It  is  what  I  taught  in  my  attic  twelve 
years  before. 

"Again,  admitting  that  the  Eloim  were  powerful  and  in- 
telligent beings  that  managed  these  things,  we  would  accuse 
them  of  being  the  authors  of  all  the  sufferings  of  Chrisna. 
And  as  they  and  the  constellation  of  Leo  were  below  the 
horizon,  and  consequently  cut  off  from  the  end  of  the 
zodiac,  there  were  but  eleven  constellations  of  the  zodiac 
to  be  seen ;  the  three  at  the  end  were  wanted,  but  those  three 
would  be  accused  of  bringing  Chrisna  into  the  troubles  which 
at  last  ended  in  his  death.  All  this  would  be  expressed  in 
the  Eastern  language  by  saying  that  Chrisna  was  persecuted 
by  those  Judoth  Ishcarioth ! ! ! ! !  [the  five  notes  of  exclama- 
tion are  the  author's].  But  the  astronomy  of  those  distant 
ages,  when  the  sun  was  at  the  south  pole  in  winter,  would 
leave  five  of  those  Decans  cut  off  from  our  view,  in  the 
latitude  of  twenty-eight  degrees;  hence  Chrisna  died  of 

8  Godfrey  Higgins  (1773-1833),  the  archeologist,  was  interested 
in  the  history  of  religious  beliefs  and  in  practical  sociology.  He 
wrote  Horae  Sabbaticae  (1826),  The  Celtic  Druids  (1827  and  1829), 
and  Anacalypsis^  an  attempt  to  draw  aside  the  veil  of  the  Saitic 
Isis;  or  an  Inquiry  into  the  Origin  of  Languages,  Nations,  and  Re- 
ligions (posthumously  published,  1836),  and  other  works.  See  also 
page  274,  infra. 


258  A    BUDGET    OF    PARADOXES. 

wounds  from  five  Decans,  but  the  whole  five  may  be  in- 
cluded in  Judoth  Ishcarioth !  for  the  phrase  means  'the  men 
that  are  wanted  at  the  extreme  parts/  Ishcarioth  is  a  com- 
pound of  ish,  a  man,  and  carat  wanted  or  taken  away,  and 
oth  the  plural  termination,  more  ancient  than  im . . . . " 

I  might  show  at  length  how.  Michael  is  the  sun,  and  the 
D'-ev-'l  in  French  Di-ob-al,  also  'L-evi-ath-an —  the  evi 
being  the  radical  part  both  of  devil  and  Imathan — is  the 
Nile,  which  the  sun  dried  up  for  Moses  to  pass:  a  battle 
celebrated  by  Jude.  Also  how  Moses,  the  same  name  as 
Muses,  is  from  mesha,  drawn  out  of  the  water,  "and  hence 
we  called  our  land  which  is  saved  from  the  water  by  the 
name  of  marsh!'  But  it  will  be  of  more  use  to  collect  the 
character  of  S.  A.  M.  from  such  correspondents  of  Notes 
and  Queries  as  have  written  after  superficial  examination. 
Great  astronomical  and  philological  attainments,  much  abil- 
ity and  learning;  had  evidently  read  and  studied  deeply; 
remarkable  for  the  originality  of  his  views  upon  the  very 
abstruse  subject  of  mythological  astronomy,  in  which  he 
exhibited  great  sagacity.  Certainly  his  views  were  original ; 
but  their  sagacity,  if  it  be  allowable  to  copy  his  own  mode 
of  etymologizing,  is  of  an  ori-gin-ale  cast,  resembling  that  of 
a  person  who  puts  to  his  mouth  liquors  both  distilled  and 
fermented. 

A  KANTESIAN  JEWELER. 

Principles  of  the  Kantesian,  or  transcendental  philosophy.     By 
Thomas  Wirgman.1    London,  1824,  8vo. 

Mr.  Wirgman's  mind  was  somewhat  attuned  to  psychol- 
ogy; but  he  was  cracky  and  vagarious.  He  had  been  a 
fashionable  jeweler  in  St.  James's  Street,  no  doubt  the  son 
or  grandson  of  Wirgman  at  "the  well-known  toy-shop  in 

JThe  work  also  appeared  in  French.  Wirgman  wrote,  or  at 
least  began,  two  other  works:  Divarication  of  the  New  Testament 
into  Doctrine  and  History;  part  I,  The  Four  Gospels  (London,  1830), 
and  Mental  Philosophy;  part  I,  Grammar  of  the  five  senses;  being 
the  first  step  to  infant  education  (London,  1838). 


A   KANTESIAN   JEWELER.  259 

St.  James's  Street/*  where  Sam  Johnson  smartened  himself 
with  silver  buckles.  (Boswell,  at.  69).  He  would  not  have 
the  ridiculous  large  ones  in  fashion;  and  he  would  give  no 
more  than  a  guinea  a  pair;  such,  says  Boswell,  in  Italics, 
were  the  principles  of  the  business:  and  I  think  this  may 
be  the  first  place  in  which  the  philosophical  word  was  brought 
down  from  heaven  to  mix  with  men.  However  this  may 
be,  my  Wirgman  sold  snuff-boxes,  among  other  things,  and 
fifty  years  ago  a  fashionable  snuff-boxer  would  be  under 
inducement,  if  not  positively  obliged,  to  have  a  stock  with 
very  objectionable  pictures.  So  it  happened  that  Wirgman 
—by  reason  of  a  trifle  too  much  candor — came  under  the 
notice  of  the  Suppression  Society,  and  ran  considerable  risk. 
Mr.  Brougham  was  his  counsel ;  and  managed  to  get  him 
acquitted.  Years  and  years  after  this,  when  Mr.  Brougham 
was  deep  in  the  formation  of  the  London  University  (now 
University  College),  Mr.  Wirgman  called  on  him.  "What 
now?"  said  Mr.  B.  with  his  most  sarcastic  look — a  very 
perfect  thing  of  its  kind — "you're  in  a  scrape  again,  I  sup- 
pose!" "No!  indeed!"  said  W.,  "my  present  object  is  to 
ask  your  interest  for  the  chair  of  Moral  Philosophy  in  the 
new  University!"  He  had  taken  up  Kant! 

Mr.  Wirgman,  an  itinerant  paradoxer,  called  on  me  in 
1831 :  he  came  to  convert  me.  "I  assure  you,"  said  he, 
"I  am  nothing  but  an  old  brute  of  a  jeweler;"  and  his  eye 
and  manner  were  of  the  extreme  of  jocosity,  as  good  in  their 
way,  as  the  satire  of  his  former  counsel.  I  mention  him  as 
one  of  that  class  who  go  away  quite  satisfied  that  they  have 
wrought  conviction.  "Now,"  said  he,  "I'll  make  it  clear  to 
you!  Suppose  a  number  of  gold-fishes  in  a  glass  bowl, 
—you  understand?  Well!  I  come  with  my  cigar  and  go 
puff,  puff,  puff,  over  the  bowl,  until  there  is  a  little  cloud 
of  smoke:  now,  tell  me,  what  will  the  gold-fishes  say  to 
that?"  "I  should  imagine,"  said  I,  "That  they  would  not 
know  what  to  make  of  it."  "By  Jove!  you're  a  Kantian;" 
said  he,  and  with  this  and  the  like,  he  left  me,  vowing  that 


260  A   BUDGET   OF    PARADOXES. 

it  was  delightful  to  talk  to  so  intelligent  a  person.  The 
greatest  compliment  Wirgman  ever  received  was  from  James 
Mill,  who  used  to  say  he  did  not  understand  Kant.  That 
such  a  man  as  Mill  should  think  this  worth  saying  is  a 
feather  in  the  cap  of  the  jocose  jeweler. 

Some  of  my  readers  will  stare  at  my  supposing  that 
Boswell  may  have  been  the  first  down-bringer  of  the  word 
principles  into  common  life ;  the  best  answer  will  be  a  prior 
instance  of  the  word  as  true  vernacular ;  it  has  never  hap- 
pened to  me  to  notice  one.  Many  words  have  very  com- 
mon uses  which  are  not  old.  Take  the  following  from 
Nichols  (Anecd.  ix.  263)  :  "Lord  Thurlow  presents  his  best 
respects  to  Mr.  and  Mrs.  Thicknesse,  and  assures  them  that 
he  knows  of  no  cause  to  complain  of  any  part  of  Mr.  Thick- 
nesse's  carriage;  least  of  all  the  circumstance  of  sending 
the  head  to  Ormond  Street."  Surely  Mr.  T.  had  lent  Lord 
T.  a  satisfactory  carriage  with  a  movable  head,  and  the 
above  is  a  polite  answer  to  inquiries.  Not  a  bit  of  it!  car- 
riage is  here  conduct,  and  the  head  is  a  bust.  The  vehicles 
of  the  rich,  at  the  time,  were  coaches,  chariots,  chaises,  etc., 
never  carriages,  which  were  rather  carts.  Gibbon  has  the 
word  for  baggage-wagons.  In  Jane  Austen's  novels  the 
word  carriage  is  established. 

WALSH'S   DELUSIONS. 

John  Walsh,1  of  Cork  (1786-1847).  This  discoverer 
has  had  the  honor  of  a  biography  from  Professor  Boole, 
who,  at  my  request,  collected  information  about  him  on  the 
scene  of  his  labors.  It  is  in  the  Philosophical  Magazine  for 
November,  1851,  and  will,  I  hope,  be  transferred  to  some 
biographical  collection  where  it  may  find  a  larger  class  of 
readers.  It  is  the  best  biography  of  a  single  hero  of  the 
kind  that  I  know.  Mr.  Walsh  introduced  himself  to  me, 

aHe  was  born  at  Shandrum,  County  Limerick,  and  supported 
himself  by  teaching  writing  and  arithmetic.  He  died  in  an  almshouse 
at  Cork. 


WALSH'S  DELUSIONS.  261 

as  he  did  to  many  others,  in  the  anterowlandian  days  of  the 
Post-office ;  his  unpaid  letters  were  double,  treble,  &c.  They 
contained  his  pamphlets,  and  cost  their  weight  in  silver:  all 
have  the  name  of  the  author,  and  all  are  in  octavo  or  in 
quarto  letter- form:  most  are  in  four  pages,  and  all  dated 
from  Cork.  I  have  the  following  by  me: 

The  Geometric  .Base,  1825.— The  theory  of  plane  angles.  1827. 
—Three  Letters  to  Dr.  Francis  Sadleir.  1838.— The  invention 
of  polar  geometry.  By  Irelandus.  1839. — The  theory  of  par- 
tial functions.  Letter  to  Lord  Brougham.  1839.— On  the  in- 
vention of  polar  geometry.  1839. — Letter  to  the  Editor  of  the 
Edinburgh  Review.  1840. — Irish  Manufacture.  A  new  method 
of  tangents.  1841. — The  normal  diameter  in  curves.  1843. — 
Letter  to  Sir  R.  Peel.  1845. — [Hints  that  Government  should 
compel  the  introduction  of  Walsh's  Geometry  into  Universi- 
ties.]— Solution  of  Equations  of  the  higher  orders.  1845. 

Besides  these,  there  is  a  Metalogia,  and  I  know  not  how 
many  others. 

Mr.  Boole,2  who  has  taken  the  moral  and  social  fea- 
tures of  Walsh's  delusions  from  the  commiserating  point 
of  view,  which  makes  ridicule  out  of  place,  has  been  obliged 
to  treat  Walsh  as  Scott's  Alan  Fairford  treated  his  client 
Peter  Peebles;  namely,  keep  the  scarecrow  out  of  court 
while  the  case  was  argued.  My  plan  requires  me  to  bring 
him  in :  and  when  he  comes  in  at  the  door,  pity  and  sym- 
pathy fly  out  at  the  window.  Let  the  reader  remember 
that  he  was  not  an  ignoramus  in  mathematics:  he  might 
have  won  his  spurs  if  he  could  have  first  served  as  an  es- 
quire. Though  so  illiterate  that  even  in  Ireland  he  never 
picked  up  anything  more  Latin  than  Irelandus,  he  was  a 
very  pretty  mathematician  spoiled  in  the  making  by  intense 
self-opinion. 

This  is  part  of  a  private  letter  to  me  at  the  back  of  a 
page  of  print:  I  had  never  addressed  a  word  to  him: 

8  George  Boole  (1815-1864),  professor  of  mathematics  at  Queens' 
College,  Cork.  His  Laws  of  Thought  (1854)  was  the  first  work  on 
the  algebra  of  logic. 


262  A  BUDGET  OF  PARADOXES. 

"There  are  no  limits  in  mathematics,  and  those  that 
assert  there  are,  are  infinite  ruffians,  ignorant,  lying  black- 
guards. There  is  no  differential  calculus,  no  Taylor's  the- 
orem, no  calculus  of  variations,  &c.  in  mathematics.  There 
is  no  quackery  whatever  in  mathematics ;  no  %  equal  to 
anything.  What  sheer  ignorant  blackguardism  that! 

"In  mechanics  the  parallelogram  of  forces  is  quackery, 
and  is  dangerous ;  for  nothing  is  at  rest,  or  in  uniform,  or 
in  rectilinear  motion,  in  the  universe.  Variable  motion  is 
an  essential  property  of  matter.  Laplace's  demonstration 
of  the  parallelogram  of  forces  is  a  begging  of  the  question ; 
and  the  attempts  of  them  all  to  show  that  the  difference 
of  twenty  minutes  between  the  sidereal  and  actual  revolu- 
tion of  the  earth  round  the  sun  arises  from  the  tugging  of 
the  Sun  and  Moon  at  the  pot-belly  of  the  earth,  without 
being  sure  even  that  the  earth  has  a  pot-belly  at  all,  is 
perfect  quackery.  The  said  difference  arising  from  and 
demonstrating  the  revolution  of  the  Sun  itself  round  some 
distant  center." 

In  the  letter  to  Lord  Brougham  we  read  as  follows: 

"I  ask  the  Royal  Society  of  London,  I  ask  the  Saxon 
crew  of  that  crazy  hulk,  where  is  the  dogma  of  their  phil- 
osophic god  now? When  the  Royal  Society  of  London, 

and  the  Academy  of  Sciences  of  Paris,  shall  have  read  this 
memorandum,  how  will  they  appear?  Like  two  cur  dogs 

in  the  paws  of  the  noblest  beast  of  the  forest Just  as 

this  note  was  going  to  press,  a  volume  lately  published  by 
you  was  put  into  my  hands,  wherein  you  attempt  to  defend 
the  fluxions  and  Principia  of  Newton.  Man !  what  are  you 
about?  You  come  forward  now  with  your  special  pleading, 
and  fraught  with  national  prejudice,  to  defend,  like  the 
philosopher  Grassi,3  the  persecutor  of  Galileo,  principles 

'Oratio  Grassi  (1582-1654),  the  Jesuit  who  became  famous  for 
his  controversy  with  Galileo  over  the  theory  of  comets.  Galileo 
ridiculed  him  in  //  Saggiatore,  although  according  to  the  modern 
view  Grassi  was  the  more  nearly  right  It  is  said  that  the  latter's 
resentment  led  to  the  persecution  of  Galileo. 


WALSH'S  DELUSIONS.  263 

and  reasoning  which,  unless  you  are  actually  insane,  or  an 
ignorant  quack  in  mathematics,  you  know  are  mathemat- 
ically false.  What  a  moral  lesson  this  for  the  students  of 
the  University  of  London  from  its  head !  Man !  demonstrate 
corollary  3,  in  this  note,  by  the  lying  dogma  of  Newton,  or 
turn  your  thoughts  to  something  you  understand. 

"WALSH   IRELANDUS." 

Mr.  Walsh — honor  to  his  memory — once  had  the  con- 
sideration to  save  me  postage  by  addressing  a  pamphlet 
under  cover  to  a  Member  of  Parliament,  with  an  explana- 
tory letter.  In  that  letter  he  gives  a  candid  opinion  of 
himself : 

(1838.)  "Mr.  Walsh  takes  leave  to  send  the  enclosed 
corrected  copy  to  Mr.  Hutton  as  one  of  the  Council  of  the 
University  of  London,  and  to  save  postage  for  the  Pro- 
fessor of  Mathematics  there.  He  will  find  in  it  geometry 
more  deep  and  subtle,  and  at  the  same  time  more  simple  and 
elegant,  than  it  was  ever  contemplated  human  genius  could 
invent." 

He  then  proceeds  to  set  forth  that  a  certain  "tomfoolery 
lemma,"  with  its  "tomfoolery"  superstructure,  "never  had 
existence  outside  the  shallow  brains  of  its  inventor,"  Euclid. 
He  then  proceeds  thus: 

"The  same  spirit  that  animated  those  philosopher^  who 
sent  Galileo  to  the  Inquisition  animates  all  the  philosophers 
of  the  present  day  without  exception.  If  anything  can  free 
them  from  the  yoke  of  error,  it  is  the  [Walsh]  problem  of 
double  tangence.  But  free  them  it  will,  how  deeply  soever 
they  may  be  sunk  into  mental  slavery — and  God  knows  that 
is  deeply  enough ;  and  they  bear  it  with  an  admirable  grace ; 
for  none  bear  slavery  with  a  better  grace  than  tyrants.  The 
lads  must  adopt  my  theory ....  It  will  be  a  sad  reverse  for 
all  our  great  professors  to  be  compelled  to  become  school- 
boys in  their  gray  years.  But  the  sore  scratch  is  to  be  com- 
pelled, as  they  had  before  been  compelled  one  thousand 
years  ago,  to  have  recourse  to  Ireland  for  instruction." 


264  A  BUDGET  OF  PARADOXES. 

The  following  "Impromptu"  is  no  doubt  by  Walsh  him- 
self :  he  was  more  of  a  poet  than  of  an  astronomer : 

"Through  ages  unfriended, 

With  sophistry  blended, 
Deep  science  in  Chaos  had  slept; 

Its  limits  were  fettered, 

Its  voters  unlettered, 
Its  students  in  movements  but  crept. 

Till,  despite  of  great  foes, 

Great  WALSH  first  arose, 
And  with  logical  might  did  unravel 

Those  mazes  of  knowledge, 

Ne'er  known  in  a  college, 
Though  sought  for  with  unceasing  travail. 

With  cheers  we  now  hail  him, 

May  success  never  fail  him, 
In  Polar  Geometrical  mining; 

Till  his  foes  be  as  tamed 

As  his  works  are  far-famed 
For  true  philosophic  refining." 

Walsh's  system  is,  that  all  mathematics  and  physics  are 
wrong:  there  is  hardly  one  proposition  in  Euclid  which  is 
demonstrated.  His  example  ought  to  warn  all  who  rely  on 
their  own  evidence  to  their  own  success.  He  was  not, 
properly  speaking,  insane;  he  only  spoke  his  mind  more 
freely -than  many  others  of  his  class.  The  poor  fellow  died 
in  the  Cork  union,  during  the  famine.  He  had  lived  a  happy 
life,  contemplating  his  own  perfections,  like  Brahma  on  the 
lotus-leaf.4 

*De  Morgan  might  have  found  much  else  for  his  satire  in  the 
letters  of  Walsh.  He  sought,  in  his  Theory  of  Partial  Functions,  to 
substitute  "partial  equations"  for  the  differential  calculus.  In  his 
diary  there  is  an  entry:  "Discovered  the  general  solution  of  numer- 
ical equations  of  the  fifth  degree  at  114  Evergreen  Street,  at  the 
Cross  of  Evergreen,  Cork,  at  nine  o'clock  in  the  forenoon  of  July  7th, 
1844 ;  exactly  twenty-two  years  after  the  invention  of  the  Geometry 
of  Partial  Equations,  and  the  expulsion  of  the  differential  calculus 
from  Mathematical  Science." 


GROWTH  OF  FREEDOM  OF  OPINION.  265 


GROWTH  OF  FREEDOM   OF  OPINION. 

The  year  1825  brings  me  to  about  the  middle  of  my 
Athenaeum  list:  that  is,  so  far  as  mere  number  of  names 
mentioned  is  concerned.  Freedom  of  opinion,  beyond  a  doubt, 
is  gaining  ground,  for  good  or  for  evil,  according  to  what 
the  speaker  happens  to  think:  admission  of  authority  is  no 
longer  made  in  the  old  way.  If  we  take  soul-cure  and  body- 
cure,  divinity  and  medicine,  it  is  manifest  that  a  change 
has  come  over  us.  Time  was  when  it  was  enough  that  dose 
or  dogma  should  be  certified  by  "II  a  ete  ordonne,  Mon- 
sieur, il  a  ete  ordonne,"1  as  the  apothecary  said  when  he 
wanted  to  operate  upon  poor  de  Porceaugnac.  Very  much 
changed:  but  whether  for  good  or  for  evil  does  not  now 
matter;  the  question  is,  whether  contempt  of  demonstration 
such  as  our  paradoxers  show  has  augmented  with  the  re- 
jection of  dogmatic  authority.  It  ought  to  be  just  the 
other  way :  for  the  worship  of  reason  is  the  system  on  which, 
if  we  trust  them,  the  deniers  of  guidance  ground  their  plan 
of  life.  The  following  attempt  at  an  experiment  on  this 
point  is  the  best  which  I  can  make ;  and,  so  far  as  I  know, 
the  first  that  ever  was  made. 

Say  that  my  list  of  paradoxers  divides  in  1825:  this  of 
itself  proves  nothing,  because  so  many  of  the  earlier  books 
are  lost,  or  not  likely  to  be  come  at.  It  would  be  a  fearful 
rate  of  increase  which  would  make  the  number  of  paradoxes 
since  1825  equal  to  the  whole  number  before  that  date.  Let 
us  turn  now  to  another  collection  of  mine,  arithmetical  books, 
of  which  I  have  published  a  list.  The  two  collections  are 
similarly  circumstanced  as  to  new  and  old  books ;  the  para- 
doxes had  no  care  given  to  the  collection  of  either;  the 
arithmetical  books  equal  care  to  both.  The  list  of  arith- 
metical books,  published  in  1847,  divides  at  1735 ;  the  para- 
doxes, up  to  1863,  divide  at  1825.  If  we  take  the  process 
which  is  most  against  the  distinction,  and  allow  every  year 

1  "It  has  been  ordered,  sir,  it  has  been  ordered." 


266  A  BUDGET  OF  PARADOXES. 

from  1847  to  1863  to  add  a  year  to  1735,  we  should  say  that 
the  arithmetical  writers  divide  at  1751.  This  rough  process 
may  serve,  with  sufficient  certainty,  to  show  that  the  propor- 
tion of  paradoxes  to  books  of  sober  demonstration  is  on  the 
increase;  and  probably,  quite  as  much  as  the  proportion  of 
heterodoxes  to  books  of  orthodox  adherence.  So  that  di- 
vinity and  medicine  may  say  to  geometry,  Don't  you  sneer : 
if  rationalism,  homoeopathy,  and  their  congeners  are  on  the 
rise  among  us,  your  enemies  are  increasing  quite  as  fast.  But 
geometry  replies — Dear  friends,  content  yourselves  with  the 
rational  inference  that  the  rise  of  heterodoxy  within  your 
pales  is  not  conclusive  against  you,  taken  alone ;  for  it  rises 
at  the  same  time  within  mine.  Store  within  your  garners 
the  precious  argument  that  you  are  not  proved  wrong 
by  increase  of  dissent;  because  there  is  increase  of  dissent 
against  exact  science.  But  do  not  therefore  even  yourselves 
to  me:  remember  that  you,  Dame  Divinity,  have  inflicted 
every  kind  of  penalty,  from  the  stake  to  the  stocks,  in  aid 
of  your  reasoning;  remember  that  you,  Mother  Medicine, 
have  not  many  years  ago  applied  to  Parliament  for  increase 
of  forcible  hindrance  of  antipharmacopceal  drenches,  pills, 
and  powders.  Who  ever  heard  of  my  asking  the  legislature 
to  fine  blundering  circle-squarers  ?  Remember  that  the  D 
in  dogma  is  the  D  in  decay ;  but  the  D  in  demonstration  is 
the  D  in  durability. 

THE   STATUS   OF  MEDICINE. 

I  have  known  a  medical  man — a  young  one — who  was 
seriously  of  the  opinion  that  the  country  ought  to  be  divided 
into  medical  parishes,  with  a  practitioner  appointed  to  each, 
and  a  penalty  for  calling  in  any  but  the  incumbent  curer. 
How  should  people  know  how  to  choose  ?  The  hair-dressers 
once  petitioned  Parliament  for  an  act  to  compel  people  to 
wear  wigs.  My  own  opinion  is  of  the  opposite  extreme,  as 
in  the  following  letter  (Examiner,  April  5,  1856)  ;  which, 
to  my  surprise,  I  saw  reprinted  in  a  medical  journal,  as  a 


THE   STATUS   OF   MEDICINE.  267 

plan  not  absolutely  to  be  rejected.  I  am  perfectly  satis- 
fied that  it  would  greatly  promote  true  medical  orthodoxy, 
the  predominance  of  well  educated  thinkers,  and  the  de- 
velopment of  their  desirable  differences. 

"SiR.  The  Medical  Bill  and  the  medical  question  gen- 
erally is  one  on  which  experience  would  teach,  if  people 
would  be  taught. 

"The  great  soul  question  took  three  hundred  years  to 
settle:  the  little  body  question  might  be  settled  in  thirty 
years,  if  the  decisions  in  the  former  question  were  studied. 

"Time  was  when  the  State  believed,  as  honestly  as  ever 
it  believed  anything,  that  it  might,  could,  and  should  find 
out  the  true  doctrine  for  the  poor  ignorant  community;  to 
which,  like  a  worthy  honest  state,  it  added  would.  Accord- 
ingly, by  the  assistance  of  the  Church,  which  undertook  the 
physic,  the  surgery,  and  the  pharmacy  of  sound  doctrine  all 
by  itself,  it  sent  forth  its  legally  qualified  teachers  into  every 
parish,  and  woe  to  the  man  who  called  in  any  other.  They 
burnt  that  man,  they  whipped  him,  they  imprisoned  him, 
they  did  everything  but  what  was  Christian  to  him,  all  for 
his  soul's  health  and  the  amendment  of  his  excesses. 

"But  men  would  not  submit.  To  the  argument  that  the 
State  was  a  father  to  the  ignorant,  they  replied  that  it  was 
at  best  the  ignorant  father  of  an  ignorant  son,  and  that  a 
blind  man  could  find  his  way  into  a  ditch  without  another 
blind  man  to  help  him,  And  when  the  State  said — But 
here  we  have  the  Church,  which  knows  all  about  it,  the 
ignorant  community  declared  that  it  had  a  right  to  judge 
that  question,  and  that  it  would  judge  it.  It  also  said  that 
the  Church  was  never  one  thing  long,  and  that  it  progressed, 
on  the  whole,  rather  more  slowly  than  the  ignorant  com- 
munity. 

"The  end  of  it  was,  in  this  country,  that  every  one  who 
chose  taught  all  who  chose  to  let  him  teach,  on  condition 
only  of  an  open  and  true  registration.  The  State  was 


268  A  BUDGET  OF  PARADOXES. 

allowed  to  patronize  one  particular  Church,  so  that  no  one 
need  trouble  himself  to  choose  a  pastor  from  the  mere  ne- 
cessity of  choosing.  But  every  church  is  allowed  its  col- 
leges, its  studies,  its  diplomas;  and  every  man  is  allowed 
his  choice.  There  is  no  proof  that  our  souls  are  worse  off 
than  in  the  sixteenth  century;  and,  judging  by  fruits,  there 
is  much  reason  to  hope  they  are  better  off. 

"Now  the  little  body  question  is  a  perfect  parallel  to  the 
great  soul  question  in  all  its  circumstances.  The  only  things 
in  which  the  parallel  fails  are  the  following :  Every  one  who 
believes  in  a  future  state  sees  that  the  soul  question  is  in- 
comparably more  important  than  the  body  question,  and 
every  one  can  try  the  body  question  by  experiment  to  a 
larger  extent  than  the  soul  question.  The  proverb,  which 
always  has  a  spark  of  truth  at  the  bottom,  says  that  every 
man  of  forty  is  either  a  fool  or  a  physician;  but  did  even 
the  proverb  maker  ever  dare  to  say  that  every  man  is  at  any 
age  either  a  fool  or  a  fit  teacher  of  religion? 

"Common  sense  points  out  the  following  settlement  of 
the  medical  question:  and  to  this  it  will  come  sooner  or 
later. 

"Let  every  man  who  chooses — subject  to  one  common 
law  of  manslaughter  for  all  the  crass  cases — doctor  the 
bodies  of  all  who  choose  to  trust  him,  and  recover  payment 
according  to  agreement  in  the  courts  of  law.  Provided 
always  that  every  person  practising  should  be  registered 
at  a  moderate  fee  in  a  register  to  be  republished  every  six 
months. 

"Let  the  register  give  the  name,  address,  and  asserted 
qualification  of  each  candidate — as  licentiate,  or  doctor,  or 
what  not,  of  this  or  that  college,  hall,  university,  &c.,  home 
or  foreign.  Let  it  be  competent  to  any  man  to  describe 
himself  as  qualified  by  study  in  public  schools  without  a 
diploma,  or  by  private  study,  or  even  by  intuition  or  divine 
inspiration,  if  he  please.  But  whatever  he  holds  his  quali- 
fication to  be,  that  let  him  declare.  Let  all  qualification 


THE  STATUS  OF   MEDICINE.  269 

which  of  its  own  nature  admits  of  proof  be  proved,  as  by 
the  diploma  or  certificate,  &c.,  leaving  things  which  cannot 
be  proved,  as  asserted  private  study,  intuition,  inspiration, 
&c.,  to  work  their  own  way. 

"Let  it  be  highly  penal  to  assert  to  the  patient  any  quali- 
fication which  is  not  in  the  register,  and  let  the  register  be 
sold  very  cheap.  Let  the  registrar  give  each  registered  prac- 
titioner a  copy  of  the  register  in  his  own  case ;  let  any  patient 
have  the  power  to  demand  a  sight  of  this  copy ;  and  let  no 
money  for  attendance  be  recoverable  in  any  case  in  which 
there  has  been  false  representation. 

"Let  any  party  in  any  suit  have  a  right  to  produce  what 
medical  testimony  he  pleases.  Let  the  medical  witness  pro- 
duce his  register,  and  let  his  evidence  be  for  the  jury,  as  is 
that  of  an  engineer  or  a  practitioner  of  any  art  which  is  not 
attested  by  diplomas. 

"Let  any  man  who  practises  without  venturing  to  put 
his  name  on  the  register  be  liable  to  fine  and  imprisonment. 

"The  consequence  would  be  that,  as  now,  anybody  who 
pleases  might  practise ;  for  the  medical  world  is  well  aware 
that  there  is  no  power  of  preventing  what  they  call  quacks 
from  practising.  But  very  different  from  what  is  now, 
every  man  who  practises  would  be  obliged  to  tell  the  whole 
world  what  his  claim  is,  and  would  run  a  great  risk  if  he 
dared  to  tell  his  patient  in  private  anything  different  from 
what  he  had  told  the  whole  world. 

"The  consequence  would  be  that  a  real  education  in 
anatomy,  physiology,  chemistry,  surgery,  and  what  is  known 
of  the  thing  called  medicine,  would  acquire  more  impor- 
tance than  it  now  has. 

"It  is  curious  to  see  how  completely  the  medical  man 
of  the  nineteenth  century  squares  with  the  priest  of  the 
sixteenth  century.  The  clergy  of  all  sects  are  now  better 
divines  and  better  men  than  they  ever  were.  They  have  lost 
Bacon's  reproach  that  they  took  a  smaller  measure  of  things 
than  any  other  educated  men ;  and  the  physicians  are  now 


270  A  BUDGET  OF  PARADOXES. 

in  this  particular  the  rearguard  of  the  learned  world ;  though 
it  may  be  true  that  the  rear  in  our  day  is  further  on  in  the 
march  than  the  van  of  Bacon's  day.  Nor  will  they  ever 
recover  the  lost  position  until  medicine  is  as  free  as  religion. 
"To  this  it  must  come.  To  this  the  public,  which  will 
decide  for  itself,  has  determined  it  shall  come.  To  this  the 
public  has,  in  fact,  brought  it,  but  on  a  plan  which  it  is  not 
desirable  to  make  permanent.  We  will  be  as  free  to  take 
care  of  our  bodies  as  of  our  souls  and  of  our  goods.  This 
is  the  profession  of  all  who  sign  as  I  do,  and  the  practice 
of  most  of  those  who  would  not  like  the  name 

"HETEROPATH." 

The  motion  of  the  Sun  in  the  Ecliptic,  proved  to  be  uniform  in 
a  circular  orbit. . .  .with  preliminary  observations  on  the  fallacy 
of  the  Solar  System.  By  Bartholomew  Prescott,1  1825,  8vo. 

The  author  had  published,  in  1803,  a  Defence  of  the 
Divine  System,  which  I  never  saw;  also,  On  the  inverted 
scheme  of  Copernicus.  The  above  work  is  clever  in  its 
satire. 

THE  CHRISTIAN  EVIDENCE  SOCIETY. 

Manifesto  of  the  Christian  Evidence  Society,  established  Nov. 
12,  1824.  Twenty-four  plain  questions  to  honest  men. 

These  are  two  broadsides  of  August  and  November, 
1826,  signed  by  Robert  Taylor,1  A.  B.,  Orator  of  the  Chris- 
tian Evidence  Society.  This  gentleman  was  a  clergyman, 

1  Bartholomew  Prescot  was  a  Liverpool  accountant.  De  Morgan 
gives  this  correct  spelling  9n  page  278.  He  died  after  1849.  His 
Inverted  Scheme  of  Copernicus  appeared  in  Liverpool  in  1822. 

1  Robert  Taylor  (1784-1844)  had  many  more  ups  and  downs  than 
De  Morgan  mentions.  He  was  a  priest  of  the  Church  of  England, 
but  resigned  his  parish  in  1818  after  preaching  against  Christianity. 
He  soon  recanted  and  took  another  parish,  but  was  dismissed  by  the 
Bishop  almost  immediately  on  the  ground  of  heresy.  As  stated  in 
the  text,  he  was  convicted  of  blasphemy  in  1827  and  was  sentenced 
to  a  year's  imprisonment,  and  again  for  two  years  on  the  same 
charge  in  1831.  He  then  married  a  woman  who  was  rich  in  money 
and  in  years,  and  was  thereupon  sued  for  breach  of  promise  by 
another  woman.  To  escape  paying  the  judgment  that  was  rendered 
against  him  he  fled  to  Tours  where  he  took  up  surgery. 


THE   CHRISTIAN    EVIDENCE   SOCIETY.  271 

and  was  convicted  of  blasphemy  in  1827,  for  which  he  suf- 
fered imprisonment,  and  got  the  name  of  the  Devil's  Chap- 
lain. The  following  are  quotations : 

"For  the  book  of  Revelation,  there  was  no  original  Greek 
at  all,  but  Erasmus  wrote  it  himself  in  Switzerland,  in  the 
year  1516.  Bishop  Marsh,2  vol.  i.  p.  320."— "Is  not  God  the 
author  of  your  reason  ?  Can  he  then  be  the  author  of  any- 
thing which  is  contrary  to  your  reason?  If  reason  be  a 
sufficient  guide,  why  should  God  give  you  any  other?  if  it 
be  not  a  sufficient  guide,  why  has  he  given  you  that?" 

1  remember  a  votary  of  the  Society  being  asked  to  substi- 
tute for  reason  "the  right  leg,"  and  for  guide  "support," 
and  to  answer  the  two  last  questions:  he  said  there  must 
be  a  quibble,  but  he  did  not  see  what.     It  is  pleasant  to 
reflect  that  the  argumentum  a  carcere3  is  obsolete.     One 
great  defect  of  it  was  that  it  did  not  go  far  enough:  there 
should  have  been  laws  against  subscriptions  for  blasphemers, 
against  dealing  at  their  shops,  and  against  rich  widows 
marrying  thefn. 

Had  I  taken  in  theology,  I  must  have  entered  books 
against  Christianity.  I  mention  the  above,  and  Paine's 
Age  of  Reason,  simply  because  they  are  the  only  English 
modern  works  that  ever  came  in  my  way  without  my  ask- 
ing for  them.  The  three  parts  of  the  Age  of  Reason 
were  published  in  Paris  1793,  Paris  1795,  and  New  York 
1807.  CarlileV  edition  is  of  London,  1818,  8vo.  It  must 
be  republished  when  the  time  comes,  to  show  what  stuff 
governments  and  clergy  were  afraid  of  at  the  beginning 
of  this  century.  I  should  never  have  seen  the  book,  if  it 

2  Herbert  Marsh,  Bishop  of  Peterborough.     See  note  9  on  page 
199. 

3  "Argument  from  the  prison." 

4  Richard  Carlile  (1790-1843),  one  of  the  leading  radicals  of  his 
time.     He  published  Hone's  parodies    (see  note  9,  page   124)    after 
they  had  been  suppressed,  and  an  edition  of  Thomas  Paine  (1818). 
He  was  repeatedly  imprisoned,  serving  nine  years  in  all.     His  con- 
tinued  conflict   with   the  authorities   proved  a  good  advertisement 
for  his  bookshop. 


272  A  BUDGET  OF  PARADOXES. 

had  not  been  prohibited :  a  bookseller  put  it  under  my  nose 
with  a  fearful  look  round  him;  and  I  could  do  no  less,  in 
common  curiosity,  than  buy  a  work  which  had  been  so  com- 
plimented by  church  and  state.  And  when  I  had  read  it, 
I  said  in  my  mind  to  church  and  state, — Confound  you! 
you  have  taken  me  in  worse  than  any  reviewer  I  ever  met 
with.  I  forget  what  I  gave  for  the  book,  but  I  ought  to 
have  been  able  to  claim  compensation  somewhere. 

THE  CABBALA. 

Cabbala  Algebraica.     Auctore   Gul.   Lud.   Christmann.1     Stutt- 
gard,  1827,  4to. 

Eighty  closely  printed  pages  of  an  attempt  to  solve  equa- 
tions of  every  degree,  which  has  a  process  called  by  the 
author  cabbala.  An  anonymous  correspondent  spells  cab- 
bala as  follows,  xa/?/?aAA,  and  makes  666  out  of  its  letters. 
This  gentleman  has  sent  me  since  my  Budget  commenced, 
a  little  heap  of  satirical  communications,  each  having  a  666 
or  two ;  for  instance,  alluding  to  my  remarks  on  the  spelling 
of  chemistry,  he  finds  the  fated  number  in  xw*l(J~  With  these 
are  challenges  to  explain  them,  and  hints  about  the  end  of  the 
world.  All  these  letters  have  different  fantastic  seals ;  one 
of  them  with  the  legend  "keep  your  temper," — another 
bearing  "bank  token  five  pence."  The  only  signature  is  a 
triangle  with  a  little  circle  in  it,  which  I  interpret  to  mean 
that  the  writer  confesses  himself  to  be  the  round  man  stuck 
in  the  three-cornered  hole,  to  be  explained  as  in  Sydney 
Smith's  joke. 

1Wilhelm  Ludwig  Christmann  (1780-1835)  was  a  protestant 
clergyman  and  teacher  of  mathematics.  For  a  while  he  taught  under 
Pestalozzi.  Disappointed  in  his  ambition  to  be  professor  of  mathe- 
matics at  Tubingen,  he  became  a  confirmed  misanthrope  and  is  said 
never  to  have  left  his  house  during  the  last  ten  years  of  his  life.  He 
wrote  several  works :  Ein  Wort  tiber  Pestalozzi  und  Pestalozzismus 
(1812);  Ars  cossae  promota  (1814);  Philosophic,  cossica  (1815); 
Aetas  argentea  cossae  (1819);  Ueber  Tradition  und  Schrift,  Logos 
und  Kabbala  (1829),  besides  the  one  mentioned  above.  The  word 
coss  in  the  above  titles  was  a  German  name  for  algebra,  from  the 
Italian  cosa  (thing),  the  name  for  the  unknown  quantity.  It  appears 
in  English  in  the  early  name  for  algebra,  "the  cossic  art." 


THE   CABBALA.  273 

There  is  a  kind  of  Cabbala  Alphabetica  which  the  in- 
vestigators of  the  numerals  in  words  would  do  well  to  take 
up:  it  is  the  formation  of  sentences  which  contain  all  the 
letters  of  the  alphabet,  and  each  only  once.  No  one  has  done 
it  with  v  and  /  treated  as  consonants ;  but  you  and  I  can 
do  it.  Dr.  Whewell2  and  I  amused  ourselves,  some  years 
ago,  with  attempts.  He  could  not  make  sense,  though  he 
joined  words :  he  gave  me 

Phiz,  styx,  wrong,  buck,  flame,  quid. 

I  gave  him  the  following,  which  he  agreed  was  "admirable 
sense" :  I  certainly  think  the  words  would  never  have  come 
together  except  in  this  way: 

I,  quartz  pyx,  who  fling  muck  beds. 

I  long  thought  that  no  human  being  could  say  this  under 
any  circumstances.  At  last  I  happened  to  be  reading  a 
religious  writer — as  he  thought  himself — who  threw  asper- 
sions on  his  opponents  thick  and  threefold.  Heyday!  came 
into  my  head,  this  fellow  flings  muck  beds;  he  must  be  a 
quartz  pyx.  And  then  I  remembered  that  a  pyx  is  a  sacred 
vessel,  and  quartz  is  a  hard  stone,  as  hard  as  the  heart  of  a 
religious  foe-curser.  So  that  the  line  is  the  motto  of  the 
ferocious  sectarian,  who  turns  his  religious  vessels  into  mud- 
holders,  for  the  benefit  of  those  who  will  not  see  what  he 
sees. 

1  can  find  no  circumstances  for  the  following,  which  I 
received  from  another: 

Fritz!  quick!  land!  hew  gypsum  box. 
From  other  quarters  I  have  the  following: 
Dumpy  quiz!  whirl  back  fogs  next. 

This  might  be  said  in  time  of  haze  to  the  queer  little  figure 
in  the  Dutch  weather-toy,  which  comes  out  or  goes  in  with 
the  change  in  the  atmosphere.  Again, 

2  See  note  4,  page  101. 


274  A  BUDGET  OF  PARADOXES. 

Export  my  fund!   Quiz  black  whigs. 

This  Squire  Western  might  have  said,  who  was  always 
afraid  of  the  whigs  sending  the  sinking-fund  over  to  Han- 
over. But  the  following  is  the  best:  it  is  good  advice  to 
a  young  man,  very  well  expressed  under  the  circumstances : 

Get  nymph;  quiz  sad  brow;  fix  luck. 

Which  in  more  sober  English  would  be,  Marry ;  be  cheer- 
ful; watch  your  business.  There  is  more  edification,  more 
religion  in  this  than  in  all  the  666-interpretations  put  to- 
gether. 

Such  things  would  make  excellent  writing  copies,  for 
they  secure  attention  to  every  letter ;  v  and  /  might  be  placed 
at  the  end. 

ON  GODFREY  HIGGINS. 

The  Celtic  Druids.  By  Godfrey  Higgins,1  Esq.  of  Skellow 
Grange,  near  Doncaster.  London,  1827,  4to. 

Anacalypsis,  or  an  attempt  to  draw  aside  the  veil  of  the  Saitic 
Isis :  or  an  inquiry  into  the  origin  of  languages,  nations,  and 

religions.  By  Godfrey  Higgins,  &c ,  London,  1836,  2 

vols.  4to. 

The  first  work  had  an  additional  preface  and  a  new  index 
in  1829.  Possibly,  in  future  time,  will  be  found  bound  up  with 
copies  of  the  second  work  two  sheets  which  Mr.  Higgins 
circulated  among  his  friends  in  1831 :  the  first  a  "Recapitu- 
lation," the  second  "Book  vi.  ch.  1." 

The  system  of  these  works  is  that — 

"The  Buddhists  of  Upper  India  (of  whom  the  Phenician 
Canaanite,  Melchizedek,  was  a  priest),  who  built  the  Pyra- 
mids, Stonehenge,  Carnac,  &c.  will  be  shown  to  have  founded 
all  the  ancient  mythologies  of  the  world,  which,  however 
varied  and  corrupted  in  recent  times,  were  originally  one, 
and  that  one  founded  on  principles  sublime,  beautiful,  and 
true." 

1  See  note  3,  page  257. 


ON  GODFREY  HIGGINS.  275 

These  works  contain  an  immense  quantity  of  learning, 
very  honestly  put  together.  I  presume  the  enormous  num- 
ber of  facts,  and  the  goodness  of  the  index,  to  be  the  rea- 
sons why  the  Anacalypsis  found  a  permanent  place  in  the 
old  reading-room  of  the  British  Museum,  even  before  the 
change  which  greatly  increased  the  number  of  books  left 
free  to  the  reader  in  that  room. 

Mr.  Higgins,  whom  I  knew  well  in  the  last  six  years 
of  his  life,  and  respected  as  a  good,  learned,  and  (in  his 
own  way)  pious  man,  was  thoroughly  and  completely  the 
man  of  a  system.  He  had  that  sort  of  mental  connection 
with  his  theory  that  made  his  statements  of  his  authorities 
trustworthy:  for,  besides  perfect  integrity,  he  had  no  bias 
towards  alteration  of  facts:  he  saw  his  system  in  the  way 
the  fact  was  presented  to  him  by  his  authority,  be  that 
what  it  might. 

He  was  very  sure  of  a  fact  which  he  got  from  any  of 
his  authorities:  nothing  could  shake  him.  Imagine  a  con- 
versation between  him  and  an  Indian  officer  who  had  paid 
long  attention  to  Hindoo  antiquities  and  their  remains:  a 
third  person  was  present,  ego  qui  scribo.  G.  H.  "You  know 
that  in  the  temples  of  I-forget-who  the  Ceres  is  always 

sculptured  precisely  as  in  Greece."  Col. ,  "I  really  do 

not  remember  it,  and  I  have  seen  most  of  these  temples." 
G.  H.  "It  is  so,  I  assure  you,  especially  at  I-forget-where." 

Col.  ,  "Well,  I  am  sure!  I  was  encamped  for  six 

weeks  at  the  gate  of  that  very  temple,  and,  except  a  little 
shooting,  had  nothing  to  do  but  to  examine  its  details, 
which  I  did,  day  after  day,  and  I  found  nothing  of  the 
kind."  It  was  of  no  use  at  all. 

Godfrey  Higgins  began  life  by  exposing  and  conquer- 
ing, at  the  expense  of  two  years  of  his  studies,  some  shock- 
ing abuses  which  existed  in  the  York  Lunatic  Asylum. 
This  was  a  proceeding  which  called  much  attention  to  the 
treatment  of  the  insane,  and  produced  much  good  effect. 
He  was  very  resolute  and  energetic.  The  magistracy  of  his 


276  A  BUDGET  OF  PARADOXES. 

time  had  scruples  about  using  the  severity  of  law  to  people 
of  such  station  as  well-to-do  farmers,  &c. :  they  would  allow 
a  great  deal  of  resistance,  and  endeavor  to  mollify  the 
rebels  into  obedience.  A  young  farmer  flatly  refused  to 
pay  under  an  order  of  affiliation  made  upon  him  by  Godfrey 
Higgins.  He  was  duly  warned;  and  persisted:  he  shortly 
found  himself  in  gaol.  He  went  there  sure  to  conquer  the 
Justice,  and  the  first  thing  he  did  was  to  demand  to  see  his 
lawyer.  He  was  told,  to  his  horror,  that  as  soon  as  he  had 
been  cropped  and  prison-dressed,  he  might  see  as  many 
lawyers  as  he  pleased,  to  be  looked  at,  laughed  at,  and 
advised  that  there  was  but  one  way  out  of  the  scrape. 
Higgins  was,  in  his  speculations,  a  regular  counterpart  of 
Bailly;  but  the  celebrated  Mayor  of  Paris  had  not  his 
nerve.  It  is  impossible  to  say,  if  their  characters  had  been 
changed,  whether  the  unfortunate  crisis  in  which  Bailly 
was  not  equal  to  the  occasion  would  have  led  to  very  differ- 
ent results  if  Higgins  had  been  in  his  place:  but  assuredly 
constitutional  liberty  would  have  had  one  chance  more. 
There  are  two  works  of  his  by  which  he  was  known,  apart 
from  his  paradoxes.  First,  An  apology  for  the  life  and 
character  of  the  celebrated  prophet  of  Arabia,  called  Mo- 
hamed,  or  the  Illustrious.  London,  8vo.  1829.  The  reader 
will  look  at  this  writing  of  our  English  Buddhist  with  sus- 
picious eye,  but  he  will  not  be  able  to  avoid  confessing  that 
the  Arabian  prophet  has  some  reparation  to  demand  at  the 
hands  of  Christians.  Next,  Hora  Sabaticcs;  or  an  attempt 
to  correct  certain  superstitions  and  vulgar  errors  respecting 
the  Sabbath.  Second  edition,  with  a  large  appendix.  Lon- 
don, 12mo.  1833.  This  book  was  very  heterodox  at  the 
time,  but  it  has  furnished  material  for  some  of  the  clergy 
of  our  day. 

I  never  could  quite  make  out  whether  Godfrey  Higgins 
took  that  system  which  he  traced  to  the  Buddhists  to  have 
a  Divine  origin,  or  to  be  the  result  of  good  men's  medita- 
tions. Himself  a  strong  theist,  and  believer  in  a  future 


ON  POPE'S  DIPPING  NEEDLE.  277 

state,  one  would  suppose  that  he  w,ould  refer  a  universal 
religion,  spread  in  different  forms  over  the  whole  earth 
from  one  source,  directly  to  the  universal  Parent.  And  this 
I  suspect  he  did,  whether  he  knew  it  or  not.  The  external 
evidence  is  balanced.  In  his  preface  he  says: 

"I  cannot  help  smiling  when  I  consider  that  the  priests 
have  objected  to  admit  my  former  book,  The  Celtic  Druids, 
into  libraries,  because  it  was  antichristian ;  and  it  has  been 
attacked  by  Deists,  because  it  was  superfluously  religious. 
The  learned  Deist,  the  Rev.  R.  Taylor  [already  mentioned], 
has  designated  me  as  the  religious  Mr.  Higgins." 

The  time  will  come  when  some  profound  historian  of 
literature  will  make  himself  much  clearer  on  the  point  than 
I  am. 

ON    POPE'S   DIPPING   NEEDLE. 

The  triumphal  Chariot  of  Friction:  or  a  familiar  elucidation  of 
the  origin  of  magnetic  attraction,  &c.  &c.  By  William  Pope.1 
London,  1829,  4to. 

Part  of  this  work  is  on  a  dipping-needle  of  the  au- 
thor's construction.  It  must  have  been  under  the  impression 
that  a  book  of  naval  magnetism  was  proposed,  that  a 
great  many  officers,  the  Royal  Naval  Club,  etc.  lent  their 
names  to  the  subscription  list.  How  must  they  have  been 
surprised  to  find,  right  opposite  to  the  list  of  subscribers, 
the  plate  presenting  "the  three  emphatic  letters,  J.  A.  O." 
And  how  much  more  when  they  saw  it  set  forth  that  if  a 
square  be  inscribed  in  a  circle,  a  circle  within  that,  then  a 
square  again,  &c.,  it  is  impossible  to  have  more  than  fourteen 
circles,  let  the  first  circle  be  as  large  as  you  please.  From 
this  the  seven  attributes  of  God  are  unfolded ;  and  further, 
that  all  matter  was  moral,  until  Lucifer  churned  it  into 
physical  "as  far  as  the  third  circle  in  Deity":  this  Lucifer, 
called  Leviathan  in  Job,  being  thus  the  moving  cause  of 

1  He  seems  to  have  written  nothing  else. 


278  A  BUDGET  OF  PARADOXES. 

chaos.    I  shall  say  no  more,  except  that  the  friction  of  the 
air  is  the  cause  of  magnetism. 

Remarks  on  the  Architecture,  Sculpture,  and  Zodiac  of  Pal- 
myra; with  a  Key  to  the  Inscriptions.  By  B.  Prescot.2  Lon- 
don, 1830,  8vo. 

Mr.  Prescot  gives  the  signs  of  the  zodiac  a  Hebrew 
origin. 

THE  JACOTOT  METHOD. 

Epitome  de  mathematiques.     Par  F.   Jacotot,1  Avocat.     3ieme 

edition,  Paris,  1830,  8vo.  (pp.  18). 
Methode  Jacotot.     Choix  de  propositions  mathematiques.     Par 

P.  Y.  Sepres.2    2nde  edition.    Paris,  1830,  8vo.     (pp.  82). 

Of  Jacotot's  method,  which  had  some  vogue  in  Paris, 
the  principle  was  Tout  est  dans  tout,3  and  the  process  Ap- 
prendre  quelque  chose,  et  a  y  rapporter  tout  le  rested  The 
first  tract  has  a  proposition  in  conic  sections  and  its  prelim- 
inaries: the  second  has  twenty  exercises,  of  which  the  first 
is  finding  the  greatest  common  measure  of  two  numbers, 
and  the  last  is  the  motion  of  a  point  on  a  surface,  acted  on 
by  given  forces.  This  is  topped  up  with  the  problem  of 
sound  in  a  tube,  and  a  slice  of  Laplace's  theory  of  the 
tides.  All  to  be  studied  until  known  by  heart,  and  all  the 
rest  will  come,  or  at  least  join  on  easily  when  it  comes. 
There  is  much  truth  in  the  assertion  that  new  knowledge 

*  See  note  I  on  page  270.    The  name  is  here  spelled  correctly. 

1  Joseph  Jacotot  (1770-1840),  the  father  of  this  Fortune  Jacotot, 
was  an  infant  prodigy.  At  nineteen  he  was  made  professor  of  the 
humanities  at  Dijon.  He  served  in  the  army,  and  then  became  pro- 
fessor of  mathematics  at  Dijon.  He  continued  in  his  chair  until 
the  restoration  of  the  Bourbons,  and  then  fled  to  Louvain.  It  was 
here  that  he  developed  the  method  with  which  his  name  is  usually 
connected.  He  wrote  a  Mathematiques  in  1827,  which  went  through 
four  editions.  The  Epitome  is  by  his  son,  Fortune. 

*  He  wrote  on  educational  topics  and  a  Sacred  History  that  went 
through  several  editions. 

'  "All  is  in  all." 

4  "Know  one  thing  and  refer  everything  else  to  it,"  as  it  is  often 
translated. 


A   DISCOURSE   ON    PROBABILITY.  279 

hooks  on  easily  to  a  little  of  the  old,  thoroughly  mastered. 
The  day  is  coming  when  it  will  be  found  out  that  crammed 
erudition,  got  up  for  examinations,  does  not  cast  out  any 
hooks  for  more. 

Lettre  a  MM.  les  Membres  de  1' Academic  Royale  des  Sciences, 
contenant  un  developpement  de  la  refutation  du  systeme  de  la 
gravitation  universelle,  qui  leur  a  ete  presentee  le  30  aout,  1830. 
Par  Felix  Passot5  Paris,  1830,  8vo. 

Works  of  this  sort  are  less  common  in  France  than  in 
England.  In  France  there  is  only  the  Academy  of  Sciences 
to  go  to:  in  England  there  is  a  reading  public  out  of  the 
Royal  Society,  &c. 

A  DISCOURSE  ON  PROBABILITY. 

About  1830  was  published,  in  the  Library  of  Useful 
Knowledge,  the  tract  on  Probability,  the  joint  work  of  the 
late  Sir  John  Lubbock1  and  Mr.  Drinkwater  (Bethune).2 
It  is  one  of  the  best  elementary  openings  of  the  subject. 
A  binder  put  my  name  on  the  outside  (the  work  was  anon- 
ymous) and  the  consequence  was  that  nothing  could  drive 
out  of  people's  heads  that  it  was  written  by  me.  I  do 
not  know  how  many  denials  I  have  made,  from  a  passage 
in  one  of  my  own  works  to  a  letter  in  the  Times :  and  I  am 
not  sure  that  I  have  succeeded  in  establishing  the  truth, 
even  now.  I  accordingly  note  the  fact  once  more.  But 
as  a  book  has  no  right  here  unless  it  contain  a  paradox — 
or  thing  counter  to  general  opinion  or  practice — I  will  pro- 
duce two  small  ones.  Sir  John  Lubbock,  with  whom  lay 
the  executive  arrangement,  had  a  strong  objection  to  the 
last  word  in  "Theory  of  Probabilities,"  he  maintained  that 
the  singular  probability,  should  be  used;  and  I  hold  him 
quite  right. 

5  A  writer  of  no  reputation. 

*Sir  John  Lubbock   (1803-1865),  banker,  scientist,  publicist,  as- 
tronomer, one  of  the  versatile  men  of  his  time. 
2  See  note  8,  page  99. 


280  A  BUDGET  OF  PARADOXES. 

The  second  case  was  this:  My  friend  Sir  J.  L.,  with  a 
large  cluster  of  intellectual  qualities,  and  another  of  social 
qualities,  had  one  point  of  character  which  I  will  not  call 
bad  and  cannot  call  good ;  he  never  used  a  slang  expression. 
To  such  a  length  did  he  carry  his  dislike,  that  he  could  not 
bear  head  and  tail,  even  in  a  work  on  games  of  chance:  so 
he  used  obverse  and  reverse.  I  stared  when  I  first  saw 
this:  but,  to  my  delight,  I  found  that  the  force  of  circum- 
stances beat  him  at  last.  He  was  obliged  to  take  an  example 
from  the  race-course,  and  the  name  of  one  of  the  horses 
was  Bessy  Bedlam  I  And  he  did  not  put  her  down  as 
Elisabeth  Bethlehem,  but  forced  himself  to  follow  the 
jockeys. 

[Almanach  Remain  sur  la  Loterie  Royale  de  France,  ou  les 
Etrennes  necessaires  aux  Actionnaires  et  Receveurs  de  la 
dite  Loterie.  Par  M.  Menut  de  St.-Mesmin.  Paris,  1830. 
I2mo. 

This  book  contains  all  the  drawings  of  the  French  lot- 
tery (two  or  three,  each  month)  from  1758  to  1830.  It  is 
intended  for  those  who  thought  they  could  predict  the 
future  drawings  from  the  past:  and  various  sets  of  sympa- 
thetic numbers  are  given  to  help  them.  The  principle  is, 
that  anything  which  has  not  happened  for  a  long  time  must 
be  soon  to  come.  At  rouge  et  noir,  for  example,  when  the  red 
has  won  five  times  running,  sagacious  gamblers  stake  on  the 
black,  for  they  think  the  turn  which  must  come  at  last  is 
nearer  than  it  was.  So  it  is:  but  observation  would  have 
shown  that  if  a  large  number  of  those  cases  had  been 
registered  which  show  a  run  of  five  for  the  red,  the  next 
game  would  just  as  often  have  made  the  run  into  six  as 
have  turned  in  favor  of  the  black.  But  the  gambling  rea- 
soner  is  incorrigible:  if  he  would  but  take  to  squaring  the 
circle,  what  a  load  of  misery  would  be  saved.  A  writer  of 
1823,  who  appeared  to  be  thoroughly  acquainted  with  the 
gambling  of  Paris  and  London,  says  that  the  gamesters  by 


A   DISCOURSE   ON    PROBABILITY.  281 

profession  are  haunted  by  a  secret  foreboding  of  their  future 
destruction,  and  seem  as  if  they  said  to  the  banker  at  the 
table,  as  the  gladiators  said  to  the  emperor,  Morituri  te 
salutant.8 

In  the  French  lottery,  five  numbers  out  of  ninety  were 
drawn  at  a  time.  Any  person,  in  any  part  of  the  country, 
might  stake  any  sum  upon  any  event  he  pleased,  as  that 
27  should  be  drawn ;  that  42  and  81  should  be  drawn ;  that 
42  and  81  should  be  drawn,  and  42  first;  and  so  on  up  to 
a  quine  determine,  if  he  chose,  which  is  betting  on  five 
given  numbers  in  a  given  order.  Thus,  in  July,  1821,  one 
of  the  drawings  was 

8      46      16      64      13. 

A  gambler  had  actually  predicted  the  five  numbers  (but  not 
their  order),  and  won  131,350  francs  on  a  trifling  stake.  M. 
Menut  seems  to  insinuate  that  the  hint  what  numbers  to 
choose  was  given  at  his  own  office.  Another  won  20,852 
francs  on  the  quaterne,  8,  16,  46,  64,  in  this  very  drawing. 
These  gains,  of  course,  were  widely  advertised :  of  the  mul- 
titudes who  lost  nothing  was  said.  The  enormous  number 
of  those  who  played  is  proved  to  all  who  have  studied 
chances  arithmetically  by  the  numbers  of  simple  quaternes 
which  were  gained:  in  1822,  fourteen;  in  1823,  six;  in 
1824,  sixteen;  in  1825,  nine,  &c. 

The  paradoxes  of  what  is  called  chance,  or  hazard,  might 
themselves  make  a  small  volume.  All  the  world  under- 
stands that  there  is  a  long  run,  a  general  average ;  but  great 
part  of  the  world  is  surprised  that  this  general  average 
should  be  computed  and  predicted.  There  are  many  re- 
markable cases  of  verification;  and  one  of  them  relates  to 
the  quadrature  of  the  circle.  I  give  some  account  of  this  and 
another.  Throw  a  penny  time  after  time  until  head  arrives, 
which  it  will  do  before  long:  let  this  be  called  a  set.  Ac- 
cordingly, H  is  the  smallest  set,  TH  the  next  smallest,  then 
TTH,  &c.  For  abbreviation,  let  a  set  in  which  seven  tails 

'"Those  about  to  die  salute  you." 


282  A  BUDGET  OF  PARADOXES. 

occur  before  head  turns  up  be  T7H.  In  an  immense  num- 
ber of  trials  of  sets,  about  half  will  be  H ;  about  a  quarter 
TH ;  about  an  eighth,  T2H.  Buffon4  tried  2,048  sets ;  and 
several  have  followed  him.  It  will  tend  to  illustrate  the 
principle  if  I  give  all  the  results ;  namely,  that  many  trials 
will  with  moral  certainty  show  an  approach— and  the  greater 
the  greater  the  number  of  trials — to  that  average  which 
sober  reasoning  predicts.  In  the  first  column  is  the  most 
likely  number  of  the  theory :  the  next  column  gives  Buffon's 
result;  the  three  next  are  results  obtained  from  trial  by 

H  .     1,024  .  1,061     .     1,048    .     1,017    .     1,039 

TH  .       512  .  494    .       507    .       547    .       480 

T*H  .       256  .  232     .       248    .       235     .       267 

T3H  .        128  .  137    .         99    ,       118    .       126 

T4H  .         64  .  56    .         71     .         72    .         67 

TsH  .         32  .  29     .         38     .         32     .         33 

T6H  .         16  .  25     .         17    .         10    .         19 

T7H  .           8  .  8    .           9    .           9    .         10 

T8H  .           4  .  6    .           5     .           3    .           3 

T9H                 2  .  3.2.4 

T'°H                1  .  1.1 

T"H  0     .  1 

T"H  0    .  0 

T'3H                1  .  1.0 

T'4H  0  0 

T'sH  1     .  1 

&c.  0.0 

2,048    .    2,048    .    2,048    .    2,048    .    2,048 

4  Georges  Louis  Leclerc  Buffon  (1707-1788),  the  well-known 
biologist.  He  also  experimented  with  burning  mirrors,  his  results 
appearing  in  his  Invention  des  miroirs  ardens  pour  bruler  a  une 
grande  distance  (1747).  The  reference  here  may  be  to  his  Resolu- 
tion des  problemes  qui  re  gar  dent  le  jeu  du  franc  carreau  (1733). 
The  prominence  of  his  Histoire  naturelle  (36  volumes,  1749-1788) 
has^  overshadowed  the  credit  due  to  him  for  his  translation  of  New- 
ton's work  on  Fluxions. 


A   DISCOURSE   ON    PROBABILITY.  283 

correspondents  of  mine.    In  each  case  the  number  of  trials 
is  2,048. 

In  very  many  trials,  then,  we  may  depend  upon  something 
like  the  predicted  average.  Conversely,  from  many  trials 
we  may  form  a  guess  at  what  the  average  will  be.  Thus, 
in  Buffon's  experiment  the  2,048  first  throws  of  the  sets 
gave  head  in  1,061  cases:  we  have  a  right  to  infer  that  in 
the  long  run  something  like  1,061  out  of  2,048  is  the  pro- 
portion of  heads,  even  before  we  know  the  reasons  for  the 
equality  of  chance,  which  tell  us  that  1,024  out  of  2,048  is 
the  real  truth.  I  now  come  to  the  way  in  which  such  con- 
siderations have  led  to  a  mode  in  which  mere  pitch-and-toss 
has  given  a  more  accurate  approach  to  the  quadrature  of  the 
circle  than  has  been  reached  by  some  of  my  paradoxers. 
What  would  my  friend5  in  No.  14  have  said  to  this?  The 
method  is  as  follows:  Suppose  a  planked  "floor  of  the  usual 
kind,  with  thin  visible  seams  between  the  planks.  Let  there 
be  a  thin  straight  rod,  or  wire,  not  so  long  as  the  breadth  of 
the  plank.  This  rod,  being  tossed  up  at  hazard,  will  either 
fall  quite  clear  of  the  seams,  or  will  lay  across  one  seam. 
Now  Buffon,  and  after  him  Laplace,  proved  the  following: 
That  in  the  long  run  the  fraction  of  the  whole  number  of 
trials  in  which  a  seam  is  intersected  will  be  the  fraction 
which  twice  the  length  of  the  rod  is  of  the  circumference 
of  the  circle  having  the  breadth  of  a  plank  for  its  diameter. 
In  1855  Mr.  Ambrose  Smith,  of  Aberdeen,  made  3,204 
trials  with  a  rod  three-fifths  of  the  distance  between  the 
planks:  there  were  1,213  clear  intersections,  and  11  contacts 
on  which  it  was  difficult  to  decide.  Divide  these  contacts 
equally,  and  we  have  1,218J  to  3,204  for  the  ratio  of  6  to 
5?r,  presuming  that  the  greatness  of  the  number  of  trials 
gives  something  near  to  the  final  average,  or  result  in  the 
long  run:  this  gives  7r  =  3.1553.  If  all  the  11  contacts  had 
been  treated  as  intersections,  the  result  would  have  been 

5  See  page  285.    This  article  was  a  supplement  to  No.  14  in  the 
Athenaum  Budget.— A.  De  M. 


284  A  BUDGET  OF  PARADOXES. 

7r  =  3.1412,  exceedingly  near.  A  pupil  of  mine  made  600 
trials  with  a  rod  of  the  length  between  the  seams,  and  got 
7r  =  3.137. 

This  method  will  hardly  be  believed  until  it  has  been 
repeated  so  often  that  "there  never  could  have  been  any 
doubt  about  it." 

The  first  experiment  strongly  illustrates  a  truth  of  the 
theory,  well  confirmed  by  practice:  whatever  can  happen 
will  happen  if  we  make  trials  enough.  Who  would  under- 
take to  throw  tail  eight  times  running?  Nevertheless,  in 
the  8,192  sets  tail  8  times  running  occurred  17  times;  9 
times  running,  9  times;  10  times  running,  twice;  11  times 
and  13  times,  each  once;  and  15  times  twice.] 

ON  CURIOSITIES  OF  ». 

1830.  The  celebrated  interminable  fraction  3. 14159. 
which  the  mathematician  calls  TT,  is  the  ratio  of  the  circum- 
ference to  the  diameter.  But  it  is  thousands  of  things 
besides.  It  is  constantly  turning  up  in  mathematics :  and  if 
arithmetic  and  algebra  had  been  studied  without  geometry, 
TT  must  have  come  in  somehow,  though  at  what  stage  or 
under  what  name  must  have  depended  upon  the  casualties 
of  algebraical  invention.  This  will  readily  be  seen  when 
it  is  stated  that  TT  is  nothing  but  four  times  the  series 

l-1/3  +  1/5-1/7  +  1/9-1/ll+.... 

ad  infinitum.1     It  would  be  wonderful  if  so  simple  a  series 


are  many  similar  series  and  products.    Among  the  more 
interesting  are  the  following: 

7r_2-2-4-4-6-6-8... 
2    1-3-3-5-5-7-7...  ' 

I     rz    ~ ~  ~""~  * 


t       2-3-4      4-5-6      6-7-8 

"6  ~~  \  3"     \      8*3    y  •  S    S^7-    S* -t""      / ' 

«=t(i L+_I L+.  . .  WJL. 

4       \  5     3*5^    5  "5**     7'57  /        \23Q 


ON  CURIOSITIES  OF  TT.  285 

had  but  one  kind  of  occurrence.  As  it  is,  our  trigonometry 
being  founded  on  the  circle,  IT  first  appears  as  the  ratio 
stated.  If,  for  instance,  a  deep  study  of  probable  fluctua- 
tion from  average  had  preceded,  TT  might  have  emerged  as 
a  number  perfectly  indispensable  in  such  problems  as :  What 
is  the  chance  of  the  number  of  aces  lying  between  a  million 
+  x  and  a  million  -  x,  when  six  million  of  throws  are  made 
with  a  die?  I  have  not  gone  into  any  detail  of  all  those 
cases  in  which  the  paradoxer  finds  out,  by  his  unassisted 
acumen,  that  results  of  mathematical  investigation  cannot 
be :  in  fact,  this  discovery  is  only  an  accompaniment,  though 
a  necessary  one,  of  his  paradoxical  statement  of  that  which 
must  be.  Logicians  are  beginning  to  see  that  the  notion 
of  horse  is  inseparably  connected  with  that  of  non-horse: 
that  the  first  without  the  second  would  be  no  notion  at  all. 
And  it  is  clear  that  the  positive  affirmation  of  that  which 
contradicts  mathematical  demonstration  cannot  but  be  ac- 
companied by  a  declaration,  mostly  overtly  made,  that  dem- 
onstration is  false.  If  the  mathematician  were  interested 
in  punishing  this  indiscretion,  he  could  make  his  denier 
ridiculous  by  inventing  asserted  results  which  would  com- 
pletely take  him  in. 

More  than  thirty  years  ago  I  had  a  friend,  now  long 
gone,  who  was  a  mathematician,  but  not  of  the  higher 
branches:  he  was,  inter  alia,  thoroughly  up  in  all  that 
relates  to  mortality,  life  assurance,  &c.  One  day,  explain- 
ing to  him  how  it  should  be  ascertained  what  the  chance 
is  of  the  survivors  of  a  large  number  of  persons  now  alive 
lying  between  given  limits  of  number  at  the  end  of  a  certain 
time,  I  came,  of  course  upon  the  introduction  of  IT,  which 
I  could  only  describe  as  the  ratio  of  the  circumference  of 
a  circle  to  its  diameter.  "Oh,  my  dear  friend !  that  must  be 
a  delusion ;  what  can  the  circle  have  to  do  with  the  numbers 
alive  at  the  end  of  a  given  time?" — "I  cannot  demonstrate 
it  to  you ;  but  it  is  demonstrated." — "Oh !  stuff !  I  think  you 
can  prove  anything  with  your  differential  calculus :  figment, 


286  A  BUDGET  OF  PARADOXES. 

depend  upon  it."  I  said  no  more;  but,  a  few  days  after- 
wards, I  went  to  him  and  very  gravely  told  him  that  I  had 
discovered  the  law  of  human  mortality  in  the  Carlisle  Table, 
of  which  he  thought  very  highly.  I  told  him  that  the  law 
was  involved  in  this  circumstance.  Take  the  table  of  ex- 
pectation of  life,  choose  any  age,  take  its  expectation  and 
make  the  nearest  integer  a  new  age,  do  the  same  with  that, 
and  so  on;  begin  at  what  age  you  like,  you  are  sure  to 
end  at  the  place  where  the  age  past  is  equal,  or  most  nearly 
equal,  to  the  expectation  to  come.  "You  don't  mean  that 
this  always  happens?" — "Try  it."  He  did  try,  again  and 
again;  and  found  it  as  I  said.  "This  is,  indeed,  a  curious 
thing;  this  is  a  discovery."  I  might  have  sent  him  about 
trumpeting  the  law  of  life :  but  I  contented  myself  with  in- , 
forming  him  that  the,  same  thing  would  happen  with  any 
table  whatsoever  in  which  the  first  column  goes  up  and 
the  second  goes  down ;  and  that  if  a  proficient  in  the  higher 
mathematics  chose  to  palm  a  figment  upon  him,  he  could 
do  without  the  circle :  a  corsair  e}  corsair e  et  demi?  the  French 
proverb  says.  "Oh!"  it  was  remarked,  "I  see,  this  was 
Milne  !"3  It  was  not  Milne :  I  remember  well  showing  the 
formula  to  him  some  time  afterwards.  He  raised  no  diffi- 
culty about  ?r;  he  knew  the  forms  of  Laplace's  results,  and 
he  was  much  interested.  Besides,  Milne  never  said  stuff! 
and  figment!  And  he  would  not  have  been  taken  in:  he 
would  have  quietly  tried  it  with  the  Northampton  and  all 
the  other  tables,  and  would  have  got  at  the  truth. 

8  "To  a  privateer,  a  privateer  and  a  half." 

3  Joshua  Milne  (1776-1851)  was  actuary  of  the  Sun  Life  Assur- 
ance Society.  He  wrote  A  Treatise  on  the  Valuation  of  Annuities 
and  Assurances  on  Lives  and  Survivorships;  on  the  Construction 
of  tables  of  mortality;  and  on  the  Probabilities  and  Expectations  of 
Life,  London,  1815.  Upon  the  basis  of  the  Carlisle  bills  of  mortality 
of  Dr.  Heysham  he  reconstructed  the  mortality  tables  then  in  use 
and  which  were  based  upon  the  Northampton  table  of  Dr.  Price.  His 
work  revolutionized  the  actuarial  science  of  the  time.  In  later  years 
he  devoted  his  attention  to  natural  history. 


EUCLID  WITHOUT  AXIOMS.  287 

EUCLID  WITHOUT  AXIOMS. 

The  first  book  of  Euclid's  Elements.  With  alterations  and 
familiar  notes.  Being  an  attempt  to  get  rid  of  axioms  alto- 
gether; and  to  establish  the  theory  of  parallel  lines,  without 
the  introduction  of  any  principle  not  common  to  other  parts  of 
the  elements.  By  a  member  of  the  University  of  Cambridge. 
Third  edition.  In  usum  serenissimae  filiolse.  London,  1830. 

The  author  was  Lieut.  Col.  (now  General)  Perronet 
Thompson,1  the  author  of  the  "Catechism  on  the  Corn 
Laws."  I  reviewed  the  fourth  edition — which  had  the  name 
of  "Geometry  without  Axioms,"  1833 — in  the  quarterly 
Journal  of  Education  for  January,  1834.  Col.  Thompson, 
who  then  was  a  contributor  to — if  not  editor  of —  the  West- 
minster Review,  replied  in  an  article  the  authorship  of  which 
could  not  be  mistaken. 

Some  more  attempts  upon  the  problem,  by  the  same 
author,  will  be  found  in  the  sequel.  They  are  all  of  acute 
and  legitimate  speculation;  but  they  do  not  conquer  the 
difficulty  in  the  manner  demanded  by  the  conditions  of  the 
problem.  The  paradox  of  parallels  does  not  contribute 
much  to  my  pages:  its  cases  are  to  be  found  for  the  most 
part  in  geometrical  systems,  or  in  notes  to  them.  Most  of 
them  consist  in  the  proposal  of  additional  postulates ;  some 
are  attempts  to  do  without  any  new  postulate.  Gen.  Perronet 
Thompson,  whose  paradoxes  are  always  constructed  on 
much  study  of  previous  writers,  has  collected  in  the  work 
above  named,  a  budget  of  attempts,  the  heads  of  which 
are  in  the  Penny  and  English  Cyclopedias,  at  "Parallels." 
He  has  given  thirty  instances,  selected  from  what  he  had 
found.2 

1  See  note  2,  page  252.    He  also  wrote  the  Theory  of  Parallels. 
The  proof  of  Euclid's  axiom  looked  for  in  the  properties  of  the 
equiangular  spiral    (London,   1840),  which  went  through   four  edi- 
tions, and  the  Theory  of  Parallels.     The  proof  that  the  three  angles 
of  a  triangle  are  equal  to  two  right  angles  looked  for  in  the  inflation 
of  the  sphere  (London,  1853),  of  which  there  were  three  editions. 

2  For  the  latest  summary,  see  W.   B.   Frankland,   Theories  of 
Parallelism,  an  historical  critique,  Cambridge,  1910. 


288  A  BUDGET  OF  PARADOXES. 

Lagrange,3  in  one  of  the  later  years  of  his  life,  imag- 
ined that  he  had  overcome  the  difficulty.  He  went  so  far 
as  to  write  a  paper,  which  he  took  with  him  to  the  Insti- 
tute, and  began  to  read  it.  But  in  the  first  paragraph  some- 
thing struck  him  which  he  had  not  observed:  he  muttered 
//  faut  que  j'y  songe  encore*  and  put  the  paper  in  his 
pocket. 


THE  LUNAR  CAUSTIC  JOKE. 

The  following  paragraph  appeared  in  the  Morning  Post, 
May  4,  1831 : 

"We  understand  that  although,  owing  to  circumstances 
with  which  the  public  are  not  concerned,  Mr.  Goulburn1 
declined  becoming  a  candidate  for  University  honors,  that 
his  scientific  attainments  are  far  from  inconsiderable.  He 
is  well  known  to  be  the  author  of  an  essay  in  the  Philosoph- 
ical Transactions  on  the  accurate  rectification  of  a  circular 
arc,  and  of  an  investigation  of  the  equation  of  a  lunar 
caustic — a  problem  likely  to  become  of  great  use  in  nautical 
astronomy." 

'Joseph  Louis  Lagrange  (1736-1813),  author  of  the  Mecanique 
analytique  (1788),  Theorie  des  fonctions  analytiques  (1797),  Traite 
de  la  resolution  des  equations  numeriques  de  tous  degres  (1798), 
Leqons  sur  le  calcul  des  fonctions  (1806),  and  many  memoirs.  Al- 
though born  in  Turin  and  spending  twenty  of  his  best  years  in  Ger- 
many, he  is  commonly  looked  upon  as  the  great  leader  of  French 
mathematicians.  The  last  twenty-seven  years  of  his  life  were  spent  in 
Paris,  and  his  remarkable  productivity  continued  to  the  time  of  his 
death.  His  genius  in  the  theory  of  numbers  was  probably  never  ex- 
celled except  by  Fermat  He  received  very  high  honors  at  the  hands 
of  Napoleon  and  was  on  the  first  staff  of  the  Ecole  polytechnique 
(1797). 

4  "I  shall  have  to  think  it  over  again." 

1  Henry  Goulburn  (1784-1856^  held  various  government  posts. 
He  was  under-secretary  for  war  and  the  colonies  (1813),  commis- 
sioner to  negotiate  peace  with  America  (1814),  chief  secretary  to 
the  Lord  Lieutenant  of  Ireland  (1821),  and  several  times  Chancellor 
of  the  Exchequer.  On  the  occasion  mentioned  by  De  Morgan  he 
was  standing  for  parliament,  and  was  successful. 


THE  LUNAR  CAUSTIC  JOKE.  289 

This  hoax — which  would  probably  have  succeeded  with 
any  journal — was  palmed  upon  the  Morning  Post,  which 
supported  Mr.  Goulburn,  by  some  Cambridge  wags  who  sup- 
ported Mr.  Lubbock,  the  other  candidate  for  the  University 
of  Cambridge.  Putting  on  the  usual  concealment,  I  may 
say  that  I  always  suspected  Dr-nkw-t-r  B-th-n-2  of  having 
a  share  in  the  matter.  The  skill  of  the  hoax  lies  in  avoiding 
the  words  "quadrature  of  the  circle,"  which  all  know,  and 
speaking  of  "the  accurate  rectification  of  a  circular  arc," 
which  all  do  not  know  for  its  synonyme.  The  Morning 
Post  next  day  gave  a  reproof  to  hoaxers  in  general,  without 
referring  to  any  particular  case.  It  must  be  added,  that 
although  there  are  caustics  in  mathematics,  there  is  no 
lunar  caustic. 

So  far  as  Mr.  Goulburn  was  concerned,  the  above  was 
poetic  justice.  He  was  the  minister  who,  in  old  time,  told 
a  deputation  from  the  Astronomical  Society  that  the  Gov- 
ernment "did  not  care  twopence  for  all  the  science  in  the 
country."  There  may  be  some  still  alive  who  remember 
this:  I  heard  it  from  more  than  one  of  those  who  were 
present,  and  are  now  gone.  Matters  are  much  changed. 
I  was  thirty  years  in  office  at  the  Astronomical  Society ; 
and,  to  my  certain  knowledge,  every  Government  of  that 
period,  Whig  and  Tory,  showed  itself  ready  to  help  with 
influence  when  wanted,  and  with  money  whenever  there 
was  an  answer  for  the  House  of  Commons.  The  following 
correction  subsequently  appeared.  Referring  to  the  hoax 
about  Mr.  Goulburn,  Messrs.  C.  H.  and  Thompson  Cooper8 
have  corrected  an  error,  by  stating  that  the  election  which 
gave  rise  to  the  hoax  was  that  in  which  Messrs.  Goulburn 

2  On  Drinkwater  Bethtme  see  note  8,  page  99. 

"Charles  Henry  Cooper  (1808-1866)  was  a  biographer  and  an- 
tiquary. He  was  town  clerk  of  Cambridge  (1849-1866)  and  wrote 
the  Annals  of  Cambridge  (1842-1853).  His  Memorials  of  Cam- 
bridge (1874)  appeared  after  his  death.  Thompson  Cooper  was  his 
son,  and  the  two  collaborated  in  the  Athenae  Cantabrigiewis  (1858). 


290  A  BUDGET  OF  PARADOXES. 

and  Yates  Peel4  defeated  Lord  Palmerston5  and  Mr.  Caven- 
dish.6 They  add  that  Mr.  Gunning,  the  well-known  Es- 
quire Bedell  of  the  University,  attributed  the  hoax  to  the 
late  Rev.  R.  Sheepshanks,  to  whom,  they  state,  are  also 
attributed  certain  clever  fictitious  biographies — of  public 
men,  as  I  understand  it — which  were  palmed  upon  the  edi- 
tor of  the  Cambridge  Chronicle,  who  never  suspected  their 
genuineness  to  the  day  of  his  death.  Being  in  most  confi- 
dential intercourse  with  Mr.  Sheepshanks,7  both  at  the  time 
and  all  the  rest  of  his  life  (twenty-five  years),  and  never 
heard  him  allude  to  any  such  things — which  were  not  in 
his  line,  though  he  had  satirical  power  of  quite  another 

*  William  Yates  Peel  (1789-1858)  was  a  brother  of  Sir  Robert 
Peel,  he  whose  name  degenerated  into  the  familiar  title  of  the 
London  "Bobby"  or  "Peeler."  Yates  Peel  was  a  member  of  parliament 
almost  continuously  from  1817  to  1852.  He  represented  Cambridge 
at  Westminster  from  1831  to  1835. 

5  Henry  John  Temple,  third  Viscount  of  Palmerston  (1784-1865), 
was  member  for  Cambridge  in  1811,  1818,  1820,  1826  (defeating 
Goulburn),  and  1830.  He  failed  of  reelection  in  1831  because  of  his 
advocacy  of  reform.  This  must  have  been  the  time  when  Goulburn 
defeated  him.  He  was  Foreign  Secretary  (1827)  and  Secretary  of 
State  for  Foreign  Affairs  (1830-1841,  and  1846-1851).  It  is  said  of 
him  that  he  "created  Belgium,  saved  Portugal  and  Spain  from  ab- 
solutism, rescued  Turkey  from  Russia  and  the  highway  to  India  from 
France."  He  was  Prime  Minister  almost  continuously  from  1855  to 
1865,  a  period  covering  the  Indian  Mutiny  and  the  American  Civil 
War. 

'William  Cavendish,  seventh  Duke  of  Devonshire  (1808-1891). 
He  was  member  for  Cambridge  from  1829  to  1831,  but  was  defeated 
in  1831  because  he  had  favored  parliamentary  reform.  He  became 
Earl  of  Burlington  in  1834,  and  Duke  of  Devonshire  in  1858.  He  was 
much  interested  in  the  promotion  of  railroads  and  in  the  iron  and 
steel  industries 

'Richard  Sheepshanks  (1794-1855)  was  a  brother  of  John  Sheep- 
shanks the  benefactor  of  art.  (See  note  3,  p.  147.)  He  was  a  fellow  of 
Trinity  College,  Cambridge,  a  fellow  of  the  Royal  Society  and  secretary 
of  the  Astronomical  Society.  Babbage  (See  note  12,  p.  207)  suspected 
him  of  advising  against  the  government  support  of  his  calculating 
machine  and  attacked  him  severely  in  his  Exposition  of  1851,  in  the 
chapter  on  The  Intrigues  of  Science.  Babbage  also  showed  that 
Sheepshanks  got  an  astronomical  instrument  of  French  make  through 
the  custom  house  by  having  Troughton's  (See note 2,  page  152)  name 
engraved  on  it.  Sheepshanks  admitted  this  second  charge,  but  wrote 
a  Letter  in  Reply  to  the  Calumnies  of  Mr.  Babbage,  which  was  pub- 
lished in  1854.  He  had  a.  highly  controversial  nature. 


ON    M.   DEMONVILLE.  291 

kind — I  feel  satisfied  he  had  nothing  to  do  with  them.  I 
may  add  that  others,  his  nearest  friends,  and  also  members 
of  his  family,  never  heard  him  allude  to  these  hoaxes  as 
their  author,  and  disbelieve  his  authorship  as  much  as  I 
do  myself.  I  say  this  not  as  imputing  any  blame  to  the 
true  author,  such  hoaxes  being  fair  election  jokes  in  all 
time,  but  merely  to  put  the  saddle  off  the  wrong  horse,  and 
to  give  one  more  instance  of  the  insecurity  of  imputed 
authorship.  Had  Mr.  Sheepshanks  ever  told  me  that  he 
had  perpetrated  the  hoax,  I  should  have  had  no  hesitation 
in  giving  it  to  him.  I  consider  all  clever  election  squibs, 
free  from  bitterness  and  personal  imputation,  as  giving  the 
multitude  good  channels  for  the  vent  of  feelings  which 
but  for  them  would  certainly  find  bad  ones. 

[But  I  now  suspect  that  Mr.  Babbage8  had  some  hand 
in  the  hoax.  He  gives  it  in  his  "Passages,  &c."  and  is  evi- 
dently writing  from  memory,  for  he  gives  the  wrong  year. 
But  he  has  given  the  paragraph,  though  not  accurately, 
yet  with  such  a  recollection  of  the  points  as  brings  sus- 
picion of  the  authorship  upon  him,  perhaps  in  conjunction 
with  D.  B.9  Both  were  on  Cavendish's  committee.  Mr. 
Babbage  adds,  that  "late  one  evening  a  cab  drove  up  in  hot 
haste  to  the  office  of  the  Morning  Post,  delivered  .the  copy 
as  coming  from  Mr.  Goulburn's  committee,  and  at  the  same 
time  ordered  fifty  extra  copies  of  the  Post  to  be  sent  next 
morning  to  their  committee-room.  I  think  the  man — the 
only  one  I  ever  heard  of — who  knew  all  about  the  cab  and 
the  extra  copies  must  have  known  more.] 

ON  M.  DEMONVILLE. 

Demonville.  —  A  Frenchman's  Christian  name  is  his 
own  secret,  unless  there  be  two  of  the  surname.  M.  Demon- 
ville is  a  very  good  instance  of  the  difference  between  a 

8  See  note  12,  page  207.    The  work  referred  to  is  Passages  from 
the  Life  of  a  Philosopher,  London,  1864. 

9  Drinkwater  Bethune.    See  note  8,  page  99. 


292  A  BUDGET  OF  PARADOXES. 

French  and  English  discoverer.  In  England  there  is  a 
public  to  listen  to  discoveries  in  mathematical  subjects  made 
without  mathematics :  a  public  which  will  hear,  and  wonder, 
and  think  it  possible  that  the  pretensions  of  the  discoverer 
have  some  foundation.  The  unnoticed  man  may  possibly 
be  right:  and  the  old  country-town  reputation  which  I  once 
heard  of,  attaching  to  a  man  who  "had  written  a  book 
about  the  signs  of  the  zodiac  which  all  the  philosophers  in 
London  could  not  answer,"  is  fame  as  far  as  it  goes.  Ac- 
cordingly, we  have  plenty  of  discoverers  who,  even  in  as- 
tronomy, pronounce  the  learned  in  error  because  of  mathe- 
matics. In  France,  beyond  the  sphere  of  influence  of  the 
Academy  of  Sciences,  there  is  no  one  to  cast  a  thought 
upon  the  matter :  all  who  take  the  least  interest  repose  entire 
faith  in  the  Institute.  Hence  the  French  discoverer  turns 
all  his  thoughts  to  the  Institute,  and  looks  for  his  only 
hearing  in  that  quarter.  He  therefore  throws  no  slur  upon 
the  means  of  knowledge,  but  would  say,  with  M.  Demon- 
ville:  "A  1'egard  de  M.  Poisson,1  j'envie  loyalement  la 
millieme  partie  de  ses  connaissances  mathematiques,  pour 
prouver  mon  systeme  d'astronomie  aux  plus  incredules."2 
This  system  is  that  the  only  bodies  of  our  system  are  the 
earth,  the  sun,  and  the  moon ;  all  the  others  being  illusions, 
caused  by  reflection  of  the  sun  and  moon  from  the  ice  of 
the  polar  regions.  In  mathematics,  addition  and  subtraction 
are  for  men;  multiplication  and  division,  which  are  in 
truth  creation  and  destruction,  are  prerogatives  of  deity. 
But  nothing  multiplied  by  nothing  is  one.  M.  Demonville 
obtained  an  introduction  to  William  the  Fourth,  who  de- 
sired the  opinion  of  the  Royal  Society  upon  his  system :  the 

1  Simeon-Denis  Poisson  (1781-1840)  was  professor  of  calculus 
and  mechanics  at  the  Ecole  polytechnique.  He  was  made  a  baron  by 
Napoleon,  and  was  raised  to  the  peerage  in  1837.  His  chief  works 
are  the  Traite  de  mecanique  (1811)  and  the  Traite  mathematique  de 
la  chaleur  (1835). 

*"As  to  M.  Poisson,  I  really  wish  I  had  a  thousandth  part  of 
his  mathematical  knowledge  that  I  might  prove  my  system  to  the 
incredulous." 


PARSE Y^S  PARADOX.  293 

answer  was  very  brief.  The  King  was  quite  right ;  so  was 
the  Society:  the  fault  lay  with  those  who  advised  His 
Majesty  on  a  matter  they  knew  nothing  about.  The  writ- 
ings of  M.  Demonville  in  my  possession  are  as  follows.3 
The  dates — which  were  only  on  covers  torn  off  in  binding 
—were  about  1831-34: 

Petit  cours  d 'astronomic*  followed  by  Sur  I'unite  mathe- 
matique. — Principes  de  la  physique  de  la  creation  implicite- 
ment  admis  dans  la  notice  sur  le  tonnerre  par  M.  Arago. — 
Question  de  longitude  sur  mer.* — Vrai  systeme  du  mondeQ 
(pp.  92).  Same  title,  four  pages,  small  type.  Same  title, 
four  pages,  addressed  to  the  British  Association.  Same  title, 
four  pages,  addressed  to  M.  Mathieu.  Same  title,  four 
pages,  on  M.  Bouvard's  report. — Resume  de  la  physique 
de  la  creation;  troisieme  par  tie  du  vrai  systeme  du  monde.1 

PARSEY'S    PARADOX. 

The  quadrature  of  the  circle  discovered,  by  Arthur  Parsey,1 
author  of  the  'art  of  miniature  painting/  Submitted  to  the 
consideration  of  the  Royal  Society,  on  whose  protection  the 
author  humbly  throws  himself.  London,  1832,  8vo. 

Mr.  Parsey  was  an  artist,  who  also  made  himself  con- 
spicuous by  a  new  view  of  perspective.  Seeing  that  the 
sides  of  a  tower,  for  instance,  would  appear  to  meet  in  a 
point  if  the  tower  were  high  enough,  he  thought  that  these 
sides  ought  to  slope  to  one  another  in  the  picture.  On  this 

This  list  includes  most  of  the  works  of  Antoine-Louis-Guenard 
Demonville.  There  was  also  the  Nouveau  systeme  du  monde. ...  et 
hypotheses  conformes  aux  experiences  sur  les  vents,  sur  la  lumiere 
et  sur  le  Huide  electro-magnetique,  Paris,  1830. 

'Paris,  1835. 
"Paris,  1833. 

c  The  second  part  appeared  in  1837.  There  were  also  editions  in 
1850  and  1852,  and  one  edition  appeared  without  date. 

1  Paris,  1842. 

1  Parsey  also  wrote  The  Art  of  Miniature  Painting  on  Ivory 
(1831),  Perspective  Rectified  (1836),  and  The  Science  of  Vision 
(1840),  the  third  being  a  revision  of  the  second. 


294  A  BUDGET  OF  PARADOXES. 

theory  he  published  a  small  work,  of  which  I  have  not  the 
title,  with  a  Grecian  temple  in  the  frontispiece,  stated,  if 
I  remember  rightly,  to  be  the  first  picture  which  had  ever 
been  drawn  in  true  perspective.  Of  course  the  building 
looked  very  Egyptian,  with  its  sloping  sides.  The  answer 
to  his  notion  is  easy  enough.  What  is  called  the  picture 
is  not  the  picture  from  which  the  mind  takes  its  perception ; 
that  picture  is  on  the  retina.  The  intermediate  picture,  as  it 
may  be  called — the  human  artist's  work — is  itself  seen  per- 
spectively.  If  the  tower  were  so  high  that  the  sides,  though 
parallel,  appeared  to  meet  in  a  point,  the  picture  must  also 
be  so  high  that  the  picture-sides,  though  parallel,  would  ap- 
pear to  meet  in  a  point.  I  never  saw  this  answer  given, 
though  I  have  seen  and  heard  the  remarks  of  artists  on  Mr. 
Parsey's  work.  I  am  inclined  to  think  it  is  commonly  sup- 
posed that  the  artist's  picture  is  the  representation  which 
comes  before  the  mind :  this  is  not  true ;  we  might  as  well 
say  the  same  of  the  object  itself.  In  July  1831,  reading  an 
article  on  squaring  the  circle,  and  finding  that  there  was  a 
difficulty,  he  set  to  work,  got  a  light  denied  to  all  mathe- 
maticians in — some  would  say  through — a  crack,  and  ad- 
vertised in  the  Times  that  he  had  done  the  trick.  He  then 
prepared  this  work,  in  which,  those  who  read  it  will  see 

how,  he  showed  that  3.14159 should  be  3.0625.     He 

might  have  found  out  his  error  by  stepping  a  draughtsman's 
circle  with  the  compasses. 

Perspective  has  not  had  many  paradoxes.  The  only 
other  one  I  remember  is  that  of  a  writer  on  perspective, 
whose  name  I  forget,  and  whose  four  pages  I  do  not  possess. 
He  circulated  remarks  on  my  notes  on  the  subject,  pub- 
lished in  the  Athen&um,  in  which  he  denies  that  the  stereo- 
graphic  projection  is  a  case  of  perspective,  the  reason 
being  that  the  whole  hemisphere  makes  too  large  a  picture 
for  the  eye  conveniently  to  grasp  at  once.  That  is  to  say, 
it  is  no  perspective  because  there  is  too  much  perspective. 


ON  A  COUPLE  OF  GEOMETRIES.  295 


ON  A  COUPLE  OF  GEOMETRIES. 

Principles  of  Geometry  familiarly  illustrated.     By  the  Rev.  W. 

Ritchie,1  LL.D.    London,  1833,  I2mo. 
A  new  Exposition  of  the  system  of  Euclid's  Elements,  being  an 

attempt  to  establish  his  work  on  a  different  basis.    By  Alfred 

Day,2  LL.D.    London,  1839,  I2mo. 

These  works  belong  to  a  small  class  which  have  the 
peculiarity  of  insisting  that  in  the  general  propositions  of 
geometry  a  proposition  gives  its  converse:  that  "Every  B 
is  A"  follows  from  "Every  A  is  B."  Dr.  Ritchie  says,  "If  it 
be  proved  that  the  equality  of  two  of  the  angles  of  a  triangle 
depends  essentially  upon  the  equality  of  the  opposite  sides, 
it  follows  that  the  equality  of  opposite  sides  depends  essen- 
tially on  the  equality  of  the  angles."  Dr.  Day  puts  it  as 
follows : 

"That  the  converses  of  Euclid,  so  called,  where  no  par- 
ticular limitation  is  specified  or  implied  in  the  leading  prop- 
osition, more  than  in  the  converse,  must  be  necessarily  true ; 
for  as  by  the  nature  of  the  reasoning  the  leading  proposition 
must  be  universally  true,  should  the  converse  be  not  so,  it 
cannot  be  so  universally,  but  has  at  least  all  the  exceptions 
conveyed  in  the  leading  proposition,  and  the  case  is  there- 
fore unadapted  to  geometric  reasoning;  or,  what  is  the 
same  thing,  by  the  very  nature  of  geometric  reasoning,  the 
particular  exceptions  to  the  extended  converse  must  be 
identical  with  some  one  or  other  of  the  cases  under  the 
universal  affirmative  proposition  with  which  we  set  forth, 
which  is  absurd." 

1  William  Ritchie  (1790-1837)  was  a  physicist  who  had  studied 
at  Paris  under  Biot  and  Gay-Lussac.    He  contributed  several  papers 
on  electricity,  heat,  and  elasticity,  and  was  looked  upon  as  a  good 
experimenter.     Besides  the  geometry  he  wrote  the  Principles  of  the 
Differential  and  Integral  Calculus  (1836). 

2  Alfred  Day  (1810-1849)  was  a  man  who  was  about  fifty  years 
ahead  of  his  time  in  his  attempt  to  get  at  the  logical  foundations  of 
geometry.     It  is  true  that  he  laid  himself  open  to  criticism,  but  his 
work  was  by  no  means  bad.    He  also  wrote  A  Treatise  on  Harmony 
(1849,  second  edition  1885),  The  Rotation  of  the  Pendulum  (1851), 
and  several  works  on  Greek  and  Latin  Grammar. 


296  A  BUDGET  OF  PARADOXES. 

On  this  I  cannot  help  transferring  to  my  reader  the 
words  of  the  Pacha  when  he  orders  the  bastinado, — May 
it  do  you  good !  A  rational  study  of  logic  is  much  wanted 
to  show  many  mathematicians,  of  all  degrees  of  proficiency, 
that  there  is  nothing  in  the  reasoning  of  mathematics  which 
differs  from  other  reasoning.  Dr.  Day  repeated  his  argu- 
ment in  A  Treatise  on  Proportion,  London,  1840,  8vo.  Dr. 
Ritchie  was  a  very  clear-headed  man.  He  published,  in 
1818,  a  work  on  arithmetic,  with  rational  explanations.  , 
This  was  too  early  for  such  an  improvement,  and  nearly 
the  whole  of  his  excellent  work  was  sold  as  waste  paper. 
His  elementary  introduction  to  the  Differential  Calculus 
was  drawn  up  while  he  was  learning  the  subject  late  in 
life.  Books  of  this  sort  are  often  very  effective  on  points 
of  difficulty. 

NEWTON  AGAIN  OBLITERATED. 

Letter  to  the  Royal  Astronomical  Society  in  refutation  of  Mis- 
taken Notions  held  in  common,  by  the  Society,  and  by  all 
the  Newtonian  philosophers.  By  Capt.  Forman,1  R.N.  Shep- 
ton-Mallet,  1833,  8vo. 

Capt.  Forman  wrote  against  the  whole  system  of  gravi- 
tation, and  got  no  notice.  He  then  wrote  to  Lord  Brougham, 
Sir  J.  Herschel,  and  others  I  suppose,  desiring  them  to 
procure  notice  of  his  books  in  the  reviews:  this  not  being 
acceded  to,  he  wrote  (in  print)  to  Lord  John  Russell2  to 
complain  of  their  "dishonest"  conduct.  He  then  sent  a 
manuscript  letter  to  the  Astronomical  Society,  inviting  con- 
troversy: he  was  answered  by  a  recommendation  to  study 

1  Walter  Forman  wrote  a  number  of  controversial  tracts.  His 
first  seems  to  have  been  A  plan  for  improving  the  Revenue  without 
adding  to  the  burdens  of  the  people,  a  letter  to  Canning  in  1813.  He 
also  wrote  A  New  Theory  of  the  Tides  (1822).  His  Letter  to  Lord 
John  Russell,  on  Lord  Brougham's  most  extraordinary  conduct;  and 
another  to  Sir  J.  Herschel,  on  the  application  of  Kepler's  third  law 
appeared  in  1832. 

8  Lord  John  Russell  (1792-1878)'  first  Earl  Russell,  was  one  of 
the  strongest  supporters  of  the  reform  measures  of  the  early  Vic- 
torian period.  He  became  prime  minister  in  1847,  and  again  in  1865. 


NEWTON  AGAIN  OBLITERATED.  297 

dynamics.  The  above  pamphlet  was  the  consequence,  in 
which,  calling  the  Council  of  the  Society  "craven  dunghill 
cocks,"  he  set  them  right  about  their  doctrines.  From  all 
I  can  learn,  the  life  of  a  worthy  man  and  a  creditable  officer 
was  completely  embittered  by  his  want  of  power  to  see  that 
no  person  is  bound  in  reason  to  enter  into  controversy 
with  every  one  who  chooses  to  invite  him  to  the  field.  This 
mistake  is  not  peculiar  to  philosophers,  whether  of  ortho- 
doxy or  paradoxy;  a  majority  of  educated  persons  imply, 
by  their  modes  of  proceeding,  that  no  one  has  a  right  to 
any  opinion  which  he  is  not  prepared  to  defend  against  all 
comers. 

David  and  Goliath,  or  an  attempt  to  prove  that  the  Newtonian 
system  of  Astronomy  is  directly  opposed  to  the  Scriptures. 
By  Wm.  Lauder,1  Sen.,  Mere,  Wilts.  Mere,  1833,  I2mo. 

Newton  is  Goliath;  Mr.  Lauder  is  David.  David  took 
five  pebbles ;  Mr.  Lauder  takes  five  arguments.  He  expects 
opposition ;  for  Paul  and  Jesus  both  met  with  it. 

Mr.  Lauder,  in  his  comparison,  seems  to  put  himself  in 
the  divinely  inspired  class.  This  would  not  be  a  fair  in- 
ference in  every  case ;  but  we  know  not  what  to  think  when 
we  remember  that  a  tolerable  number  of  cyclometers  have 
attributed  their  knowledge  to  direct  revelation.  The  works 
of  this  class  are  very  scarce ;  I  can  only  mention  one  or  two 
from  Montucla.2  Alphonso  Cano  de  Molina,3  in  the  last 
century,  upset  all  Euclid,  and  squared  the  circle  upon  the 
ruins ;  he  found  a  follower,  Janson,  who  translated  him  from 
Spanish  into  Latin.  He  declared  that  he  believed  in  Euclid, 
until  God,  who  humbles  the  proud,  taught  him  better.  One 
Paul  Yvon,  called  from  his  estate  de  la  Leu,  a  merchant  at 
Rochelle,  supported  by  his  book-keeper,  M.  Pujos,  and  a 

1  Lauder  seems  never  to  have  written  anything  else. 

2  See  note  i,  page  40. 

3  The  names  of  Alphonso  Cano  de  Molina,  Yvon,  and  Robert 
Sara  have  no  standing  in  the  history  of  the  subject  beyond  what 
would  be  inferred  from  De  Morgan's  remark. 


298  A  BUDGET  OF  PARADOXES. 

Scotchman,  John  Dunbar,  solved  the  problem  by  divine 
grace,  in  a  manner  which  was  to  convert  all  Jews,  Infidels, 
etc.  There  seem  to  have  been  editions  of  his  work  in  1619 
and  1628,  and  a  controversial  "Examen"  in  1630,  by  Robert 
Sara.  There  was  a  noted  discussion,  in  which  Mydorge,4 
Hardy,5  and  others  took  part  against  de  la  Leu.  I  cannot 
find  this  name  either  in  Lipenius6  or  Murhard,7  and  I 
should  not  have  known  the  dates  if  it  had  not  been  for 
one  of  the  keenest  bibliographers  of  any  time,  my  friend 
Prince  Balthasar  Boncompagni,8  who  is  trying  to  find  copies 
of  the  works,  and  has  managed  to  find  copies  of  the  titles. 
In  1750,  Henry  Sullamar,  an  Englishman,  squared  the  circle 
by  the  number  of  the  Beast:  he  published  a  pamphlet  every 
two  or  three  years ;  but  I  cannot  find  any  mention  of  him  in 
English  works.9  In  France,  in  1753,  M.  de  Causans,10  of 
the  Guards,  cut  a  circular  piece  of  turf,  squared  it,  and 

4  Claude  Mydorge  (1585-1647),  an  intimate  friend  of  Descartes, 
was  a  dilletante  in  mathematics  who  read  much  but  accomplished 
little.  His  Recreations  mathematiques  is  his  chief  work.  Boncom- 
pagni published  the  "Problemes  de  Mydorge"  in  his  Bulletino. 

6  Claude  Hardy  was  born  towards  the  end  of  the  i6th  century 
and  died  at  Paris  in  1678.  In  1625  he  edited  the  Data  Euclidis, 
publishing  the  Greek  text  with  a  Latin  translation.  He  was  a  friend 
of  Mydorge  and  Descartes,  but  an  opponent  of  Fermat. 

6  That  is,  in  the  Bibliotheca  Realis  of  Martin  Lipen,  or  Lipenius 
(1630-1692),   which   appeared   in   six   folio  volumes,   at   Frankfort, 
1675-1685. 

7  See  note  4,  page  43. 

8  Baldassare  Boncompagni  (1821-1894)  was  the  greatest  general 
collector  of  mathematical  works  that  ever  lived,  possibly  excepting 
Libri.     His  magnificent   library  was   dispersed  at   his   death.     His 
Bulletino    (1868-1887)    is  one  of  the  greatest  source  books  on  the 
history  of  mathematics  that  we  have.     He  also  edited  the  works  of 
Leonardo  of  Pisa. 

9  He  seems  to  have  attracted  no  attention  since  De  Morgan's 
search,  for  he  is  not  mentioned  in  recent  bibliographies. 

10  Joseph-Louis  Vincens  de  Mouleon  de  Causans  was  born  about 
the  beginning  of  the   i8th  century.     He  was  a  Knight  of  Malta, 
colonel  in  the  infantry,  prince  of  Conti,  and  governor  of  the  princi- 
pality of  Orange.    His  works  on  geometry  are  the  Prospectus  apolo- 
getique  pour  la  quadrature  du  cercle  (1753),  and  La  vraie  geometrie 
transcendante  (1754). 


SIR  JOHN    HERSCHEL.  299 

deduced  original  sin  and  the  Trinity.  He  found  out  that 
the  circle  was  equal  to  the  square  in  which  it  is  inscribed; 
and  he  offered  a  reward  for  detection  of  any  error,  and 
actually  deposited  10,000  francs  as  earnest  of  300,000.  But 
the  courts  would  not  allow  any  one  to  recover. 

SIR  JOHN  HERSCHEL. 

1834.  In  this  year  Sir  John  Herschel1  set  up  his  tel- 
escope at  Feldhausen,  Cape  of  Good  Hope.  He  did  much 
for  astronomy,  but  not  much  for  the  Budget  of  Paradoxes. 
He  gives  me,  however,  the  following  story.  He  showed  a 
resident  a  remarkable  blood-red  star,  and  some  little  time 
after  he  heard  of  a  sermon  preached  in  those  parts  in  which 
it  was  asserted  that  the  statements  of  the  Bible  must  be 
true,  for  that  Sir  J.  H.  had  seen  in  his  telescope  "the  very 
place  where  wicked  people  go." 

But  red  is  not  always  the  color.  Sir  J.  Herschel  has  in 
his  possession  a  letter  written  to  his  father,  Sir  W.  H.,2 
dated  April  3,  1787,  and  signed  "Eliza  Cumyns,"  begging 
to  know  if  any  of  the  stars  be  indigo  in  color,  "because,  if 
there  be,  I  think  it  may  be  deemed  a  strong  conjectural  illus- 
tration of  the  expression,  so  often  used  by  our  Saviour  in 
the  Holy  Gospels,  that  'the  disobedient  shall  be  cast  into 
outer  darkness' ;  for  as  the  Almighty  Being  can  doubtless 
confine  any  of  his  creatures,  whether  corporeal  or  spiritual, 
to  what  part  of  his  creation  He  pleases,  if  therefore  any  of 
the  stars  (which  are  beyond  all  doubt  so  many  suns  to 
other  systems)  be  of  so  dark  a  color  as  that  above  men- 
tioned, they  may  be  calculated  to  give  the  most  insufferable 
heat  to  those  dolorous  systems  dependent  upon  them  (and 
to  reprobate  spirits  placed  there) ,  without  one  ray  of  cheer- 
ful light ;  and  may  therefore  be  the  scenes  of  future  punish- 
ments." This  letter  is  addressed  to  Dr.  Heirschel  at  Slow. 
Some  have  placed  the  infernal  regions  inside  the  earth,  but 

1  See  note  5,  page  80. 

2  See  note  6,  page  81. 


300  A  BUDGET  OF  PARADOXES. 

others  have  filled  this  internal  cavity — for  cavity  they  will 
have — with  refulgent  light,  and  made  it  the  abode  of  the 
blessed.  It  is  difficult  to  build  without  knowing  the  num- 
ber to  be  provided  for.  A  friend  of  mine  heard  the  follow- 
ing (part)  dialogue  between  two  strong  Scotch  Calvinists: 
"Noo!  hoo  manny  d'ye  thank  there  are  of  the  alact  on  the 
arth  at  this  moment? — Eh!  mabbee  a  doozen — Hoot!  mon! 
nae  so  mony  as  thot !" 

THE  NAUTICAL  ALMANAC. 

1834.  From  1769  to  1834  the  Nautical  Almanac  was 
published  on  a  plan  which  gradually  fell  behind  what  was 
wanted.  In  1834  the  new  series  began,  under  a  new  super- 
intendent (Lieut.  W.  S.  Stratford).1  There  had  been  a  long 
scientific  controversy,  which  would  not  be  generally  in- 
telligible. To  set  some  of  the  points  before  the  reader,  I 
reprint  a  cutting  which  I  have  by  me.  It  is  from  the 
Nautical  Magazine,  but  I  did  hear  that  some  had  an  idea 
that  it  was  in  the  Nautical  Almanac  itself.  It  certainly  was 
not,  and  I  feel  satisfied  the  Lords  of  the  Admiralty  would 
not  have  permitted  the  insertion ;  they  are  never  in  advance 
of  their  age.  The  Almanac  for  1834  was  published  in  July 
1833. 

THE  NEW  NAUTICAL  ALMANAC— Extract  from  the  Trimum 
Mobile/  and  'Milky  Way  Gazette/  Communicated  by  AERO- 
LITH. 

A  meeting  of  the  different  bodies  composing  the  Solar 
System  was  this  day  held  at  the  Dragon's  Tail,  for  the 
purpose  of  taking  into  consideration  the  alterations  and 
amendments  introduced  into  the  New  Nautical  Almanac. 
The  honorable  luminaries  had  been  individually  summoned 

1  Lieut.  William  Samuel  Stratford  (1791-1853),  was  in  active 
service  during  the  Napoleonic  wars  but  retired  from  the  army  in 
1815.  He  was  first  secretary  of  the  Astronomical  Society  (1820) 
and  became  superintendent  of  the  Nautical  Almanac  in  1831.  With 
Francis  Baily  he  compiled  a  star  catalogue,  and  wrote  on  Halley's 
(1835-1836)  and  Encke's  (1838)  comets. 


THE  NAUTICAL  ALMANACK.  301 

by  fast-sailing  comets,  and  there  was  a  remarkably  full  at- 
tendance. Among  the  visitors  we  observed  several  nebulae, 
and  almost  all  the  stars  whose  proper  motions  would  admit 
of  their  being  present. 

The  SUN  was  unanimously  called  to  the  focus.  The 
small  planets  took  the  oaths,  and  their  places,  after  a  short 
discussion,  in  which  it  was  decided  that  the  places  should 
be  those  of  the  Almanac  itself,  with  leave  reserved  to  move 
for  corrections. 

Petitions  were  presented  from  a  and  8  Ursae  Minoris, 
complaining  of  being  put  on  daily  duty,  and  praying  for 
an  increase  of  salary. — Laid  on  the  plane  of  the  ecliptic. 

The  trustees  of  the  eccentricity2  and  inclination  funds 
reported  a  balance  of  .00001  in  the  former,  and  a  deficit 
of  0".009  in  the  latter.  This  announcement  caused  con- 
siderable surprise,  and  a  committee  was  moved  for,  to  as- 
certain which  of  the  bodies  had  more  or  less  than  his  share. 
After  some  discussion,  in  which  the  small  planets  offered 
to  consent  to  a  reduction,  if  necessary,  the  motion  was 
carried. 

The  FOCAL  BODY  then  rose  to  address  the  meeting.  He 
remarked  that  the  subject  on  which  they  were  assembled 
was  one  of  great  importance  to  the  routes  and  revolutions 
of  the  heavenly  bodies.  For  himself,  though  a  private 
arrangement  between  two  of  his  honourable  neighbours 
(here  he  looked  hard  at  the  Earth  and  Venus)  had  pre- 
vented his  hitherto  paying  that  close  attention  to  the  pre- 
dictions of  the  Nautical  Almanac  which  he  declared  he  al- 
ways had  wished  to  do;  yet  he  felt  consoled  by  knowing 
that  the  conductors  of  that  work  had  every  disposition  to 
take  his  peculiar  circumstances  into  consideration.  He  de- 
clared that  he  had  never  passed  the  wires  of  a  transit  with- 
out deeply  feeling  his  inability  to  adapt  himself  to  the 
present  state  of  his  theory;  a  feeling  which  he  was  afraid 
had  sometimes  caused  a  slight  tremor  in  his  limb.  Before 

*  See  Sir  J.  Herschel's  Astronomy,  p.  369. — A.  De  M. 


302  A  BUDGET  OF  PARADOXES. 

he  sat  down,  he  expressed  a  hope  that  honourable  lumi- 
naries would  refrain  as  much  as  possible  from  eclipsing 
each  other,  or  causing  mutual  peturbations.  Indeed,  he 
should  be  very  sorry  to  see  any  interruption  of  the  harmony 
of  the  spheres.  (Applause.) 

The  several  articles  of  the  New  Nautical  Almanac  were 
then  read  over  without  any  comment ;  only  we  observed 
that  Saturn  shook  his  ring  at  every  novelty,  and  Jupiter 
gave  his  belt  a  hitch,  and  winked  at  the  satellites  at  page 
21  of  each  month. 

The  MOON  rose  to  propose  a  resolution.  No  one,  he 
said,  would  be  surprised  at  his  bringing  this  matter  forward 
in  the  way  he  did,  when  it  was  considered  in  how  complete 
and  satisfactory  a  manner  his  motions  were  now  repre- 
sented. He  must  own  he  had  trembled  when  the  Lords  of 
the  Admiralty  dissolved  the  Board  of  Longitude,  but  his 
tranquillity  was  more  than  reestablished  by  the  adoption 
of  the  new  system.  He  did  not  know  but  that  any  little 
assistance  he  could  give  in  Nautical  Astronomy  was  be- 
coming of  less  and  less  value  every  day,  owing  to  the 
improvement  of  chronometers.  But  there  was  one  thing, 
of  which  nothing  could  deprive  him — he  meant  the  regu- 
lation of  the  tides.  And,  perhaps,  when  his  attention  was 
not  occupied  by  more  than  the  latter,  he  should  be  able  to 
introduce  a  little  more  regularity  into  the  phenomena.  ( Here 
the  honourable  luminary  gave  a  sort  of  modest  libration, 
which  convulsed  the  meeting  with  laughter.)  They  might 
laugh  at  his  natural  infirmity  if  they  pleased,  but  he  could 
assure  them  it  arose  only  from  the  necessity  he  was  under, 
when  young,  of  watching  the  motions  of  his  worthy  primary. 
He  then  moved  a  resolution  highly  laudatory  of  the  altera- 
tions which  appeared  in  the  New  Nautical  Almanac. 

The  EARTH  rose,  to  second  the  motion.  His  honour- 
able satellite  had  fully  expressed  his  opinions  on  the  sub- 
ject. He  joined  his  honourable  friend  in  the  focus  in  wish- 
ing to  pay  every  attention  to  the  Nautical  Almanac,  but, 


THE  NAUTICAL  ALMANACK.  303 

really,  when  so  important  an  alteration  had  taken  place  in 
his  magnetic  pole3  (hear)  and  there  might,  for  aught  he 
knew,  be  a  successful  attempt  to  reach  his  pole  of  rotation, 
he  thought  he  could  not  answer  for  the  preservation  of  the 
precession  in  its  present  state.  (Here  the  hon.  luminary, 
scratching  his  side,  exclaimed,  as  he  sat  down,  "More  steam- 
boats— confound  'em!") 

An  honourable  satellite  (whose  name  we  could  not  learn) 
proposed  that  the  resolution  should  be  immediately  des- 
patched, corrected  for  refraction,  when  he  was  called  to 
order  by  the  Focal  Body,  who  reminded  him  that  it  was 
contrary  to  the  moving  orders  of  the  system  to  take  cog- 
nizance of  what  passed  inside  the  atmosphere  of  any  planet. 

SATURN  and  PALLAS  rose  together.  (Cries  of  "New 
member!"  and  the  former  gave  way.)  The  latter,  in  a 
long  and  eloquent  speech,  praised  the  liberality  with  which 
he  and  his  colleagues  had  at  length  been  relieved  from 
astronomical  disqualifications.  He  thought  that  it  was 
contrary  to  the  spirit  of  the  laws  of  gravitation  to  exclude 
any  planet  from  office  on  account  of  the  eccentricity  or  in- 
clination of  his  orbit.  Honourable  luminaries  need  not  talk 
of  the  want  of  convergency  of  his  series.  What  had  they 
to  do  with  any  private  arrangements  between  him  and  the 
general  equations  of  the  system?  (Murmurs  from  the 
opposition.)  So  long  as  he  obeyed  the  laws  of  motion,  to 
which  he  had  that  day  taken  a  solemn  oath,  he  would  ask, 
were  old  planets,  which  were  now  so  well  known  that 
nobody  trusted  them,  to.  ... 

The  FOCAL  BODY  said  he  was  sorry  to  break  the  continu- 
ity of  the  proceedings,  but  he  thought  that  remarks  upon 
character,  with  a  negative  sign,  would  introduce  differ- 

3  Captain  Ross  had  just  stuck  a  bit  of  brass  there.— A.  De  M. 

Sir  James  Clark  Ross  (1800-1862)  was  a  rear  admiral  in  the 
British  navy  and  an  arctic  and  antarctic  explorer  of  prominence. 
De  Morgan's  reference  is  to  Ross's  discovery  of  the  magnetic  pole 
on  June  i,  1831.  In  1838  he  was  employed  by  the  Admiralty  on  a 
magnetic  survey  of  the  United  Kingdom.  He  was  awarded  the 
gold  medal  of  the  geographical  societies  of  London  and  Paris  in  1842. 


304  A  BUDGET  OF  PARADOXES. 

ences  of  too  high  an  order.  The  honourable  luminary  must 
eliminate  the  expression  which  he  had  brought  out,  in 
finite  terms,  and  use  smaller  inequalities  in  future.  (Hear, 
hear.) 

PALLAS  explained,  that  he  was  far  from  meaning  to 
reflect  upon  the  orbital  character  of  any  planet  present. 
He  only  meant  to  protest  against  being  judged  by  any  laws 
but  those  of  gravitation,  and  the  differential  calculus:  he 
thought  it  most  unjust  that  astronomers  should  prevent  the 
small  planets  from  being  observed,  and  then  reproach  them 
with  the  imperfections  of  the  tables,  which  were  the  result 
of  their  own  narrow-minded  policy.  (Cheers.) 

SATURN  thought  that,  as  an  old  planet,  he  had  not  been 
treated  with  due  respect.  (Hear,  from  his  satellites.)  He 
had  long  foretold  the  wreck  of  the  system  from  the  friends 
of  innovation.  Why,  he  might  ask,  were  his  satellites  to 
be  excluded,  when  small  planets,  trumpery  comets,  which 
could  not  keep  their  mean  distances  (cries  of  oh!  oh!), 
double  stars,  with  graphical  approximations,  and  such  ob- 
scure riff-raff  of  the  heavens  (great  uproar)  found  room 
enough.  So  help  him  Arithmetic,  nothing  could  come  of 
it,  but  a  stoppage  of  all  revolution.  His  hon.  friend  in  the 
focus  might  smile,  for  he  would  be  a  gainer  by  such  an 
event;  but  as  for  him  (Saturn),  he  had  something  to  lose, 
and  hon.  luminaries  well  knew  that,  whatever  they  might 
think  under  an  atmosphere,  above  it  continual  revolution 
was  the  only  way  of  preventing  perpetual  anarchy.  As  to 
the  hon.  luminary  who  had  risen  before  him,  he  was  not 
surprised  at  his  remarks,  for  he  had  invariably  observed  that 
he  and  his  colleagues  allowed  themselves  too  much  latitude. 
The  stability  of  the  system  required  that  they  should  be 
brought  down,  and  he,  for  one,  would  exert  all  his  powers 
of  attraction  to  accomplish  that  end.  If  other  bodies  would 
cordially  unite  with  him,  particularly  his  noble  friend  next 
him,  than  whom  no  luminary  possessed  greater  weight — 

JUPITER  rose  to  order*     He  conceived  his  noble  friend 


THE  NAUTICAL  ALMANACK.  305 

had  no  right  to  allude  to  him  in  that  manner,  and  was  much 
surprised  at  his  proposal,  considering  the  matters  which 
remained  in  dispute  between  them.  In  the  present  state 
of  affairs,  he  would  take  care  never  to  be  in  conjunction 
with  his  hon.  neighbour  one  moment  longer  than  he  could 
help.  (Cries  of  "Order,  order,  no  long  inequalities,"  during 
which  he  sat  down.) 

SATURN  proceeded  to  say,  that  he  did  not  know  till  then 
that  a  planet  with  a  ring  could  affront  one  who  had  only  a 
belt,  by  proposing  mutual  co-operation.  He  would  now 
come  to  the  subject  under  discussion.  He  should  think 
meanly  of  his  hon.  colleagues  if  they  consented  to  bestow 
their  approbation  upon  a  mere  astronomical  production. 
Had  they  forgotten  that  they  once  were  considered  the 
arbiters  of  fate,  and  the  prognosticators  of  man's  destiny? 
What  had  lost  them  that  proud  position?  Was  it  not  the 
infernal  march  of  intellect,  which,  after  having  turned  the 
earth  topsy-turvy,  was  now  disturbing  the  very  universe? 
For  himself  (others  might  do  as  they  pleased),  but  he 
stuck  to  the  venerable  Partridge,4  and  the  Stationers'  Com- 
pany, and  trusted  that  they  would  outlive  infidels  and  an- 
archists, whether  of  Astronomical  or  Diffusion  of  Knowl- 
edge Societies.  (Cries  of  oh!  oh!) 

MARS  said  he  had  been  told,  for  he  must  confess  he  had 
not  seen  the  work,  that  the  places  of  the  planets  were  given 
for  Sundays.  This,  he  must  be  allowed  to  say,  was  an  in- 
decorum he  had  not  expected ;  and  he  was  convinced  the 
Lords  of  the  Admiralty  had  given  no  orders  to  that  effect. 
He  hoped  this  point  would  be  considered  in  the  measure 
which  had  been  introduced  in  another  place,  and  that  some 

4  John  Partridge  (1644-1715),  the  well-known  astrologer  and 
almanac  maker.  Although  bound  to  a  shoemaker  in  his  early  boy- 
hood, he  had  acquired  enough  Latin  at  the  age  of  eighteen  to  read 
the  works  of  the  astrologers.  He  then  mastered  Greek  and  Hebrew 
and  studied  medicine.  In  1680  he  began  the  publication  of  his  al- 
manac, the  Merlinus  Liberatus,  a  book  that  acquired  literary  celeb- 
rity largely  through  the  witty  comments  upon  it  by  such  writers  as 
Swift  and  Steele. 


306  A  BUDGET  OF  PARADOXES. 

one  would  move  that  the  prohibition  against  travelling  on 
Sundays  extend  to  the  heavenly  as  well  as  earthly  bodies. 

Several  of  the  stars  here  declared,  that  they  had  been 
much  annoyed  by  being  observed  on  Sunday  evenings, 
during  the  hours  of  divine  service. 

The  room  was  then  cleared  for  a  division,  but  we  are 
unable  to  state  what  took  place.  Several  comets-at-arms 
were  sent  for,  and  we  heard  rumors  of  a  personal  collision 
having  taken  place  between  two  luminaries  in  opposition. 
We  were  afterwards  told  that  the  resolution  was  carried 
by  a  majority,  and  the  luminaries  elongated  at  2  h.  15  m. 
33,41  s.  sidereal  time. 

*  *  *  It  is  reported,  but  we  hope  without  foundation,  that 
Saturn,  and  several  other  discontented  planets,  have  ac- 
cepted an  invitation  from  Sirius  to  join  his  system,  on  the 
most  liberal  appointments.  We  believe  the  report  to  have 
originated  in  nothing  more  than  the  discovery  of  the  annual 
parallax  of  Sirius  from  the  orbit  of  Saturn;  but  we  may 
safely  assure  our  readers  that  no  steps  have  as  yet  been 
taken  to  open  any  communication. 

We  are  also  happy  to  state,  that  there  is  no  truth  in  the 
rumor  of  the  laws  of  gravitation  being  about  to  be  re- 
pealed. We  have  traced  this  report,  and  find  it  originated 
with  a  gentleman  living  near  Bath  (Captain  Forman, R.N),5 
whose  name  we  forbear  to  mention. 

A  great  excitement  has  been  observed  among  the  neb- 
ulae, visible  to  the  earth's  southern  hemisphere,  particularly 
among  those  which  have  not  yet  been  discovered  from 
thence.  We  are  at  a  loss  to  conjecture  the  cause,  but  we 
shall  not  fail  to  report  to  our  readers  the  news  of  any  move- 
ment which  may  take  place.  (Sir  J.  Herschel's  visit.  He 
could  just  see  this  before  he  went  out.) 

6  See  note  i  on  page  296. 


WOODLEY'S  DIVINE  SYSTEM.  307 


WOODLEY'S  DIVINE  SYSTEM. 

A  Treatise  on  the  Divine  System  of  the  Universe,  by  Captain 
Woodley,  R.N.,1  and  as  demonstrated  by  his  Universal  Time- 
piece, and  universal  method  of  determining  a  ship's  longitude 
by  the  apparent  true  place  of  the  moon;  with  an  introduction 
refuting  the  solar  system  of  Copernicus,  the  Newtonian  phi- 
losophy, and  mathematics.  1834.2  8vo. 

Description  of  the  Universal  Time-piece.    (4pp.  I2mo.) 

I  think  this  divine  system  was  published  several  years 
before,  and  was  republished  with  an  introduction  in  1834.3 
Capt.  Woodley  was  very  sure  that  the  earth  does  not  move : 
he  pointed  out  to  me,  in  a  conversation  I  had  with  him, 
something — I  forget  what — in  the  motion  of  the  Great 
Bear,  visible  to  any  eye,  which  could  not  possibly  be  if  the 
earth  moved.  He  was  exceedingly  ignorant,  as  the  follow- 
ing quotation  from  his  account  of  the  usual  opinion  will 
show: 

"The  north  pole  of  the  Earth's  axis  deserts,  they  say, 
the  north  star  or  pole  of  the  Heavens,  at  the  rate  of  1°  in 
71%  years. .  .The  fact  is,  nothing  can  be  more  certain  than 
that  the  Stars  have  not  changed  their  latitudes  or  declina- 
tions one  degree  in  the  last  71%  years." 

This  is  a  strong  specimen  of  a  class  of  men  by  whom 
all  accessible  persons  who  have  made  any  name  in  science 
are  hunted.  It  is  a  pity  that  they  cannot  be  admitted  into 
scientific  societies,  and  allowed  fairly  to  state  their  cases, 
and  stand  quiet  cross-examination,  being  kept  in  their  an- 
swers very  close  to  the  questions,  and  the  answers  written 
down.  I  am  perfectly  satisfied  that  if  one  meeting  in  the 
year  were  devoted  to  the  hearing  of  those  who  chose  to 
come  forward  on  such  conditions,  much  good  would  be 
done.  But  I  strongly  suspect  few  would  come  forward 

1  William  Woodley  also  published  several  almanacs  (1838,  1839, 
1840)  after  his  rejection  by  the  Astronomical  Society  in  1834. 

2  It  appeared  at  London. 

8  The  first  edition  appeared  in  1830,  also  at  London. 


308  A  BUDGET  OF  PARADOXES. 

at  first,  and  none  in  a  little  while:  and  I  have  had  some 
experience  of  the  method  I  recommend,  privately  tried. 
Capt.  Woodley  was  proposed,  a  little  after  1834,  as  a  Fellow 
of  the  Astronomical  Society;  and,  not  caring  whether  he 
moved  the  sun  or  the  earth,  or  both — I  could  not  have 
stood  neither — I  signed  the  proposal.  I  always  had  a  sneak- 
ing kindness  for  paradoxers,  such  a  one,  perhaps,  as  Petit 
Andre  had  for  his  lambs,  as  he  called  them.  There  was  so 
little  feeling  against  his  opinions,  that  he  only  failed  by  a 
fraction  of  a  ball.  Had  I  myself  voted,  he  would  have 
been  elected ;  but  being  engaged  in  conversation,  and  not 
having  heard  the  slightest  objection  to  him,  I  did  not  think 
it  worth  while  to  cross  the  room  for  the  purpose.  I  re- 
gretted this  at  the  time,  but  had  I  known  how  ignorant  he 
was  I  should  not  have  supported  him.  Probably  those  who 
voted  against  him  knew  more  of  his  book  than  I  did. 

I  remember  no  other  instance  of  exclusion  from  a  scien- 
tific society  on  the  ground  of  opinion,  even  if  this  be  one ; 
of  which  it  may  be  that  ignorance  had  more  to  do  with  it 
than  paradoxy.  Mr.  Frend,4  a  strong  anti-Newtonian,  was 
a  Fellow  of  the  Astronomical  Society,  and  for  some  years 
in  the  Council.  Lieut.  Kerigan5  was  elected  to  the  Royal 
Society  at  a  time  when  his  proposers  must  have  known  that 
his  immediate  object  was  to  put  F.R.S.  on  the  title-page  of 
a  work  against  the  tides.  To  give  all  I  know,  I  may  add 
that  the  editor  of  some  very  ignorant  bombast  about  the 
"forehead  of  the  solar  sky,"  who  did  not  know  the  differ- 
ence between  Bailly*  and  Baity,7  received  hints  which  in- 
duced him  to  withdraw  his  proposal  for  election  into  the 
Astronomical  Society.  But  this  was  an  act  of  kindness ; 

4  See  note  i,  page  196. 

6  Thomas  Kerigan  wrote  The  Young  Navigator's  Guide  to  the 
siderial  and  planetary  parts  of  Nautical  Astronomy  (London,  1821, 
second  edition  1828),  a  work  on  eclipses  (London,  1844),  and  the 
work  on  tides  (London,  1847)  to  which  De  Morgan  refers. 

8  Jean  Sylvain  Bailly,  who  was  guillotined.    See  note  i,  page  166. 
T  See  note  2,  page  309. 


ON  JOHN  FLAMSTEED.  309 

for  if  he  had  seen  Mr.  Baily  in  the  chair,  with  his  head  on, 
he  might  have  been  political  historian  enough  to  faint  away. 

De  la  formation  des  Corps.  Par  Paul  Laurent.8  Nancy,  1834, 
8vo. 

Atoms,  and  ether,  and  ovules  or  eggs,  which  are  planets, 
and  their  eggs,  which  are  satellites.  These  speculators  can 
create  worlds,  in  which  they  cannot  be  refuted ;  but  none  of 
them  dare  attack  the  problem  of  a  grain  of  wheat,  and  its 
passage  from  a  seed  to  a  plant,  bearing  scores  of  seeds  like 
what  it  was  itself. 

ON  JOHN  FLAMSTEED. 

An  account  of  the  Rev.  John  Flamsteed,1  the  First  Astronomer- 
Royal.  ...  By  Francis  Baily,2  Esq.  London,  1835,  4to-  Supple- 
ment, London,  1837,  4to. 

My  friend  Francis  Baily  was  a  paradoxer:  he  brought 
forward  things  counter  to  universal  opinion.  That  Newton 
was  impeccable  in  every  point  was  the  national  creed;  and 
failings  of  temper  and  conduct  would  have  been  utterly 
disbelieved,  if  the  paradox  had  not  come  supported  by  very 
unusual  evidence.  Anybody  who  impeached  Newton  on 
existing  evidence  might  as  well  have  been  squaring  the 
circle,  for  any  attention  he  would  have  got.  About  this 
book  I  will  tell  a  story.  It  was  published  by  the  Admiralty 
for  distribution ;  and  the  distribution  was  entrusted  to  Mr. 
Baily.  On  the  eve  of  its  appearance,  rumors  of  its  extra- 
ordinary revelations  got  about,  and  persons  of  influence 
applied  to  the  Admiralty  for  copies.  The  Lords  were  in  a 
difficulty :  but  on  looking  at  the  list  they  saw  names,  as  they 

8  Laurent  seems  to  have  had  faint  glimpses  of  the  modern  theory 
of  matter.  He  is,  however,  unknown. 

1  See  note  4,  page  87. 

2  Francis   Baily    (1774-1844)    was   a  London   stockbroker.     His 
interest  in  science  in  general  and  in  astronomy  in  particular  led  to 
his  membership  in  the  Royal  Society  and  to  his  presidency  of  the 
Astronomical  Society.     He  wrote  on  interest  and  annuities   (1808), 
but  his  chief  works  were  on  astronomy. 


310  A  BUDGET  OF  PARADOXES. 

thought,  which  were  so  obscure  that  they  had  a  right  to 
assume  Mr.  Baily  had  included  persons  who  had  no  claim 
to  such  a  compliment  as  presentation  from  the  Admiralty. 
The  Secretary  requested  Mr.  Baily  to  call  upon  him.  "Mr. 
Baily,  my  Lords  are  inclined  to  think  that  some  of  the  per- 
sons in  this  list  are  perhaps  not  of  that  note  which  would 
justify  their  Lordships  in  presenting  this  work." — "To  whom 
does  your  observation  apply,  Mr.  Secretary  ?" — "Well,  now, 
let  us  examine  the  list;  let  me  see;  now, — now, — now, — 
come! — here's  Gauss3 — who's  Gauss'?" — "Gauss,  Mr.  Sec- 
retary, is  the  oldest  mathematician  now  living,  and  is  gen- 
erally thought  to  be  the  greatest."— "O-o-oh !  Well,  Mr. 
Baily,  we  will  see  about  it,  and  I  will  write  you  a  letter." 
The  letter  expressed  their  Lordships'  perfect  satisfaction 
with  the  list. 

There  was  a  controversy  about  the  revelations  made  in 
this  work ;  but  as  the  eccentric  anomalies  took  no  part  in  it, 
there  is  nothing  for  my  purpose.  The  following  valentine 
from  Mrs.  Flamsteed.4  which  I  found  among  Baily's  papers, 
illustrates  some  of  the  points: 

"3  Astronomers'  Row,  Paradise :  February  14,  1836. 

"Dear  Sir, — I  suppose  you  hardly  expected  to  receive  a 
letter  from  me,  dated  from  this  place;  but  the  truth  is,  a 
gentleman  from  our  street  was  appointed  guardian  angel  to 
the  American  Treaty,  in  which  there  is  some  astronomical 
question  about  boundaries.  He  has  got  leave  to  go  back  to 
fetch  some  instruments  which  he  left  behind,  and  I  take  this 
opportunity  of  making  your  acquaintance.  That  America 
has  become  a  wonderful  place  since  I  was  down  among 
you;  you  have  no  idea  how  grand  the  fire  at  New  York 

'If  the  story  is  correctly  told  Baily  must  have  enjoyed  his 
statement  that  Gauss  was  "the  oldest  mathematician  now  living." 
As  a  matter  of  fact  he  was  then  only  58,  three  years  the  junior  of 
Baily  himself.  Gauss  was  born  in  1777  and  died  in  1855,  and  Baily 
was  quite  right  in  saying  that  he  was  "generally  thought  to  be  the 
greatest"  mathematician  then  living. 

'Margaret  Cooke,  who  married  Flamsteed  in  1692. 


ON  JOHN  FLAMSTEED.  311 

looked  up  here.  Poor  dear  Mr.  Flamsteed  does  not  know 
I  am  writing  a  letter  to  a  gentleman  on  Valentine's  day ;  he 
is  walked  out  with  Sir  Isaac  Newton  (they  are  pretty  good 
friends  now,  though  they  do  squabble  a  little  sometimes) 
and  Sir  William  Herschel,  to  see  a  new  nebula.  Sir  Isaac 
says  he  can't  make  out  at  all  how  it  is  managed ;  and  I  am 
sure  I  cannot  help  him.  I  never  bothered  my  head  about 
those  things  down  below,  and  I  don't  intend  to  begin  here. 
"I  have  just  received  the  news  of  your  having  written 
a  book  about  my  poor  dear  man.  It's  a  chance  that  I  heard 
it  at  all ;  for  the  truth  is,  the  scientific  gentlemen  are  some- 
how or  other  become  so  wicked,  and  go  so  little  to  church, 
that  very  few  of  them  are  considered  fit  company  for  this 
place.  If  it  had  not  been  for  Dr.  Brinkley,5  who  came  here 
of  course,  I  should  not  have  heard  about  it.  He  seems  a 
nice  man,  but  is  not  yet  used  to  our  ways.  As  to  Mr.  Hal- 
ley,6  he  is  of  course  not  here;  which  is  lucky  for  him,  for 
Mr.  Flamsteed  swore  the  moment  he  caught  him  in  a  place 
where  there  are  no  magistrates,  he  would  make  a  sacrifice 
of  him  to  heavenly  truth.  It  was  very  generous  in  Mr.  F. 
not  appearing  against  Sir  Isaac  when  he  came  up,  for  I  am 
told  that  if  he  had,  Sir  Isaac  would  not  have  been  allowed 
to  come  in  at  all.  I  should  have  been  sorry  for  that,  for  he 
is  a  companionable  man  enough,  only  holds  his  head  rather 
higher  than  he  should  do.  I  met  him  the  other  day  walking 
with  Mr.  Whiston,7  and  disputing  about  the  deluge.  'Well, 
Mrs.  Flamsteed/  says  he,  'does  old  Poke-the-Stars  under- 
stand gravitation  yet?'  Now  you  must  know  that  is  rather 
a  sore  point  with  poor  dear  Mr.  Flamsteed.  He  says  that 
Sir  Isaac  is  as  crochetty  about  the  moon  as  ever ;  and  as  to 

E  John  Brinkley  (1763-1835),  senior  wrangler,  first  Smith's  prize- 
man (1788),  Andrews  professor  of  astronomy  at  Dublin,  first  As- 
tronomer Royal  for  Ireland  (1792),  F.R.S.  (1803),  Copley  medallist, 
president  of  the  Royal  Society  and  Bishop  of  Cloyne.  His  Elements 
of  Astronomy  appeared  in  1808. 

"  See  note  7,  page  124. 
7  See  note  3,  page  133. 


312  A  BUDGET  OF  PARADOXES. 

what  some  people  say  about  what  has  been  done  since  his 
time,  he  says  he  should  like  to  see  somebody  who  knows 
something  about  it  of  himself.  For  it  is  very  singular  that 
none  of  the  people  who  have  carried  on  Sir  Isaac's  notions 
have  been  allowed  to  come  here. 

"I  hope  you  have  not  forgotten  to  tell  how  badly  Sir 
Isaac  used  Mr.  Flamsteed  about  that  book.  I  have  never 
quite  forgiven  him;  as  for  Mr.  Flamsteed,  he  says  that  as 
long  as  he  does  not  come  for  observations,  he  does  not  care 
about  it,  and  that  he  will  never  trust  him  with  any  papers 
again  as  long  as  he  lives.  I  shall  never  forget  what  a  rage 
he  came  home  in  when  Sir  Isaac  had  called  him  a  puppy. 
He  struck  the  stairs  all  the  way  up  with  his  crutch,  and  said 
puppy  at  every  step,  and  all  the  evening,  as  soon  as  ever 
a  star  appeared  in  the  telescope,  he  called  it  puppy.  I  could 
not  think  what  was  the  matter,  and  when  I  asked,  he  only 
called  me  puppy. 

"I  shall  be  very  glad  to  see  you  if  you  come  our  way. 
Pray  keep  up  some  appearances,  and  go  to  church  a  little. 
St.  Peter  is  always  uncommonly  civil  to  astronomers,  and  in- 
deed to  all  scientific  persons,  and  never  bothers  them  with 
many  questions.  If  they  can  make  anything  out  of  the  case, 
he  is  sure  to  let  them  in.  Indeed,  he  says,  it  is  perfectly 
out  of  the  question  expecting  a  mathematician  to  be  as  re- 
ligious as  an  apostle,  but  that  it  is  as  much  as  his  place  is 
worth  to  let  in  the  greater  number  of  those  who  come.  So 
try  if  you  cannot  manage  it,  for  I  am  very  curious  to  know 
whether  you  found  all  the  letters.  I  remain,  dear  sir,  your 
faithful  servant, 

"MARGARET  FLAMSTEED. 

Francis  Baily,  Esq. 

"P.S.  Mr.  Flamsteed  has  come  in,  and  says  he  left  Sir 
Isaac  riding  cockhorse  upon  the  nebula,  and  poring  over  it 
as  if  it  were  a  book.  He  has  brought  in  his  old  acquaint- 
ance Ozanam,8  who  says  that  it  was  always  his  maxim  on 

8  See  note  7,  page  161. 


ON  STEVIN.  313 

earth,  that  'il  appartient  aux  docteurs  de  Sorbonne  de  dis- 
puter,  au  Pape  de  prononcer,  et  au  mathematicien  d'aller  en 
Paradis  en  ligne  perpendiculaire.'  "9 

ON  STEVIN. 

The  Secretary  of  the  Admiralty  was  completely  extin- 
guished. I  can  recall  but  two  instances  of  demolition  as 
complete,  though  no  doubt  there  are  many  others.  The  first 
is  in 

Simon  Stevin1  and  M.  Dumortier.     Nieuport,  1845,  I2mo. 

M.  Dumortier  was  a  member  of  the  Academy  of  Brus- 
sels :  there  was  a  discussion,  I  believe,  about  a  national 
Pantheon  for  Belgium.  The  name  of  Stevinus  suggested 
itself  as  naturally  as  that  of  Newton  to  an  Englishman; 
probably  no  Belgian  is  better  known  to  foreigners  as  illus- 
trious in  science.  Stevinus  is  great  in  the  Mecanique  Ana- 
lytique  of  Lagrange  f  Stevinus  is  great  in  the  Tristram 
Shandy  of  Sterne.  M.  Dumortier,  who  believed  that  not 
one  Belgian  in  a  thousand  knew  Stevinus,  and  who  confesses 
with  ironical  shame  that  he  was  not  the  odd  man,  protested 
against  placing  the  statue  of  an  obscure  man  in  the  Pan- 
theon, to  give  foreigners  the  notion  that  Belgium  could 
show  nothing  greater.  The  work  above  named  is  a  slash- 
ing retort:  any  one  who  knows  the  history  of  science  ever 
so  little  may  imagine  what  a  dressing  was  given,  by  mere 
extract  from  foreign  writers.  The  tract  is  a  letter  signed 
J.  du  Fan,  but  this  is  a  pseudonym  of  Mr.  Van  de  Weyer.3 
The  Academician  says  Stevinus  was  a  man  who  was  not 

"Tt  becomes  the  doctors  of  the  Sorbonne  to  dispute,  the  Pope 
to  decree,  and  the  mathematician  to  go  to  Paradise  on  a  perpen- 
dicular line." 

1  See  note  10,  page  83. 
8  See  note  3,  page  288. 

s  Sylvain  van  de  Weyer,  who  was  born  at  Louvain  in  1802.  He 
was  a  jurist  and  statesman,  holding  the  portfolio  for  foreign  affairs 
(1831-1833),  and  being  at  one  time  ambassador  to  England. 


314  A  BUDGET  OF  PARADOXES. 

without  merit  for  the  time  at  which  he  lived:  Sir!  is  the 
answer,  he  was  as  much  before  his  own  time  as  you  are 
behind  yours.  How  came  a  man  who  had  never  heard  of 
Stevinus  to  be  a  member  of  the  Brussels  Academy  ? 

The  second  story  was  told  me  by  Mr.  Crabb  Robinson,4 
who  was  long  connected  with  the  Times,  and  intimately  ac- 
quainted with  Mr.  W***.5  When  W***  was  an  under- 
graduate at  Cambridge,  taking  a  walk,  he  came  to  a  stile, 
on  which  sat  a  bumpkin  who  did  not  make  way  for  him: 
the  gown  in  that  day  looked  down  on  the  town.  "Why  do 
you  not  make  way  for  a  gentleman?" — "Eh?" — "Yes,  why 
do  you  not  move?  You  deserve  a  good  hiding,  and  you 
shall  get  it  if  you  don't  take  care!"  The  bumpkin  raised 
his  muscular  figure  on  its  feet,  patted  his  menacer  on  the 
head,  and  said,  very  quietly, — "Young  man!  I'm  Cribb."6 
W***  seized  the  great  pugilist's  hand,  and  shook  it  warmly, 
got  him  to  his  own  rooms  in  college,  collected  some  friends, 
and  had  a  symposium  which  lasted  until  the  large  end  of 
the  small  hours. 

FINLEYSON  AS  A  PARADOXER. 

God's  Creation  of  the  Universe  as  it  is,  in  support  of  the  Scrip- 
tures.   By  Mr.  Finleyson.1    Sixth  Edition,  1835,  8vo. 

4  Henry    Crabb    Robinson    (1775-1867),    correspondent    of    the 
Times  at  Altona  and  in  the   Peninsula,  and  later   foreign  editor. 
He  was  one  of  the  founders  of  the  Athenaeum  Club  and  of  University 
College,  London.     He  seems  to  have  known  pretty  much  every  one 
of  his  day,  and  his  posthumous  Diary  attracted  attention  when  it 
appeared. 

5  Was  this  Whewell,  who  was  at  Trinity  from  1812  to  1816  and 
became  a  fellow  in  1817? 

8  Tom  Cribb  (1781-1848)  the  champion  pugilist.  He  had  worked 
as  a  coal  porter  and  hence  received  his  nickname,  the  Black  Dia- 
mond. 

1John  Finleyson,  or  Finlayson,  was  born  in  Scotland  in  1770 
and  died  in  London  in  1854.  He  published  a  number  of  pamphlets 
that  made  a  pretense  to  being  scientific.  Among  his  striking  phrases 
and  sentences  are  the  statements  that  the  stars  were  made  "to  amuse 
us  in  observing  them";  that  the  earth  is  "not  shaped  like  a  garden 
turnip  as  the  Newtonians  make  it,"  and  that  the  stars  are  "oval- 
shaped  immense  masses  of  frozen  water."  The  first  edition  of  the 
work  here  mentioned  appeared  at  London  in  1830. 


FINLEYSON   AS  A  PARADOXER.  315 

This  writer,  by  his  own  account,  succeeded  in  delivering 
the  famous  Lieut.  Richard  Brothers2  from  the  lunatic 
asylum,  and  tending  him,  not  as  a  keeper  but  as  a  disciple, 
till  he  died.  Brothers  was,  by  his  own  account,  the  nephew 
of  the  Almighty,  and  Finleyson  ought  to  have  been  the 
nephew  of  Brothers.  For  Napoleon  came  to  him  in  a 
vision,  with  a  broken  sword  and  an  arrow  in  his  side,  be- 
seeching help:  Finleyson  pulled  out  the  arrow,  but  refused 
to  give  a  new  sword;  whereby  poor  Napoleon,  though  he 
got  off  with  life,  lost  the  battle  of  Waterloo.  This  story 
was  written  to  the  Duke  of  Wellington,  ending  with  "I 
pulled  out  the  arrow,  but  left  the  broken  sword.  Your 
Grace  can  supply  the  rest,  and  what  followed  is  amply  re- 
corded in  history."  The  book  contains  a  long  account  of 
applications  to  Government  to  do  three  things:  to  pay 
2,000/.  for  care  taken  of  Brothers,  to  pay  10,000/.  for  dis- 
covery of  the  longitude,  and  to  prohibit  the  teaching  of 
the  Newtonian  system,  which  makes  God  a  liar.  The  suc- 
cessive administrations  were  threatened  that  they  would 
have  to  turn  out  if  they  refused,  which,  it  is  remarked, 
came  to  pass  in  every  case.  I  have  heard  of  a  joke  of  Lord 
Macaulay,  that  the  House  of  Commons  must  be  the  Beast 
of  the  Revelations,  since  658  members,  with  the  officers 
necessary  for  the  action  of  the  House,  make  666.  Macaulay 
read  most  things,  and  the  greater  part  of  the  rest:  so  that 
he  might  be  suspected  of  having  appropriated  as  a  joke 
one  of  Finleyson's  serious  points — "I  wrote  Earl  Grey3 
upon  the  13th  of  July,  1831,  informing  him  that  his  Reform 

2  Richard  Brothers  (1757-1824)  was  a  native  of  Newfoundland. 
He  went  to  London  when  he  was  about  30,  and  a  little  later  set  forth 
his  claim  to  being  a  descendant  of  David,  prince  of  the  Hebrews, 
and  ruler  of  the  world.     He  was  confined  as  a  criminal  lunatic  in 
1795  but  was  released  in  1806. 

3  Charles  Grey  (1764-1845),  second  Earl  Grey,  Viscount  Howick, 
was  then  Prime  Minister.    The  Reform  Bill  was  introduced  and  de- 
feated in  1831.     The  following  year,  with  the  Royal  guarantees  to 
allow  him  to  create  peers,  he  finally  carried  the  bill  in  spite  of  "the 
number  of  the  beast." 


316  A  BUDGET  OF  PARADOXES. 

Bill  could  not  be  carried,  as  it  reduced  the  members  below 
the  present  amount  of  658,  which,  with  the  eight  principal 
clerks  or  officers  of  the  House,  make  the  number  666." 
But  a  witness  has  informed  me  that  Macaulay's  joke  was 
made  in  his  hearing  a  great  many  years  before  the  Reform 
Bill  was  proposed ;  in  fact,  when  both  were  students  at 
Cambridge.  Earl  Grey  was,  according  to  Finleyson,  a  des- 
cendant of  Uriah  the  Hittite.  For  a  specimen  of  Lieut. 
Brothers,  this  book  would  be  worth  picking  up.  Perhaps 
a  specimen  of  the  Lieutenant's  poetry  may  be  acceptable: 
Brothers  loquitur,  remember: 

"Jerusalem !  Jerusalem !  shall  be  built  again ! 

More  rich,  more  grand  then  ever; 
And  through  it  shall  Jordan  flow!(!) 

My  people's  favourite  river. 
There  I'll  erect  a  splendid  throne, 

And  build  on  the  wasted  place; 
To  fulfil  my  ancient  covenant 

To  King  David  and  his  race. 
******** 

"Euphrates'  stream  shall  flow  with  ships, 

And  also  my  wedded  Nile; 
And  on  my  coast  shall  cities  rise, 

Each  one  distant  but  a  mile. 
******* 

"My  friends  the  Russians  on  the  north 

With  Persees  and  Arabs  round, 
Do  show  the  limits  of  my  land, 

Here!  Here!  then  I  mark  the  ground." 

ON   THEOLOGICAL   PARADOXERS. 

Among  the  paradoxers  are  some  of  the  theologians  who 
in  their  own  organs  of  the  press  venture  to  criticise  science. 
These  may  hold  their  ground  when  they  confine  themselves 
to  the  geology  of  long  past  periods  and  to  general  cosmog- 
ony :  for  it  is  the  tug  of  Greek  against  Greek ;  and  both  sides 
deal  much  in  what  is  grand  when  called  hypothesis,  petty 
when  called  supposition.  And  very  often  they  are  not  con- 
spicuous when  they  venture  upon  things  within  knowledge ; 


ON  THEOLOGICAL  PARADOXERS. 


317 


wrong,  but  not  quite  wrong  enough  for  a  Budget  of  Para- 
doxes. One  case,  however,  is  destined  to  live,  as  an  in- 
stance of  a  school  which  finds  writers,  editors,  and  readers. 
The  double  stars  have  been  seen  from  the  seventeenth  cen- 
tury, and  diligently  observed  by  many  from  the  time  of  Wm. 
Herschel,  who  first  devoted  continuous  attention  to  them. 
The  year  1836  was  that  of  a  remarkable  triumph  of  astro- 
nomical prediction.  The  theory  of  gravitation  had  been 
applied  to  the  motion  of  binary  stars  about  each  other,  in 
elliptic  orbits,  and  in  that  year  the  two  stars  of  y  Virginis, 
as  had  been  predicted  should  happen  within  a  few  years  of 
that  time — for  years  are  small  quantities  in  such  long  revo- 
lutions— the  two  stars  came  to  their  nearest:  in  fact,  they 
appeared  to  be  one  as  much  with  the  telescope  as  without  it. 
This  remarkable  turning-point  of  the  history  of  a  long  and 
widely-known  branch  of  astronomy  was  followed  by  an 
article  in  the  Church  of  England  Quarterly  Review  for 
April  1837,  written  against  the  Useful  Knowledge  Society. 
The  notion  that  there  are  any  such  things  as  double  stars 
is  (p.  460)  implied  to  be  imposture  or  delusion,  as  in  the 
following  extract.  I  suspect  that  I  myself  am  the  Sidrophel, 
and  that  my  companion  to  the  maps  of  the  stars,  written  for 
the  Society  and  published  in  1836,  is  the  work  to  which  the 
writer  refers: 

"We  have  forgotten  the  name  of  that  Sidrophel  who 
lately  discovered  that  the  fixed  stars  were  not  single  stars, 
but  appear  in  the  heavens  like  soles  at  Billingsgate,  in  pairs ; 
while  a  second  astronomer,  under  the  influence  of  that  com- 
petition in  trade  which  the  political  economists  tell  us  is 
so  advantageous  to  the  public,  professes  to  show  us,  through 
his  superior  telescope,  that  the  apparently  single  stars  are 
really  three.  Before  such  wondrous  mandarins  of  science, 
how  continually  must  homunculi  like  ourselves  keep  in  the 
background,  lest  we  come  between  the  wind  and  their 
nobility." 

If  the  homunculus  who  wrote  this  be  still  above  ground, 


318  A  BUDGET  OF  PARADOXES. 

how  devoutly  must  he  hope  he  may  be  able  to  keep  in  the 
background  !  But  the  chief  blame  falls  on  the  editor.  The 
title  of  the  article  is: 

''The  new  school  of  superficial  pantology;  a  speech  in- 
tended to  be  delivered  before  a  defunct  Mechanics'  Insti- 
tute. By  Swallow  Swift,  late  M.P.  for  the  Borough  of 
Cockney-Cloud,  Witsbury  :  reprinted  Balloon  Island,  Bubble 
year,  month  Ventose.  Long  live  Charlatan!" 

As  a  rule,  orthodox  theologians  should  avoid  humor,  a 
weapon  which  all  history  shows  to  be  very  difficult  to  employ 
in  favor  of  establishment,  and  which,  nine  times  out  of  ten, 
leaves  its  wielder  fighting  on  the  side  of  heterodoxy.  Theo- 
logical argument,  when  not  enlivened  by  bigotry,  is  seldom 
worse  than  narcotic:  but  theological  fun,  when  not  covert 
heresy,  is  almost  always  sialagogue.  The  article  in  question 
is  a  craze,  which  no  editor  should  have  admitted,  except  after 
severe  inspection  by  qualified  persons.  The  author  of  this 
wit  committed  a  mistake  which  occurs  now  and  then  in  old 
satire,  the  confusion  between  himself  and  the  party  aimed 
at.  He  ought  to  be  reviewing  this  fictitious  book,  but  every 
now  and  then  the  article  becomes  the  book  itself;  not  by 
quotation,  but  by  the  writer  forgetting  that  he  is  not  Mr. 
Swallow  Swift,  but  his  reviewer.  In  fact  he  and  Mr.  S. 
Swift  had  each  had  a  dose  of  the  Devil's  Elixir.  A  novel 
so  called,  published  about  forty  years  ago,  proceeds  upon 
a  legend  of  this  kind.  If  two  parties  both  drink  of  the 
elixir,  their  identities  get  curiously  intermingled  ;  each  turns 
up  in  the  character  of  the  other  throughout  the  three  vol- 
umes, without  having  his  ideas  clear  as  to  whether  he  be 
himself  or  the  other.  There  is  a  similar  confusion  in  the 
answer  made  to  the  famous  E  pistole?  Obscurorum  Viro- 
it is  headed  Lamentationes  Obscurorum  Virorum.2 


1The  letters  of  obscure  men,  the  Epistola  obscurorum  virorum 
ad  venerabilem  virum  Magistrum  Ortuinum  Gratium  Dauentriensem, 
by  Joannes  Crotus,  Ulrich  von  Hutten,  and  others  appeared  at 
Venice  about  1516. 

2  The  lamentations  of  obscure  men,  the  Lamentationes  obscuro- 


ON  THEOLOGICAL  PARADOXERS.  319 

This  is  not  a  retort  of  the  writer,  throwing  back  the  impu- 
tation: the  obscure  men  who  had  been  satirized  are  them- 
selves made,  by  name,  to  wince  under  the  disapprobation 
which  the  Pope  had  expressed  at  the  satire  upon  themselves. 

Of  course  the  book  here  reviewed  is  a  transparent  for- 
gery. But  I  do  not  know  how  often  it  may  have  happened 
that  the  book,  in  the  journals  which  always  put  a  title  at  the 
head,  may  have  been  written  after  the  review.  About  the 
year  1830  a  friend  showed  me  the  proof  of  an  article  of  his 
on  the  malt  tax,  for  the  next  number  of  the  Edinburgh 
Review.  Nothing  was  wanting  except  the  title  of  the  book 
reviewed;  I  asked  what  it  was.  He  sat  down,  and  wrote 
as  follows  at  the  head,  "The  Maltster's  Guide  (pp.  124)," 
and  said  that  would  do  as  well  as  anything. 

But  I  myself,  it  will  be  remarked,  have  employed  such 
humor  as  I  can  command  "in  favor  of  establishment." 
What  it  is  worth  I  am  not  to  judge ;  as  usual  in  such  cases, 
those  who  are  of  my  cabal  pronounce  it  good,  but  cyclom- 
eters and  other  paradoxers  either  call  it  very  poor,  or  com- 
mend it  as  sheer  buffoonery.  Be  it  one  or  the  other,  I  ob- 
serve that  all  the  effective  ridicule  is,  in  this  subject,  on 
the  side  of  establishment.  This  is  partly  due  to  the  diffi- 
culty of  quizzing  plain  and  sober  demonstration ;  but  so 
much,  if  not  more,  to  the  ignorance  of  the  paradoxers. 
For  that  which  cannot  be  ridiculed,  can  be  turned  into  ridi- 
cule by  those  who  know  how.  But  by  the  time  a  person 
is  deep  enough  in  negative  quantities,  and  impossible  quan- 
tities, to  be  able  to  satirize  them,  he  is  caught,  and  being 
inclined  to  become  a  user,  shrinks  from  being  an  abuser. 
Imagine  a  person  with  a  gift  of  ridicule,  and  knowledge 
enough,  trying  his  hand  on  the  junction  of  the  assertions 
which  he  will  find  in  various  books  of  algebra.  First,  that 
a  negative  quantity  has  no  logarithm ;  secondly,  that  a  neg- 

rum  virorum,  non  prohibcte  per  sedem  Apostolicam.  Epistola  D. 
Erasmi  Roterodami  -.quid  de  obscuris  sentiat,  by  G.  Ortwinus,  ap- 
peared at  Cologne  in.  1518: 


320  A  BUDGET  OF  PARADOXES. 

ative  quantity  has  no  square  root ;  thirdly,  that  the  first 
non-existent  is  to  the  second  as  the  circumference  of  a 
circle  to  its  diameter.  One  great  reason  of  the  allowance 
of  such  unsound  modes  of  expression  is  the  confidence  felt 
by  the  writers  that  V  ~~  1  anc^  ^°S  (~~  1)  w^  niake  their  way, 
however  inaccurately  described.  I  heartily  wish  that  the 
cyclometers  had  knowledge  enough  to  attack  the  weak 
points  of  algebraical  diction :  they  would  soon  work  a  bene- 
ficial change.3 

AN  EARLY  METEOROLOGIST. 

Recueil  de  ma  vie,  mes  ouvrages  et  mes  pensees.    Par  Thomas 
Ignace  Marie  Forster.1     Brussels,  1836,  I2mo. 

Mr.  Forster,  an  Englishman  settled  at  Bruges,  was  an 
observer  in  many  subjects,  but  especially  in  meteorology. 
He  communicated  to  the  Astronomical  Society,  in  1848,  the 
information  that,  in  the  registers  kept  by  his  grandfather, 
his  father,  and  himself,  beginning  in  1767,  new  moon  on 
Saturday  was  followed,  nineteen  times  out  of  twenty,  by 
twenty  days  of  rain  and  wind.  This  statement  being  pub- 
lished in  the  Athen&um,  a  cluster  of  correspondents  averred 
that  the  belief  is  common  among  seamen,  in  all  parts  of  the 
world,  and  among  landsmen  too.  Some  one  quoted  a  dis- 
tich: 

"Saturday's  moon  and  Sunday's  full 
Never  were  fine  and  never  wull." 

8  The  criticism  was  timely  when  De  Morgan  wrote  it.  At  present 
it  would  have  but  little  force  with  respect  to  the  better  class  of 
algebras. 

1  Thomas  Ignatius  Maria  Forster  (1789-1860)  was  more  of  a 
man  than  one  would  infer  from  this  satire  upon  his  theory.  He 
was  a  naturalist,  astronomer,  and  physiologist.  In  1812  he  published 
his  Researches  about  Atmospheric  Phenomena,  and  seven  years  later 
(July  3,  1819)  he  discovered  a  comet.  With  Sir  Richard  Phillips 
he  founded  a  Meteorological  Society,  but  it  was  short  lived.  He 
declined  a  fellowship  in  the  Royal  Society  because  he  disapproved 
of  certain  of  its  rules,  so  that  he  had  a  recognized  standing  in  his 
day.  The  work  mentioned  by  De  Morgan  is  the  second  edition, 
the  first  having  appeared  at  Frankfort  on  the  Main  in  1835  under 
the  title,  Recueil  des  ouvrages  et  des  pensees  d'un  physicien  et 
metaphysicien. 


AN   EARLY   METEOROLOGIST.  321 

Another  brought  forward: 

"If  a  Saturday's  moon 
Comes  once  in  seven  years  it  comes  too  soon." 

Mr.  Forster  did  not  say  he  was  aware  of  the  proverbial 
character  of  the  phenomenon.  He  was  a  very  eccentric 
man.  He  treated  his  dogs  as  friends,  and  buried  them  with 
ceremony.  He  quarrelled  with  the  cure  of  his  parish,  who 
remarked  that  he  could  not  take  his  dogs  to  heaven  with 
him.  I  will  go  nowhere,  said  he,  where  I  cannot  take  my 
dog.  He  was  a  sincere  Catholic :  but  there  is  a  point  beyond 
which  even  churches  have  no  influence. 

The  following  is  some  account  of  the  announcement  of 
1849.  The  Athenaum  (Feb.  17),  giving  an  account  of  the 
meeting  of  the  Astronomical  Society  in  December,  1858, 
says: 

"Dr.  Forster  of  Bruges,  who  is  well  known  as  a  meteor- 
ologist, made  a  communication  at  which  our  readers  will 
stare :  he  declares  that  by  journals  of  the  weather  kept  by  his 
grandfather,  father,  and  himself,  ever  since  1767,  to  the 
present  time,  whenever  the  new  moon  has  fallen  on  a  Satur- 
day, the  following  twenty  days  have  been  wet  and  windy,  in 
nineteen  cases  out  of  twenty.  In  spite  of  our  friend  Zadkiel2 
and  the  others  who  declare  that  we  would  smother  every 
truth  that  does  not  happen  to  agree  with  us,  we  are  glad 
to  see  that  the  Society  had  the  sense  to  publish  this  com- 
munication, coming,  as  it  does,  from  a  veteran  observer, 
and  one  whose  love  of  truth  is  undoubted.  It  must  be 
that  the  fact  is  so  set  down  in  the  journals,  because  Dr. 
Forster  says  it:  and  whether  it  be  only  a  fact  of  the  jour- 
nals, or  one  of  the  heavens,  can  soon  be  tried.  The  new 
moon  of  March  next,  falls  on  Saturday  the  24th,  at  2  in  the 
afternoon.  We  shall  certainly  look  out." 

2  Zadkiel,  whose  real  name  was  Richard  James  Morrison  (1795- 
1874),  was  in  his  early  years  an  officer  in  the  navy.  In  1831  he 
began  the  publication  of  the  Herald  of  Astrology,  which  was  con- 
tinued as  Zadkiel9 s  Almanac.  His  name  became  familiar  through- 
out Great  Britain  as  a  result. 


322  A  BUDGET  OF  PARADOXES. 

The  following  appeared  in  the  number  of  March  31 : 
"The  first  Saturday  Moon  since  Dr.  Forster's  announce- 
ment came  off  a  week  ago.  We  had  previously  received 
a  number  of  letters  from  different  correspondents — all  to 
the  effect  that  the  notion  of  new  moon  on  Saturday  bringing 
wet  weather  is  one  of  widely  extended  currency.  One  cor- 
respondent (who  gives  his  name)  states  that  he  has  con- 
stantly heard  it  at  sea,  and  among  the  farmers  and  peas- 
antry in  Scotland,  Ireland,  and  the  North  of  England.  He 
proceeds  thus:  'Since  1826,  nineteen  years  of  the  time  I 
have  spent  in  a  seafaring  life.  I  have  constantly  observed, 
though  unable  to  account  for,  the  phenomenon.  I  have  also 
heard  the  stormy  qualities  of  a  Saturday's  moon  remarked 
by  American,  French,  and  Spanish  seamen;  and,  still  more 
distant,  a  Chinese  pilot,  who  was  once  doing  duty  on  board 
my  vessel  seemed  to  be  perfectly  cognizant  of  the  fact.' 
So  that  it  seems  we  have,  in  giving  currency  to  what  we 
only  knew  as  a  very  curious  communication  from  an  earnest 
meteorologist,  been  repeating  what  is  common  enough 
among  sailors  and  farmers.  Another  correspondent  affirms 
that  the  thing  is  most  devoutly  believed  in  by  seamen ;  who 
would  as  soon  sail  on  a  Friday  as  be  in  the  Channel  after 
a  Saturday  moon. — After  a  tolerable  course  of  dry  weather, 
there  was  some  snow,  accompanied  by  wind  on  Saturday 
last,  here  in  London ;  there  were  also  heavy  louring  clouds. 
Sunday  was  cloudy  and  cold,  with  a  little  rain ;  Monday 
was  louring,  Tuesday  unsettled ;  Wednesday  quite  over- 
clouded, with  rain  in  the  morning.  The  present  occasion 
shows  only  a  general  change  of  weather  with  a  tendency 
towards  rain.  If  Dr.  Forster's  theory  be  true,  it  is  decidedly 
one  of  the  minor  instances,  as  far  as  London  weather  is  con- 
cerned.— It  will  take  a  good  deal  of  evidence  to  make  us 
believe  in  the  omen  of  a  Saturday  Moon.  But,  as  we  have 
said  of  the  Poughkeepsie  Seer,  the  thing  is  very  curious 
whether  true  or  false.  Whence  comes  this  universal  proverb 
— and  a  hundred  others — while  the  meteorological  observer 


AN   EARLY   METEOROLOGIST.  323 

cannot,  when  he  puts  down  a  long  series  of  results,  detect 
any  weather  cycles  at  all  ?  One  of  our  correspondents  wrote 
us  something  of  a  lecture  for  encouraging,  he  said,  the 
notion  that  names  could  influence  the  weather.  He  mis- 
takes the  question.  If  there  be  any  weather  cycles  depend- 
ing on  the  moon,  it  is  possible  that  one  of  them  may  be  so 
related  to  the  week  cycle  of  seven  days,  as  to  show  recur- 
rences which  are  of  the  kind  stated,  or  any  other.  For  ex- 
ample, we  know  that  if  the  new  moon  of  March  fall  on  a 
Saturday  in  this  year,  it  will  most  probably  fall  on  a  Satur- 
day nineteen  years  hence.  This  is  not  connected  with  the 
spelling  of  Saturday — but  with  the  connection  between  the 
motions  of  the  sun  and  moon.  Nothing  but  the  Moon  can 
settle  the  question — and  we  are  willing  to  wait  on  her  for 
further  information.  If  the  adage  be  true,  then  the  phi- 
losopher has  missed  what  lies  before  his  eyes ;  if  false,  then 
the  world  can  be  led  by  the  nose  in  spite  of  the  eyes.  Both 
these  things  happen  sometimes ;  and  we  are  willing  to  take 
whichever  of  the  two  solutions  is  borne  out  by  future  facts. 
In  the  mean  time,  we  announce  the  next  Saturday  Moon 
for  the  18th  of  August." 

How  many  coincidences  are  required  to  establish  a  law 
of  connection?  It  depends  on  the  way  in  which  the  mind 
views  the  matter  in  question.  Many  of  the  paradoxers  are 
quite  set  up  by  a  very  few  instances.  I  will  now  tell  a  story 
about  myself,  and  then  ask  them  a  question. 

So  far  as  instances  can  prove  a  law,  the  following  is 
proved :  no  failure  has  occurred.  Let  a  clergyman  be  known 
to  me,  whether  by  personal  acquaintance  or  correspondence, 
or  by  being  frequently  brought  before  me  by  those  with 
whom  I  am  connected  in  private  life:  that  clergyman  does 
not,  except  in  few  cases,  become  a  bishop ;  but  if  he  become 
a  bishop,  he  is  sure,  first  or  last,  to  become  an  arch-bishop. 
This  has  happened  in  every  case.  As  follows: 

1.  My  last  schoolmaster,  a  former  Fellow  of  Oriel,  was 


324  A  BUDGET  OF  PARADOXES. 

a  very  intimate  college  friend  of  Richard  Whately,3  a 
younger  man.  Struck  by  his  friend's  talents,  he  used  to 
talk  of  him  perpetually,  and  predict  his  future  eminence. 
Before  I  was  sixteen,  and  before  Whately  had  even  given  his 
Bampton  Lectures,  I  was  very  familiar  with  his  name,  and 
some  of  his  sayings.  I  need  not  say  that  he  became  Arch- 
bishop of  Dublin. 

2.  When  I  was  a  child,  a  first  cousin  of  John  Bird  Sum- 
ner* married  a  sister  of  my  mother.    I  cannot  remember  the 
time  when  I  first  heard  his  name,  but  it  was  made  very 
familiar  to  me.    In  time  he  became  Bishop  of  Chester,  and 
then,  Archbishop  of  Canterbury.     My  reader  may  say  that 
Dr.  C.  R.  Sumner,5  Bishop  of  Winchester,  has  just  as  good  a 
claim:  but  it  is  not  so:  those  connected  with  me  had  more 
knowledge  of  Dr.  J.  B.  Sumner  ;•  and  said  nothing,  or  next 
to  nothing,  of  the  other.     Rumor  says  that  the  Bishop  of 
Winchester  has  declined  an  Archbishopric :  if  so,  my  rule  is 
a  rule  of  gradations. 

3.  Thomas  Musgrave,7  Fellow  of  Trinity  College,  Cam- 
bridge, was  Dean  of  the  college  when   I  was  an  under- 
graduate: this  brought  me  into  connection  with  him,  he 
giving  impositions  for  not  going  to  chapel,  I  writing  them 
out  according.     We  had  also  friendly  intercourse  in  after 
life ;  I  forgiving,  he  probably  forgetting.    Honest  Tom  Mus- 

8  See  note  1,  page  246. 

*  Sumner  (1780-1862)  was  an  Eton  boy.  He  went  to  King's 
College,  Cambridge,  and  was  elected  fellow  in  1801.  He  took  many 
honors,  and  in  1807  became  M.A.  He  was  successively  Canon  of 
Durham  (1820),  Bishop  of  Chester  (1828),  and  Archbishop  of 
Canterbury  (1848).  Although  he  voted  for  the  Catholic  Relief  Bill 
(1829)  and  the  Reform  Bill  (1832),  he  opposed  the  removal  of 
Jewish  disabilities. 

"Charles  Richard  Sumner  (1790-1874)  was  not  only  Bishop  of 
Winchester  (1827),  but  also  Bishop  of  Llandaff  and  Dean  of  St. 
Paul's,  London  (1826).  He  lost  the  king's  favor  by  voting  for  the 
Catholic  Relief  Bill. 

6  John  Bird  Sumner,  brother  of  Charles  Richard. 

'Thomas  Musgrave  (1788-1860)  became  Fellow  of  Trinity  in 
1812,  and  senior  proctor  in  1831.  He  was  also  Dean  of  Bristol. 


AN    EARLY    METEOROLOGIST.  325 

grave,  as  he  used  to  be  called,  became  Bishop  of  Hereford, 
and  Archbishop  of  York. 

4.  About  the  time  when  I  went  to  Cambridge,  I  heard 
a  great  deal  about  Mr.  C.  T.  Longley,8  of*  Christchurch, 
from  a  cousin  of  my  own  of  the  same  college,  long  since 
deceased,  who  spoke  of  him  much,  and  most  affectionately. 
Dr.  Longley  passed  from  Durham  to  York,  and  thence  to 
Canterbury.     I  cannot  quite  make  out  the  two  Archbishop- 
rics ;  I  do  not  remember  any  other  private  channel  through 
which  the  name  came  to  me:  perhaps  Dr.  Longley,  having 
two  strings  to  his  bow,  would  have  been  one  archbishop  if 
I  had  never  heard  of  him. 

5.  When  Dr.  Wm.  Thomson9  was  appointed  to  the  see 
of  Gloucester  in  1861,  he  and  I  had  been  correspondents 
on  the  subject  of  logic — on  which  we  had  both  written — for 
about  fourteen  years.     On  his  elevation  I  wrote  to  him, 
giving  the  preceding  instances,  and  informing  him  that  he 
would  certainly  be  an  Archbishop.    The  case  was  a  strong 
one,  and  the  law  acted  rapidly ;  for  Dr.  Thomson's  elevation 
to  the  see  of  York  took  place  in  1862. 

Here  are  five  cases;  and  there  is  no  opposing  instance. 
I  have  searched  the  almanacs  since  1828,  and  can  find  no 
instance  of  a  Bishop  not  finally  Archbishop  of  whom  I  had 
known  through  private  sources,  direct  or  indirect.  Now 
what  do  my  paradoxers  say?  Is  this  a  pre-established  har- 
mony, or  a  chain  of  coincidences?  And  how  many  in- 
stances will  it  require  to  establish  a  law?10 

"Charles  Thomas  Longley  (1794-1868)  was  educated  at  West- 
minster School  and  at  Christ  Church,  Oxford.  He  became  M.A.  in 
1818  and  D.D.  in  1829.  Besides  the  bishoprics  mentioned  he  was 
Bishop  of  Ripon  (1836-1856),  and  before  that  was  headmaster  of 
Harrow  (1829-1836). 

"Thomson  (1819-1890)  was  scholar  and  fellow  of  Queen's  Col- 
lege, Oxford.  He  became  chaplain  to  the  Queen  in  1859. 

10  This  is  worthy  of  the  statistical  psychologists  of  the  present 
day. 


326  A  BUDGET  OF  PARADOXES. 


THE  HERSCHEL  HOAX. 

Some  account  of  the  great  astronomical  discoveries  lately  made 
by  Sir  John  Herschel  at  the  Cape  of  Good  Hope.  Second 
Edition.  London,  I2mo.  1836. 

This  is  a  curious  hoax,  evidently  written  by  a  person 
versed  in  astronomy  and  clever  at  introducing  probable 
circumstances  and  undesigned  coincidences.1  It  first  ap- 
peared in  a  newspaper.  It  makes  Sir  J.  Herschel  discover 
men,  animals,  etc.  in  the  moon,  of  which  much  detail  is 
given.  There  seems  to  have  been  a  French  edition,  the 
original,  and  English  editions  in  America,  whence  the 
work  came  into  Britain:  but  whether  the  French  was  pub- 
lished in  America  or  at  Paris  I  do  not  know.  There  is  no 
doubt  that  it  was  produced  in  the  United  States,  by  M. 
Nicollet,2  an  astronomer,  once  of  Paris,  and  a  fugitive  of 
some  kind.  About  him  I  have  heard  two  stories.  First 
that  he  fled  to  America  with  funds  not  his  own,  and  that  this 
book  was  a  mere  device  to  raise  the  wind.  Secondly,  that 
he  was  a  protege  of  Laplace,  and  of  the  Polignac  party, 
and  also  an  outspoken  man.  That  after  the  revolution  he 
was  so  obnoxious  to  the  republican  party  that  he  judged  it 
prudent  to  quit  France;  which  he  did  in  debt,  leaving 
money  for  his  creditors,  but  not  enough,  with  M.  Bouvard. 
In  America  he  connected  himself  with  an  assurance  office. 

1  The  famous  Moon  Hoax  was  written  by  Richard  Adams  Locke, 
who  was  born  in  New  York  in  1800  and  died  in  Staten  Island  in 
1871.  He  was  at  one  time  editor  of  the  Sun,  and  the  Hoax  appeared 
in  that  journal  in  1835.  It  was  reprinted  in  London  (1836)  and 
Germany,  and  was  accepted  seriously  by  most  readers.  It  was  pub- 
lished in  book  form  in  New  York  in  1852  under  the.  title  The  Moon 
Hoax.  Locke  also  wrote  another  hoax,  the  Lost  Manuscript  of 
Mungo  Park,  but  it  attracted  relatively  little  attention. 

*It  is  true  that  Jean-Nicolas  Nicollet  (1756-1843)  was  at  that 
time  in  the  United  States,  but  there  does  not  seem  to  be  any  very 
tangible  evidence  to  connect  him  with  the  story.  He  was  secretary 
and  librarian  of  the  Paris  observatory  (1817),  member  of  the 
Bureau  of  Longitudes  (1822),  and  teacher  of  mathematics  in  the 
Lycee  Louis-le-Grand.  Having  lost  his  money  through  speculations 
he  left  France  for  the  United  States  in  1831  and  became  connected 
with  the  government  survey  of  the  Mississippi  Valley. 


SOME   MORE   METEOROLOGY.  327 

The  moon-story  was  written,  and  sent  to  France,  chiefly 
with  the  intention  of  entrapping  M.  Arago,  Nicollet's  es- 
pecial foe,  into  the  belief  of  it.  And  those  who  narrate 
this  version  of  the  story  wind  up  by  saying  that  M.  Arago 
was  entrapped,  and  circulated  the  wonders  through  Paris, 
until  a  letter  from  Nicollet  to  M.  Bouvard3  explained  the 
hoax.  I  have  no  personal  knowledge  of  either  story:  but 
as  the  poor  man  had  to  endure  the  first,  it  is  but  right  that 
the  second  should  be  told  with  it. 

SOME  MORE  METEOROLOGY. 

The  Weather  Almanac  for  the  Year  1838.    By  P.  Murphy,1  Esq., 
M.N.S. 

By  M.  N.  S.  is  meant  member  of  no  society.  This  al- 
manac bears  on  the  title-page  two  recommendations.  The 
Morning  Post  calls  it  one  of  the  most  important-if-true 
publications  of  our  generation.  The  Times  says:  "If  the 
basis  of  his  theory  prove  sound,  and  its  principles  be  sanc- 
tioned by  a  more  extended  experience,  it  is  not  too  much  to 
say  that  the  importance  of  the  discovery  is  equal  to  that 
of  the  longitude."  Cautious  journalist!  Three  times  that 
of  the  longitude  would  have  been  too  little  to  say.  That  the 
landsman  might  predict  the  weather  of  all  the  year,  at  its 
beginning,  Jack  would  cheerfully  give  up  astronomical 
longitude — the  problem — altogether,  and  fall  back  on  chro- 
nometers with  the  older  Ls,  lead,  latitude,  and  look-out, 
applied  to  dead-reckoning.  Mr.  Murphy  attempted  to  give 
the  weather  day  by  day :  thus  the  first  seven  days  of  March 

=  This  was  Alexis  Bouvard  (1767-1843),  who  made  most  of  the 
computations  for  Laplace's  Mecanique  celeste  (1793).  He  discovered 
eight  new  comets  and  calculated  their  orbits.  In  his  tables  of 
Uranus  (1821)  he  attributed  certain  perturbations  to  the  presence 
of  an  undiscovered  planet,  but  unlike  Leverrier  and  Adams  he  did 
not  follow  up  this  clue  and  thus  discover  Neptune. 

1  Patrick  Murphy  (1782-1847)  awoke  to  find  himself  famous 
because  of  his  natural  guess  that  there  would  be  very  cold  weather 
on  January  20,  although  that  is  generally  the  season  of  lowest  tem- 
perature. It  turned  out  that  his  forecasts  were  partly  right  on  168 
days  and  very  wrong  on  197  days. 


328  A  BUDGET  OF  PARADOXES. 

bore  Changeable ;  Rain ;  Rain  ;  Rain  -  win d ;  Changeable  ; 
Fair;  Changeable.  To  aim  at  such  precision  as  to  put  a 
fair  day  between  two  changeable  ones  by  weather  theory 
was  going  very  near  the  wind  and  weather  too.  Murphy 
opened  the  year  with  cold  and  frost ;  and  the  weather  did  the 
same.  But  Murphy,  opposite  to  Saturday,  January  20,  put 
down  "Fair,  Probable  lowest  degree  of  winter  temperature." 
When  this  Saturday  came,  it  was  not  merely  the  probably 
coldest  of  1838,  but  certainly  the  coldest  of  many  consecu- 
tive years.  Without  knowing  anything  of  Murphy,  I  felt 
it  prudent  to  cover  my  nose  with  my  glove  as  I  walked  the 
street  at  eight  in  the  morning.  The  fortune  of  the  Almanac 
was  made.  Nobody  waited  to  see  whether  the  future  would 
dement  the  prophecy :  the  shop  was  beset  in  a  manner  which 
brought  the  police  to  keep  order ;  and  it  was  said  that  the 
Almanac  for  1838  was  a  gain  of  5,000/.  to  the  owners.  It 
very  soon  appeared  that  this  was  only  a  lucky  hit:  the 
weather-prophet  had  a  modified  reputation  for  a  few  years ; 
and  is  now  no  more  heard  of.  A  work  of  his  will  presently 
appear  in  the  list. 

THE  GREAT  PYRAMIDS. 

Letter  from  Alexandria  on  the  evidence  of  the  practical  appli- 
cation of  the  quadrature  of  the  circle  in  the  great  pyramids  of 
Gizeh.  By  H.  C.  Agnew,1  Esq.  London,  1838,  4to. 

1  He  seems  to  have  written  nothing  else.  If  one  wishes  to  enter 
into  the  subject  of  the  mathematics  of  the  Great  Pyramid  there  is 
an  extensive  literature  awaiting  him.  Richard  William  Howard  Vyse 
(1784-1853)  published  in  1840  his  Operations  carried  on  at  the  Pyra- 
mids of  Gieeh  in  1837,  and  in  this  he  made  a  beginning  of  a  scien- 
tific metrical  study  of  the  subject.  Charles  Piazzi  Smyth  (1819- 
1900),  astronomer  Royal  for  Scotland  (1845-1888)  was  much  carried 
away  with  the  number  mysticism  of  the  Great  Pyramid,  so  much  so  that 
he  published  in  1864  a  work  entitled  Our  Inheritance  in  the  Great 
Pyramid,  in  which  his  vagaries  were  set  forth.  Although  he  was 
then  a  Fellow  of  the  Royal  Society  (1857),  his  work  was  so  ill  re- 
ceived that  when  he  offered  a  paper  on  the  subject  it  was  rejected 
(1874)  and  he  resigned  in  consequence  of  this  action.  The  latest 
and  perhaps  the  most  scholarly  of  all  investigators  of  the  subject 
is  William  Matthew  Flinders  Petrie  (born  in  1853),  Edwards  pro- 
fessor of  Egyptology  at  University  College,  London,  whose  Pyra- 
mids and  Temples  of  Gizeh  (1883)  and  subsequent  works  are  justly 
esteemed  as  authorities. 


THE  MATHEMATICS  OF  A  CREED.  329 

Mr.  Agnew  detects  proportions  which  he  thinks  were 
suggested  by  those  of  the  circumference  and  diameter  of  a 
circle. 

THE  MATHEMATICS  OF  A  CREED. 

The  creed  of  St.  Athanasius  proved  by  a  mathematical  parallel. 
Before  you  censure,  condemn,  or  approve;  read,  examine,  and 
understand.  E.  B.  REViLO.1  London,  1839,  8vo. 

This  author  really  believed  himself,  and  was  in  earnest. 
He  is  not  the  only  person  who  has  written  nonsense  by  con- 
founding the  mathematical  infinite  (of  quantity)  with  what 
speculators  now  more  correctly  express  by  the  unlimited, 
the  unconditioned,  or  the  absolute.  This  tract  is  worth 
preserving,  as  the  extreme  case  of  a  particular  kind.  The 
following  is  a  specimen.  Infinity  being  represented  by  00, 
as  usual,  and  /,  s,  g,  being  finite  integers,  the  three  Persons 
are  denoted  by  oo^  (woo)*,  oo^  the  finite  fraction  m  repre- 
senting human  nature,  as  opposed  to  oo.  The  clauses  of  the 
Creed  are  then  given  with  their  mathematical  parallels.  I 
extract  a  couple : 

"But  the  Godhead  of  the  "It  has  been  shown  that 
Father,  of  the  Son,  and  of  oo/,  cos,  and  (wOO)*,  to- 
the  Holy  Ghost,  is  all  one:  gether,  are  but  00,  and  that 
the  glory  equal,  the  Majesty  each  is  oo,  and  any  magni- 
co-eternal.  tude  in  existence  represented 

kby   00   always   was   and   al- 
ways will  be:  for  it  cannot 
be  made,  or  destroyed,  and 
yet  exists. 
*As   De  Morgan  subsequently  found,  this  name  reversed  be- 
comes  Oliver  B...e,  for  Oliver  Byrne,  one  of  the  odd  characters 
among  the  minor  mathematical  writers  of  the  middle  of  the  last 
century.     One  of  his  most  curious  works  is  The  first  six  Books  of 
the  Elements  of  Euclid;  in  which  coloured  diagrams  and  symbols 
are  used  instead  of  letters  (1847).     There  is  some  merit  in  speak- 
ing of  the  red  triangle  instead  of  the  triangle  ABC,  but  not  enough 
to  give  the  method  any  standing.    His  Dual  Arithmetic  (1863-1867) 
was  also  a  curious  work. 


330  A  BUDGET  OF  PARADOXES. 

"Equal  to  the  Father,  as          "(wOO)*  is  equal  to  oof  as 

touching  his   Godhead:  and  touching  00,  but  inferior  to 

inferior   to   the   Father,    as  cof  as  touching  m:  because 

touching  his  Manhood."  m  is  not  infinite." 

I  might  have  passed  this  over,  as  beneath  even  my 
present  subject,  but  for  the  way  in  which  I  became  ac- 
quainted with  it.  A  bookseller,  not  the  publisher,  handed 
it  to  me  over  his  counter:  one  who  had  published  mathe- 
matical works.  He  said,  with  an  air  of  important  communi- 
cation, Have  you  seen  this,  Sir!  In  reply,  I  recommended 

him  to  show  it  to  my  friend  Mr. ,  for  whom  he  had 

published  mathematics.  Educated  men,  used  to  books  and  to 
the  converse  of  learned  men,  look  with  mysterious  wonder 
on  such  productions  as  this :  for  which  reason  I  have  made 
a  quotation  which  many  will  judge  had  better  have  been 
omitted.  But  it  would  have  been  an  imposition  on  the  pub- 
lic if  I  were,  omitting  this  and  some  other  uses  of  the 
Bible  and  Common  Prayer,  to  pretend  that  I  had  given  a 
true  picture  of  my  school. 

[Since  the  publication  of  the  above,  it  has  been  stated 
that  the  author  is  Mr.  Oliver  Byrne,  the  author  of  the  Dual 
Arithmetic  mentioned  further  on:  E.  B.  Revilo  seems  to  be 
obviously  a  reversal.] 

LOGIC   HAS   NO    PARADOXERS. 

Old  and  new  logic  contrasted :  being  an  attempt  to  elucidate,  for 
ordinary  comprehension,  how  Lord  Bacon  delivered  the  human 
mind  from  its  2,000  years'  enslavement  under  Aristotle.  By 
Justin  Brenan.1  London,  1839,  I2mo. 

Logic,  though  the  other  exact  science,  has  not  had  the 
sort  of  assailants  who  have  clustered  about  mathematics. 
There  is  a  sect  which  disputes  the  utility  of  logic,  but  there 
are  no  special  points,  like  the  quadrature  of  the  circle,  which 

1  Brenan  also  wrote  on  English  composition  (1829),  a  work  that 
went  through  fourteen  editions  by  1865 ;  a  work  entitled  The  For- 
eigner's English  Conjugator  (1831),  and  a  work  on  the  national 
debt. 


LOGIC  HAS  NO  PARADOXERS.  331 

excite  dispute  among  those  who  admit  other  things.  The 
old  story  about  Aristotle  having  one  logic  to  trammel  us, 
and  Bacon  another  to  set  us  free, — always  laughed  at  by 
those  who  really  knew  either  Aristotle  or  Bacon, — now 
begins  to  be  understood  by  a  large  section  of  the  educated 
world.  The  author  of  this  tract  connects  the  old  logic  with 
the  indecencies  of  the  classical  writers,  and  the  new  with 
moral  purity:  he  appeals  to  women,  who,  "when  they  see 
plainly  the  demoralizing  tendency  of  syllogistic  logic,  they 
will  no  doubt  exert  their  powerful  influence  against  it,  and 
support  the  Baconian  method."  This  is  the  only  work 
against  logic  which  I  can  introduce,  but  it  is  a  rare  one,  I 
mean  in  contents.  I  quote  the  author's  idea  of  a  syllogism : 

"The  basis  of  this  system  is  the  syllogism.  This  is  a 
form  of  couching  the  substance  of  your  argument  or  in- 
vestigation into  one  short  line  or  sentence — then  corrobo- 
rating or  supporting  it  in  another,  and  drawing  your  con- 
clusion or  proof  in  a  third." 

On  this  definition  he  gives  an  example,  as  follows :  "Every 
sin  deserves  death,"  the  substance  of  the  "argument  or  in- 
vestigation." Then  comes,  "Every  unlawful  wish  is  a  sin," 
which  "corroborates  or  supports"  the  preceding:  and,  lastly, 
"therefore  every  unlawful  wish  deserves  death,"  which  is 
the  "conclusion  or  proof."  We  learn,  also,  that  "sometimes 
the  first  is  called  the  premises  (sic),  and  sometimes  the 
first  premiss";  as  also  that  "the  first  is  sometimes  called 
the  proposition,  or  subject,  or  affirmative,  and  the  next  the 
predicate,  and  sometimes  the  middle  term."  To  which  is 
added,  with  a  mark  of  exclamation  at  the  end,  "but  in  ana- 
lyzing the  syllogism,  there  is  a  middle  term,  and  a  predicate 
too,  in  each  of  the  lines!"  It  is  clear  that  Aristotle  never 
enslaved  this  mind. 

I  have  said  that  logic  has  no  paradoxers,  but  I  was 
speaking  of  old  time.  This  science  has  slept  until  our  own 
day:  Hamilton2  says  there  has  been  "no  progress  made  in 

a  See  note  7,  page  1 12. 


332  A   BUDGET  OF   PARADOXES. 

the  general  development  of  the  syllogism  since  the  time  of 
Aristotle ;  and  in  regard  to  the  few  partial  improvements, 
the  professed  historians  seem  altogether  ignorant."  But  in 
our  time,  the  paradoxer,  the  opponent  of  common  opinion, 
has  appeared  in  this  field.  I  do  not  refer  to  Prof.  Boole,3 
who  is  not  a  paradoxer,  but  a  discoverer:  his  system  could 
neither  oppose  nor  support  common  opinion,  for  its  grounds 
were  not  in  the  conception  of  any  one.  I  speak  especially 
of  two  others,  who  fought  like  cat  and  dog:  one  was  dog- 
matical, the  other  categorical.  The  first  was  Hamilton  him- 
self— Sir  William  Hamilton  of  Edinburgh,  the  metaphysi- 
cian,(  not  Sir  William  Rowan  Hamilton*  of  Dublin,  the 
mathematician  J  a  combination  of  peculiar  genius  with  un- 
precedented learning,  erudite  in  all  he  could  want  except 
mathematics,  for  which  he  had  no  turn,  and  in  which  he 
had  not  even  a  schoolboy's  knowledge,  thanks  to  the  Oxford 
of  his  younger  day.  The  other  was  the  author  of  this 
work,  so  fully  described  in  Hamilton's  writings  that  there 
is  no  occasion  to  describe  him  here.  I  shall  try  to  say  a  few 
words  in  common  language  about  the  paradoxers. 

Hamilton's  great  paradox  was  the  quantification  of  the 
predicate;  a  fearful  phrase,  easily  explained.  We  all  know 
that  when  we  say  "Men  are  animals/'  a  form  wholly  un- 
quantified  in  phrase,  we  speak  of  all  men,  but  not  of  all 
animals:  it  is  some  or  all,  some  may  be  all  for  aught  the 
proposition  says.  This  some-may-be-all-for-aught-we-say, 
or  not-none,  is  the  logician's  some.  One  would  suppose 

8  See  note  2,  page  261. 

*Sir  William  Rowan  Hamilton  (1805-1865),  the  discoverer  of 
quaternions  (1852),  was  an  infant  prodigy,  competing  with  Zerah 
Colburn  as  a  child.  He  was  a  linguist  of  remarkable  powers,  being 
able,  at  thirteen  years  of  age,  to  boast  that  he  knew  as  many  languages 
as  he  had  lived  years.  When  only  sixteen  he  found  an  error  in 
Laplace's  Mecanique  celeste.  When  only  twenty-two  he  was  ap- 
pointed Andrews  professor  of  astronomy,  and  he  soon  after  became 
Astronomer  Royal  of  Ireland.  He  was  knighted  in  1835.  His  earlier 
work  was  on  optics,  his  Theory  of  Systems  of  Rays  appearing  in 
1823.  In  1827  he  published  a  paper  on  the  principle  of  Varying  Ac* 
tion.  He  also  wrote  on  dynamics. 


LOGIC  HAS  NO  PARADOXERS.  333 

that  "all  men  are  some  animals,"  would  have  been  the  log- 
ical phrase  in  all  time:  but  the  predicate  never  was  quanti- 
fied. The  few  who  alluded  to  the  possibility  of  such  a  thing 
found  reasons  for  not  adopting  it  over  and  above  the  great 
reason,  that  Aristotle  did  not  adopt  it.  For  Aristotle  never 
ruled  in  physics  or  metaphysics  in  the  old  time  with  near  so 
much  of  absolute  sway  as  he  has  ruled  in  logic  down  to  our 
own  time.  The  logicians  knew  that  in  the  proposition  "all 
men  are  animals"  the  "animal"  is  not  universal,  but  particu- 
lar yet  no  one  dared  to  say  that  all  men  are  some  animals, 
and  to  invent  the  phrase,  "some  animals  are  all  men"  until 
Hamilton  leaped  the  ditch,  and  not  only  completed  a  system 
of  enunciation,  but  applied  it  to  syllogism. 

My  own  case  is  as  peculiar  as  his:  I  have  proposed  to 
introduce  mathematical  thought  into  logic  to  an  extent  which 
makes  the  old  stagers  cry: 

"St.  Aristotle !  what  wild  notions ! 
Serve  a  ne  exeat  regno6  on  him !" 

Hard  upon  twenty  years  ago,  a  friend  and  opponent 
who  stands  high  in  these  matters,  and  who  is  not  nearly 
such  a  sectary  of  Aristotle  and  establishment  as  most,  wrote 
to  me  as  follows :  "It  is  said  that  next  to  the  man  who  forms 
the  taste  of  the  nation,  the  greatest  genius  is  the  man  who 
corrupts  it.  I  mean  therefore  no  disrespect,  but  very  much 
the  reverse,  when  I  say  that  I  have  hitherto  always  consid- 
ered you  as  a  great  logical  heresiarch."  Coleridge  says  he 
thinks  that  it  was  Sir  Joshua  Reynolds  who  made  the  re- 
mark: which,  to  copy  a  bull  I  once  heard,  I  cannot  deny, 
because  I  was  not  there  when  he  said  it.  My  friend  did  not 
call  me  to  repentance  and  reconciliation  with  the  church: 
I  think  he  had  a  guess  that  I  was  a  reprobate  sinner.  My 
offences  at  that  time  were  but  small:  I  went  on  spinning 
syllogism  systems,  all  alien  from  the  common  logic,  until  I 
had  six,  the  initial  letters  of  which,  put  together,  from  the 

8  "Let  him  not  leave  the  kingdom," — a  legal  phrase. 


334  A  BUDGET  OF  PARADOXES. 

names  I  gave  before  I  saw  what  they  would  make,  bar  all 
repentance  by  the  words 

RUE  NOT! 

leaving  to  the  followers  of  the  old  school  the  comfortable 
option  of  placing  the  letters  thus: 

TRUE?  NO! 

It  should  however  be  stated  that  the  question  is  not 
about  absolute  truth  or  falsehood.  No  one  denies  that  any- 
thing I  call  an  inference  is  an  inference:  they  say  that  my 
alterations  are  extra-logical-,  that  they  are  material,  not 
formal',  and  that  logic  is  a  formal  science. 

The  distinction  between  material  and  formal  is  easily 
made,  where  the  usual  perversions  are  not  required.  A  form 
is  an  empty  machine,  such  as  "Every  X  is  Y";  it  may  be 
supplied  with  matter,  as  in  "Every  man  is  animal"  The 
logicians  will  not  see  that  their  formal  proposition,  "Every 
X  is  Y,"  is  material  in  three  points,  the  degree  of  assertion, 
the  quantity  of  the  proposition,  and  the  copula.  The  purely 
formal  proposition  is  "There  is  the  probability  a  that  X 
stands  in  the  relation  L  to  Y."  The  time  will  come  when  it 
will  be  regretted  that  logic  went  without  paradoxers  for 
two  thousand  years:  and  when  much  that  has  been  said  on 
the  distinction  of  form  and  matter  will  breed  jokes. 

I  give  one  instance  of  one  mood  of  each  of  the  systems, 
in  the  order  of  the  letters  first  written  above. 

Relative. — In  this  system  the  formal  relation  is  taken, 
that  is,  the  copula  may  be  any  whatever.  As  a  material  in- 
stance, in  which  the  relations  are  those  of  consanguinity  (of 
men  understood),  take  the  following:  X  is  the  brother  of 
Y ;  X  is  not  the  uncle  of  Z ;  therefore,  Z  is  not  the  child  of 
Y.  The  discussion  of  relation,  and  of  the  objections  to  the 
extension,  is  in  the  Cambridge  Transactions,  Vol.  X,  Part  2  ; 
a  crabbed  conglomerate. 

Undecided. — In  this  system  one  premise,  and  want  of 
power  over  another,  infer  want  of  power  over  a  conclusion. 


LOGIC  HAS  NO  PARADOXERS.  335 

As  "Some  men  are  not  capable  of  tracing  consequences ;  we 
cannot  be  sure  that  there  are  beings  responsible  for  conse- 
quences who  are  incapable  of  tracing  consequences;  there- 
fore, we  cannot  be  sure  that  all  men  are  responsible  for  the 
consequences  of  their  actions." 

Exemplar. — This,  long  after  it  suggested  itself  to  me  as 
a  means  of  correcting  a  defect  in  Hamilton's  system,  I  saw 
to  be  the  very  system  of  Aristotle  himself,  though  his  fol- 
lowers have  drifted  into  another.  It  makes  its  subject  and 
predicate  examples,  thus:  Any  one  man  is  an  animal;  any 
one  animal  is  a  mortal ;  therefore,  any  one  man  is  a  mortal. 

Numerical. — Suppose  100  Ys  to  exist:  then  if  70  Xs 
be  Ys,  and  40  Zs  be  Ys,  it  follows  that  10  Xs  (at  least)  are 
Zs.  Hamilton,  whose  mind  could  not  generalize  on  sym- 
bols, saw  that  the  word  most  would  come  under  this  system, 
and  admitted,  as  valid,  such  a  syllogism  as  "most  Ys  are 
Xs;  most  Ys  are  Zs;  therefore,  some  Xs  are  Zs." 

Onymatic. — This  is  the  ordinary  system  much  enlarged 
in  prepositional  forms.  It  is  fully  discussed  in  my  Syllabus 
of  Logic. 

Transposed. — In  this  syllogism  the  quantity  in  one  prem- 
ise is  transposed  into  the  other.  As,  some  Xs  are  not  Ys; 
for  every  X  there  is  a  Y  which  is  Z ;  therefore,  some  Zs  are 
not  Xs. 

Sir  William  Hamilton  of  Edinburgh  was  one  of  the  best 
friends  and  allies  I  ever  had.  When  I  first  began  to  publish 
speculation  on  this  subject,  he  introduced  me  to  the  logical 
world  as  having  plagiarized  from  him.  This  drew  their 
attention:  a  mathematician  might  have  written  about  logic 
under  forms  which  had  something  of  mathematical  look 
long  enough  before  the  Aristotelians  would  have  troubled 
themselves  with  him:  as  was  done  by  John  Bernoulli,6 

0  Probably  De  Morgan  is  referring  to  Johann  Bernoulli  III  (1744- 
1807),  who  edited  Lambert's  Logische  und  philosophische  Abhand- 
lungen,  Berlin,  1782.  He  was  astronomer  of  the  Academy  of  Sci- 
ences at  Berlin. 


336  A  BUDGET  OF  PARADOXES. 

James  Bernoulli,7  Lambert,8  and  Gergonne ;°  who,  when  our 
discussion  began,  were  not  known  even  to  omnilegent  Ham- 
ilton. He  retracted  his  accusation  of  wilful  theft  in  a  manly 
way  when  he  found  it  untenable;  but  on  this  point  he 
wavered  a  little,  and  was  convinced  to  the  last  that  I  had 
taken  his  principle  unconsciously.  He  thought  I  had  done 
the  same  with  Ploucquet10  and  Lambert.  It  was  his  pet 
notion  that  I  did  not  understand  the  commonest  principles  of 
logic,  that  I  did  not  always  know  the  difference  between  the 
middle  term  of  a  syllogism  and  its  conclusion.  It  went 
against  his  grain  to  imagine  that  a  mathematician  could  be 
a  logician.  So  long  as  he  took  me  to  be  riding  my  own 
hobby,  he  laughed  consumedly:  but  when  he  thought  he 
could  make  out  that  I  was  mounted  behind  Ploucquet  or 
Lambert,  the  current  ran  thus :  "It  would  indeed  have  been 
little  short  of  a  miracle  had  he,  ignorant  even  of  the  common 
principles  of  logic,  been  able  of  himself  to  rise  to  generali- 
zation so  lofty  and  so  accurate  as  are  supposed  in  the  pecu- 
liar doctrines  of  both  the  rival  logicians,  Lambert  and 
Ploucquet — how  useless  soever  these  may  in  practice  prove 
to  be."  All  this  has  been  sufficiently  discussed  elsewhere: 
"but,  masters,  remember  that  I  am  an  ass." 

I  know  that  I  never  saw  Lambert's  work  until  after  all 
Hamilton  supposed  me  to  have  taken  was  written:  he  him- 
self, who  read  almost  everything,  knew  nothing  about  it 
until  after  I  did.  I  cannot  prove  what  I  say  about  my 
knowledge  of  Lambert :  but  the  means  of  doing  it  may  turn 
up.  For,  by  the  casual  turning  up  of  an  old  letter,  I  have 

T  Jacob  Bernoulli  (1654-1705)  was  one  of  the  two  brothers  who 
founded  the  famous  Bernoulli  family  of  mathematicians,  the  other 
being  Johann  I.  His  Ars  conjectandi  (1713),  published  posthu- 
mously, was  the  first  distinct  treatise  on  probabilities. 

'Johann  Heinrich  Lambert  (1728-1777)  was  one  of  the  most 
learned  men  of  his  time.  Although  interested  chiefly  in  mathematics, 
he  wrote  also  on  science,  logic,  and  philosophy. 

'Joseph  Diez  Gergonne  (1771-1859),  a  soldier  under  Napoleon, 
and  founder  of  the  Annalcs  de  mathematiques  (1810). 

"Gottfried  Ploucquet  (1716-1790)  was  at  first  a  clergyman,  but 
afterwards  became  professor  of  logic  at  Tubingen. 


LOGIC  HAS  NO  PARADOXERS.  337 

found  the  means  of  clearing  myself  as  to  Ploucquet.  Ham- 
ilton assumed  that  (unconsciously)  I  took  from  Ploucquet 
the  notion  of  a  logical  notation  in  which  the  symbol  of  the 
conclusion  is  seen  in  the  joint  symbols  of  the  premises.  For 
example,  in  my  own  fashion  I  write  down  (  .  )  (  .  ),  two 
symbols  of  premises.  By  these  symbols  I  see  that  there  is 
a  valid  conclusion,  and  that  it  may  be  written  in  symbol  by 
striking  out  the  two  middle  parentheses,  which  gives  (  .  .  ) 
and  reading  the  two  negative  dots  as  an  affirmative.  And 
so  I  see  in  (  .  )  (  .  )  that  (  )  is  the  conclusion.  This, 
in  full,  is  the  perception  that  "all  are  either  Xs  or  Ys"  and 
"all  are  either  Ys  or  Zs"  necessitates  "some  Xs  are  Zs." 
Now  in  Ploucquet's  book  of  1763,  is  found,  "Deleatur  in 
praemissis  medius ;  id  quod  restat  indicat  conclusionem."11 
In  the  paper  in  which  I  explain  my  symbols — which  are 
altogether  different  from  Ploucquet's — there  is  found  "Erase 
the  symbols  of  the  middle  term;  the  remaining  symbols 
show  the  inference."  There  is  very  great  likeness:  and  I 
would  have  excused  Hamilton  for  his  notion  if  he  had  fairly 
given  reference  to  the  part  of  the  book  in  which  his  quota- 
tion was  found.  For  I  had  shown  in  my  Formal  Logic  what 
part  of  Ploucquet's  book  I  had  used:  and  a  fair  disputant 
would  either  have  strengthened  his  point  by  showing  that 
I  had  been  at  his  part  of  the  book,  or  allowed  me  the  ad- 
vantage of  it  being  apparent  that  I  had  not  given  evidence 
of  having  seen  that  part  of  the  book.  My  good  friend, 
though  an  honest  man,  was  sometimes  unwilling  to  allow 
due  advantage  to  controversial  opponents. 

But  to  my  point.  The  only  work  of  Ploucquet  I  ever 
saw  was  lent  me  by  my  friend  Dr.  Logan,12  with  whom  I 
have  often  corresponded  on  logic,  etc.  I  chanced  (in  1865) 

1  "In  the  premises  let  the  middle  term  be  omitted ;  what  remains 
indicates  the  conclusion." 

"Probably  Sir  William  Edmond  Logan  (1789-1875),  who  be- 
came so  interested  in  geology  as  to  be  placed  at  the  head  of  the  geo- 
logical survey  of  Canada  (1842).  The  University  of  Montreal  con- 
ferred the  title  LL.D.  upon  him,  and  Napoleon  III  gave  him  the 
cross  of  the  Legion  of  Honor. 


338  A  BUDGET  OF  PARADOXES. 

to  turn  up  the  letter  which  he  sent  me  (Sept.  12,  1847)  with 
the  book.  Part  of  it  runs  thus:  "I  congratulate  you  on 
your  success  in  your  logical  researches  [that  is,  in  asking 
for  the  book,  I  had  described  some  results].  Since  the 
reading  of  your  first  paper  I  have  been  satisfied  as  to  the 
possibility  of  inventing  a  logical  notation  in  which  the 
rationale  of  the  inference  is  contained  in  the  symbol,  though 
I  never  attempted  to  verify  it  [what  I  communicated,  then, 
satisfied  the  writer  that  I  had  done  and  communicated  what 
he,  from  my  previous  paper,  suspected  to  be  practicable]. 
I  send  you  Ploucquet's  dissertation ' 

It  now  being  manifest  that  I  cannot  be  souring  grapes 
which  have  been  taken  from  me,  I  will  say  what  I  never 
said  in  print  before.  There  is  not  the  slightest  merit  in 
making  the  symbols  of  the  premises  yield  that  of  the  con- 
clusion by  erasure :  the  thing  must  do  itself  in  every  system 
which  symbolizes  quantities.  For  in  every  syllogism  (ex- 
cept the  inverted  Bramantip  of  the  Aristotelians)  the  con- 
clusion is  manifest  in  this  way  without  symbols.  This 
Bramantip  destroys  system  in  the  Aristotelian  lot:  and  cir- 
cumstances which  I  have  pointed  out  destroy  it  in  Hamil- 
ton's own  collection.  But  in  that  enlargement  of  the  re- 
puted Aristotelian  system  which  I  have  called  onymatic, 
and  in  that  correction  of  Hamilton's  system  which  I  have 
called  exemplar,  the  rule  of  erasure  is  universal,  and  may 
be  seen  without  symbols. 

Our  first  controversy  was  in  1846.  In  1847,  in  my 
Formal  Logic,  I  gave  him  back  a  little  satire  for  satire, 
just  to  show,  as  I  stated,  that  I  could  employ  ridicule  if  I 
pleased.  He  was  so  offended  with  the  appendix  in  which 
this  was  contained,  that  he  would  not  accept  the  copy  of  the 
book  I  sent  him,  but  returned  it.  Copies  of  controversial 
works,  sent  from  opponent  to  opponent,  are  not  presents,  in 
the  usual  sense :  it  was  a  marked  success  to  make  him  angry 
enough  to  forget  this.  It  had  some  effect  however:  during 
the  rest  of  his  life  I  wished  to  avoid  provocation;  for  I 


LOGIC  HAS  NO  PARADOXERS.  339 

could  not  feel  sure  that  excitement  might  not  produce  con- 
sequences. I  allowed  his  slashing  account  of  me  in  the 
Discussions  to  pass  unanswered :  and  before  that,  when  he 
proposed  to  open  a  controversy  in  the  Athenceum  upon  my 
second  Cambridge  paper,  I  merely  deferred  the  dispute  until 
the  next  edition  of  my  Formal  Logic.  I  cannot  expect  the 
account  in  the  Discussions  to  amuse  an  unconcerned  reader 
as  much  as  it  amused  myself:  but  for  a  cut-and-thrust, 
might-and-main,  tooth-and-nail,  hammer-and-tongs  assault, 
I  can  particularly  recommend  it.  I  never  knew,  until  I  read 
it,  how  much  I  should  enjoy  a  thundering  onslought  on 
myself,  done  with  racy  insolence  by  a  master  hand,  to  whom 
my  good  genius  had  whispered  Ita  feri  ut  se  sentiat  emori.™ 
Since  that  time  I  have,  as  the  Irishman  said,  become  "dry 
moulded  for  want  of  a  bating."  Some  of  my  paradoxers 
have  done  their  best:  but  theirs  is  mere  twopenny — "small 
swipes,"  as  Peter  Peebles  said.  Brandy  for  heroes !  I  hope  a 
reviewer  or  two  will  have  mercy  on  me,  and  will  give  me  as 
good  discipline  as  Strafford  would  have  given  Hampden 
and  his  set:  "much  beholden,"  said  he,  "should  they  be  to 
any  one  that  should  thoroughly  take  pains  with  them  in 
that  kind" — meaning  objective  flagellation.  And  I  shall 
be  the  same  to  any  one  who  will  serve  me  so — but  in  a 
literary  and  periodical  sense:  my  corporeal  cuticle  is  as 
thin  as  my  neighbors'. 

Sir  W.  H.  was  suffering  under  local  paralysis  before 
our  controversy  commenced:  and  though  his  mind  was 
quite  unaffected,  a  retort  of  as  downright  a  character  as  the 
attack  might  have  produced  serious  effect  upon  a  person 
who  had  shown  himself  sensible  of  ridicule.  Had  a  second 
attack  of  his  disorder  followed  an  answer  from  me,  I  should 
have  been  held  to  have  caused  it :  though,  looking  at  Hamil- 
ton's genial  love  of  combat,  I  strongly  suspected  that  a 
retort  in  kind 

u  "So  strike  that  he  may  think  himself  to  die." 


340  A  BUDGET  OF  PARADOXES. 

"Would  cheer  his  heart,  and  warm  his  blood, 
And  make  him  fight,  and  do  him  good." 

But  I  could  not  venture  to  risk  it.  So  all  I  did,  in  reply  to 
the  article  in  the  Discussions,  was  to  write  to  him  the  follow- 
ing note:  which,  as  illustrating  an  etiquette  of  controversy, 
I  insert. 

"I  beg  to  acknowledge  and  thank  you  for. . .  It  is  neces- 
sary that  I  should  say  a  word  on  my  retention  of  this  work, 
with  reference  to  your  return  of  the  copy  of  my  Formal 
Logic,  which  I  presented  to  you  on  its  publication :  a  return 
made  on  the  ground  of  your  disapproval  of  the  account  of 
our  controversy  which  that  work  contained.  According  to 
my  view  of  the  subject,  any  one  whose  dealing  with  the 
author  of  a  book  is  specially  attacked  in  it,  has  a  right  to 
expect  from  the  author  that  part  of  the  book  in  which  the 
attack  is  made,  together  with  so  much  of  the  remaining  part 
as  is  fairly  context.  And  I  hold  that  the  acceptance  by  the 
party  assailed  of  such  work  or  part  of  a  work  does  not  imply 
any  amount  of  approval  of  the  contents,  or  of  want  of  dis- 
approval. On  this  principle  (though  I  am  not  prepared 
to  add  the  word  alone)  I  forwarded  to  you  the  whole  of  my 
work  on  Formal  Logic  and  my  second  Cambridge  Memoir. 
And  on  this  principle  I  should  have  held  you  wanting  in  due 
regard  to  my  literary  rights  if  you  had  not  forwarded  to 
me  your  asterisked  pages,  with  all  else  that  was  necessary 
to  a  full  understanding  of  their  scope  and  meaning,  so  far 
as  the  contents  of  the  book  would  furnish  it.  For  the  re- 
maining portion,  which  it  would  be  a  hundred  pities  to  sepa- 
rate from  the  pages  in  which  I  am  directly  concerned,  I  am 
your  debtor  on  another  principle;  and  shall  be  glad  to  re- 
main so  if  you  will  allow  me  to  make  a  feint  of  balancing 
the  account  by  the  offer  of  two  small  works  on  subjects  as 
little  connected  with  our  discussion  as  the  Epistolce  Ob- 
scurorum  Virorum,  or  the  Lutheran  dispute.  I  trust  that 
by  accepting  my  Opuscula  you  will  enable  me  to  avoid  the 


SOME   DOGGEREL   AND    COUNTER   DOGGEREL.  341 

use  of  the  knife,  and  leave  me  to  cut  you  up  with  the  pen  as 
occasion  shall  serve,  I  remain,  etc.     (April  21,  1852)." 

I  received  polite  thanks,  but  not  a  word  about  the  body 
of  the  letter:  my  argument,  I  suppose,  was  admitted. 

SOME  DOGGEREL  AND  COUNTER  DOGGEREL. 

I  find  among  my  miscellaneous  papers  the  following 
jeu  d' esprit,  or  jeu  de  betise*  whichever  the  reader  pleases 
—I  care  not — intended,  before  I  saw  ground  for  abstaining, 
to  have,  as  the  phrase  is,  come  in  somehow.  I  think  I  could 
manage  to  bring  anything  into  anything:  certainly  into  a 
Budget  of  Paradoxes.  Sir  W.  H.  rather  piqued  himself  upon 
some  caniculars,  or  doggerel  verses,  which  he  had  put  to- 
gether in  memoriam  [technicam]  of  the  way  in  which 
A  E  I  O  are  used  in  logic :  he  added  U,  Y,  for  the  addition 
of  meet,  etc.,  to  the  system.  I  took  the  liberty  of  concocting 
some  counter-doggerel,  just  to  show  that  a  mathematician 
may  have  architectonic  power  as  well  as  a  metaphysician. 

DOGGEREL. 
BY  SIR  W.  HAMILTON. 

A  it  affirms  of  this,  these,  all, 

Whilst  E  denies  of  any; 
I  it  affirms  (whilst  O  denies) 

Of  some  (or  few,  or  many). 

Thus  A  affirms,  as  E  denies, 

And  definitely  either; 
Thus  I  affirms,  as  O  denies, 

And  definitely  neither. 

A  half,  left  semidefinite, 

Is  worthy  of  its  score ; 
U,  then,  affirms,  as  Y  denies, 

This,  neither  less  nor  more. 

Indefinito-definites, 
I,  UI,  YO,  last  we  come; 

1  "Witticism  or  piece  of  stupidity." 


342  A  BUDGET  OF  PARADOXES. 

And  this  affirms,  as  that  denies 
Of  more,  most  (half,  plus,  some). 

COUNTER  DOGGEREL. 

BY   PROF.  DE  MORGAN. 

(1847.) 

GREAT  A  affirms  of  all; 

Sir  William  does  so  too: 
When  the  subject  is  "my  suspicion," 

And  the  predicate  "must  be  true." 

Great  E  denies  of  all ; 

Sir  William  of  all  but  one: 
When  he  speaks  about  this  present  time, 

And  of  those  who  in  logic  have  done. 

Great  I  takes  up  but  some-, 

Sir  William!  my  dear  soul! 
Why  then  in  all  your  writings, 

Does  "Great  I"  fill2  the  whole! 

Great  O  says  some  are  not; 

Sir  William's  readers  catch, 
That  some  (modern)  Athens  is  not  without 

An  Aristotle  to  match. 

"A  half,  left  semi-definite, 

Is  worthy  of  its  score:" 
This  looked  very  much  like  balderdash, 

And  neither  less  nor  more. 

It  puzzled  me  like  anything; 

In  fact,  it  puzzled  me  worse: 
Isn't  schoolman's  logic  hard  enough, 

Without  being  in  Sibyl's  verse? 

SA  very  truculently  unjust  assertion:  for  Sir  W.  was  as  great 
a  setter  up  of  some  as  he  was  a  puller  down  of  others.  His  writings 
are  a  congeries  of  praises  and  blames,  both  cruel  smart,  as  they  say 
in  the  States.  But  the  combined  instigation  of  prose,  rhyme,  and 
retort  would  send  Aristides  himself  to  Tartarus,  if  it  were  not  pretty 
certain  that  Minos  would  grant  a  stet  processus  under  the  circum- 
stances. The  first  two  verses  are  exaggerations  standing  on  a  basis 
of  truth.  ^  The  fourth  verse  is  quite  true :  Sir  W.  H.  was  an  Edin- 
burgh Aristotle,  with  the  difference  of  ancient  and  modern  Athens 
well  marked,  especially  the  perfervidum  ingenium  Scotorum. — 
A.  De  M. 


SOME  DOGGEREL  AND  COUNTER  DOGGEREL.      343 

At  last,  thinks  I,  'tis  German; 

And  I'll  try  it  with  some  beer ! 
The  landlord  asked  what  bothered  me  so, 

And  at  once  he  made  it  clear. 

It's  half-and-half,  the  gentleman  means ; 

Don't  you  see  he  talks  of  score? 
That's  the  bit  of  memorandum 

That  we  chalk  behind  the  door. 

Semi-definite  's  outlandish ; 

But  I  see,  in  half  a  squint, 
That  he  speaks  of  the  lubbers  who  call  for  a  quart, 

When  they  can't  manage  more  than  a  pint. 

Now  I'll  read  it  into  English, 
And  then  you'll  answer  me  this : 

If  it  isn't  good  logic  all  the  world  round, 
I  should  like  to  know  what  is? 

When  you  call  for  a  pot  of  half-and-half, 
If  you're  lost  to  sense  of  shame, 

You  may  leave  it  semi-definite, 
But  you  pay  for  it  all  just  the  same. 
*  *  *  * 

I  am  unspeakably  comforted  when  I  look  over  the  above 
in  remembering  that  the  question  is  not  whether  it  be  Pin- 
daric or  Horatian,  but  whether  the  copy  be  as  good  as  the 
original.  And  I  say  it  is :  and  will  take  no  denial. 

Long  live — long  will  live — the  glad  memory  of  William 
Hamilton,  Good,  Learned,  Acute,  and  Disputatious!  He 
fought  upon  principle:  the  motto  of  his  book  is: 

"Truth,  like  a  torch,  the  more  it's  shook  it  shines." 

There  is  something  in  this;  but  metaphors,  like  puddings, 
quarrels,  rivers,  and  arguments,  always  have  two  sides  to 
them.  For  instance, 

"Truth,  like  a  torch,  the  more  it's  shook  it  shines ; 

But  those  who  want  to  use  it,  hold  it  steady. 
They  shake  the  flame  who  like  a  glare  to  gaze  at, 
They  keep  it  still  who  want  a  light  to  see  by." 


344  A  BUDGET  OF  PARADOXES. 


ANOTHER  THEORY  OF  PARALLELS. 

Theory  of  Parallels.  The  proof  of  Euclid's  axiom  looked  for  in 
the  properties  of  the  Equiangular  Spiral.  By  Lieut-Col.  G. 
Perronet  Thompson.1  The  same,  second  edition,  revised  and 
corrected.  The  same,  third  edition,  shortened,  and  freed  from 
dependence  on  the  theory  of  limits.  The  same,  fourth  edition, 
ditto,  ditto.  All  London,  1840,  Svo. 

To  explain  these  editions  it  should  be  noted  that  General 
Thompson  rapidly  modified  his  notions,  and  republished  his 
tracts  accordingly. 

SOME   PRIMITIVE  DARWINISM. 

Vestiges  of  the  Natural  History  of  Creation.1  London,  1840, 
I2mo. 

This  is  the  first  edition  of  this  celebrated  work.  Its 
form  is  a  case  of  the  theory :  the  book  is  an  undeniable  duo- 
decimo, but  the  size  of  its  paper  gives  it  the  look  of  not  the 
smallest  of  octavos.  Does  not  this  illustrate  the  law  of 
development,  the  gradation  of  families,  the  transference  of 
species,  and  so  on?  If  so,  I  claim  the  discovery  of  this 
esoteric  testimony  of  the  book  to  its  own  contents ;  I  defy 
any  one  to  point  out  the  reviewer  who  has  mentioned  it. 
The  work  itself  is  decribed  by  its  author  as  "the  first  at- 
tempt to  connect  the  natural  sciences  into  a  history  of 
creation."  The  attempt  was  commenced,  and  has  been 
carried  on,  both  with  marked  talent,  and  will  be  continued. 
Great  advantage  will  result:  at  the  worst  we  are  but  in  the 
alchemy  of  some  new  chemistry,  or  the  astrology  of  some 
new  astronomy.  Perhaps  it  would  be  as  well  not  to  be 
too  sure  on  the  matter,  until  we  have  an  antidote  to  possible 
consequences  as  exhibited  under  another  theory,  on  which 

1  See  note  2,  p.  252.  There  was  also  a  Theory  of  Parallels  that  dif- 
fered from  these,  London,  1853,  second  edition  1856,  third  edition  1856. 

/The  work  was  written  by  Robert  Chambers  (1802-1871),  the 
Edinburgh  publisher,  a  friend  of  Scott  and  of  many  of  his  contem- 
poraries in  the  literary  field.  He  published  the  Vestiges  of  the  Nat- 
ural History  of  Creation  in  1844,  not  1840. 


ON  RELIGIOUS  INSURANCE.  345 

it  is  as  reasonable  to  speculate  as  on  that  of  the  Vestiges. 
I  met  long  ago  with  a  splendid  player  on  the  guitar,  who 
assured  me,  and  was  confirmed  by  his  friends,  that  he 
never  practised,  except  in  thought,  and  did  not  possess  an 
instrument:  he  kept  his  fingers  acting  in  his  mind,  until 
they  got  their  habits ;  and  thus  he  learnt  the  most  difficult 
novelties  of  execution.  Now  what  if  this  should  be  a 
minor  segment  of  a  higher  law?  What  if,  by  constantly 
thinking  of  ourselves  as  descended  from  primeval  monkeys, 
we  should — if  it  be  true — actually  get  our  tails  again  ?  What 
if  the  first  man  who  was  detected  with  such  an  appendage 
should  be  obliged  to  confess  himself  the  author  of  the 
Vestiges — a  person  yet  unknown — who  would  naturally 
get  the  start  of  his  species  by  having  had  the  earliest  habit 
of  thinking  on  the  matter?  I  confess  I  never  hear  a  man 
of  note  talk  fluently  about  it  without  a  curious  glance  at 
his  proportions,  to  see  whether  there  may  be  ground  to 
conjecture  that  he  may  have  more  of  "mortal  coil"  than 
others,  in  anaxyridical  concealment.  I  do  not  feel  sure  that 
even  a  paternal  love  for  his  theory  would  induce  him,  in  the 
case  I  am  supposing,  to  exhibit  himself  at  the  British  Asso- 
ciation, 

With  a  hole  behind  which  his  tail  peeped  through. 

The  first  sentence  of  this  book  (1840)  is  a  cast  of  the  log, 
which  shows  our  rate  of  progress.  "It  is  familiar  knowl- 
edge that  the  earth  which  we  inhabit  is  a  globe  of  some- 
what less  than  8,000  miles  in  diameter,  being  one  of  a 
series  of  eleven  which  revolve  at  different  distances  around 
the  sun."  The  eleven\  Not  to  mention  the  Iscariot  which 
Le  Verrier  and  Adams  calculated  into  existence,  there  is 
more  than  a  septuagint  of  new  planetoids. 

ON  RELIGIOUS  INSURANCE. 

The  Constitution  and  Rules  of  the  Ancient  and  Universal  'Bene- 
fit Society'  established  by  Jesus  Christ,  exhibited,  and  its 
advantages  and  claims  maintained,  against  all  Modern  and 


346  A  BUDGET  OF  PARADOXES. 

merely  Human  Institutions  of  the  kind :  A  Letter  very  respect- 
fully addressed  to  the  Rev.  James  Everett,1  and  occasioned 
by  certain  remarks  made  by  him,  in  a  speech  to  the  Members 
of  the  'Wesleyan  Centenary  Institute'  Benefit  Society.  Dated 
York,  Dec.  7,  1840.  By  Thomas  Smith.2  I2mo,  (pp.  8.) 

The  Wesleyan  minister  addressed  had  advocated  provision 
against  old  age,  etc. :  the  writer  declares  all  private  provision 
tin-Christian.  After  decent  maintenance  and  relief  of  fam- 
ily claims  of  indigence,  he  holds  that  all  the  rest  is  to  go 
to  the  "Benefit  Society,"  of  which  he  draws  up  the  rules, 
in  technical  form,  with  chapters  of  "Officers,"  "Contribu- 
tors" etc.,  from  the  Acts  of  the  Apostles,  etc.,  and  some  of 
the  early  Fathers.  He  holds  that  a  Christian  may  not  "make 
a  private  provision  against  the  contingencies  of  the  future" : 
and  that  the  great  "Benefit  Society"  is  the  divinely-ordained 
recipient  of  all  the  surplus  of  his  income;  capital,  beyond 
what  is  necessary  for  business,  he  is  to  have  none.  A  real 
good  speculator  shuts  his  eyes  by  instinct,  when  opening 
them  would  not  serve  the  purpose:  he  has  the  vizor  of  the 
Irish  fairy  tale,  which  fell  of  itself  over  the  eyes  of  the 
wearer  the  moment  he  turned  them  upon  the  enchanted  light 
which  would  have  destroyed  him  if  he  had  caught  sight 
of  it.  "Whiles  it  remained,  was  it  not  thine  own?  and 
after  it  was  sold,  was  it  (the  purchase-money)  not  in  thine 
own  power?"  would  have  been  awkward  to  quote,  and  ac- 
cordingly nothing  is  stated  except  the  well-known  result, 
which  is  rule  3,  cap.  5,  "Prevention  of  Abuses."  By  putting 
his  principles  together,  the  author  can  be  made,  logically, 
to  mean  that  the  successors  of  the  apostles  should  put  to 
death  all  contributors  who  are  detected  in  not  paying  their 
full  premiums. 

Everett  (1784-1872)  was  at  that  time  a  good  Wesleyan,  but  was 
expelled  from  the  ministry  in  1849  for  having  written  Wesleyan 
Takings  and  as  under  suspicion  for  having  started  the  Fly  Sheets 
in  1845.  In  1857  he  established  the  United  Methodist  Free  Church. 

2  Smith  was  a  Primitive  Methodist  preacher.  He  also  wrote 
an  Earnest  Address  to  the  Methodists  (1841)  and  The  Wealth 
Question  (1840?). 


THE  TWO  OLD   PARADOXES   AGAIN.  347 

I  have  known  one  or  two  cases  in  which  policy-holders 
have  surrendered  their  policies  through  having  arrived  at 
a  conviction  that  direct  provision  is  unlawful.  So  far  as 
I  could  make  it  out,  these  parties  did  not  think  it  unlawful 
to  lay  by  out  of  income,  except  when  this  was  done  in  a 
manner  which  involved  calculation  of  death-chances.  It  is 
singular  they  did  not  see  that  the  entrance  of  chance  of 
death  was  the  entrance  of  the  very  principle  of  the  benefit 
society  described  in  the  Acts  of  the  Apostles.  The  family 
of  the  one  who  died  young  received  more  in  proportion  to 
premiums  paid  than  the  family  of  one  who  died  old.  Every 
one  who  understands  life  assurance  sees  that — bonus  apart 
— the  difference  between  an  assurance  office  and  a  savings 
bank  consists  in  the  adoption,  pro  tanto,  of  the  principle 
of  community  of  goods.  In  the  original  constitution  of 
the  oldest  assurance  office,  the  Amicable  Society,  the  plan 
with  which  they  started  was  nothing  but  this:  persons  of 
all  ages  under  forty-five  paid  one  common  premium,  and  the 
proceeds  were  divided  among  the  representatives  of  those 
who  died  within  the  year. 

THE  TWO  OLD  PARADOXES  AGAIN. 

[I  omitted  from  its  proper  place  a  manuscript  quadra- 
ture (3.1416  exactly)  addressed  to  an  eminent  mathemati- 
cian, dated  in  1842  from  the  debtor's  ward  of  a  country 
gaol.  The  unfortunate  speculator  says,  "I  have  labored 
many  years  to  find  the  precise  ratio."  I  have  heard  of  sev- 
eral cases  in  which  squaring  the  circle  has  produced  an  in- 
ability to  square  accounts.  I  remind  those  who  feel  a  kind 
of  inspiration  to  employ  native  genius  upon  difficulties, 
without  gradual  progression  from  elements,  that  the  call 
is  one  which  becomes  stronger  and  stronger,  and  may  lead, 
as  it  has  led,  to  abandonment  of  the  duties  of  life,  and  all 
the  consequences.] 


348  A   BUDGET  OF  PARADOXES. 

1842.  Provisional  Prospectus  of  the  Double  Acting  Rotary 
Engine  Company.  Also  Mechanic's  Magazine,  March  26, 
1842. 

Perpetual  motion  by  a  drum  with  one  vertical  half  in 
mercury,  the  other  in  a  vacuum :  the  drum,  I  suppose,  work- 
ing round  forever  to  find  an  easy  position.  Steam  to  be 
superseded :  steam  and  electricity  convulsions  of  nature 
never  intended  by  Providence  for  the  use  of  man.  The 
price  of  the  present  engines,  as  old  iron,  will  buy  new  en- 
gines that  will  work  without  fuel  and  at  no  expense.  Guaran- 
teed by  the  Count  de  Predaval,1  the  discoverer.  I  was  to 
have  been  a  Director,  but  my  name  got  no  further  than 
ink,  and  not  so  far  as  official  notification  of  the  honor, 
partly  owing  to  my  having  communicated  to  the  Mechan- 
ic's Magazine  information  privately  given  to  me,  which 
gave  premature  publicity,  and  knocked  up  the  plan. 

An  Exposition  of  the  Nature,  Force,  Action,  and  other  prop- 
erties of  Gravitation  on  the  Planets.  London,  1842,  I2mo. 

An  Investigation  of  the  principles  of  the  Rules  for  determining 
the  Measures  of  the  Areas  and  Circumferences  of  Circular 
Plane  Surfaces  . . .  London,  1844,  8vo. 

These  are  anonymous ;  but  the  author  (whom  I  believe 
to  be  Mr.  Denison,2  presently  noted)  is  described  as  author 
of  a  new  system  of  mathematics,  and  also  of  mechanics.  He 
had  need  have  both,  for  he  shows  that  the  line  which  has 
a  square  equal  to  a  given  circle,  has  a  cube  equal  to  the 
sphere  on  the  same  diameter :  that  is,  in  old  mathematics,  the 
diameter  is  to  the  circumference  as  9  to  16 !  Again,  admitting 
that  the  velocities  of  planets  in  circular  orbits  are  inversely  as 
the  square  roots  of  their  distances,  that  is,  admitting  Kepler's 
law,  he  manages  to  prove  that  gravitation  is  inversely  as 
the  square  root  of  the  distance:  and  suspects  magnetism 
of  doing  the  difference  between  this  and  Newton's  law. 

JHe  wrote  the  Nouveau  traite  de  Balistique,  Paris,  1837. 

8  Joseph  Denison,  known  to  fame  only  through  De  Morgan. 
See  also  page  353. 


THE  DUPLICATION  PROBLEM.  349 

Magnetism  and  electricity  are,  in  physics,  the  member  of 
parliament  and  the  cabman  —  at  every  man's  bidding,  as 
Henry  Warburton3  said. 

The  above  is  an  outrageous  quadrature.  In  the  pre- 
ceding year,  1841,  was  published  what  I  suppose  at  first  to 
be  a  Maori  quadrature,  by  Maccook.  But  I  get  it  from  a 
cutting  out  of  some  French  periodical,  and  I  incline  to 
think  that  it  must  be  by  a  Mr.  M'Cook.  He  makes  TT  to  be 


THE  DUPLICATION  PROBLEM. 

Refutation  of  a  Pamphlet  written  by  the  Rev.  John  Mackey, 
R.C.P.,1  entitled  "A  method  of  making  a  cube  double  of  a 
cube,  founded  on  the  principles  of  elementary  geometry," 
wherein  his  principles  are  proved  erroneous,  and  the  required 
solution  not  yet  obtained.  By  Robert  Murphy.2  Mallow,  1824, 
I2mo. 

This  refutation  was  the  production  of  an  Irish  boy  of 
eighteen  years  old,  self-educated  in  mathematics,  the  son 
of  a  shoemaker  at  Mallow.  He  died  in  1843,  leaving  a 
name  which  is  well  known  among  mathematicians.  His 
works  on  the  theory  of  equations  and  on  electricity,  and  his 
papers  in  the  Cambridge  Transactions,  are  all  of  high 
genius.  The  only  account  of  him  which  I  know  of  is  that 
which  I  wrote  for  the  Supplement  of  the  Penny  Cyclopcedia. 
He  was  thrown  by  his  talents  into  a  good  income  at  Cam- 
bridge, with  no  social  training  except  penury,  and  very  little 
intellectual  training  except  mathematics.  He  fell  into  dissi- 
pation, and  his  scientific  career  was  almost  arrested:  but 
he  had  great  good  in  him,  to  my  knowledge.  A  sentence  in 

'The  radical  (1784?-  1858),  advocate  of  the  founding  of  London 
university  (1826),  of  medical  reform  (1827-1834),  and  of  the  repeal 
of  the  duties  on  newspapers  and  corn,  and  an  ardent  champion  of 
penny  postage. 

1  I.  e.,  Roman  Catholic  Priest. 

2  Murphy   (1806-1843)    showed  extraordinary  powers  in  mathe- 
matics even  before  the  age  of  thirteen.    He  became  a  fellow  of  Caius 
College,  Cambridge,  in  1829,  dean  in  1831,  and  examiner  in  mathe- 
matics in  London  University  in  1838. 


350  A  BUDGET  OF  PARADOXES. 

a  letter  from  the  late  Dean  Peacock3  to  me — giving  some 
advice  about  the  means  of  serving  Murphy — sets  out  the 
old  case:  "Murphy  is  a  man  whose  special  education  is  in 
advance  of  his  general;  and  such  men  are  almost  always 
difficult  subjects  to  manage."  This  article  having  been 
omitted  in  its  proper  place,  I  put  it  at  1843,  the  date  of 
Murphy's  death. 

A   NEW   VALUE   OF   «-. 

The  Invisible  Universe  disclosed;  or,  the  real  Plan  and  Govern- 
ment of  the  Universe.  By  Henry  Coleman  Johnson,  Esq. 
London,  1843,  8vo. 

The  book  opens  abruptly  with: 

"First  demonstration.  Concerning  the  centre:  showing 
that,  because  the  centre  is  an  innermost  point  at  an  equal 
distance  between  two  extreme  points  of  a  right  line,  and 
from  every  two  relative  and  opposite  intermediate  points, 
it  is  composed  of  the  two  extreme  internal  points  of  each 
half  of  the  line;  each  extreme  internal  point  attracting 
towards  itself  all  parts  of  that  half  to  which  it  belongs. . ." 

Of  course  the  circle  is  squared :  and  the  circumference  is 
diameters. 

SOME  MODERN  ASTROLOGY. 

Combination  of  the  Zodiacal  and  Cometical  Systems.  Printed 
for  the  London  Society,  Exeter  Hall.  Price  Sixpence,  (n.  d. 
1843-) 

What  this  London  Society  was,  or  the  "combination," 
did  not  appear.  There  was  a  remarkable  comet  in  1843, 
the  tail  of  which  was  at  first  confounded  with  what  is  called 
the  zodiacal  light.  This  nicely-printed  little  tract,  evidently 
got  up  with  less  care  for  expense  than  is  usual  in  such 
works,  brings  together  all  the  announcements  of  the  as- 
tronomers, and  adds  a  short  head  and  tail  piece,  which  I 
shall  quote  entire.  As  the  announcements  are  very  ordinary 

8  See  note  2,  page  196. 


SOME  MODERN  ASTROLOGY.  351 

astronomy,  the  reader  will  be  able  to  detect,  if  detection  be 
possible,  what  is  the  meaning  and  force  of  the  "Combina- 
tion of  the  Zodiacal  and  Cometical  Systems": 

"Premonition.  It  has  pleased  the  AUTHOR  of  CREATION 
to  cause  (to  His  human  and  reasoning  Creatures  of  this 
generation,  by  a  'combined'  appearance  in  His  Zodiacal  and 
Cometical  system)  a  'warning  Crisis'  of  universal  concern- 
ment to  this  our  GLOBE.  It  is  this  'Crisis'  that  has  so  gen- 
erally 'ROUSED'  at  this  moment  the  'nations  throughout  the 
Earth'  that  no  equal  interest  has  ever  before  been  excited 
by  MAN  ;  unless  it  be  in  that  caused  by  the  ' PAGAN-TEMPLE 
IN  ROME/  which  is  recorded  by  the  elder  Pliny,  'Nat.  Hist/ 
i.  23.  iii.  3.  HARDOUIN." 

After  the  accounts  given  by  the  unperceiving  astronomers, 
comes  what  follows: 

"Such  has  been  (hitherto)  the  only  object  discerned  by 
the  Wise  of  this  World,'  in  this  twofold  union  of  the  'Zo- 
diacal' and  'Cometical'  systems :  yet  it  is  nevertheless  a  most 
'Thrilling  Warning'  to  all  the  inhabitants  of  this  precarious 
and  transitory  EARTH.  We  have  no  authorized  intimation 
or  reasonable  prospective  contemplation,  of  'current  time' 
beyond  a  year  1860,  of  the  present  century ;  or  rather,  ex- 
cept 'the  interval  which  may  now  remain  from  the  present 
year  1843,  to  a  year  I860'  (^ue'pas  'EEHKONTA— 'threescore 
or  sixty  days' — 7  have  appointed  each  "DAY"  for  a  "YEAR,"  ' 
Ezek.  iv.  6)  :  and  we  know,  from  our  'common  experience' 
how  speedily  such  a  measure  of  time  will  pass  away. 

"No  words  can  be  'more  explicit  than  these  of  OUR 
BLESSED  LORD:  viz.  THIS  GOSPEL  of  the  Kingdom  shall  be 
preached  in  ALL  the  EARTH,  for  a  Witness  to  ALL  NATIONS; 
AND  THEN,  shall  the  END  COME/  The  'next  18  years'  must 
therefore  supply  the  interval  of  the  'special  Episcopal  fore- 
runners.' 

(Matt.  xxiv.  14.) 

"See  the  'JEWISH  INTELLIGENCER'  of  the  present  month 
(April),  p.  153,  for  the  'Debates  in  Parliament,'  respecting 


352  A  BUDGET  OF  PARADOXES. 

the  BISHOP  OF  JERUSALEM,  viz.  Dr.  Bowring,1  Mr.  Hume,2 
Sir  R.  Inglis,3  Sir  R.  Peel,4  Viscount  Palmerston.5" 

I  have  quoted  this  at  length,  to  show  the  awful  threats 
which  were  published  at  a  time  of  some  little  excitement 
about  the  phenomenon,  under  the  name  of  the  London 
Society.  The  assumption  of  a  corporate  appearance  is  a 
very  unfair  trick:  and  there  are  junctures  at  which  harm 
might  be  done  by  it. 

THE   NUMBER   OF  THE   BEAST. 

Wealth  the  name  and  number  of  the  Beast,  666,  in  the  Book  of 
Revelation,     [by  John  Taylor.1]     London,  1844,  8vo. 

Whether  Junius  or  the  Beast  be  the  more  difficult  to 
identify,  must  be  referred  to  Mr.  Taylor,  the  only  person 
who  has  attempted  both.  His  cogent  argument  on  the 
political  secret  is  not  unworthily  matched  in  his  treatment 
of  the  theological  riddle.  He  sees  the  solution  in  cforopia, 
which  occurs  in  the  Acts  of  the  Apostles  as  the  word  for 
wealth  in  one  of  its  most  disgusting  forms,  and  makes  666 
in  the  most  straightforward  way.  This  explanation  has  as 
good  a  chance  as  any  other.  The  work  contains  a  general 

*Sir  John  Bowring  (1792-1872),  the  linguist,  writer,  and  trav- 
eler, member  of  many  learned  societies  and  a  writer  of  high  repu- 
tation in  his  time.  His  works  were  not,  however,  of  genuine  merit. 

3  Joseph  Hume  (1777-1855)  served  as  a  surgeon  with  the  British 
army  in  India  early  in  the  nineteenth  century.    He  returned  to  Eng- 
land in  1808  and  entered  parliament  as  a  radical  in  1812.     He  was 
much  interested  in  all  reform  movements. 

'Sir  Robert  Harry  Inglis  (1786-1855),  a  strong  Tory,  known 
for  his  numerous  addresses  in  the  House  of  Commons  rather  than 
for  any  real  ability. 

4  Sir  Robert  Peel    (1788-1850)   began  his  parliamentary  career 
in  1809  and  was  twice  prime  minister.   He  was  prominent  in  most  of 
the  great  reforms  of  his  time. 

B  See  note  5,  page  290. 

1  John  Taylor  (1781-1864)  was  a  publisher,  and  published  several 
pamphlets  opposed  to  Peel's  currency  measures.  De  Morgan  refers 
to  his  work  on  the  Junius  question.  This  was  done  early  in  his 
career,  and  resulted  in  A  Discovery  of  the  author  of  the  Letters  of 
Junius  (1813),  and  The  Identity  of  Junius  with  a  distinguished  liv- 
ing character  established  (1816),  this  being  Sir  Philip  Francis. 


EASTER  DAY  PARADOXERS.  353 

attempt  at  explanation  of  the  Apocalypse,  and  some  history 
of  opinion  on  the  subject.  It  has  not  the  prolixity  which 
is  so  common  a  fault  of  apocalyptic  commentators. 

A  practical  Treatise  on  Eclipses. ..  .with  remarks  on  the  anom- 
alies of  the  present  Theory  of  the  Tides.  By  T.  Kerigan,2 
F.R.S.  1844,  8vo. 

Containing  also  a  refutation  of  the  theory  of  the  tides, 
and  afterwards  increased  by  a  supplement,  "Additional 
facts  and  arguments  against  the  theory  of  the  tides,"  in 
answer  to  a  short  notice  in  the  Athenceum  journal.  Mr. 
Kerigan  was  a  lieutenant  in  the  Navy:  he  obtained  ad- 
mission to  the  Royal  Society  just  before  the  publication  of 
his  book. 

A  new  theory  of  Gravitation.  By  Joseph  Denison,3  Esq.  Lon- 
don, 1844,  I2mo. 

Commentaries  on  the  Principia.  By  the  author  of  'A  new  theory 
of  Gravitation.'  London,  1846,  8vo. 

Honor  to  the  speculator  who  can  be  put  in  his  proper 
place  by  one  sentence,  be  that  place  where  it  may. 

"But  we  have  shown  that  the  velocities  are  inversely  as 
the  square  roots  of  the  mean  distances  from  the  sun ;  where- 
fore, by  equality  of  ratios,  the  forces  of  the  sun's  gravita- 
tion upon  them  are  also  inversely  as  the  square  roots  of  their 
distances  from  the  sun." 

EASTER  DAY  PARADOXERS. 

In  the  years  1818  and  1845  the  full  moon  fell  on  Easter 
Day,  having  been  particularly  directed  to  fall  before  it  in 
the  act  for  the  change  of  style  and  in  the  English  missals 
and  prayer-books  of  all  time:  perhaps  it  would  be  more 
correct  to  say  that  Easter  Day  was  directed  to  fall  after 
the  full  moon ;  "but  the  principle  is  the  same."  No  explana- 
tion was  given  in  1818,  but  Easter  was  kept  by  the  tables, 

2  See  note  5,  page  308. 

3  See  page  348. 


354  A  BUDGET  OF  PARADOXES. 

in  defiance  of  the  rule,  and  of  several  protests.  A  chrono- 
logical panic  was  beginning  in  December  1844,  which  was 
stopped  by  the  Times  newspaper  printing  extracts  from  an 
article  of  mine  in  the  Companion  to  the  Almanac  for  1845, 
which  had  then  just  appeared.  No  one  had  guessed  the 
true  reason,  which  is  that  the  thing  called  the  moon  in  the 
Gregorian  Calendar  is  not  the  moon  of  the  heavens,  but 
a  fictitious  imitation  put  wrong  on  purpose,  as  will  pres- 
ently appear,  partly  to  keep  Easter  out  of  the  way  of  the 
Jews'  Passover,  partly  for  convenience  of  calculation.  The 
apparent  error  happens  but  rarely;  and  all  the  work  will 
perhaps  have  to  be  gone  over  next  time.  I  now  give  two 
bits  of  paradox. 

Some  theologians  were  angry  at  this  explanation.  A 
review  called  the  Christian  Observer  (of  which  Christian- 
ity I  do  not  know)  got  up  a  crushing  article  against  me. 
I  did  not  look  at  it,  feeling  sure  that  an  article  on  such  a 
subject  which  appeared  on  January  1,  1845,  against  a 
publication  made  in  December  1844,  must  be  a  second-hand 
job.  But  some  years  afterwards  (Sept.  10,  1850),  the  re- 
views, etc.  having  been  just  placed  at  the  disposal  of  readers 
in  the  old  reading-room  of  the  Museum,  I  made  a  tour  of 
inspection,  came  upon  my  critic  on  his  perch,  and  took  a 
look  at  him.  I  was  very  glad  to  remember  this,  for,  though 
expecting  only  second-hand,  yet  even  of  this  there  is  good 
and  bad;  and  I  expected  to  find  some  hints  in  the  good 
second-hand  of  a  respectable  clerical  publication.  I  read 
on,  therefore,  attentively,  but  not  long:  I  soon  came  to  the 
information  that  some  additions  to  Delambre's1  statement 
of  the  rule  for  finding  Easter,  belonging  to  distant  years, 
had  been  made  by  Sir  Harris  Nicolas!2  Now  as  I  myself 
furnished  my  friend  Sir  H.  N.  with  Delambre's  digest  of 

1  See  note  3,  page  160. 

_2Sir  Nicholas  Harris  Nicolas  (1799-1848)  was  a  reformer  in 
various  lines, — the  Record  Commission,  the  Society  of  Antiquaries, 
and  the  British  Museum, — and  his  work  was  not  without  good  results. 


EASTER  DAY  PARADOXERS.  355' 

Clavius's3  rule,  which  I  translated  out  of  algebra  into  com- 
mon language  for  the  purpose,  I  was  pretty  sure  this  was 
the  ignorant  reading  of  a  person  to  whom  Sir  H.  N.  was 
the  highest  arithmetical  authority  on  the  subject.  A  person 
pretending  to  chronology,  without  being  able  to  distinguish 
the  historical  points — so  clearly  as  they  stand  out — in  which 
Sir  H.  N.  speaks  with  authority,  from  the  arithmetical 
points  of  pure  reckoning  on  which  he  does  not  pretend  to 
do  more  than  directly  repeat  others,  must  be  as  fit  to  talk 
about  the  construction  of  Easter  Tables  as  the  Spanish  are 
to  talk  French.  I  need  hardly  say  that  the  additions  for 
distant  years  are  as  much  from  Clavius  as  the  rest:  my 
reviewer  was  not  deep  enough  in  his  subject  to  know  that 
Clavius  made  and  published,  from  his  rules,  the  full  table 
up  to  A.  D.  5000,  for  all  the  movable  feasts  of  every  year ! 
I  gave  only  a  glance  at  the  rest :  I  found  I  was  either  knave 
or  fool,  with  a  leaning  to  the  second  opinion;  and  I  came 
away  satisfied  that  my  critic  was  either  ignoramus  or  novice, 
with  a  leaning  to  the  first.  I  afterwards  found  an  ambiguity 
of  expression  in  Sir  H.  N.'s  account — whether  his  or  mine 
I  could  not  tell — which  might  mislead  a  novice  or  content 
an  ignoramus,  but  would  have  been  properly  read  or  further 
inquired  into  by  a  competent  person. 

The  second  case  is  this.  Shortly  after  the  publication 
of  my  article,  a  gentleman  called  at  my  house,  and,  finding 
I  was  not  at  home,  sent  up  his  card — with  a  stylish  west-end 
club  on  it — to  my  wife,  begging  for  a  few  words  on  pressing 
business.  With  many  well-expressed  apologies,  he  stated 
that  he  had  been  alarmed  by  hearing  that  Prof.  De  M.  had 
an  intention  of  altering  Easter  next  year.  Mrs.  De  M.  kept 
her  countenance,  and  assured  him  that  I  had  no  such  inten- 
tion, and  further,  that  she  greatly  doubted  my  having  the 
power  to  do  it.  Was  she  quite  sure  ?  his  authority  was  very 
good:  fresh  assurances  given.  He  was  greatly  relieved, 
for  he  had  some  horses  training  for  after  Easter,  which 

3  See  note  5,  page  69. 


356  A  BUDGET  OF  PARADOXES. 

would  not  be  ready  to  run  if  it  were  altered  the  wrong  way. 
A  doubt  comes  over  him :  would  Mrs.  De  M..  in  the  event 
of  her  being  mistaken,  give  him  the  very  earliest  informa- 
tion ?  Promise  given  ;  profusion  of  thanks  ;  more  apologies ; 
and  departure. 

Now,  candid  reader! — or  uncandid  either! — which  most 
deserves  to  be  laughed  at  ?  A  public  instructor,  who  under- 
takes to  settle  for  the  world  whether  a  reader  of  Clavius, 
the  constructor  of  the  Gregorian  Calendar,  is  fool  or  knave, 
upon  information  derived  from  a  compiler — in  this  matter — 
of  his  own  day ;  or  a  gentleman  of  horse  and  dog  associa- 
tions, who,  misapprehending  something  which  he  heard 
about  a  current  topic,  infers  that  the  reader  of  Clavius  had 
the  ear  of  the  Government  on  a  proposed  alteration.  I  suppose 
the  querist  had  heard  some  one  say,  perhaps,  that  the  day 
ought  to  be  set  right,  and  some  one  else  remark  that  I  might 
be  consulted,  as  the  only  person  who  had  discussed  the 
matter  from  the  original  source  of  the  Calendar. 

To  give  a  better  chance  of  the  explanation  being  at  once 
produced,  next  time  the  real  full  moon  and  Easter  Day  shall 
fall  together,  I  insert  here  a  summary  which  was  printed 
in  the  Irish  Prayer-book  of  the  Ecclesiastical  Society.  If 
the  amusement  given  by  paradoxers  should  prevent  a  use- 
less discussion  some  years  hence,  I  and  the  paradoxers  shall 
have  done  a  little  good  between  us — at  any  rate,  I  have 
done  my  best  to  keep  the  heavy  weight  afloat  by  tying 
bladders  to  it.  I  think  the  next  occurrence  will  be  in  1875. 

EASTER    DAY. 

In  the  years  1818  and  1845,  Easter  Day,  as  given  by  the 
rules  in  24  Geo.  II  cap.  23.  (known  as  the  act  for  the 
change  of  style)  contradicted  the  precept  given  in  the  pre- 
liminary explanations.  The  precept  is  as  follows: 

"Easter  Day,  on  which  the  rest"  of  the  moveable  feasts 
"depend,  is  always  the  First  Sunday  after  the  Full  Moon, 
which  happens  upon  or  next  after  the  Twenty-first  Day  of 


EASTER  DAY  PARADOXERS.  357 

March]  and  if  the  Full  Moon  happens  upon  a  Sunday, 
Easter  Day  is  the  Sunday  after." 

But  in  1818  and  1845,  the  full  moon  fell  on  a  Sunday, 
and  yet  the  rules  gave  that  same  Sunday  for  Easter  Day. 
Much  discussion  was  produced  by  this  circumstance  in  1818 : 
but  a  repetition  of  it  in  1845  was  nearly  altogether  prevented 
by  a  timely4  reference  to  the  intention  of  those  who  con- 
ducted the  Gregorian  reformation  of  the  Calendar.  Never- 
theless, seeing  that  the  apparent  error  of  the  Calendar  is 
due  to  the  precept  in  the  Act  of  Parliament,  which  is  both 
erroneous  and  insufficient,  and  that  the  difficulty  will  recur 
so  often  as  Easter  Day  falls  on  the  day  of  full  moon,  it  may 
be  advisable  to  select  from  the  two  articles  cited  in  the  note 
such  of  their  conclusions  and  rules,  without  proof  or  con- 
troversy, as  will  enable  the  reader  to  understand  the  main 
points  of  the  Easter  question,  and,  should  he  desire  it,  to 
calculate  for  himself  the  Easter  of  the  old  or  new  style,  for 
any  given  year. 

1.  In  the  very  earliest  age  of  Christianity,  a  controversy 
arose  as  to  the  mode  of  keeping  Easter,  some  desiring  to 
perpetuate  the  Passover,  others  to  keep  the  festival  of  the 
Resurrection.  The  first  afterwards  obtained  the  name  of 
Quartadecimans,  from  their  Easter  being  always  kept  on 
the  fourteenth  day  of  the  moon  (Exod.  xii.  18,  Levit.  xxiii. 
5.).  But  though  it  is  unquestionable  that  a  Judaizing  party 
existed,  it  is  also  likely  that  many  dissented  on  chrono- 
logical grounds.  It  is  clear  that  no  perfect  anniversary  can 
take  place,  except  when  the  fourteenth  of  the  moon,  and 
with  it  the  passover,  falls  on  a  Friday.  Suppose,  for  in- 
stance, it  falls  on  a  Tuesday:  one  of  three  things  must  be 

*In  the  Companion  to  the  Almanac  for  1845  is  a  paper  by  Prof. 
De  Morgan,  "On  the  Ecclesiastical  Calendar,"  the  statements  of 
which,  so  far  as  concerns  the  Gregorian  Calendar,  are  taken  direct 
from  the  work  of  Clavius,  the  principal  agent  in  the  arrangement  of 
the  reformed  reckoning.  This  was  followed,  in  the  Companion  to  the 
Almanac  for  1846,  by  a  second  paper,  by  the  same  author,  headed 
"On  the  Earliest  Printed  Almanacs,"  much  of  which  is  written  in 
direct  supplement  to  the  former  article. — S.  E.  De  Morgan. 


358  A  BUDGET  OF  PARADOXES. 

done.  Either  (which  seems  never  to  have  been  proposed) 
the  crucifixion  and  resurrection  must  be  celebrated  on  Tues- 
day and  Sunday,  with  a  wrong  interval ;  or  the  former  on 
Tuesday,  the  latter  on  Thursday,  abandoning  the  first  day 
of  the  week;  or  the  former  on  Friday,  and  the  latter  on 
Sunday,  abandoning  the  paschal  commemoration  of  the  cru- 
cifixion. 

The  last  mode  has  been,  as  every  one  knows,  finally 
adopted.  The  disputes  of  the  first  three  centuries  did  not 
turn  on  any  calendar  questions.  The  Easter  question  was 
merely  the  symbol  of  the  struggle  between  what  we  may 
call  the  Jewish  and  Gentile  sects  of  Christians :  and  it  nearly 
divided  the  Christian  world,  the  Easterns,  for  the  most  part, 
being  Quartadecimans.  It  is  very  important  to  note  that 
there  is  no  recorded  dispute  about  a  method  of  predicting 
the  new  moon,  that  is,  no  general  dispute  leading  to  forma- 
tion of  sects:  there  may  have  been  difficulties,  and  discus- 
sions about  them.  The  Metonic  cycle,  presently  mentioned, 
must  have  been  used  by  many,  perhaps  most,  churches. 

2.  The  question  came  before  the  Nicene  Council  (A.  D. 
325)  not  as  an  astronomical,  but  as  a  doctrinal,  question: 
it  was,  in  fact,  this,  Shall  the  passover*  be  treated  as  a  part 
of  Christianity?  The  Council  resolved  this  question  in  the 
negative,  and  the  only  information  on  its  premises  and  con- 
clusion, or  either,  which  comes  from  itself,  is  contained  in 
the  following  sentence  of  the  synodical  epistle,  which  epistle 
is  preserved  by  Socrates6  and  Theodoret.7  "We  also  send 

5  It  may  be  necessary  to  remind  some  English  readers  that  in 
Latin  and  its  derived  European  languages,  what  we  call  Easter  is 
called  the  passover  (pascha).  The  Quartadecimans  had  the  name 
on  their  side :  a  possession  which  often  is,  in  this  world,  nine  points 
of  the  law.— A.  De  M. 

fl  Socrates  Scholasticus  was  born  at  Constantinople  c.  379,  and 
died  after  439.  His  Historia  Ecclesiastic  a  (in  Greek)  covers  the 
period  from  Constantine  the  Great  to  about  439,  and  includes  the 
Council  of  Nicaea.  The  work  was  printed  in  Paris  1544. 

7Theodoretus  or  Theodoritus  was  born  at  Antioch  and  died 
about  457.  He  was  one  of  the  greatest  divines  of  the  fifth  century, 
a  man  of  learning,  piety,  and  judicial  mind,  and  a  champion  of  free- 
dom of  opinion  in  all  religious  matters. 


EASTER  DAY  PARADOXERS.  359 

you  the  good  news  concerning  the  unanimous  consent  of  all 
in  reference  to  the  celebration  of  the  most  solemn  feast  of 
Easter,  for  this  difference  also  has  been  made  up  by  the 
assistance  of  your  prayers:  so  that  all  the  brethren  in  the 
East,  who  formerly  celebrated  this  festival  at  the  same 
time  as  the  Jews,  will  in  future  conform  to  the  Romans  and 
to  us,  and  to  all  who  have  of  old  observed  our  manner  of 
celebrating  Easter."  This  is  all  that  can  be  found  on  the 
subject:  none  of  the  stories  about  the  Council  ordaining 
the  astronomical  mode  of  finding  Easter,  and  introducing 
the  Metonic  cycle  into  ecclesiastical  reckoning,  have  any 
contemporary  evidence:  the  canons  which  purport  to  be 
those  of  the  Nicene  Council  do  not  contain  a  word  about 
Easter;  and  this  is  evidence,  whether  we  suppose  those 
canons  to  be  genuine  or  spurious. 

3.  The  astronomical  dispute  about  a  lunar  cycle  for  the 
prediction  of  Easter  either  commenced,  or  became  prom- 
inent, by  the  extinction  of  greater  ones,  soon  after  the  time 
of  the  Nicene  Council.  Pope  Innocent  I8  met  with  difficulty 
in  414.  S.  Leo,9  in  454,  ordained  that  Easter  of  455  should 
be  April  24;  which  is  right.  It  is  useless  to  record  details 
of  these  disputes  in  a  summary:  the  result  was,  that  in  the 
year  463,  Pope  Hilarius10  employed  Victorinus11  of  Aqui- 
taine  to  correct  the  Calendar,  and  Victorinus  formed  a  rule 
which  lasted  until  the  sixteenth  century.  He  combined  the 
Metonic  cycle  and  the  solar  cycle  presently  described.  But 

8  He  died  in  417.     He  was  a  man  of  great  energy  and  of  high 
attainments. 

9  He  died  in  461,  having  reigned  as  pope  for  twenty-one  years. 
It  was  he  who  induced  Attila  to  spare  Rome  in  452. 

10  He  succeeded  Leo  as  pope  in  461,  and  reigned  for  seven  years. 

"Victorinus  or  Victorius  Marianus  seems  to  have  been  born  at 
Limoges.  He  was  a  mathematician  and  astronomer,  and  the  cycle 
mentioned  by  De  Morgan  is  one  of  532  years,  a  combination  of  the 
Metonic  cycle  of  19  years  with  the  solar  cycle  of  28  years.  His 
canon  was  published  at  Antwerp  in  1633  or  1634,  De  doctrina  tem- 
porum  sive  commentarius  in  Victorii  Aquitani  et  aliorum  canones 
pas  c  hales. 


360  A  BUDGET  OF  PARADOXES. 

this  cycle  bears  the  name  of  Dionysius  Exiguus,12  a  Scythian 
settled  at  Rome,  about  A.  D.  530,  who  adapted  it  to  his  new 
yearly  reckoning,  when  he  abandoned  the  era  of  Diocletian 
as  a  commencement,  and  constructed  that  which  is  now  in 
common  use. 

4.  With  Dionysius,  if  not  before,  terminated  all  differ- 
ence as  to  the  mode  of  keeping  Easter  which  is  of  historical 
note:  the  increasing  defects  of  the  Easter  Cycle  produced 
in  time  the  remonstrance  of  persons  versed  in  astronomy, 
among  whom   may  be  mentioned   Roger  Bacon,13    Sacro- 
bosco,14  Cardinal  Cusa,15  Regiomontanus,18  etc.     From  the 
middle  of  the  sixth  to  that  of  the  sixteenth  century,  one 
rule  was  observed. 

5.  The  mode  of  applying  astronomy  to  chronology  has 
always  involved  these  two  principles.     First,  the  actual  po- 
sition of  the  heavenly  body  is  not  the  object  of  considera- 
tion, but  what  astronomers  call  its  mean  place,  which  may 
be  described  thus.     Let  a  fictitious  sun  or  moon  move  in 
the  heavens,  in  such  manner  as  to  revolve  among  the  fixed 
stars  at  an  average  rate,  avoiding  the  alternate  accelerations 
and  retardations  which  take  place  in  every  planetary  mo- 
tion.    Thus  the  fictitious   (say  mean)   sun  and  moon  are 
always  very  near  to  the  real  sun  and  moon.    The  ordinary 
clocks  show  time  by  the  mean,  not  the  real,  sun :  and  it  was 
always  laid  down  that  Easter  depends  on  the  opposition 
(or  full  moon)  of  the  mean  sun  and  moon,  not  of  the  real 
ones.    Thus  we  see  that,  were  the  Calendar  ever  so  correct 

"  He  went  to  Rome  about  497,  and  died  there  in  540.  He  wrote 
his  Liber  de  paschate  in  525,  and  it  was  in  this  work  that  the  Chris- 
tian era  was  first  used  for  calendar  purposes. 

11  See  note  6,  page  126. 

"Johannes  de  Sacrobosco  (Holy  wood),  or  John  of  Holywood. 
The  name  was  often  written,  without  regard  to  its  etymology, 
Sacrobusto.  He  was  educated  at  Oxford  and  taught  in  Paris  until 
his  death  (1256).  He  did  much  to  make  the  Hindu-Arabic  numer- 
als known  to  European  scholars. 

11  See  note  2,  page  44. 
"  See  note  2,  page  48. 


EASTER  DAY  PARADOXERS.  361 

as  to  the  mean  moon,  it  would  be  occasionally  false  as  to  the 
true  one:  if,  for  instance,  the  opposition  of  the  mean  sun 
and  moon  took  place  at  one  second  before  midnight,  and  that 
of  the  real  bodies  only  two  seconds  afterwards,  the  calendar 
day  of  full  moon  would  be  one  day  before  that  of  the  com- 
mon almanacs.  Here  is  a  way  in  which  the  discussions  of 
1818  and  1845  might  have  arisen:  the  British  legislature  has 
defined  the  moon  as  the  regulator  of  the  paschal  calendar. 
But  this  was  only  a  part  of  the  mistake. 

6.  Secondly,  in  the  absence  of  perfectly  accurate  knowl- 
edge of  the  solar  and  lunar  motion  (and  for  convenience, 
even  if  such  knowledge  existed),  cycles  are,  and  always  have 
been  taken,  which  serve  to  represent  those  motions  nearly. 
The  famous  Metonic  cycle,  which  is  introduced  into  eccle- 
siastical chronology  under  the  name  of  the  cycle  of  the 
golden  numbers,  is  a  period  of  19  Julian17  years.     This 
period,  in  the  old  Calendar,  was  taken  to  contain  exactly 
235  lunations,  or  intervals  between  new  moons,  of  the  mean 
moon.    Now  the  state  of  the  case  is : 

19  average  Julian  years  make  6939  days  18  hours. 

235  average  lunations  make  6939  days  16  hours  31 
minutes. 

So  that  successive  cycles  of  golden  numbers,  supposing 
the  first  to  start  right,  amount  to  making  the  new  moons 
fall  too  late,  gradually,  so  that  the  mean  moon  of  this  cycle 
gains  1  hour  29  minutes  in  19  years  upon  the  mean  moon 
of  the  heavens,  or  about  a  day  in  300  years.  When  the 
Calendar  was  reformed,  the  calendar  new  moons  were  four 
days  in  advance  of  the  mean  moon  of  the  heavens :  so  that, 
for  instance,  calendar  full  moon  on  the  18th  usually  meant 
real  full  moon  on  the  14th. 

7.  If  the  difference  above  had  not  existed,  the  moon  of 
the  heavens  (the  mean  moon  at  least),  would  have  returned 

"The  Julian  year  is  a  year  of  the  Julian  Calendar,  in  which 
there  is  leap  year  every  fourth  year.  Its  average  length  is  therefore 
365  days  and  a  quarter.— A.  De  M. 


362  A  BUDGET  OF  PARADOXES. 

permanently  to  the  same  days  of  the  month  in  19  years ; 
with  an  occasional  slip  arising  from  the  unequal  distribu- 
tion of  the  leap  years,  of  which  a  period  contains  sometimes 
five  and  sometimes  four.  As  a  general  rule,  the  days  of 
new  and  full  moon  in  any  one  year  would  have  been  also 
the  days  of  new  and  full  moon  of  a  year  having  19  more 
units  in  its  date.  Again,  if  there  had  been  no  leap  years, 
the  days  of  the  month  would  have  returned  to  the  same 
days  of  the  week  every  seven  years.  The  introduction  of 
occasional  29ths  of  February  disturbs  this,  and  makes  the 
permanent  return  of  month  days  to  week  days  occur  only 
after  28  years.  If  all  had  been  true,  the  lapse  of  28  times  19, 
or  532  years,  would  have  restored  the  year  in  every  point: 
that  is,  A.  D.  1,  for  instance,  and  A.  D.  533,  would  have  had 
the  same  almanac  in  every  matter  relating  to  week  days, 
month  days,  sun,  and  moon  (mean  sun  and  moon  at  least). 
And  on  the  supposition  of  its  truth,  the  old  system  of  Diony- 
sius  was  framed.  Its  errors,  are,  first,  that  the  moments 
of  mean  new  moon  advance  too  much  by  1  h.  29  m.  in  19 
average  Julian  years;  secondly,  that  the  average  Julian 
year  of  365 J  days  is  too  long  by  llm.  10s. 

8.  The  Council  of  Trent,  moved  by  the  representations 
made  on  the  state  of  the  Calendar,  referred  the  considera- 
tion of  it  to  the  Pope.  In  1577,  Gregory  XIII18  submitted 
to  the  Roman  Catholic  Princes  and  Universities  a  plan  pre- 
sented to  him  by  the  representatives  of  Aloysius  Lilius,19 
then  deceased.  This  plan  being  approved  of,  the  Pope  nomi- 
nated a  commission  to  consider  its  details,  the  working  mem- 
ber of  which  was  the  Jesuit  Clavius.  A  short  work  was 
prepared  by  Clavius,  descriptive  of  the  new  Calendar:  this 

18Ugo  Buoncompagno  (1502-1585)  was  elected  pope  in  1572. 

19  He  was  a  Calabrian,  and  as  early  as  1552  was  professor  of 
medicine  at  Perugia.  In  1576  his  manuscript  on  the  reform  of  the 
calendar  was  presented  to  the  Roman  Curia  by  his  brother,  An- 
tonius.  The  manuscript  was  not  printed  and  it  has  not  been  pre- 
served. 


EASTER  DAY  PARADOXERS.  363 

was  published20  in  1582,  with  the  Pope's  bull  (dated  Febru- 
ary 24,  1581)  prefixed.  A  larger  work  was  prepared  by 
Clavius,  containing  fuller  explanation,  and  entitled  Romani 
Calendarii  a  Gregorio  XIII.  Pontifice  Maximo  restituti  Ex- 
plicatio.  This  was  published  at  Rome  in  1603,  and  again 
in  the  collection  of  the  works  of  Clavius  in  1612. 

9.  The  following  extracts  from  Clavius  settle  the  question 
of  the  meaning  of  the  term  moon,  as  used  in  the  Calendar : 

"Who,  except  a  few  who  think  they  are  very  sharp- 
sighted  in  this  matter,  is  so  blind  as  not  to  see  that  the  14th 
of  the  moon  and  the  full  moon  are  not  the  same  things  in 

the  Church  of  God? Although  the  Church,  in  finding  the 

new  moon,  and  from  it  the  14th  day,  uses  neither  the  true 
nor  the  mean  motion  of  the  moon,  but  measures  only  ac- 
cording to  the  order  of  a  cycle,  it  is  nevertheless  undeniable 
that  the  mean  full  moons  found  from  astronomical  tables  are 
of  the  greatest  use  in  determining  the  cycle  which  is  to  be 

preferred the  new  moons  of  which  cycle,  in  order  to 

the  due  celebration  of  Easter,  should  be  so  arranged  that 
the  14th  days  of  those  moons,  reckoning  from  the  day  of 
new  moon  inclusive,  should  not  fall  two  or  more  days  before 
the  mean  full  moon,  but  only  one  day,  or  else  on  the  very 
day  itself,  or  not  long  after.  And  even  thus  far  the  Church 
need  not  take  very  great  pains ....  for  it  is  sufficient  that  all 
should  reckon  by  the  14th  day  of  the  moon  in  the  cycle,  even 
though  sometimes  it  should  be  more  than  one  day  before  or 
after  the  mean  full  moon ....  We  have  taken  pains  that  in 
our  cycle  the  new  moons  should  follow  the  real  new  moons, 
so  that  the  14th  of  the  moon  should  fall  either  the  day  be- 
fore the  mean  full  moon,  or  on  that  day,  or  not  long  after ; 
and  this  was  done  on  purpose,  for  if  the  new  moon  of  the 
cycle  fell  on  the  same  day  as  the  mean  new  moon  of  the 

20  The  title  of  this  work,  which  is  the  authority  on  all  points  of 
the  new  Calendar,  is  Kalendarium  Gregorianum  Perpetuum.  Cum 
Privilegio  Summi  Pontificis  Et  Aliorum  Principum.  Roma,  Ex 
Officina  Dominici  Bascz.  MDLXXXII.  Cum  Licentia  Superiorum 
(quarto,  pp.  60).— A.  De  M. 


364  A  BUDGET  OF  PARADOXES. 

astronomers,  it  might  chance  that  we  should  celebrate  Easter 
on  the  same  day  as  the  Jews  or  the  Quartadeciman  heretics, 
which  would  be  absurd,  or  else  before  them,  which  would 
be  still  more  absurd." 

From  this  it  appears  that  Clavius  continued  the  Calen- 
dar of  his  predecessors  in  the  choice  of  the  fourteenth  day 
of  the  moon.  Our  legislature  lays  down  the  day  of  the  full 
moon:  and  this  mistake  appears  to  be  rather  English  than 
Protestant;  for  it  occurs  in  missals  published  in  the  reign 
of  Queen  Mary.  The  calendar  lunation  being  29|  days, 
the  middle  day  is  the  fifteenth  day,  and  this  is  and  was 
reckoned  as  the  day  of  the  full  moon.  There  is  every 
right  to  presume  that  the  original  passover  was  a  feast  of 
the  real  full  moon :  but  it  is  most  probable  that  the  moons 
were  then  reckoned,  not  from  the  astronomical  conjunction 
with  the  sun,  which  nobody  sees  except  at  an  eclipse,  but 
from  the  day  of  -first  visibility  of  the  new  moon.  In  fine 
climates  this  would  be  the  day  or  two  days  after  conjunction  ; 
and  the  fourteenth  day  from  that  of  first  visibility  inclusive, 
would  very  often  be  the  day  of  full  moon.  The  following 
is  then  the  proper  correction  of  the  precept  in  the  Act  of 
Parliament : 

Easter  Day,  on  which  the  rest  depend,  is  always  the 
First  Sunday  after  the  fourteenth  day  of  the  calendar  moon 
which  happens  upon  or  next  after  the  Twenty-first  day  of 
March,  according  to  the  rules  laid  down  for  the  construction 
of  the  Calendar-,  and  if  the  fourteenth  day  happens  upon  a 
Sunday,  Easter  Day  is  the  Sunday  after. 

10.  Further,  it  appears  that  Clavius  valued  the  celebra- 
tion of  the  festival  after  the  Jews,  etc.,  more  than  astronom- 
ical correctness.  He  gives  comparison  tables  which  would 
startle  a  believer  in  the  astronomical  intention  of  his  Calen- 
dar: they  are  to  show  that  a  calendar  in  which  the  moon  is 
always  made  a  day  older  than  by  him,  represents  the  heavens 
better  than  he  has  done,  or  meant  to  do.  But  it  must  be 
observed  that  this  diminution  of  the  real  moon's  age  has 


EASTER  DAY  PARADOXERS.  365 

a  tendency  to  make  the  English  explanation  often  practically 
accordant  with  the  Calendar.  For  the  fourteenth  day  of 
Clavius  is  generally  the  fifteenth  day  of  the  mean  moon  of 
the  heavens,  and  therefore  most  often  that  of  the  real 
moon.  But  for  this,  1818  and  1845  would  not  have  been 
the  only  instances  of  our  day  in  which  the  English  precept 
would  have  contradicted  the  Calendar. 

11.  In  the  construction  of  the  Calendar,  Clavius  adopted 
the  ancient  cycle  of  532  years,  but,  we  may  say,  without 
ever  allowing  it  to  run  out.  At  certain  periods,  a  shift  is 
made  from  one  part  of  the  cycle  into  another.  This  is  done 
whenever  what  should  be  Julian  leap  year  is  made  a  com- 
mon year,  as  in  1700,  1800,  1900,  2100,  etc.  It  is  also  done 
at  certain  times  to  correct  the  error  of  1  h.  19  m.,  before 
referred  to,  in  each  cycle  of  golden  numbers :  Clavius,  to 
meet  his  view  of  the  amount  of  that  error,  put  forward 
the  moon's  age  a  day  8  times  in  2,500  years.  As  we  cannot 
enter  at  full  length  into  the  explanation,  we  must  content 
ourselves  with  giving  a  set  of  rules,  independent  of  tables, 
by  which  the  reader  may  find  Easter  for  himself  in  any 
year,  either  by  the  old  Calendar  or  the  new.  Any  one  who 
has  much  occasion  to  find  Easters  and  movable  feasts  should 
procure  Francceur's21  tables. 

12.  Rule  for  determining  Easter  Day  of  the  Gregorian 
Calendar  in  any  year  of  the  new  style.  To  the  several  parts 

*a  Manueh-Roret.  Theorie  du  Calendrier  et  collection  de  tous 

les  Calendriers  des  Annees  passees  et  futures Par  L.  B.  Fran- 

cceur,. .  .Paris,  a  la  librairie  encyclopedique  de  Roret,  rue  Haute- 
feuille,  10  bis.  1842.  (i2mo.)  In  this  valuable  manual,  the  35 
possible  almanacs  are  given  at  length,  with  such  preliminary  tables 
as  will  enable  any  one  to  find,  by  mere  inspection,  which  almanac 
he  is  to  choose  for  any  year,  whether  of  old  or  new  style.  [1866. 
I  may  now  refer  to  my  own  Book  of  Almanacs,  for  the  same  pur- 
pose].—A.  De  M. 

Louis  Benjamin  Francceur  (1773-1849),  after  holding  positions 
in  the  Ecole  polytechnique  (1804)  and  the  Lycee  Charlemagne 
(1805),  became  professor  of  higher  algebra  in  the  University  of 
Paris  (1809).  His  Cours  complet  des  mathematiques  pures  was  well 
received,  and  he  also  wrote  on  mechanics,  astronomy,  and  geodesy. 


366  A  BUDGET  OF  PARADOXES. 

of  the  rule  are  annexed,  by  way  of  example,  the  results  for 
the  year  1849. 

I.  Add  i  to  the  given  year.    ( 1850) . 

II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting 
the  remainder.     (462). 

III.  Take  16  from  the  centurial  figures  of  the  given  year,  if  it  can 

be  done,  and  take  the  remainder.     (2). 

IV.  Take  the  quotient  of  III.   divided  by  4,   neglecting  the   re- 

mainder,    (o). 

V.  From  the  sum  of  L,  II.,  and  IV.,  subtract  III.     (2310). 
VI.  Find  the  remainder  of  V.  divided  by  7.     (o). 
VII.  Subtract  VI.   from  7;   this  is  the  number  of  the  dominical 

letter  A  B  C  D I F  G      (7 ;  dominical  letter  G>  • 

VIII.  Divide  I.  by  19,  the  remainder  (or  19,  if  no  remainder)  is  the 
golden  number.    (7). 

IX.  From  the  centurial  figures  of  the  year  subtract  17,  divide  by 

25,  and  keep  the  quotient,     (o). 

X.  Subtract  IX.  and  15  from  the  centurial  figures,  divide  by  3, 
and  keep  the  quotient,     (i). 

XL  To  VIII.  add  ten  times  the  next  less  number,  divide  by  30,  and 

keep  the  remainder.     (7). 

XII.  To  XL  add  X.  and  IV.,  and  take  away  III.,  throwing  out 
thirties,  if  any.  If  this  give  24,  change  it  into  25.  If  25, 
change  it  into  26,  whenever  the  golden  number  is  greater 
than  ii.  If  o,  change  it  into  30.  Thus  we  have  the  epact,  or 
age  of  the  Calendar  moon  at  the  beginning  of  the  year.  (6). 

When  the  Epact  is  23,  or  less.        When  the  Epact  is  greater  than  23. 


XIII.  Subtract   XII.,   the   epact, 

from  45.     (39). 

XIV.  Subtract   the    epact    from 

27,  divide  by  7,  and 
keep  the  remainder,  or 
7,  if  there  be  no  re- 
mainder. (7). 


XIII.  Subtract   XII.,   the   epact, 

from  75. 

XIV.  Subtract   the    epact   from 

57,  divide  by  7,  and 
keep  the  remainder,  or 
7,  if  there  be  no  re- 
mainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides,  if 
XIV.  be  greater  than  VII.,)  and  subtract  XIV.,  the  result 
is  the  day  of  March,  or  if  more  than  31,  subtract  31,  and 


EASTER  DAY  PARADOXERS. 


367 


the  result  is  the  day  of  April,  on  which  Easter   Sunday 
falls.     (39;  Easter  Day  is  April  8). 

In  the  following  examples,  the  several  results  leading 
to  the  final  conclusion  are  tabulated. 


GIVEN  YEAR 

1592 

1637 

1723 

1853 

2018 

4686 

I. 

1593 

1638 

1724 

1854 

2019 

4687 

II. 

398 

409 

430 

463 

504 

1171 

III. 



0 

1 

2 

4 

30 

IV. 



0 

0 

0 

1 

7 

V. 

1991 

2047 

2153 

2315 

2520 

5835 

VI. 

3 

3 

4 

5 

0 

4 

VII. 

4 

4 

3 

2 

7 

3 

VIII. 

16 

4 

14 

11 

5 

13 

IX. 





0 

0 

0 

1 

X. 

0 

0 

0 

1 

1 

10 

XL 

16 

4 

24 

21 

15 

13 

XII. 

16 

4 

23 

20 

13 

0  say  30 

XIII. 

29 

41 

22 

25 

32 

45 

XIV. 

4 

2 

4 

7 

7 

6 

XV. 

29 

43 

28 

27 

32 

49 

Easter  Day' 

Mar.  29 

Apr.  12 

Mar.  28 

Mar.  27 

Apr.  1 

Apr.  18 

13.  Rule  for  determining  Easter  Day  of  the  Antegrego- 
rian  Calendar  in  any  year  of  the  old  style.  To  the  several 
parts  of  the  rule  are  annexed,  by  way  of  example,  the  results 
for  the  year  1287.  The  steps  are  numbered  to  correspond 
with  the  steps  of  the  Gregorian  rule,  so  that  it  can  be  seen 
what  augmentations  the  latter  requires. 

I.  Set  down  the  given  year.     (1287). 
II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting 

the  remainder  (321). 

V.  Take  4  more  than  the  sum  of  I.  and  II.     (1612). 
VI.  Find  the  remainder  of  V.  divided  by  7.     (2). 
VII.  Subtract  VI.  from  7;  this  is  the  number  of  the  dominical 


letter 


ABCDEFG 


(5;  dominical  letter  E). 


1234567. 

VIII.  Divide  one  more  than  the  given  year  by  19,  the  remainder 

(or  19  if  no  remainder)  is  the  golden  number.     (15). 
XII.  Divide  3  less  than  n  times  VIII.  by  30;  the  remainder  (or  30 
if  there  be  no  remainder)  is  the  epact     (12). 


368  A  BUDGET  OF  PARADOXES. 


When  the  Epact  is  23,  or  less.        When  the  Epact  is  greater  than  23. 


XIII.  Subtract   XII.,   the  epact, 

from  45.     (33). 

XIV.  Subtract   the   epact    from 

27,  divide  by  7,  and 
keep  the  remainder,  or 
7,  if  there  be  no  re- 
mainder, (i). 


XIII.  Subtract   XII.,   the   epact, 

from  75. 

XIV.  Subtract   the    epact   from 

57,  divide  by  7,  and 
keep  the  remainder,  or 
7,  if  there  be  no  re- 
mainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides  if 
XIV.  be  greater  than  VII.,)  and  subtract  XIV.,  the  result 
is  the  day  of  March,  or  if  more  than  31,  subtract  31,  and  the 
result  is  the  day  of  April,  on  which  Easter  Sunday  (old 
style)  falls.  (37;  Easter  Day  is  April  6). 

These  rules  completely  represent  the  old  and  new  Cal- 
endars, so  far  as  Easter  is  concerned.  For  further  explana- 
tion we  must  refer  to  the  articles  cited  at  the  commence- 
ment. 

The  annexed  is  the  table  of  new  and  full  moons  of  the 
Gregorian  Calendar,  cleared  of  the  errors  made  for  the 
purpose  of  preventing  Easter  from  coinciding  with  the 
Jewish  Passover. 

The  second  table  (page  370)  contains  e pacts,  or  ages  of 
the  moon  at  the  beginning  of  the  year:  thus  in  1913,  the 
epact  is  22,  in  1868  it  is  6.  This  table  goes  from  1850  to 
1999:  should  the  New  Zealander  not  have  arrived  by  that 
time,  and  should  the  churches  of  England  and  Rome  then 
survive,  the  epact  table  may  be  continued  from  their  liturgy- 
books.  The  way  of  using  the  table  is  as  follows :  Take  the 
epact  of  the  required  year,  and  find  it  in  the  first  or  last 
column  of  the  first  table,  in  line  with  it  are  seen  the  calendar 
days  of  new  and  full  moon.  Thus,  when  the  epact  is  17, 
the  new  and  full  moons  of  March  fall  on  the  13th  and  28th. 
The  result  is,  for  the  most  part,  correct:  but  in  a  minority 
of  cases  there  is  an  error  of  a  day.  When  this  happens,  the 
error  is  almost  always  a  fraction  of  a  day  much  less  than 
twelve  hours.  Thus,  when  the  table  gives  full  moon  on  the 
27th,  and  the  real  truth  is  the  28th,  we  may  be  sure  it  is  early 


Jan. 

Feb. 

Mar 

Apr. 

May 

June 

July 

Aug 

Sep. 

Oct. 

Nov 

Dec. 

1  \ 

ag 
14 

27 
13 

29 
M 

27 
13 

27 

12 

25 
ii 

25 

IO 

23 
9 

22 

7 

21 

7 

20 
5 

19 
5 

i   1 

2  { 

28 
13 

26 

12 

28 
U 

26 

13 

26 
ii 

24 

IO 

24 
9 

32 

8 

31 

6 

20 

6 

19 

4 

18 

4 

f  2 

3 

37 
12 

25 
II 

27 

12 

25 
ii 

25 

10 

23 
9 

3 

21 

7 

20 

5 

19 

5 

18 
3 

17 
3 

1  3 

4 

26 
ii 

24 
IO 

26 
II 

24 

IO 

24 

9 

22 
8 

22 

7 

20 
6 

19 

4 

18 

4 

17 

a 

16 

2,31 

El 

5  ; 

25 

10 

23 

9 

25 
IO 

23 

9 

'i 

21 

7 

21 

6 

19 
5 

18 
3 

17 
3 

16 

i 

15 
1,30 

1  ^ 

6  { 

24 
9 

22 
8 

24 

9 

22 
8 

22 

7 

20 
6 

20 

5 

18 

4 

17 

a 

16 
2,31 

15 
30 

14 
29 

1  ^ 

7  { 

23 

21 

7 

1 

21 

7 

21 

6 

19 
5 

19 

4 

17 
3 

16 

15 
i,3° 

14 
29 

Ii 

f  7 

8  | 

22 
7 

20 

6 

22 

7 

20 

6 

20 

5 

18 

4 

18 
3 

16 
2,31 

15 
3° 

14 
29 

3 

12 

27 

8 

9 

21 

6 

19 

5 

21 

6 

19 

5 

19 

4 

17 
3 

17 

a 

15 
1,30 

14 
29 

X 

12 
27 

II 
26 

9 

10  j 

20 

5 

18 

4 

20 
5 

18 

4 

18 
3 

16 

2 

16 
i.3i 

14 
29 

U 

12 

27j 

II 
26 

10 
25 

10 

11] 

i9 

4 

17 
3 

19 
4 

17 
3 

17 

2 

IS 
1,30 

15 
30 

Ji 

12 
27 

II 

26 

IO 

25 

9 

24 

1  H 

12  { 

18 
3 

16 

2 

18 
3 

16 

2 

16 
i,3i 

14 
29 

14 
29 

12 
27 

II 
26 

10 

25 

9 
24 

8 
23 

i  12 

13  | 

17 

2 

15 

17 

2 

IS 

1,30 

IS 
30 

11 

11 

ii 
26 

IO 
25 

9 

24 

8 
23 

7 

22 

f  13 

14  j 

16 
1.3* 

14 

16 
i»3i 

14 
29 

14 
29 

12 
27 

12 
27 

IO 

25 

9 
24 

8 
23 

7 

22 

6 

21 

i  i4 

15  { 

I  I5 
1  3° 

3 

15 

30 

Ii 

Ii 

II 
26 

II 
26 

9 

24 

8 
23 

7 
22 

6 

21 

5 

20 

1  I5 

16  | 

14 
29 

12 
27 

14 
29 

12 
27 

12 
27 

IO 
25 

IO 
25 

8 
23 

7 

22 

6 

21 

5 
20 

4 
19 

i  16 

17  | 

ij 

II 
26 

ii 

II 
26 

II 
26 

9 
24 

9 

24 

7 

22 

6 

21 

5 
20 

4 
19 

,1 

{  17 

18  j 

12 

27 

IO 
25 

12 
27 

IO 
25 

IO 
25 

8 
23 

8 
23 

6 

21 

5 

20 

4 
19 

,1 

2 
17 

18 

191 

II 
26 

9 

24 

II 
26 

9 

24 

9 

24 

7 

22 

7 

22 

5 

20 

4 
19 

18 

2 
17 

'A' 

19 

20  { 

IO 
25 

8 
23 

10 
25 

8 
23 

6 
21 

6 

21 

4 
19 

,i 

2 
17 

'A1 

30 

is 

20 

21 

9 
24 

7 

22 

9 
24 

7 

22 

7 

22 

5 

20 

5 

20 

j 

2 
17 

'ft1 

29 
15 

29 
14 

21 

22 

8 
23 

6 

21 

8 
23 

6 

21 

6 

21 

4 
19 

4 
19 

2 
17 

1,30 

16 

30 

u 

28 
14 

28 

13 

f  22 

23 

7 

22 

5 

20 

7 

22 

5 

20 

5 
20 

ii 

18 

1,31 

16 

29 

15 

29 

•-14.- 

27 
13 

27 

12 

23 

24  j 

6 
21 

19 

21 

19 

19 

17 

17 

1,30 
'5 

29 

'4 

28 
*3 

27 

12 

26 
II 

}  24 

25 

S 

20 

4 
19 

5 
20 

4 
19 

j 

2 
17 

'$ 

29 
15 

28 
13 

27 
13 

26 
II 

25 
II 

25 

26  i 

4 
19 

,| 

4 
19 

j 

2 
17 

1,30 

16 

30 
15 

28 
14 

27 

12 

26 

12 

25 
IO 

24 
IO 

}  26 

27  | 

,1 

2 
17 

,1 

2 

17 

H1 

16 

29 

15 

29 
14 

27 
13 

26 
II 

25 
II 

24 

9 

23 

9 

27 

28  j 

2 
*7 

I 

16 

2 
17 

i,3p 
16 

30 
15 

28 
14 

28 
13 

26 

12 

25 
IO 

24 
IO 

2i 

22 

8 

28 

29  j 

1,3,1 

16 

15 

1,31 

16 

29 
15 

29 
14 

27 
13 

27 

12 

25 
II 

24 

9 

23 

9 

22 

7 

21 

7 

29 

30  j 

30 

15 

28 
14 

30 

u 

28 
14 

28 
13 

26 

12 

26 
II 

24 
10 

2i 

22 
8 

21 

6 

20 
6 

30 

Jan. 

Feb. 

Mar. 

Apr. 

May 

'une 

Tuly 

Aug. 

Sep. 

Oct. 

Nov. 

Dec. 

370 


A  BUDGET  OF  PARADOXES. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

g 

185 

17 

28 

19 

20 

2 

12 

23 

4 

15 

26 

186 

7 

18 

30 

11 

22 

3 

14 

25 

6 

17 

187 

28 

9 

20 

1 

12 

23 

4 

15 

26 

7 

188 

18 

30 

11 

22 

3 

14 

25 

6 

17 

28 

189 

9 

21 

1 

12 

23 

4 

15 

26 

7 

18 

190 

29 

10 

21 

2 

13 

24 

5 

16 

27 

8 

191 

19 

30 

11 

22 

3 

14 

26 

6 

17 

29 

192 

10 

21 

2 

13 

24 

5 

16 

27 

8 

19 

193 

30 

11 

22 

3 

14 

26 

6 

17 

29 

10 

194 

21 

2 

13 

24 

5 

16 

27 

8 

19 

30 

195 

11 

22 

3 

14 

26 

6 

17 

29 

10 

21 

196 

2 

13 

24 

5 

16 

27 

8 

19 

30 

11 

197 

22 

3 

14 

26 

6 

17 

29 

10 

21 

2 

198 

13 

24 

5 

16 

27 

8 

19 

30 

11 

22 

199 

3 

14 

26 

6 

17 

29 

10 

21 

2 

13 

on  the  28th.    For  example,  the  year  1867.    The  epact  is  25, 
and  we  find  in  the  table: 

J.        F.         M.      AP.      M.        JU.     JL.    AU.       S.       O.      N.        D. 

New  ....    5+    4        5+4        3+2   1,31   29    28-  27    26      25 
Full  ....  20      19-  20      19-  18      17     16     15    13-  13    11+  11 

When  the  truth  is  the  day  after  +  is  written  after  the 
date;  when  the  day  before,  — .  Thus,  the  new  moon  of 
March  is  on  the  6th ;  the  full  moon  of  April  is  on  the  18th. 


EASTER  DAY  PARADOXERS.  371 

I  now  introduce  a  small  paradox  of  my  own;  and  as  I 
am  not  able  to  prove  it,  I  am  compelled  to  declare  that 
any  one  who  shall  dissent  must  be  either  very  foolish  or 
very  dishonest,  and  will  make  me  quite  uncomfortable  about 
the  state  of  his  soul.  This  being  settled  once  for  all,  I  pro- 
ceed to  say  that  the  necessity  of  arriving  at  the  truth  about 
the  assertions  that  the  Nicene  Council  laid  down  astronom- 
ical tests  led  me  to  look  at  Fathers,  Church  histories,  etc. 
to  an  extent  which  I  never  dreamed  of  before.  One  con- 
clusion which  I  arrived  at  was,  that  the  Nicene  Fathers  had 
a  knack  of  sticking  to  the  question  which  many  later  councils 
could  not  acquire.  In  our  own  day,  it  is  not  permitted 
to  Convocation  seriously  to  discuss  any  one  of  the  points 
which  are  bearing  so  hard  upon  their  resources  of  defence 
— the  cursing  clauses  of  the  Athanasian  Creed,  for  example. 
And  it  may  be  collected  that  the  prohibition  arises  partly 
from  fear  that  there  is  no  saying  where  a  beginning,  if 
allowed,  would  end.  There  seems  to  be  a  suspicion  that 
debate,  once  let  loose,  would  play  up  old  Trent  with  the 
liturgy,  and  bring  the  whole  book  to  book.  But  if  any  one 
will  examine  the  real  Nicene  Creed,  without  the  augmen- 
tation, he  will  admire  the  way  in  which  the  framers  stuck 
to  the  point,  and  settled  what  they  had  to  decide,  according  to 
their  view  of  it.  With  such  a  presumption  of  good  sense 
in  their  favor,  it  becomes  easier  to  believe  in  any  claim  which 
may  be  made  on  their  behalf  to  tact  or  sagacity  in  settling 
any  other  matter.  And  I  strongly  suspect  such  a  claim  may 
be  made  for  them  on  the  Easter  question. 

I  collect  from  many  little  indications,  both  before  and 
after  the  Council,  that  the  division  of  the  Christian  world 
into  Judaical  and  Gentile,  though  not  giving  rise  to  a  sec- 
tarian distinction  expressed  by  names,  was  of  far  greater 
force  and  meaning  than  historians  prominently  admit.  I 
took  note  of  many  indications  of  this,  but  not  notes,  as  it  was 
not  to  my  purpose.  If  it  were  so,  we  must  admire  the  dis- 
cretion of  the  Council.  The  Easter  question  was  the  fight- 


372  A  BUDGET  OF  PARADOXES. 

ing  ground  of  the  struggle:  the  Eastern  or  Judaical  Chris- 
tians, with  some  varieties  of  usage  and  meaning,  would 
have  the  Passover  itself  to  be  the  great  feast,  but  taken  in 
a  Christian  sense;  the  Western  or  Gentile  Christians,  would 
have  the  commemoration  of  the  Resurrection,  connected 
with  the  Passover  only  by  chronology.  To  shift  the  Passover 
in  time,  under  its  name,  Pascha,  without  allusion  to  any  of 
the  force  of  the  change,  was  gently  cutting  away  the  ground 
from  under  the  feet  of  the  Conservatives.  And  it  was  done 
in  a  very  quiet  way:  no  allusion  to  the  precise  character  of 
the  change ;  no  hint  that  the  question  was  about  two  different 
festivals:  "all  the  brethren  in  the  East,  who  formerly  cele- 
brated this  festival  at  the  same  time  as  the  Jews,  will  in  fu- 
ture conform  to  the  Romans  and  to  us."  The  Judaizers 
meant  to  be  keeping  the  Passover  as  a  Christian  feast :  they 
are  gently  assumed  to  be  keeping,  not  the  Passover,  but  a 
Christian  feast;  and  a  doctrinal  decision  is  quietly,  but  effi- 
ciently, announced  under  the  form  of  a  chronological  ordi- 
nance. Had  the  Council  issued  theses  of  doctrine,  and  ex- 
communicated all  dissentients,  the  rupture  of  the  East  and 
West  would  have  taken  place  earlier  by  centuries  than  it  did. 
The  only  place  in  which  I  ever  saw  any  part  of  my  paradox 
advanced,  was  in  an  article  in  the  Examiner  newspaper, 
towards  the  end  of  1866,  after  the  above  was  written. 

A  story  about  Christopher  Clavius,  the  workman  of  the 
new  Calendar.  I  chanced  to  pick  up  "Albertus  Pighius 
Campensis  de  sequinoctiorum  solsticiorumque  inventione .  . . 
Ejusdem  de  ratione  Paschalis  celebrationis,  De  que  Restitu- 
tione  ecclesiastici  Kalendarii,"  Paris,  1520,  folio.22  On  the 
title-page  were  decayed  words  followed  by  ".  .hristophor.  . 
C.  .ii,  1556  (or  8),"  the  last  blank  not  entirely  erased  by 
time,  but  showing  the  lower  halves  of  an  /  and  of  an  a,  and 

M  Albertus  Pighius,  or  Albert  Pigghe,  was  born  at  Kempen  c. 
1490  and  died  at  Utrecht  in  1542.  He  was  a  mathematician  and  a 
firm  defender  of  the  faith,  asserting  the  supremacy  of  the  Pope  and 
attacking  both  Luther  and  Calvin.  He  spent  some  time  in  Rome. 
His  greatest  work  was  his  Hierarchic?  ecclesiastics  assertio  (1538). 


A  COUPLE  OF  MINOR  PARADOXES.  373 

rather  too  much  room  for  a  v.  It  looked  very  like  E  Libris 
Christophori  Clavii  1556.  By  the  courtesy  of  some  members 
of  the  Jesuit  body  in  London,  I  procured  a  tracing  of  the 
signature  of  Clavius  from  Rome,  and  the  shapes  of  the 
letters,  and  the  modes  of  junction  and  disjunction,  put  the 
matter  beyond  question.  Even  the  extra  space  was  ex- 
plained;  he  wrote  himself  Clawius.  Now  in  1556,  Clavius 
was  nineteen  years  old :  it  thus  appears  probable  that  the 
framer  of  the  Gregorian  Calendar  was  selected,  not  merely 
as  a  learned  astronomer,  but  as  one  who  had  attended  to  the 
calendar,  and  to  works  on  its  reformation,  from  early  youth. 
When  on  the  subject  I  found  reason  to  think  that  Clavius 
had  really  read  this  work,  and  taken  from  it  a  phrase  or  two 
and  a  notion  or  two.  Observe  the  advantage  of  writing  the 
baptismal  name  at  full  length. 

A  COUPLE  OF  MINOR  PARADOXES. 

The  discovery  of  a  general  resolution  of  all  superior  finite  equa- 
tions, of  every  numerical  both  algebraick  and  transcendent 
form.  By  A.  P.  Vogel,1  mathematician  at  Leipzick.  Leipzick 
and  London,  1845,  8vo. 

This  work  is  written  in  the  English  of  a  German  who 
has  not  mastered  the  idiom:  but  it  is  always  intelligible.  It 
professes  to  solve  equations  of  every  degree  "in  a  more  ex- 
tent sense,  and  till  to  every  degree  of  exactness."  The  gen- 
eral solution  of  equations  of  all  degrees  is  a  vexed  question, 
which  cannot  have  the  mysterious  interest  of  the  circle  prob- 
lem, and  is  of  a  comparatively  modern  date.2  Mr.  Vogel 

1This  was  A.  F.  yogel.  The  work  was  his  translation  from 
the  German  edition  which  appeared  at  Leipsic  the  same  year,  Ent- 
deckung  einer  numerischen  General-Auflosung  aller  hoheren  end- 
lichen  Gleichungen  von  jeder  beliebigen  algebraischen  und  transcen- 
denten  Form. 

"The  latest  edition  of  Burnside  and  Panton's  Theory  of  Equa- 
tions has  this  brief  summary  of  the  present  status  of  the  problem: 
"Demonstrations  have  been  given  by  Abel  and  Wantzel  (see  Serret's 
Cours  d'Algebre  Superieure,  Art  516)^  of  the  impossibility  of  re- 
solving algebraically  equations  unrestricted  in  form,  of  a  degree 
higher  than  the  fourth.  A  transcendental  solution,  however,  of  the 


374  A  BUDGET  OF  PARADOXES. 

announces  a  forthcoming  treatise  in  which  are  resolved  the 
"last  impossibilities  of  pure  mathematics." 

Elective  Polarity  the  Universal  Agent.  By  Frances  Barbara 
Burton,  authoress  of  'Astronomy  familiarized/  'Physical  As- 
tronomy/ &c.  London,  1845,  8vo.3 

The  title  gives  a  notion  of  the  theory.  The  first  sentence 
states,  that  12,500  years  ago  a  Lyrae  was  the  pole-star,  and 
attributes  the  immense  magnitude  of  the  now  fossil  animals 
to  a  star  of  such  "polaric  intensity  as  Vega  pouring  its 
magnetic  streams  through  our  planet."  Miss  Burton  was 
a  lady  of  property,  and  of  very  respectable  acquirements, 
especially  in  Hebrew;  she  was  eccentric  in  all  things. 

1867. — Miss  Burton  is  revived  by  the  writer  of  a  book 
on  meteorology  which  makes  use  of  the  planets :  she  is  one 
of  his  leading  minds.4 

SPECULATIVE  THOUGHT  IN  ENGLAND. 

In  the  year  1845  the  old  Mathematical  Society  was 
merged  in  the  Astronomical  Society.  The  circle-squarers, 
etc.,  thrive  more  in  England  than  in  any  other  country: 
there  are  most  weeds  where  there  is  the  largest  crop.  Specu- 
lation, though  not  encouraged  by  our  Government  so  much 
as  by  those  of  the  Continent,  has  had,  not  indeed  such 
forcing,  but  much  wider  diffusion:  few  tanks,  but  many 
rivulets.  On  this  point  I  quote  from  the  preface  to  the 
reprint  of  the  work  of  Ramchundra,1  which  I  superintended 
for  the  late  Court  of  Directors  of  the  East  India  Company. 

quintic  has  been  given  by  M.  Hermite,  in  a  form  involving  elliptic 
integrals." 

*  There  was  a  second  edition  of  this  work  in  1846.  The  author's 
Astronomy  Simplified  was  published  in  1838,  and  the  Thoughts  on 
Physical  Astronomy  in  1840,  with  a  second  edition  in  1842. 

*This  was  The  Science  of  the  Weather,  by  several  authors 

edited  by  B.,  Glasgow,  1867. 

1This  was  Y.  Ramachandra,  son  of  Sundara  Lala.  He  was  a 
teacher  of  science  in  Delhi  College,  and  the  work  to  which  De 
Morgan  refers  is  A  Treatise  on  problems  of  Maxima  and  Minima 
solved  by  Algebra,  which  appeared  at  Calcutta  in  1850.  De  Morgan's 
edition  was  published  at  London  nine  years  later. 


SPECULATIVE  THOUGHT  IN  ENGLAND.  375 

"That  sound  judgment  which  gives  men  well  to  know 
what  is  best  for  them,  as  well  as  that  faculty  of  invention 
which  leads  to  development  of  resources  and  to  the  increase 
of  wealth  and  comfort,  are  both  materially  advanced,  per- 
haps cannot  rapidly  be  advanced  without,  a  great  taste  for 
pure  speculation  among  the  general  mass  of  the  people, 
down  to  the  lowest  of  those  who  can  read  and  write.  Eng- 
land is  a  marked  example.  Many  persons  will  be  surprised 
at  this  assertion.  They  imagine  that  our  country  is  the 
great  instance  of  the  refusal  of  all  unpractical  knowledge  in 
favor  of  what  is  useful.  I  affirm,  on  the  contrary,  that  there 
is  no  country  in  Europe  in  which  there  has  been  so  wide 
a  diffusion  of  speculation,  theory,  or  what  other  unpractical 
word  the  reader  pleases.  In  our  country,  the  scientific  so- 
ciety  is  always  formed  and  maintained  by  the  people;  in 
every  other,  the  scientific  academy — most  aptly  named — 
has  been  the  creation  of  the  government,  of  which  it  has 
never  ceased  to  be  the  nursling.  In  all  the  parts  of  England 
in  which  manufacturing  pursuits  have  given  the  artisan 
some  command  of  time,  the  cultivation  of  mathematics  and 
other  speculative  studies  has  been,  as  is  well  known,  a  very 
frequent  occupation.  In  no  other  country  has  the  weaver 
at  his  loom  bent  over  the  Principia  of  Newton ;  in  no  other 
country  has  the  man  of  weekly  wages  maintained  his  own 
scientific  periodical.  With  us,  since  the  beginning  of  the 
last  century,  scores  upon  scores — perhaps  hundreds,  for  I 
am  far  from  knowing  all — of  annuals  have  run,  some  their 
ten  years,  some  their  half-century,  some  their  century  and 
a  half,  containing  questions  to  be  answered,  from  which 
many  of  our  examiners  in  the  universities  have  culled  mate- 
rials for  the  academical  contests.  And  these  questions  have 
always  been  answered,  and  in  cases  without  number  by  the 
lower  order  of  purchasers,  the  mechanics,  the  weavers,  and 
the  printers'  workmen.  I  cannot  here  digress  to  point  out 
the  manner  in  which  the  concentration  of  manufactures, 
and  the  general  diffusion  of  education,  have  affected  the 


376  A  BUDGET  OF  PARADOXES. 

state  of  things ;  I  speak  of  the  time  during  which  the  present 
system  took  its  rise,  and  of  the  circumstances  under  which 
many  of  its  most  effective  promoters  were  trained.  In  all 
this  there  is  nothing  which  stands  out,  like  the  state-nour- 
ished academy,  with  its  few  great  names  and  brilliant  single 
achievements.  This  country  has  differed  from  all  others  in 
the  wide  diffusion  of  the  disposition  to  speculate,  which 
disposition  has  found  its  place  among  the  ordinary  habits 
of  life,  moderate  in  its  action,  healthy  in  its  amount." 

THE  OLD  MATHEMATICAL  SOCIETY. 

Among  the  most  remarkable  proofs  of  the  diffusion  of 
speculation  was  the  Mathematical  Society,  which  flourished 
from  1717  to  1845.  Its  habitat  was  Spitalfields,  and  I  think 
most  of  its  existence  was  passed  in  Crispin  Street.  It  was 
originally  a  plain  society,  belonging  to  the  studious  artisan. 
The  members  met  for  discussion  once  a  week ;  and  I  believe 
I  am  correct  in  saying  that  each  man  had  his  pipe,  his  pot, 
and  his  problem.  One  of  their  old  rules  was  that,  "If  any 
member  shall  so  far  forget  himself  and  the  respect  due  to 
the  Society  as  in  the  warmth  of  debate  to  threaten  or  offer 
personal  violence  to  any  other  member,  he  shall  be  liable  to 
immediate  expulsion,  or  to  pay  such  fine  as  the  majority  of 
the  members  present  shall  decide."  But  their  great  rule, 
printed  large  on  the  back  of  the  title  page  of  their  last  book 
of  regulations,  was  "By  the  constitution  of  the  Society,  it 
is  the  duty  of  every  member,  if  he  be  asked  any  mathematical 
or  philosophical  question  by  another  member,  to  instruct 
him  in  the  plainest  and  easiest  manner  he  is  able."  We  shall 
presently  see  that,  in  old  time,  the  rule  had  a  more  homely 
form. 

I  have  been  told  that  De  Moivre1  was  a  member  of  this 

1  Abraham  de  Moivre  (1667-1754),  French  refugee  in  London, 
poor,  studying  under  difficulties,  was  a  man  with  tastes  in  some  re- 
spects like  those  of  De  Morgan.  For  one  thing,  he  was  a  lover  of 
books,  and  he  had  a  good  deal  of  interest  in  the  theory  of  probabili- 
ties to  which  De  Morgan  also  gave  much  thought.  His  introduction 


THE    OLD    MATHEMATICAL    SOCIETY.  377 

Society.  This  I  cannot  verify:  circumstances  render  it  un- 
likely ;  even  though  the  French  refugees  clustered  in  Spital- 
fields;  many  of  them  were  of  the  Society,  which  there  is 
some  reason  to  think  was  founded  by  them.  But  Dolland,2 
Thomas  Simpson,3  Saunderson,4  Crossley,5  and  others  of 
known  name,  were  certainly  members.  The  Society  grad- 
ually declined,  and  in  1845  was  reduced  to  nineteen  mem- 
bers. An  arrangement  was  made  by  which  sixteen  of  these 
members,  who  where  not  already  in  the  Astronomical  Society 
became  Fellows  without  contribution,  all  the  books  and  other 
property  of  the  old  Society  being  transferred  to  the  new  one. 
I  was  one  of  the  committee  which  made  the  preliminary 
inquiries,  and  the  reason  of  the  decline  was  soon  manifest. 
The  only  question  which  could  arise  was  whether  the  mem- 
bers of  the  society  of  working  men — for  this  repute  still 
continued — were  of  that  class  of  educated  men  who  could 
associate  with  the  Fellows  of  the  Astronomical  Society  on 
terms  agreeable  to  all  parties.  We  found  that  the  artisan 
element  had  been  extinct  for  many  years;  there  was  not  a 
man  but  might,  as  to  education,  manners,  and  position,  have 
become  a  Fellow  in  the  usual  way.  The  fact  was  that  life 
in  Spitalfields  had  become  harder:  and  the  weaver  could 

of  imaginary  quantities  into  trigonometry  was  an  event  of  importance 
in  the  history  of  mathematics,  and  the  theorem  that  bears  his  name, 
(cos0  +  tsin0)«  =  cosM0  +  ismn<t>,  is  one  of  the  most  important 
ones  in  all  analysis. 

"John  Dolland    (1706-1761),  the  silk  weaver  who  became  the 
greatest  maker  of  optical  instruments  in  his  time. 

Thomas  Simpson  (1710-1761),  also  a  weaver,  taking  his  leisure 
from  his  loom  at  Spitalfields  to  teach  mathematics.  His  New  Treat- 
ise on  Fluxions  (1737)  was  written  only  two  years  after  he  began 
working  in  London,  and  six  years  later  he  was  appointed  professor 
of  mathematics  at  Woolwich.  He  wrote  many  works  on  mathe- 
matics and  Simpson's  Formulas  for  computing  trigonometric  tables 
are  still  given  in  the  text-books. 

4  Nicholas  Saunderson  (1682-1739),  the  blind  mathematician.  He 
lost  his  eyesight  through  smallpox  ^when  only  a  year  old.    At  the  age 
of  25  he  began  lecturing  at  Cambridge  on  the  principles  of  the  New- 
tonian philosophy.    His  Algebra,  in  two  large  volumes,  was  long  the 
standard  treatise  on  the  subject. 

5  He  was  not  in  the  class  with  the  others  mentioned. 


378  A  BUDGET  OF  PARADOXES. 

only  live  from  hand  to  mouth,  and  not  up  to  the  brain.  The 
material  of  the  old  Society  no  longer  existed. 

In  1798,  experimental  lectures  were  given,  a  small  charge 
for  admission  being  taken  at  the  door :  by  this  hangs  a  tale — 
and  a  song.  Many  years  ago,  I  found  among  papers  of  a 
deceased  friend,  who  certainly  never  had  anything  to  do 
with  the  Society,  and  who  passed  all  his  life  far  from  Lon- 
don, a  song,  headed  "Song  sung  by  the  Mathematical  So- 
ciety in  London,  at  a  dinner  given  Mr.  Fletcher,8  a  solicitor, 
who  had  defended  the  Society  gratis/'  Mr.  Williams,7  the 
Assistant  Secretary  of  the  Astronomical  Society,  formerly 
Secretary  of  the  Mathematical  Society,  remembered  that  the 
Society  had  had  a  solicitor  named  Fletcher  among  the  mem- 
bers. Some  years  elapsed  before  it  struck  me  that  my  old 
friend  Benjamin  Gompertz,8  who  had  long  been  a  member, 
might  have  some  recollection  of  the  matter.  The  following 
is  an  extract  of  a  letter  from  him  (July  9,  1861)  : 

"As  to  the  Mathematical  Society,  of  which  I  was  a  mem- 
ber when  only  18  years  of  age,  [Mr.  G.  was  born  in  1779], 
having  been,  contrary  to  the  rules,  elected  under  the  age  of 
21.  How  I  came  to  be  a  member  of  that  Society — and  con- 
tinued so  until  it  joined  the  Astronomical  Society,  and  was 
then  the  President — was :  I  happened  to  pass  a  bookseller's 
small  shop,  of  second-hand  books,  kept  by  a  poor  taylor, 
but  a  good  mathematician,  John  Griffiths.  I  was  very 
pleased  to  meet  a  mathematician,  and  I  asked  him  if  he  would 
give  me  some  lessons ;  and  his  reply  was  that  I  was  more 
capable  to  teach  him,  but  he  belonged  to  a  society  of  mathe- 
maticians, and  he  would  introduce  me.  I  accepted  the  offer, 
and  I  was  elected,  and  had  many  scholars  then  to  teach,  as 

a  Not  known  in  the  literature  of  mathematics. 

7  Probably  J.  Butler  Williams  whose  Practical  Geodesy  appeared 
in  1842,  with  a  third  edition  in  1855. 

"Benjamin  Gompertz  (1779-1865)  was  debarred  as  a  Jew  from 
a  university  education.  He  studied  mathematics  privately  and  be- 
came president  of  the  Mathematical  Society.  De  Morgan  knew  him 
professionally  through  the  fact  that  he  was  prominent  in  actuarial 
work. 


THE    OLD    MATHEMATICAL    SOCIETY.  379 

one  of  the  rules  was,  if  a  member  asked  for  information, 
and  applied  to  any  one  who  could  give  it,  he  was  obliged  to 
give  it,  or  fine  one  penny.  Though  I  might  say  much  with 
respect  to  the  Society  which  would  be  interesting,  I  will  for 
the  present  reply  only  to  your  question.  I  well  knew  Mr. 
Fletcher,  who  was  a  very  clever  and  very  scientific  person. 
He  did,  as  solicitor,  defend  an  action  brought  by  an  informer 
against  the  Society — I  think  for  5,000/. — for  giving  lectures 
to  the  public  in  philosophical  subjects  [i.  e.,  for  unlicensed 
public  exhibition  with  money  taken  at  the  doors].  I  think 
the  price  for  admission  was  one  shilling,  and  we  used  to 
have,  if  I  rightly  recollect,  from  two  to  three  hundred  visi- 
tors. Mr.  Fletcher  was  successful  in  his  defence,  and  we  got 
out  of  our  trouble.  There  was  a  collection  made  to  reward 
his  services,  but  he  did  not  accept  of  any  reward:  and  I 
think  we  gave  him  a  dinner,  as  you  state,  and  enjoyed 
ourselves ;  no  doubt  with  astronomical  songs  and  other 
songs;  but  my  recollection  does  not  enable  me  to  say  if 
the  astronomical  song  was  a  drinking  song.  I  think  the 
anxiety  caused  by  that  action  was  the  cause  of  some  of  the 
members'  death.  [They  had,  no  doubt,  broken  the  law  in 
ignorance ;  and  by  the  sum  named,  the  informer  must  have 
been  present,  and  sued  for  a  penalty  on  every  shilling  he 
could  prove  to  have  been  taken]/' 

I  by  no  means  guarantee  that  the  whole  song  I  proceed 
to  give  is  what  was  sung  at  the  dinner:  I  suspect,  by  the 
completeness  of  the  chain,  that  augmentations  have  been 
made.  My  deceased  friend  was  just  the  man  to  add  some 
verses,  or  the  addition  may  have  been  made  before  it  came 
into  his  hands,  or  since  his  decease,  for  the  scraps  contain- 
ing the  verses  passed  through  several  hands  before  they 
came  into  mine.  We  may,  however,  be  pretty  sure  that  the 
original  is  substantially  contained  in  what  is  given,  and 
that  the  character  is  therefore  preserved.  I  have  had  my- 
self to  repair  damages  every  now  and  then,  in  the  way  of 
conjectural  restoration  of  defects  caused  by  ill-usage. 


380  A  BUDGET  OF  PARADOXES. 


THE  ASTRONOMER'S  DRINKING  SONG. 

"Whoe'er  would  search  the  starry  sky, 

Its  secrets  to  divine,  sir, 
Should  take  his  glass — I  mean,  should  try 

A  glass  or  two  of  wine,  sir ! 
True  virtue  lies  in  golden  mean, 

And  man  must  wet  his  clay,  sir; 
Join  these  two  maxims,  and  'tis  seen 

He  should  drink  his  bottle  a  day,  sir ! 

"Old  Archimedes,  reverend  sage! 

By  trump  of  fame  renowned,  sir, 
Deep  problems  solved  in  every  page, 

And  the  sphere's  curved  surface  found,1  sir : 
Himself  he  would  have  far  outshone, 

And  borne  a  wider  sway,  sir, 
Had  he  our  modern  secret  known, 

And  drank  a  bottle  a  day,  sir ! 

"When  Ptolemy,2  now  long  ago, 

Believed  the  earth  stood  still,  sir, 
He  never  would  have  blundered  so, 

Had  he  but  drunk  his  fill,  sir : 
He'd  then  have  felt3  it  circulate, 

And  would  have  learnt  to  say,  sir, 
The  true  way  to  investigate 

Is  to  drink  your  bottle  a  day,  sir ! 

"Copernicus,4  that  learned  wight, 

The  glory  of  his  nation, 
With  draughts  of  wine  refreshed  his  sight, 
And  saw  the  earth's  rotation; 

1  Referring  to  the  contributions  of  Archimedes  (287-212  B.C.) 
to  the  mensuration  of  the  sphere. 

*The  famous  Alexandrian  astronomer  (c.  87 — c.  165  A.  D.), 
author  of  the  Almagest,  a  treatise  founded  on  the  works  of  Hip- 
parchus. 

"Dr.  Whewell,  when  I  communicated  this  song  to  him,  started 
the  opinion,  which  I  had  before  him,  that  this  was  a  very  good  idea, 
of  which  too  little  was  made.— A.  De  M. 

*  See  note  3,  page  76. 


THE  ASTRONOMER'S  DRINKING  SONG.  381 

Each  planet  then  its  orb  described, 

The  moon  got  under  way,  sir; 
These  truths  from  nature  he  imbibed 

For  he  drank  his  bottle  a  day,  sir ! 

"The  noble5  Tycho  placed  the  stars, 

Each  in  its  due  location; 
He  lost  his  nose6  by  spite  of  Mars, 

But  that  was  no  privation : 
Had  he  but  lost  his  mouth,  I  grant 

He  would  have  felt  dismay,  sir, 
Bless  you !  he  knew  what  he  should  want 

To  drink  his  bottle  a  day,  sir ! 

"Cold  water  makes  no  lucky  hits ; 

On  mysteries  the  head  runs : 
Small  drink  let  Kepler7  time  his  wits 

On  the  regular  polyhedrons : 
He  took  to  wine,  and  it  changed  the  chime, 

His  genius  swept  away,  sir, 
Through  area  varying8  as  the  time 

At  the  rate  of  a  bottle  a  day,  sir ! 

"Poor  Galileo,8  forced  to  rat 

Before  the  Inquisition, 
E  pur  si  muove10  was  the  pat 
He  gave  them  in  addition : 

e  The  common  epithet  of  rank :  nobilis  Tycho,  as  he  was  a  noble- 
man.   The  writer  had  been  at  history. — A.  De  M. 
See  note  3,  page  76. 

*  He  lost  it  in  a  duel,  with  Manderupius  Pasbergius.    A  contem- 
porary, T.  B.  Laurus,  insinuates  that  they  fought  to  settle  which  was 
the  best  mathematician !    This  seems  odd,  but  it  must  be  remembered 
they  fought  in  the  dark,  "in  tenebris  densis" ;  and  it  is  a  nice  problem 
to  shave  off  a  nose  in  the  dark,  without  any  other  harm. — A.  De  M. 

Was  this  T.  B.  Laurus  Joannes  Baptista  Laurus  or  Giovanni 
Battista  Lauro  (1581-1621),  the  poet  and  writer? 

T  See  note  3,  page  76. 

*  Referring  to  Kepler's  celebrated  law  of  planetary  motion.     He 
had  previously  wasted  his  time  on  analogies  between  the  planetary 
orbits  and  the  polyhedrons. — A.  De  M. 

9  See  note  3,  page  76. 

10  "It  does  move  though." 


382  A  BUDGET  OF  PARADOXES. 

He  meant,  whate'er  you  think  you  prove, 

The  earth  must  go  its  way,  sirs ; 
Spite  of  your  teeth  I'll  make  it  move, 

For  I'll  drink  my  bottle  a  day,  sirs! 

"Great  Newton,  who  was  never  beat 

Whatever  fools  may  think,  sir; 
Though  sometimes  he  forgot  to  eat, 

He  never  forgot  to  drink,  sir: 
Descartes11  took  nought  but  lemonade, 

To  conquer  him  was  play,  sir; 
The  first  advance  that  Newton  made 

Was  to  drink  his  bottle  a  day,  sirl 

"D'Alembert,12  Euler,18  and  Clairaut,14 

Though  they  increased  our  store,  sir, 
Much  further  had  been  seen  to  go 

Had  they  tippled  a  little  more,  sir ! 
Lagrange15  gets  mellow  with  Laplace,16 

And  both  are  wont  to  say,  sir, 
The  philosophe  who's  not  an  ass 

Will  drink  his  bottle  a  day,  sir ! 

"Astronomers !  what  can  avail 

Those  who  calumniate  us ; 
Experiment  can  never  fail 

With  such  an  apparatus : 
Let  him  who'd  have  his  merits  known 

Remember  what  I  say,  sir; 
Fair  science  shines  on  him  alone 

Who  drinks  his  bottle  a  day,  sir ! 

11  As  great  a  lie  as  ever  was  told:  but  in  1800  a  compliment  to 
Newton  without  a  fling  at  Descartes  would  have  been  held  a  lopsided 
structure. — A.  De  M. 

"  Jean-le-Rond  D'Alembert  (1717-1783),  the  foundling  who  was 
left  on  the  steps  of  Jean-le-Rond  in  Paris,  and  who  became  one  of 
the  greatest  mathematical  physicists  and  astronomers  of  his  century. 

"Leonhard  Euler  (1707-1783),  friend  of  the  Bernoullis,  the 
greatest  of  Swiss  mathematicians,  prominent  in  the  theory  of  num- 
bers, and  known  for  discoveries  in  all  lines  of  mathematics  as  then 
studied. 

14  See  notes  2,  3,  page  219. 

15  See  note  3,  page  288. 
la  See  note  6,  page  255. 


LE  VERRIER'S  PLANET.  383 

"How  light  we  reck  of  those  who  mock 

By  this  we'll  make  to  appear,  sir, 
We'll  dine  by  the  sidereal17  clock 

For  one  more  bottle  a  year,  sir : 
But  choose  which  pendulum  you  will, 

You'll  never  make  your  way,  sir, 
Unless  you  drink — and  drink  your  fill, — 

At  least  a  bottle  a  day,  sir !" 

Old  times  are  changed,  old  manners  gone! 

There  is  a  new  Mathematical  Society,18  and  I  am,  at  this 
present  writing  (1866),  its  first  President.  We  are  very 
high  in  the  newest  developments,  and  bid  fair  to  take  a  place 
among  the  scientific  establishments.  Benjamin  Gompertz, 
who  was  President  of  the  old  Society  when  it  expired,  was 
the  link  betwreen  the  old  and  new  body:  he  was  a  member 
of  ours  at  his  death.  But  not  a  drop  of  liquor  is  seen  at  our 
meetings,  except  a  decanter  of  water :  all  our  heavy  is  a  fer- 
mentation of  symbols ;  and  we  do  not  draw  it  mild.  There 
is  no  penny  fine  for  reticence  or  occult  science ;  and  as  to  a 
song!  not  the  ghost  of  a  chance. 

1826.  The  time  may  have  come  when  the  original  docu- 
ments connected  with  the  discovery  of  Neptune  may  be 
worth  revising.  The  following  are  extracts  from  the 
Athenaum  of  October  3  and  October  17: 

LE  VERRIER'S1  PLANET. 

We  have  received,  at  the  last  moment  before  making  up 
for  press,  the  following  letter  from  Sir  John  Herschel,2 

"The  siderial  day  is  about  four  minutes  short  of  the  solar; 
there  are  366  sidereal  days  in  the  year. — A.  De  M. 

18  The  founding  of  the  London  Mathematical  Society  is  dis- 
cussed by  Mrs.  De  Morgan  in  her  Memoir  (p.  281).  The  idea  came 
from  a  conversation  between  her  brilliant  son,  George  Campbell  De 
Morgan,  and  his  friend  Arthur  Cowper  Ranyard  in  1864.  The  meet- 
ing of  organization  was  held  on  Nov.  7,  1864,  with  Professor  De 
Morgan  in  the  chair,  and  the  first  regular  meeting  on  January  16, 
1865. 

1  See  note  8,  page  43. 

2  See  note  5,  page  80. 


384  A   BUDGET  OF  PARADOXES. 

in  reference  to  the  matter  referred  to  in  the  communication 
from  Mr.  Hind3  given  below: 

"Collingwood,  Oct.  1. 

"In  my  address  to  the  British  Association  assembled  at 
Southampton,  on  the  occasion  of  my  resigning  the  chair  to 
Sir  R.  Murchison,4  I  stated,  among  the  remarkable  astro- 
nomical events  of  the  last  twelvemonth,  that  it  had  added  a 
new  planet  to  our  list, — adding,  'it  has  done  more, — it  has 
given  us  the  probable  prospect  of  the  discovery  of  another. 
We  see  it  as  Columbus  saw  America  from  the  shores  of 
Spain.  Its  movements  have  been  felt,  trembling  along  the 
far-reaching  line  of  our  analysis,  with  a  certainty  hardly 
inferior  to  that  of  ocular  demonstration/ — These  expres- 
sions are  not  reported  in  any  of  the  papers  which  profess 
to  give  an  account  of  the  proceedings,  but  I  appeal  to  all 
present  whether  they  were  not  used. 

"Give  me  leave  to  state  my  reasons  for  this  confidence ; 
and,  in  so  doing,  to  call  attention  to  some  facts  which  de- 
serve to  be  put  on  record  in  the  history  of  this  noble  dis- 
covery. On  July  12,  1842,  the  late  illustrious  astronomer, 
Bessel,5  honored  me  with  a  visit  at  my  present  residence. 
On  the  evening  of  that  day,  conversing  on  the  great  work 
of  the  planetary  reductions  undertaken  by  the  Astronomer 
Royal6 — then  in  progress,  and  since  published,7 — M.  Bessel 
remarked  that  the  motions  of  Uranus,  as  he  had  satisfied 

'John  Russell  Hind  (b.  1823),  the  astronomer.  Between  1847 
and  1854  he  discovered  ten  planetoids. 

4  Sir  Roderick  Impey  Murchison  (1792-1871),  the  great  geolo- 
gist. He  was  knighted  in  1846  and  devoted  the  latter  part  of  his 
life  to  the  work  of  the  Royal  Geographical  Society  and  to  the  geol- 
ogy of  Scotland. 

6Friedrich  Wilhelm  Bessel  (1784-1846),  the  astronomer  and 
physicist.  He  was  professor  of  astronomy  at  Konigsberg. 

6  This  was  the  Reduction  of  the  Observations  of  Planets  made 
....  from  1750  to  1830:  computed. ..  .under  the  superintendence  of 
George  Biddell  Airy  (1848).  See  note  2,  page  85. 

T  The  expense  of  this  magnificent  work  was  defrayed  by  Govern- 
ment grants,  obtained,  at  the  instance  of  the  British  Association,  in 
1833.— A.  De  M. 


LE  VERRIER'S  PLANET.  385 

himself  by  careful  examination  of  the  recorded  observations, 
could  not  be  accounted  for  by  the  perturbations  of  the  known 
planets;  and  that  the  deviations  far  exceeded  any  possible 
limits  of  error  of  observation.  In  reply  to  the  question, 
Whether  the  deviations  in  question  might  not  be  due  to  the 
action  of  an  unknown  planet? — he  stated  that  he  considered 
it  highly  probable  that  such  was  the  case, — being  systematic, 
and  such  as  might  be  produced  by  an  exterior  planet.  I 
then  inquired  whether  he  had  attempted,  from  the  indica- 
tions afforded  by  these  perturbations,  to  discover  the  position 
of  the  unknown  body, — in  order  that  'a  hue  and  cry'  might 
be  raised  for  it.  From  his  reply,  the  words  of  which  I  do 
not  call  to  mind,  I  collected  that  he  had  not  then  gone  into 
that  inquiry ;  but  proposed  to  do  so,  having  now  completed 
certain  works  which  had  occupied  too  much  of  his  time. 
And,  accordingly,  in  a  letter  which  I  received  from  him 
after  his  return  to  Konigsberg,  dated  November  14,  1842, 
he  says, — 'In  reference  to  our  conversation  at  Collingwood, 
I  announce  to  you  (melde  ich  Ihnen)  that  Uranus  is  not 
forgotten/  Doubtless,  therefore,  among  his  papers  will  be 
found  some  researches  on  the  subject. 

"The  remarkable  calculations  of  M.  Le  Verrier — which 
have  pointed  out,  as  now  appears,  nearly  the  true  situation 
of  the  new  planet,  by  resolving  the  inverse  problem  of  the 
perturbations — if  uncorroborated  by  repetition  of  the  numer- 
ical calculations  by  another  hand,  or  by  independent  investi- 
gation from  another  quarter,  would  hardly  justify  so  strong 
an  assurance  as  that  conveyed  by  my  expressions  above 
alluded  to.  But  it  was  known  to  me,  at  that  time,  (I  will 
take  the  liberty  to  cite  the  Astronomer  Royal  as  my  author- 
ity) that  a  similar  investigation  had  been  independently  en- 
tered into,  and  a  conclusion  as  to  the  situation  of  the  new 
planet  very  nearly  coincident  with  M.  Le  Verrier's  arrived 
at  (in  entire  ignorance  of  his  conclusions),  by  a  young 
Cambridge  mathematician,  Mr.  Adams  ;8 — who  will,  I  hope, 

*  See  note  7,  page  43. 


386  A  BUDGET  OF  PARADOXES. 

pardon  this  mention  of  his  name  (the  matter  being  one  of 
great  historical  moment), — and  who  will,  doubtless,  in  his 
own  good  time  and  manner,  place  his  calculations  before  the 
public. 

"J.  F.  W.  HERSCHEL." 

Discovery  of  Le  Verrier's  Planet. 

Mr.  Hind  announces  to  the  Times  that  he  has  received 
a  letter  from  Dr.  Briinnow,  of  the  Royal  Observatory  at 
Berlin,  giving  the  very  important  information  that  Le  Ver- 
rier's planet  was  found  by  M.  Galle,  on  the  night  of  Sep- 
tember 23.  "In  announcing  this  grand  discovery,"  he  says, 
"I  think  it  better  to  copy  Dr.  Briinnow's9  letter." 

"Berlin,  Sept.  25. 

"My  dear  Sir. — M.  Le  Verrier's  planet  was  discovered 
here  the  23d  of  September,  by  M.  Galle.10  It  is  a  star  of 
the  8th  magnitude,  but  with  a  diameter  of  two  or  three 
seconds.  Here  are  its  places: 

h,  m.  s.  R.  A.  Declination. 

Sept.  23,  12    0  14'6  M.T.          328°  19'  16'0"         —13°  24'    8'2" 
Sept.  24.     8  54  40'9  M.T.          328°  18'  14'3"         —13°  24'  29'7' 

The  planet  is  now  retrograde,  its  motion  amounting  daily 
to  four  seconds  of  time. 

"Yours  most  respectfully,  BRUNNOW." 

"This  discovery,"  Mr.  Hind  says,  "may  be  justly  con- 
sidered one  of  the  greatest  triumphs  of  theoretical  astron- 
omy;" and  he  adds,  in  a  postscript,  that  the  planet  was  ob- 
served at  Mr.  Bishop's11  Observatory,  in  the  Regent's  Park, 

"Franz  Friedrich  Ernst  Briinnow  (1821-1891)  was  at  that  time 
or  shortly  before  director  of  the  observatory  at  Diisseldqrf.  He  then 
went  to  Berlin  and  thence  (1854)  to  Ann  Arbor,  Michigan.  He 
then  went  to  Dublin  and  finally  became  Royal  Astronomer  of  Ire- 
land. 

"Johann  Gottfried  Galle  (1812-1910),  at  that  time  connected 
with  the  Berlin  observatory,  and  later  professor  of  astronomy  at 
Breslau. 

"George  Bishop  (1785-1861),  in  whose  observatory  in  Regent's 
Park  important  observations  were  made  by  Dawes,  Hind,  and  Marth. 


THE    NEW    PLANET.  387 

on  Wednesday  night,  notwithstanding  the  moonlight  and 
hazy  sky.    "It  appears  bright,"  he  says,  "and  with  a  power 
of  320  I  can  see  the  disc.     The  following  position  is  the 
result  of  instrumental  comparisons  with  33  Aquarii: 
Sept.  30,  at  8h.  16m.  21s.  Greenwich  mean  time — 

Right  ascension  of  planet 21h.  52m.  47*  15s. 

South  declination 13°  27'  20"." 

THE  NEW  PLANET. 

"Cambridge  Observatory,  Oct.  15. 

"The  allusion  made  by  Sir  John  Herschel,  in  his  letter 
contained  in  the  Athenceum  of  October  3,  to  the  theoretical 
researches  of  Mr.  Adams,  respecting  the  newly-discovered 
planet,  has  induced  me  to  request  that  you  would  make  the 
following  communication  public.  It  is  right  that  I  should 
first  say  that  I  have  Mr.  Adams's  permission  to  make  the 
statements  that  follow,  so  far  as  they  relate  to  his  labors. 
I  do  not  propose  to  enter  into  a  detail  of  the  steps  by  which 
Mr.  Adams  was  led,  by  his  spontaneous  and  independent 
researches,  to  a  conclusion  that  a  planet  must  exist  more 
distant  than  Uranus.  The  matter  is  of  too  great  historical 
moment  not  to  receive  a  more  formal  record  than  it  would 
be  proper  to  give  here.  My  immediate  object  is  to  show, 
while  the  attention  of  the  scientific  public  is  more  particu- 
larly directed  to  the  subject,  that,  with  respect  to  this  re- 
markable discovery,  English  astronomers  may  lay  claim  to 
some  merit. 

"Mr.  Adams  formed  the  resolution  of  trying,  by  calcula- 
tion, to  account  for  the  anomalies  in  the  motion  of  Uranus 
on  the  hypothesis  of  a  more  distant  planet,  when  he  was  an 
undergraduate  in  this  university,  and  when  his  exertions 
for  the  academical  distinction,  which  he  obtained  in  January 
1843,  left  him  no  time  for  pursuing  the  research.  In  the 
course  of  that  year,  he  arrived  at  an  approximation  to  the 
position  of  the  supposed  planet ;  which,  however,  he  did  not 
consider  to  be  worthy  of  confidence,  on  account  of  his  not 


388  A  BUDGET  OF  PARADOXES. 

having  employed  a  sufficient  number  of  observations  of 
Uranus.  Accordingly,  he  requested  my  intervention  to  ob- 
tain for  him  the  early  Greenwich  observations,  then  in  course 
of  reduction ; — which  the  Astronomer  Royal  immediately 
supplied,  in  the  kindest  possible  manner.  This  was  in  Febru- 
ary, 1844.  In  September,  1845,  Mr.  Adams  communicated 
to  me  values  which  he  had  obtained  for  the  heliocentric 
longitude,  excentricity  of  orbit,  longitude  of  perihelion,  and 
mass,  of  an  assumed  exterior  planet, — deduced  entirely  from 
unaccounted-for  perturbations  of  Uranus.  The  same  re- 
sults, somewhat  corrected,  he  communicated,  in  October,  to 
the  Astronomer  Royal.  M.  Le  Verrier,  in  an  investigation 
which  was  published  in  June  of  1846,  assigned  very  nearly 
the  same  heliocentric  longitude  for  the  probable  position  of 
the  planet  as  Mr.  Adams  had  arrived  at,  but  gave  no  results 
respecting  its  mass  and  the  form  of  its  orbit.  The  coinci- 
dence as  to  position  from  two  entirely  independent  investi- 
gations naturally  inspired  confidence;  and  the  Astronomer 
Royal  shortly  after  suggested  the  employing  of  the  North- 
umberland telescope  of  this  observatory  in  a  systematic 
search  after  the  hypothetical  planet;  recommending,  at  the 
same  time,  a  definite  plan  of  operations.  I  undertook  to 
make  the  search, — and  commenced  observing  on  July  29. 
The  observations  were  directed,  in  the  first  instance,  to  the 
part  of  the  heavens  which  theory  had  pointed  out  as  the 
most  probable  place  of  the  planet ;  in  selecting  which  I  was 
guided  by  a  paper  drawn  up  for  me  by  Mr.  Adams.  Not 
having  hour  xxi.  of  the  Berlin  star-maps — of  the  publica- 
tion of  which  I  was  not  aware — I  had  to  proceed  on  the 
principle  of  comparison  of  observations  made  at  intervals. 
On  July  30,  I  went  over  a  zone  9'  broad,  in  such  a  manner 
as  to  include  all  stars  to  the  eleventh  magnitude.  On 
August  4,  I  took  a  broader  zone  and  recorded  a  place  of 
the  planet.  My  next  observations  were  on  August  12; 
when  I  met  with  a  star  of  the  eighth  magnitude  in  the  zone 
which  I  had  gone  over  on  July  30, — and  which  did  not  then 


THE  NEW  PLANET.  389 

contain  this  star.  Of  course,  this  was  the  planet ; — the  place 
of  which  was,  thus,  recorded  a  second  time  in  four  days 
of  observing.  A  comparison  of  the  observations  of  July  30 
and  August  12  would,  according  to  the  principle  of  search 
which  I  employed,  have  shown  me  the  planet.  I  did  not 
make  the  comparison  till  after  the  detection  of  it  at  Berlin — 
partly  because  I  had  an  impression  that  a  much  more  ex- 
tensive search  was  required  to  give  any  probability  of  dis- 
covery— and  partly  from  the  press  of  other  occupation.  The 
planet,  however,  was  secured,  and  two  positions  of  it  re- 
corded six  weeks  earlier  here  than  in  any  other  observatory, 
— and  in  a  systematic  search  expressly  undertaken  for  that 
purpose.  I  give  now  the  positions  of  the  planet  on  August 
4  and  August  12. 


Greenwich  mean  time. 

"R.A.      21h.  58m.  14 '70s. 


Aug.  4,  13h.  36m.  25s..  .  -  ,  Ay  p  D   ^  ^f     ^^ 


j  R.A. 
Aug.l2)13h.3m.26s....-{NJ)JX 


21h.  57m.  26 -13s. 
103°  2r         0'2" 


"From  these  places  compared  with  recent  observations 
Mr.  Adams  has  obtained  the  following  results : 

Distance  of  the  planet  from  the  sun 30*05 

Inclination  of  the  orbit 1°  45' 

Longitude  of  the  descending  node 309°  43' 

Heliocentric  longitude,  Aug.  4 326°  39' 

"The  present  distance  from  the  sun  is,  therefore,  thirty 
times  the  earth's  mean  distance; — which  is  somewhat  less 
than  the  theory  had  indicated.  The  other  elements  of  the 
orbit  cannot  be  approximated  to  till  the  observations  shall 
have  been  continued  for  a  longer  period. 

"The  part  taken  by  Mr.  Adams  in  the  theoretical  search 
after  this  planet  will,  perhaps,  be  considered  to  justify  the 
suggesting  of  a  name.  With  his  consent,  I  mention  Oceanus 
as  one  which  may  possibly  receive  the  votes  of  astronomers. 


390  A  BUDGET  OF  PARADOXES. 

— I  have  authority  to  state  that  Mr.  Adams's  investigations 
will  in  a  short  time,  be  published  in  detail. 

"J.    CHALLIS."1 

ASTRONOMICAL  POLICE  REPORT. 

"An  ill-looking  kind  of  a  body,  who  declined  to  give  any 
name,  was  brought  before  the  Academy  of  Sciences,  charged 
with  having  assaulted  a  gentleman  of  the  name  of  Uranus 
in  the  public  highway.  The  prosecutor  was  a  youngish 
looking  person,  wrapped  up  in  two  or  three  great  coats; 
and  looked  chillier  than  anything  imaginable,  except  the 
prisoner, — whose  teeth  absolutely  shook,  all  the  time. 

Policeman  Le  Verrier1  stated  that  he  saw  the  prosecutor 
walking  along  the  pavement, — and  sometimes  turning  side- 
ways, and  sometimes  running  up  to  the  railings  and  jerking 
about  in  a  strange  way.  Calculated  that  somebody  must  be 
pulling  his  coat,  or  otherwise  assaulting  him.  It  was  so 
dark  that  he  could  not  see ;  but  thought,  if  he  watched  the 
direction  in  which  the  next  odd  move  was  made,  he  might 
find  out  something.  When  the  time  came,  he  set  Briinnow, 
a  constable  in  another  division  of  the  same  force,  to  watch 
where  he  told  him ;  and  Briinnow  caught  the  prisoner  lurk- 
ing about  in  the  very  spot, — trying  to  look  as  if  he  was 
minding  his  own  business.  Had  suspected  for  a  long  time 
that  somebody  was  lurking  about  in  the  neighborhood. 
Briinnow  was  then  called,  and  deposed  to  his  catching  the 
prisoner  as  described. 

M.  Arago. — Was  the  prosecutor  sober? 

Le  Verrier. — Lord,  yes,  your  worship ;  no  man  who  had 
a  drop  in  him  ever  looks  so  cold  as  he  did. 

M.  Arago. — Did  you  see  the  assault? 

Le  Verrier. — I  can't  say  I  did ;  but  I  told  Briinnow 
exactly  how  he'd  be  crouched  down, — just  as  he  was. 

1  James  Challis  (1803-1882),  director  of  the  Cambridge  observa- 
tory, and  successor  of  Airy  as  Plumian  professor  of  astronomy. 

1  On  Leverrier  and  Arago  see  note  8,  page  43,  and  note  7,  page  243. 


ASTRONOMICAL  POLICE  REPORT.  391 

M.  Arago  (to  Brunnow). — Did  you  see  the  assault? 

Briinnow. — No,  your  worship  ;  but  I  caught  the  prisoner. 

M.  Arago. — How  did  you  know  there  was  any  assault 
at  all? 

Le  Verrier. — I  reckoned  it  couldn't  be  otherwise,  when 
I  saw  the  prosecutor  making  those  odd  turns  on  the  pave- 
ment. 

M .  Arago.— You.  reckon  and  you  calculate !  Why,  you'll 
tell  me,  next,  that  you  policemen  may  sit  at  home  and  find 
out  all  that's  going  on  in  the  streets  by  arithmetic.  Did  you 
ever  bring  a  case  of  this  kind  before  me  till  now? 

Le  Verrier. — Why,  you  see,  your  worship,  the  police 
are  growing  cleverer  and  cleverer  every  day.  We  can't 
help  it : — it  grows  upon  us. 

M.  Arago. — You're  getting  too  clever  for  me.  What 
does  the  prosecutor  know  about  the  matter? 

The  prosecutor  said,  all  he  knew  was  that  he  was  pulled 
behind  by  somebody  several  times.  On  being  further  ex- 
amined, he  said  that  he  had  seen  the  prisoner  often,  but 
did  not  know  his  name,  nor  how  he  got  his  living ;  but  had 
understood  he  was  called  Neptune.  He  himself  had  paid 
rates  and  taxes  a  good  many  years  now.  Had  a  family  of 
six, — two  of  whom  got  their  own  living. 

The  prisoner  being  called  on  for  his  defence,  said  that  it 
was  a  quarrel.  He  had  pushed  the  prosecutor — and  the 
prosecutor  had  pushed  him.  They  had  known  each  other 
a  long  time,  and  were  always  quarreling ; — he  did  not  know 
why.  It  was  their  nature,  he  supposed.  He  further  said, 
that  the  prosecutor  had  given  a  false  account  of  himself; — 
that  he  went  about  under  different  names.  Sometimes  he 
was  called  Uranus,  sometimes  Herschel,  and  sometimes 
Georgium  Sidus ;  and  he  had  no  character  for  regularity 
in  the  neighborhood.  Indeed,  he  was  sometimes  not  to  be 
seen  for  a  long  time  at  once. 

The  prosecutor,  on  being  asked,  admitted,  after  a  little 
hesitation,  that  he  had  pushed  and  pulled  the  prisoner  too. 


392  A  BUDGET  OF  PARADOXES. 

In  the  altercation  which  followed,  it  was  found  very  diffi- 
cult to  make  out  which  began : — and  the  worthy  magistrate 
seemed  to  think  they  must  have  begun  together. 

M.  Arago. — Prisoner,  have  you  any  family? 

The  prisoner  declined  answering  that  question  at  present. 
He  said  he  thought  the  police  might  as  well  reckon  it  out 
whether  he  had  or  not. 

M.  Arago  said  he  didn't  much  differ  from  that  opinion. 
— He  then  addressed  both  prosecutor  and  prisoner ;  and  told 
them  that  if  they  couldn't  settle  their  differences  without 
quarreling  in  the  streets,  he  should  certainly  commit  them 
both  next  time.  In  the  meantime,  he  called  upon  both  to 
enter  into  their  own  recognizances ;  and  directed  the  police 
to  have  an  eye  upon  both, — observing  that  the  prisoner 
would  be  likely  to  want  it  a  long  time,  and  the  prosecutor 
would  be  not  a  hair  the  worse  for  it." 

This  quib  was  written  by  a  person  who  was  among  the 
astronomers :  and  it  illustrates  the  fact  that  Le  Verrier  had 
sole  possession  of  the  field  until  Mr.  Challis's  letter  appeared. 
Sir  John  Herschel's  pervious  communication  should  have 
paved  the  way:  but  the  wonder  of  the  discovery  drove  it 
out  of  many  heads.  There  is  an  excellent  account  of  the 
whole  matter  in  Professor  Grant's2  History  of  Physical 
Astronomy.  The  squib  scandalized  some  grave  people,  who 
wrote  severe  admonitions  to  the  editor.  There  are  formalists 
who  spend  much  time  in  writing  propriety  to  journals,  to 
which  they  serve  as  foolometers.  In  a  letter  to  the  Athe- 
nceum,  speaking  of  the  way  in  which  people  hawk  fine  terms 
for  common  things,  I  said  that  these  people  ought  to  have 
a  new  translation  of  the  Bible,  which  should  contain  the 
verse  "gentleman  and  lady,  created  He  them."  The  editor 
was  handsomely  fired  and  brimstoned ! 

'Robert  Grant's  (1814-1892)  History  of  Physical  Astronomy 
from  the  ^Earliest  Ages  to  the  Middle  of  the  Nineteenth  Century 
appeared  in  1852.  He  was  professor  of  astronomy  and  director  of 
the  observatory  at  Glasgow. 


A  NEW   THEORY   OF  TIDES.  393 


A  NEW  THEORY  OF  TIDES. 

A  new  theory  of  the  tides:  in  which  the  errors  of  the  usual 
theory  are  demonstrated;  and  proof  shewn  that  the  full  moon 
is  not  the  cause  of  a  concomitant  spring  tide,  but  actually  the 
cause  of  the  neaps.... By  Commr.  Debenham,1  R.N.  London, 
1846,  8vo. 

The  author  replied  to  a  criticism  in  the  Athenaum,  and 
I  remember  how,  in  a  very  few  words,  he  showed  that  he 
had  read  nothing  on  the  subject.  The  reviewer  spoke  of 
the  forces  of  the  planets  (i.  e.,  the  Sun  and  Moon)  on  the 
ocean,  on  which  the  author  remarks,  "But  N.B.  the  Sun  is 
no  planet,  Mr.  Critic."  Had  he  read  any  of  the  actual  in- 
vestigations on  the  usual  theory,  he  would  have  known  that 
to  this  day  the  sun  and  moon  continue  to  be  called  planets — 
though  the  phrase  is  disappearing — in  speaking  of  the  tides ; 
the  sense,  of  course,  being  the  old  one,  wandering  bodies. 

A  large  class  of  the  paradoxers,  when  they  meet  with 
something  which  taken  in  their  sense  is  absurd,  do  not  take 
the  trouble  to  find  out  the  intended  meaning,  but  walk  off 
with  the  words  laden  with  their  own  first  construction.  Such 
men  are  hardly  fit  to  walk  the  streets  without  an  interpreter. 
I  was  startled  for  a  moment,  at  the  time  when  a  recent  happy 
— and  more  recently  happier — marriage  occupied  the  public 
thoughts,  by  seeing  in  a  haberdasher's  window,  in  staring 
large  letters,  an  unpunctuated  sentence  which  read  itself  to 
me  as  "Princess  Alexandra!  collar  and  cuff!"  It  imme- 
diately occurred  to  me  that  had  I  been  any  one  of  some 
scores  of  my  paradoxers,  I  should,  no  doubt,  have  proceeded 
to  raise  the  mob  against  the  unscrupulous  person  who  dared 
to  hint  to  a  young  bride  such  maleficent — or  at  least  immel- 
lificent — conduct  towards  her  new  lord.  But,  as  it  was,  cer- 
tain material  contexts  in  the  shop  window  suggested  a  less 

1  John  Debenham  was  more  interested  in  religion  than  in  astron- 
omy. He  wrote  The  Strait  Gate;  or,  the  true  scripture  doctrine  of 
salvation  clearly  explained,  London,  1843,  and  Tractatus  de  magis  et 
Bethlehema  stella  et  Christi  in  deserto  tentatione,  privately  printed 
at  London  in  1845. 


394  A  BUDGET  OF   PARADOXES. 

savage  explanation.  A  paradoxer  should  not  stop  at  reading 
the  advertisements  of  Newton  or  Laplace :  he  should  learn  to 
look  at  the  stock  of  goods. 

I  think  I  must  have  an  eye  for  double  readings,  when 
presented :  though  I  never  guess  riddles.  On  the  day  on 
which  I  first  walked  into  the  Panizzi  reading  room2 — as  it 
ought  to  be  called — at  the  Museum,  I  began  my  circuit  of 
the  wall-shelves  at  the  ladies'  end :  and  perfectly  coincided  in 
the  propriety  of  the  Bibles  and  theological  works  being 
placed  there.  But  the  very  first  book  I  looked  on  the  back 
of  had,  in  flaming  gold  letters,  the  following  inscription — • 
"Blast  the  Antinomians  !"3  If  a  line  had  been  drawn  below 
the  first  word,  Dr.  Blast's  history  of  the  Antinomians  would 
not  have  been  so  fearfully  misinterpreted.  It  seems  that 
neither  the  binder  nor  the  arranger  of  the  room  had  caught 
my  reading.  The  book  was  removed  before  the  catalogue 
of  books  of  reference  was  printed. 

AN  ASTRONOMICAL  PARADOXER. 

Two  systems  of  astronomy :  first,  the  Newtonian  system,  showing 
the  rise  and  progress  thereof,  with  a  short  historical  account ;  the 
general  theory  with  a  variety  of  remarks  thereon :  second,  the 
system  in  accordance  with  the  Holy  Scriptures,  showing  the 
rise  and  progress  from  Enoch,  the  seventh  from  Adam,  the 
prophets,  Moses,  and  others,  in  the  first  Testament;  our  Lord 
Jesus  Christ,  and  his  apostles,  in  the  new  or  second  Testament ; 
Reeve  and  Muggleton,  in  the  third  and  last  Testament;  with 
a  variety  of  remarks  thereon.  By  Isaac  Frost.1  London,  1846, 
4to. 

"More  properly  the  Sydney  Smirke  reading  room,  since  it  was 
built  from  his  designs. 

*  The  Antinomians  were  followers  of  Johannes  Agricola  (1494- 
1566).  They  believed  that  Christians  as  such  were  released  from  all 
obligations  to  the  Old  Testament.  Some  went  so  far  as  to  assert 
that,  since  all  Christians  were  sanctified,  they  could  not  lose  this 
sanctity  even  though  they  disobeyed  God.  The  sect  was  prominent 
in  England  in  the  seventeenth  century,  and  was  transferred  to  New 
England.  Here  it  suffered  a  check  in  the  condemnation  of  Mrs.  Ann 
Hutchinson  (1636)  by  the  Newton  Synod. 

1  Aside  from  this  work  and  his  publications  on  Reeve  and 
Muggleton  he  wrote  nothing.  With  Joseph  Frost  he  published  A  list 


AN   ASTRONOMICAL   PARADOXER.  395 

A  very  handsomely  printed  volume,  with  beautiful  plates. 
Many  readers  who  have  heard  of  Muggletonians  have  never 
had  any  distinct  idea  of  Lodowick  Muggleton,2  the  inspired 
tailor,  (1608-1698)  who  about  1650  received  his  commission 
from  heaven,  wrote  a  Testament,  founded  a  sect,  and  de- 
scended to  posterity.  Of  Reeve3  less  is  usually  said ;  accord- 
ing to  Mr.  Frost,  he  and  Muggleton  are  the  two  "witnesses." 
I  shall  content  myself  with  one  specimen  of  Mr.  Frost's 
science : 

"I  was  once  invited  to  hear  read  over  'Guthrie4  on  As- 
tronomy,' and  when  the  reading  was  concluded  I  was  asked 
my  opinion  thereon ;  when  I  said,  'Doctor,  it  appears  to  me 
that  Sir  I.  Newton  has  only  given  two  proofs  in  support  of 
his  theory  of  the  earth  revolving  round  the  sun :  all  the  rest 
is  assertion  without  any  proofs.' — 'What  are  they?'  inquired 
the  Doctor.— 'Well/  I  said,  'they  are,  first,  the  power  of 

of  Books  and  general  index  to  J.  Reeve  and  L.  Muggleton's  works 
(1846),  Divine  Songs  of  the  Muggletonians  (1829),  and  the  work 
mentioned  on  page  396.  The  works  of  J.  Reeve  and  L.  Muggleton 
(1832). 

'About  1650  he  and  his  cousin  John  Reeve  (1608-1658)  began 
to  have  visions.  As  part  of  their  creed  they  taught  that  astronomy 
was  opposed  by  the  Bible.  They  asserted  that  the  sun  moves  about 
the  earth,  and  Reeve  figured  out  that  heaven  was  exactly  six  miles 
away.  Both  Muggleton  and  Reeve  were  imprisoned  for  their  uni- 
tarian  views.  Muggleton  wrote  a  Transcendant  Spirituall  Treatise 
(1652).  I  have  before  me  A  true  Interpretation  of  All  the  Chief 

Texts of  the  whole  Book  of  the  Revelation  of  St.  'John By 

Lodozvick  Muggleton,  one  of  the  two  last  Commissioned  Witnesses 
&  Prophets  of  the  onely  high,  immortal,  glorious  God,  Christ  Jesus 
(1665),  in  which  the  interpretation  of  the  "number  of  the  beast" 
occupies  four  pages  without  arriving  anywhere. 

*In  1652  he  was,  in  a  vision,  named  as  the  Lord's  "last  mes- 
senger," with  Muggleton  as  his  "mouth,"  and  died  six  years  later, 
probably  of  nervous  tension  resulting  from  his  divine  "illumination." 
He  was  the  more  spiritual  of  the  two. 

4  William  Guthrie  (1708-1770)  was  a  historian  and  political 
writer.  His  History  of  England  (1744-1751)  was  the  first  attempt 
to  base  history  on  parliamentary  records.  He  also  wrote  a  General 
History  of  Scotland  in  10  volumes  (1767).  The  work  to  which  Frost 
refers  is  the  Geographical,  Historical,  and  Commercial  Grammar 
(1770)  which  contained  an  astronomical  part  by  J.  Ferguson.  By 
1827  it  had  passed  through  24  editions. 


396  A  BUDGET  OF  PARADOXES. 

attraction  to  keep  the  earth  to  the  sun ;  the  second  is  the 
power  of  repulsion,  by  virtue  of  the  centrifugal  motion  of 
the  earth:  all  the  rest  appears  to  me  assertion  without 
proof.'  The  Doctor  considered  a  short  time  and  then  said, 
'It  certainly  did  appear  so.'  I  said,  'Sir  Isaac  has  certainly 
obtained  the  credit  of  completing  the  system,  but  really  he 
has  only  half  done  his  work.' — 'How  is  that/  inquired  my 
friend  the  Doctor.  My  reply  was  this:  'You  will  observe 
his  system  shows  the  earth  traverses  round  the  sun  on  an 
inclined  plane;  the  consequence  is,  there  are  four  powers 
required  to  make  his  system  complete: 

1st.  The  power  of  attraction. 

2ndly.  The  power  of  repulsion. 

3rdly.  The  power  of  ascending  the  inclined  plane. 

4thly.    The  power  of  descending  the  inclined  plane 

You  will  thus  easily  see  the  four  powers  required,  and 
Newton  has  only  accounted  for  two ;  the  work  is  therefore 
only  half  done/  Upon  due  reflection  the  Doctor  said,  'It 
certainly  was  necessary  to  have  these  four  points  cleared 
up  before  the  system  could  be  said  to  be  complete.' " 

I  have  no  doubt  that  Mr.  Frost,  and  many  others  on 
my  list,  have  really  encountered  doctors  who  could  be 
puzzled  by  such  stuff  as  this,  or  nearly  as  bad,  among  the 
votaries  of  existing  systems,  and  have  been  encouraged 
thereby  to  print  their  objections.  But  justice  requires  me 
to  say  that  from  the  words  "power  of  repulsion  by  virtue 
of  the  centrifugal  motion  of  the  earth,"  Mr.  Frost  may  be 
suspected  of  having  something  more  like  a  notion  of  the 
much-mistaken  term  "centrifugal  force"  than  many  para- 
doxers  of  greater  fame.  The  Muggletonian  sect  is  not  alto- 
gether friendless:  over  and  above  this  handsome  volume, 
the  works  of  Reeve  and  Muggleton  were  printed,  in  1832, 
in  three  quarto  volumes.  See  Notes  and  Queries,  ist  Series, 
v,  80 ;  3d  Series,  iii,  303. 


AN   ASTRONOMICAL   PARADOXER.  397 

[The  system  laid  down  by  Mr.  Frost,  though  intended 
to  be  substantially  that  of  Lodowick  Muggleton,  is  not  so 
vagarious.  It  is  worthy  of  note  how  very  different  have 
been  the  fates  of  two  contemporary  paradoxers,  Muggleton 
and  George  Fox.5  They  were  friends  and  associates,6  and 
commenced  their  careers  about  the  same  time,  1647-1650. 
The  followers  of  Fox  have  made  their  sect  an  institution, 
and  deserve  to  be  called  the  pioneers  of  philanthropy.  But 
though  there  must  still  be  Muggletonians,  since  expensive 
books  are  published  by  men  who  take  the  name,  no  sect  of 
that  name  is  known  to  the  world.  Nevertheless,  Fox  and 
Muggleton  are  men  of  one  type,  developed  by  the  same 
circumstances :  it  is  for  those  who  investigate  such  men  to 
point  out  why  their  teachings  have  had  fates  so  different. 
Macaulay  says  it  was  because  Fox  found  followers  of  more 
sense  than  himself.  True  enough:  but  why  did  Fox  find 
such  followers  and  not  Muggleton?  The  two  were  equally 
crazy,  to  all  appearance:  and  the  difference  required  must 
be  sought  in  the  doctrines  themselves. 

Fox  was  not  a  rational  man :  but  the  success  of  his  sect 
and  doctrines  entitles  him  to  a  letter  of  alteration  of  the 
phrase  which  I  am  surprised  has  not  become  current.  When 
Conduitt,7  the  husband  of  Newton's  half-niece,  wrote  a 
circular  to  Newton's  friends,  just  after  his  death,  inviting 
them  to  bear  their  parts  in  a  proper  biography,  he  said,  "As 
Sir  I.  Newton  was  a  national  man,  I  think  every  one  ought 
to  contribute  to  a  work  intended  to  do  him  justice."  Here 
is  the  very  phrase  which  is  often  wanted  to  signify  that 


G  George  Fox  (1624-1691),  founder  of  the  Society  of  Friends;  a 
mystic  and  a  disciple  of  Boehme.  He  was  eight  times  imprisoned  for 
heresy. 

6  If  they  were  friends  they  were  literary  antagonists,  for  Mug- 
gleton wrote  against  Fox  The  Neck  of  the  Quakers  Broken  (1663), 
and  Fox  replied  in  1667.  Muggleton  also  wrote  A  Looking  Glass  for 
George  Fox. 

'John  Conduitt  (1688-1737),  who  married  (1717)  Newton's 
half  niece,  Mrs.  Katherine  Barton.  See  note  6,  page  136. 


398  A  BUDGET  OF  PARADOXES. 

celebrity  which  puts  its  mark,  good  or  bad,  on  the  national 
history,  in  a  manner  which  cannot  be  asserted  of  many 
notorious  or  famous  historical  characters.  Thus  George 
Fox  and  Newton  are  both  national  men.  Dr.  Roget's8 
Thesaurus  gives  more  than  fifty  synonyms  —  colleagues 
would  be  the  better  word — of  "celebrated"  any  one  of 
which  might  be  applied,  either  in  prose  or  poetry,  to  New- 
ton or  to  his  works,  no  one  of  which  comes  near  to  the 
meaning  which  Conduitt's  adjective  immediately  suggests. 
The  truth  is,  that  we  are  too  monarchical  to  be  national. 
We  have  the  Queen's  army,  the  Queen's  navy,  the  Queen's 
highway,  the  Queen's  English,  etc. ;  nothing  is  national  ex- 
cept the  debt.  That  this  remark  is  not  new  is  an  addition 
to  its  force;  it  has  hardly  been  repeated  since  it  was  first 
made.  It  is  some  excuse  that  nation  is  not  vernacular  Eng- 
lish: the  country  is  our  word,  and  country  man  is  appro- 
priated.] 


Astronomical  Aphorisms,  or  Theory  of  Nature ;  founded  on  the 
immutable  basis  of  Meteoric  Action.  By  P.  Murphy,9  Esq. 
London,  1847,  12mo. 

This  is  by  the  framer  of  the  Weather  Almanac,  who 
appeals  to  that  work  as  corroborative  of  his  theory  of  plan- 
etary temperature,  years  after  all  the  world  knew  by  ex- 
perience that  this  meteorological  theory  was  just  as  good 
as  the  others. 


"Probably  Peter  Mark  Roget's  (1779-1869)  Thesaurus  of  Eng- 
lish Words  (1852)  is  not  much  used  at  present,  but  it  went  through 
28  editions  in  his  lifetime.  Few  who  use  the  valuable  work  are 
aware  that  Roget  was  a  professor  of  physiology  at  the  Royal  Insti- 
tution (London),  that  he  achieved  his  title  of  F.  R.  S.  because  of  his 
work  in  perfecting  the  slide  rule,  and  that  he  followed  Sir  John 
Herschel  as  secretary  of  the  Royal  Society. 

*  See  note  1,  page  327.  This  work  went  into  a  second  edition  in 
the  year  of  its  first  publication. 


THEISM    INDEPENDENT  OF   REVELATION.  399 

The  conspiracy  of  the  Bullionists  as  it  affects  the  present  system 
of  the  money  laws.  By  Caleb  Quotem.  Birmingham,  1847, 
8vo.  (pp.  16). 

This  pamphlet  is  one  of  a  class  of  which  I  know  very 
little,  in  which  the  effects  of  the  laws  relating  to  this  or 
that  political  bone  of  contention  are  imputed  to  deliberate 
conspiracy  of  one  class  to  rob  another  of  what  the  one  knew 
ought  to  belong  to  the  other.  The  success  of  such  writers 
in  believing  what  they  have  a  bias  to  believe,  would,  if  they 
knew  themselves,  make  them  think  it  equally  likely  that  the 
inculpated  classes  might  really  believe  what  it  is  their  in- 
terest to  believe.  The  idea  of  a  guilty  understanding  ex- 
isting among  fundholders,  or  landholders,  or  any  holders, 
all  the  country  over,  and  never  detected  except  by  bouncing 
pamphleteers,  is  a  theory  which  should  have  been  left  for 
Cobbett10  to  propose,  and  for  Apella  to  believe.11 

[August,  1866.  A  pamphlet  shows  how  to  pay  the 
National  Debt.  Advance  paper  to  railways,  etc.,  receivable 
in  payment  of  taxes.  The  railways  pay  interest  and  prin- 
cipal in  money,  with  which  you  pay  your  national  debt,  and 
redeem  your  notes.  Twenty-five  years  of  interest  redeems 
the  notes,  and  then  the  principal  pays  the  debt.  Notes  to 
be  kept  up  to  value  by  penalties.] 


THEISM  INDEPENDENT  OF  REVELATION. 

The  Reasoner.    No.  45.    Edited  by  G.  J.  Holyoake.1    Price  2d. 
Is  there  sufficient  proof  of  the  existence  of  God?  8vo.   1847. 

This  acorn  of  the  holy  oak  was  forwarded  to  me  with 
a  manuscript  note,  signed  by  the  editor,  on  the  part  of  the 

10  See  note  1,  page  177. 

11  See  note  4,  page  233. 

1  George  Jacob  Holyoake  (1817-1906)  entered  into  a  controver- 
sial life  at  an  early  age.  In  1841  he  was  imprisoned  for  six  months 
for  blasphemy.  He  founded  and  edited  The  Reasoner  (Vols.  1-26, 
1846-1861).  In  his  later  life  he  did  much  to  promote  cooperation 
among  the  working  class. 


400  A  BUDGET  OF   PARADOXES. 

"London  Society  of  Theological  Utilitarians,"  who  say, 
"they  trust  you  may  be  induced  to  give  this  momentous 
subject  your  consideration."  The  supposition  that  a  middle- 
aged  person,  known  as  a  student  of  thought  on  more  subjects 
than  one,  had  that  particular  subject  yet  to  begin,  is  a  speci- 
men of  what  I  will  call  the  assumption-trick  of  controversy, 
a  habit  which  pervades  all  sides  of  all  subjects.  The  tract  is 
a  proof  of  the  good  policy  of  letting  opinions  find  their 
level,  without  any  assistance  from  the  Court  of  Queen's 
Bench.  Twenty  years  earlier  the  thesis  would  have  been 
positive,  "There  is  sufficient  proof  of  the  non-existence  of 
God,"  and  bitter  in  its  tone.  As  it  stands,  we  have  a  mod- 
erate and  respectful  treatment — wrong  only  in  making  the 
opponent  argue  absurdly,  as  usually  happens  when  one 
side  invents  the  other — of  a  question  in  which  a  great  many 
Christians  have  agreed  with  the  atheist:  that  question  be- 
ing— Can  the  existence  of  God  be  proved  independently  of 
revelation?  Many  very  religious  persons  answer  this  ques- 
tion in  the  negative,  as  well  as  Mr.  Holyoake.  And,  this 
point  being  settled,  all  who  agree  in  the  negative  separate 
into  those  who  can  endure  scepticism,  and  those  who  can- 
not: the  second  class  find  their  way  to  Christianity.  This 
very  number  of  The  Reasoner  announces  the  secession  of 
one  of  its  correspondents,  and  his  adoption  of  the  Christian 
faith.  This  would  not  have  happened  twenty  years  before : 
nor,  had  it  happened,  would  it  have  been  respectfully  an- 
nounced. 

There  are  people  who  are  very  unfortunate  in  the  ex- 
pression of  their  meaning.  Mr.  Holyoake,  in  the  name  of 
the  "London  Society"  etc.,  forwarded  a  pamphlet  on  the 
existence  of  God,  and  said  that  the  Society  trusted  I  "may 
be  induced  to  give"  the  subject  my  "consideration."  How 
could  I  know  the  Society  was  one  person,  who  supposed 
I  had  arrived  at  a  conclusion  and  wanted  a  "guiding  word"  ? 
But  so  it  seems  it  was:  Mr.  Holyoake,  in  the  English 


THEISM    INDEPENDENT   OF   REVELATION.  401 

Leader  of  October  15,  1864,  and  in  a  private  letter  to  me, 
writes  as  follows : 

"The  gentleman  who  was  the  author  of  the  argument, 
and  who  asked  me  to  send  it  to  Mr.  De  Morgan,  never 
assumed  that  that  gentleman  had  'that  particular  subject 
to  begin' — on  the  contrary,  he  supposed  that  one  whom  we 
all  knew  to  be  eminent  as  a  thinker  had  come  to  a  conclusion 
upon  it,  and  would  perhaps  vouchsafe  a  guiding  word  to 
one  who  was,  as  yet,  seeking  the  solution  of  the  Great  Prob- 
lem of  Theology.  I  told  my  friend  that  'Mr.  De  Morgan 
was  doubtless  preoccupied,  and  that  he  must  be  content  to 
wait.  On  some  day  of  courtesy  and  leisure  he  might  have 
the  kindness  to  write/  Nor  was  I  wrong — the  answer  ap- 
pears in  your  pages  at  the  lapse  of  seventeen  years." 

I  suppose  Mr.  Holyoake's  way  of  putting  his  request 
was  the  stylus  curio?  of  the  Society.  A  worthy  Quaker 
who  was  sued  for  debt  in  the  King's  Bench  was  horrified 
to  find  himself  charged  in  the  declaration  with  detaining 
his  creditor's  money  by  force  and  arms,  contrary  to  the  peace 
of  our  Lord  the  King,  etc.  It's  only  the  stylus  curioe,  said 
a  friend:  I  don't  know  curio? ,  said  the  Quaker,  but  he 
shouldn't  style  us  peace-breakers. 

The  notion  that  the  won-existence  of  God  can  be  proved, 
has  died  out  under  the  light  of  discussion:  had  the  only 
lights  shone  from  the  pulpit  and  the  prison,  so  great  a 
step  would  never  have  been  made.  The  question  now  is 
as  above.  The  dictum  that  Christianity  is  "part  and  parcel 
of  the  law  of  the  land"  is  also  abrogated :  at  the  same  time, 
and  the  coincidence  is  not  an  accident,  it  is  becoming  some- 
what nearer  the  truth  that  the  law  of  the  land  is  part  and 
parcel  of  Christianity.  It  must  also  be  noticed  that  Chris- 
tianity was  part  and  parcel  of  the  articles  of  war]  and  so 
was  duelling.  Any  officer  speaking  against  religion  was  to 
be  cashiered ;  and  any  officer  receiving  an  affront  without, 
in  the  last  resort,  attempting  to  kill  his  opponent,  was  also 
to  be  cashiered.  Though  somewhat  of  a  book-hunter,  I 


402  A  BUDGET  OF  PARADOXES. 

have  never  been  able  to  ascertain,  the  date  of  the  collected 
remonstrances  of  the  prelates  in  the  House  of  Lords  against 
this  overt  inculcation  of  murder,  under  the  soft  name  of 
satisfaction:  it  is  neither  in  Watt,2  nor  in  Lowndes,3  nor  in 
any  edition  of  Brunet  ;*  and  there  is  no  copy  in  the  British 
Museum.  Was  the  collected  edition  really  published? 

[The  publication  of  the  above  in  the  Athenceum  has  not 
produced  reference  to  a  single  copy.  The  collected  edition 
seems  to  be  doubted.  I  have  even  met  one  or  two  persons 
who  doubt  the  fact  of  the  Bishops  having  remonstrated  at 
all:  but  their  doubt  was  founded  on  an  absurd  supposition, 
namely,  that  it  was  no  business  of  theirs ;  that  it  was  not  the 
business  of  the  prelates  of  the  church  in  union  with  the 
state  to  remonstrate  against  the  Crown  commanding  mur- 
der! Some  say  that  the  edition  was  published,  but  under 
an  irrelevant  title,  which  prevented  people  from  knowing 
what  it  was  about.  Such  things  have  happened:  for  ex- 
ample, arranged  extracts  from  Wellington's  general  orders, 
which  would  have  attracted  attention,  fell  dead  under  the 
title  of  "Principles  of  War."  It  is  surmised  that  the  book 
I  am  looking  for  also  contains  the  protests  of  the  Reverend 
bench  against  other  things  besides  the  Thou-shalt-do-murder 
of  the  Articles  (of  war),  and  is  called  "First  Elements  of 
Religion"  or  some  similar  title.  Time  clears  up  all  things.] 

8  See  note  6,  page  102. 

'William  Thomas  Lowndes  (1798-1843),  whose  Bibliographer's 
Manual  of  English  Literature,  4  vols.,  London,  1834  (also  1857-1864, 
and  1869)  is  a  classic  in  its  line. 

4  Jacques  Charles  Brunet  (1780-1867),  the  author  of  the  great 
French  bibliography,  the  Manuel  du  Libraire  (1810). 


RETURN       CIRCULATION  DEPARTMENT 

TO  •fr        202  Main  Library 

LOAN  PERIOD 
HOME  USE 


ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 

1-month  loans  may  be  renewed  by  calling  642-3405 

6-month  loans  may  be  recharged  by  bringing  books  to  Circulation  Desk 

Renewals  and  recharges  may  be  made  4  days  prior  to  due  date 

DUE   ASM  STAMPED   BELOW 


'NOV.-  3  1977 


IE&.CIILKW 


LIBRARY  USE 


MOV  30 1987 


MAY     9 


2  9  1P98 


CIRCULATION  D  =PT 


CIRCULATION  DE>I 


FORM  NO.  DD  6, 


UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
BERKELEY,  CA   94720 


U.C.  BERKELEY  LIBRARIES