Royal  Society.  227 
and  that  while  I  do  not  know  what  exactly  is  the  meaning  of  the 
ratio 
3  shillings  :  6  yards, 
I  am  enabled  to  assert  that  there  is  a  connexion  between  5  shillings 
and  6  yards  in  the  nature  of  a  ratio,  and  subject  to  the  rules  of  pro- 
portion, which  is  the  same  as  the  connexion  between  5  shillings  and 
10  yards,  whatever  that  may  be.  To  deny  this  appears  to  me  to 
imply  an  objection  to  concrete  arithmetic  generally.  I  do  not  assert 
that  the  ratio  is  definite."  It  is  much  to  be  regretted  that  Mr. 
Merrifield  did  not  omit  this  altogether,  or  else  that  he  did  not  ex- 
plain his  views  more  fully.  Had  he  taken  the  latter  course,  we  are 
sure  that  his  explanation  would  have  been  clear  of  objection.  But 
as  the  note  stands,  it  is  very  liable  to  mislead.  We  need  hardly  say 
that  such  a  proportion  as 
3  shillings  :  6  yards  : :  5  shillings  :  10  yards 
is  commonly  held  to  be  merely  an  improper  mode  of  stating  that  the 
ratio  of  3  shillings  to  5  shillings  is  equal  to  the  ratio  of  6  yards  to 
10  yards  ;  and  it  is  by  no  means  obvious  that  the  common  view  does 
not  go  to  the  bottom  of  the  matter.  At  all  events,  Mr.  Merri- 
field could  hardly  complain  if  from  his  premises  we  were  to  draw  the 
conclusion  that 
3  shillings  +  6  yards  :  6  yards  :  :  5  shillings +10  yards  :  10  yards. 
But  what  meaning  can  be  attached  to  this  proportion,  beyond  a  rela- 
tion between  the  bare  numbers,  it  is  hard  to  see.     Of  course  if  it 
is  merely  a  question  of  numbers,  there  is  no  difficulty ;  but  this,  to 
all  appearance,  is  not  Mr.  Merrifield's  meaning. 
Our  notice  of  the  remaining  part  of  the  work  must  be  brief.  The 
treatise  on  Mensuration  comprises  all  the  most  useful  rules  for  find- 
ing areas  and  volumes  ;  and  though  there  is  no  attempt  to  give 
formal  proofs  of  the  rules,  their  dependence  on  known  geometrical 
theorems  is  shown  with  great  clearness,  and  their  use  illustrated  by 
a  sufficiency  of  examples.  Mr.  Merrifield's  powers  of  exposition 
are  perhaps  seen  to  most  advantage  in  this  part  of  the  volume.  The 
book  as  a  whole,  however,  is  exceedingly  well  done ;  in  fact,  we 
are  inclined  to  think  that,  of  all  the  works  hitherto  published  in 
Messrs.  Longman's  series,  this  comes  most  nearly  up  to  the  notion 
of  a  text-book  adapted  "  for  the  self-instruction  of  working  men." 
XXVIII.  Proceedings  of  Learned  Societies. 
ROYAL  SOCIETY. 
[Continued  from  p.  154.] 
Nov.  16,  18/1. — General  Sir  Edward  Sabine,  K.C.B.,  President,  in 
the  Chair. 
rFHE  following  communication  was  read : — 
■*-  "Considerations  on  the  Abrupt  Change  at  Boiling  or  Conden- 
sing in  reference  to  the  Continuity  of  the  Fluid  State  of  Matter."  By 
Professor  James  Thomson,  LL.D. 
When  we  find  a  substance  capable  of  existing  in  two  fluid  states 
Q2 
