Atomic  Hypothesis  and  Dissected  {Structural)  Formula.     251 
The  well-known  numerical  relationships  between  the  combi- 
ning numbers  of  allied  elements  (e.  g.  Li  +  K  =  2Na,  K  +  Cs  = 
2B,b,  Cl  +  I  =  2Br,  P  +  Sb  =  2As,  &c.)  and  the  regular  progres- 
sion in  physical  and  chemical  properties  observable  in  members 
of  the  same  family  according  as  their  combining  numbers  are 
higher  (e.  g.  CI,  gas  j  Br,  liquid  5  1,  solid  j  Mg,  Ca,  Sr,  Ba  :  N, 
P,  V,  As,  Sb,  Bi :  &c.)  are  either  consequences  of,  or  closely 
related  to,  these  "  periodic  laws/' 
17.  Chemical  reactions  may  be  expressed  by  equations  when 
one  or  more  formulae  occur  on  each  side  of  the  sign  of  equality; 
the  most  general  form  in  which  such  equations  may  be  put  is 
AB  +  CD=AC+BD, 
where  A,  B,  C,  D  represent  portions  of  formulae  which  are  asso- 
ciated together  differently  in  the  resulting  products  from  what 
they  are  in  the  generators. 
If  AB,  CD,  AC,  BD  are  the  formulae  of  two  generators  and 
two  products  respectively,  the  reaction  is  said  to  be  one  of  double 
decomposition ;  and  to  the  portions  of  formulae  A,  B,  C,  D  the 
terms  Groups  or  Radicals  are  applied.     Thus  the  equations 
CH4  +  C12  =  C1H  +  CH3C1,  ...  (1) 
0H2  +  PC15  =  2C1H  +  PC130,  ...  (2) 
NH3  +  CHC13=3C1H  +  NCH     ....     (3) 
represent  double  decompositions ;  and  on  inspecting  them  it  is 
noticeable  that  the  formulae  of  the  resulting  products  may  be 
deduced  from  those  of  the  generators  by  replacing  certain  sym- 
bols in  one  generator  by  certain  others  in  the  other  generator, 
i.  e.  substituting  one  group  for  another.  Thus  in  equation  (!) 
the  symbol  CI  is  substituted  for  H  in  the  formula  CH4,  produ- 
cing CH3C1;  or  the  group  or  radical  CH3  is  replaced  by  CI, 
forming  C1H ;  while  CI  is  replaced  in  CI2  by  H,  forming  C1H ; 
or  the  radical  CH3  is  substituted  for  CI  in  CI2,  producing  CH3C1. 
Similarly  in  equation  (2),  PCI3  replaces  H2  in  H20,  forming 
PC130;  and  CI2  replaces  0  in  H2  0,  forming  H2C12  or  2HC1; 
or  otherwise,  0  replaces  CI2  in  PCI5,  forming  PCI3  0 ;  while  H2 
replaces  PCI3,  forming  H2C12  or  2HC1. 
Asrain  in  equation  (3),  N  replaces  CI3  in  CH  CI3,  producing 
CHN;  or  H3  replaces  CH,  forming  H3 CI3 or  3HC1;  while  CH 
replaces  H3  in  NH3,  forming  NCH ;  or  CI3  replaces  N,  produ- 
cing CI3  H3  or  3C1H. 
A  radical,  therefore,  is  one  or  more  symbols  and  suffixes 
transferable  from  one  formula  to  another,  the  process  indicated 
by  such  transfer  being  a  given  chemical  change  or  reaction ; 
hence  the  employment  of  the  word  radical  necessarily  involves 
the  idea  of  a  reaction.  The  term  combining  number  is  applied 
to  a  radical  to  indicate  the  sum  obtained  by  multiplying  the 
