394  Royal  Society : — Mr.  D.  M'Farlane  on  the 
was  obtained,  where  y  is  the  value  of  a  scale-division  in  terms  of  a 
degree  Centigrade,  and  x  the  galvanometer  deflection  ;  and  the  differ- 
ence of  temperature  of  the  junctions  is  therefore 
^=0°0924^+0°-0000227^2, 
from  which  the  numbers  in  col.  II.  of  the  following  Tables  were  cal- 
culated. 
The  method  adopted  in  reducing  the  observations  was  this  : — 
Each  single  set  of  readings  was  arranged  in  a  vertical  column,  and 
the  whole  series  placed  side  by  side  with  corresponding  numbers  in 
the  same  horizontal  line  ;  the  means  of  the  horizontal  lines  were 
formed  into  a  similar  column,  and  divided  into  groups,  each  consist- 
ing of  four  consecutive  numbers,  and  the  means  of  these  groups 
form  the  numbers  in  col.  I.  of  the  Tables. 
Col.  II.  contains  the  differences  of  the  temperatures  of  the  junc- 
tions at  intervals  of  four  minutes,  corresponding  to  the  mean  deflec- 
tions in  col.  I. 
Col.  III.  contains  the  common  logarithms  of  the  numbers  in  col.  II. 
Col.  IV.  contains  the  differences  of  the  successive  numbers  in  col. 
III.  divided  by  4. 
Col.  V.  is  formed  from  col.  IV.,  by  multiplying  by  the  Napierian 
logarithm  of  10,  and  is  the  rate  at  which  the  difference  of  tem- 
perature varies  per  minute. 
Col.  VI.  shows  the  quantity  of  heat  emitted  from  the  ball  in 
gramme-water  units  per  square  centimetre  per  second  per  degree  of 
difference  of  temperatures,  and  is  formed  by  multiplying  the  numbers 
in  col.  V.  by  009385*,  a  constant  depending  on  the  surface  of  the 
ball  and  its  capacity  for  heat. 
The  numbers  found  in  cols.  VI.  and  VII.  were  plotted  on  squared 
paper,  and  a  mean  curve  drawn  through  the  points;  and,  assuming 
the  quantity  of  heat  emitted  to  be  represented  by  the  formula  cc—a 
-\-bt-\-cf,  where  t  is  the  difference  of  temperature,  the  coordinates 
of  the  curve  were  employed  to  determine  a,  b,  andc;  and  col.  VIII. , 
calculated  by  the  formula,  is  added  to  show  the  degree  of  approxi- 
mation to  which  the  results  of  the  experiment  are  represented  by  it. 
*  The  surface  of  the  ball  was  50-26  sq.  centimetres,  and  its  capacity  for  heat 
28.31  gramme-water  units.  Let x  denote  the  heat  emitted  per  second,  per  sq. 
centimetre  per  degree  of  difference  of  temperature,  and  C  the  rate  at  which  the 
difference  of  temperature  varies  per  minute  ;  then 
xx  60x50-26 
28-31        ~C' 
and  therefore 
#=•009385  C. 
