and  the  Magnetic  Relations  of  the  Heavenly  Bodies.       483 
After  having  fully  discussed  the  materials  of  observation, 
D'Arrest  concludes  his  research  with  a  comparison  of  the  re- 
sults obtained,  in  the  following  manner : — 
(Pp.  99,  100.)  "The  sums  for  the  different  years  are,  in  de- 
grees Reaumur  for  Berlin  at  noon,  as  follows  : 
1st 
Obs. 
2nd 
Obs. 
3rd 
Obs. 
4th 
Obs. 
group. 
group. 
group. 
group. 
j  1836-37. 
1181 
14 
1277 
14 
820 
13 
872 
13 
1837-38 
82  0 
13 
934 
13 
86-6 
14 
112-9 
14 
1838-39. 
1251 
14 
974 
13 
956 
13 
93  5 
13 
1839-40. 
98-9 
13 
126  3 
14 
1083 
14 
112  5 
13 
1840-41. 
97-4 
13 
103-7 
13 
98-8 
13 
116-4 
14 
1841-42. 
1251 
14 
1382 
14 
111-4 
13 
1101 
13 
1842-43. 
1011 
13 
113-6 
13 
1325 
14 
1161 
14 
1843-44. 
1170 
14 
131-5 
13 
107-0 
13 
100-9 
13 
1844-45. 
941 
13 
1001 
14 
989 
14 
89-2 
13 
1845-46. 
1261 
14 
1153 
13 
132-7 
13 
131-8 
14 
Suras  ... 
10851 
1  135 
1147-2 
134 
1053-8 
134 
10706 
134 
(t  We  have  therefore  for  the  meridian  M,  which  was  turned 
towards  the  earth  at  the  Berlin  noon,  July  1,  1836, 
Mean  temperature  in  degrees  Centigrade  10-0475 
For  the  meridian  M  +  90°               „  10-6989 
„         M  +  180°            „  9-8300 
M  +  2700             „  9-9863 
A  mere  glance  at  these  numbers  shows  that  these  observations 
do  not  lead  to  the  coefficient  determined  above,  but  indicate  a 
much  greater  variation  in  temperature  arising  from  the  sun's  ro- 
tation. It  is  impossible  to  express  by  three  constants  the  four 
values  deduced  from  the  Berlin  observations,  as  this  has  been 
done  for  Konigsberg;  and  we  must  therefore  draw  an  interpola- 
ting line  of  about  the  following  form : 
Mean  temperature  =10' 1406  +  0-3724  sin  (16°  59'  +  m) 
-03615  sin  (33°  57'  + 2m). 
The  degrees  are  Centigrade,  and  m  runs  through  its  values  in 
27*26  days.  The  curve  has  two  maxima  and  two  minima,  found 
by  the  equation 
cos(16°59'  +  m) 
cos  2(1 6°  59' +  m)     avoft' 
The  solution  gives 
cos  (16°  59'  +  m)  =  +0-12753 +  071850, 
and  hence  for  the 
212 
