MATHEMATICS: W. B. FORD 
431 
FeO 
NiO 
CoO 
CaO 
BaO 
MgO 
MnO 
SrO 
NasO 
K2O 
U2O 
H20(Ign.) 
P2O6 
S 
Cu 
C 
CI 
F 
CO2 
SO3 
Ni,Mn \ 
Cu, Sn / 
I 
14.58 
0.48^ 
0.066 
2.42 
none 
22.67 
0.29^ 
none 
0.878 
0.2V 
trace 
0.75" 
0.26'' 
1.8012 
0.01413 
0.1514 
0.0815 
? 
? 
100.04^ 
II 
3.35 
0.03 
4.81 
0.10 
3.77 
0.09 
0.04 
3.29 
3.02 
0.01 
2.05 
0.25 
0.10 
0.03 
0.06 
0.10 
0.70 
0.02 
100.00 
' Average of 46 determinations 
- Average of 42 determinations. 
3 Average of 50 determinations. 
* Average of 41 determinations. 
5 Average of 19 determinations. 
^ Average of 6 determinations. 
^ Average of 33 determinations 
* Average of 49 determinations. 
» Average of 44 determinations. 
10 Average of 15 determinations. 
Ill 
16.435 
1.758 
22.884 
0.556 
0.943 
0.328 
.839 
100.00 
IV 
16.13 
0.21 
2.31 
22.42 
0.18 
0.81 
0.20 
0.20 
0.03 
1.98 
0.06 
0.02 
99.82 
" Average of 44 determinations. 
•2 Average of 51 determinations. 
I' Average of 16 determinations 
" Average of 8 determinations. 
IS Averaere of 5 determinations. 
The detailed results of these investigations on the chemical and 
mineralogical constituents of meteorites begun in 1912 under a grant 
from the National Academy will be printed as a Memoir in the series 
of Memoirs of the National A cademy. 
ON THE REPRESENTATION OF ARBITRARY FUNCTIONS BY 
DEFINITE INTEGRALS 
By Walter B. Ford 
DEPARTMENT OF MATHEMATICS. UNIVERSITY OF MICHIGAN 
Presented to the Academy, May 27. 1915 
Let / {x) be any function of the real variable x defined and with|/ {x)\ 
integrable throughout the interval {a, h) and having limited total fluc- 
tuation in the neighborhood of the particular point x = a {a < a >h). 
Then, if (p (n, x - a) he sl function of the parameter n and of x-a satisfy- 
ing certain well known conditions the integral 
(a) = r / (x) <p (n, X -a) dx (1) 
