584 Proceedings of the Boy at Society 
V 
u 
A u 
Ahi 
A 3 u 
A % 
A b u 
A 3 u 
0 
0 
0*49 
0-49 
0*49 
0-49 
0-49 
0-49 
1 
0 
0-49 
0-49 
0-49 
0-49 
0*49 
0-49 
200 
o’ 
6-49 
6-49 
0-49 
0-49 
0-49 
0*4*9 
giving for u m the value 0, whereas if computed according to the 
method of successive differences, the result is u m = 308. 
If, however, we augment the sixth difference by two units in its 
last place, leaving the other differences unchanged, we get 
p 
u 
A 1 ^ 
A % 
A 3 u 
A % 
A b u 
A % 
0 
0 
0-49 
0-49 
0-49 
0-49 
0-49 
0-51 
1 
0 
0-49 
0*49 
0-49 
0-49 
0-50 
0-51 
2 
0 
0-49 
0-49 
0-49 
0-50 
0*51 
0-51 
3 
0 
0-49 
0-49 
0-50 
0-51 
0-52 
0-51 
4 
0 
0-49 
0*50 
0-51 
0-52 
0*53 
0*51 
5 
0 
0*50 
0-51 
0-52 
0*53 
0-54 
0*51 
6 
1 
0-51 
0-52 
0-53 
0-54 
0-55 
0-51 
50 
45 
0-95 
0-96 
0-97 
0*98 
0*99 
0-51 
100 
95 
1-45 
T46 
1-47 
1-48 
1-49 
0*51 
150 
190 
2-41 
2-43 
2*45 
2-47 
1-99 
0-51 
195 
327 
3-80 
3-84 
3-78 
3-37 
2-44 
0-51 
196 
331 
3-84 
3*88 
3-81 
3-39 
2-45 
0-51 
197 
335 
3-88 
3-92 
3-84 
3-41 
2*46 
0-51 
198 
339 
3*92 
3-96 
3-87 
3-43 
2-47 
0-51 
199 
343 
3-96 
4-00 
3-90 
3-45 
2-48 
0-51 
200 
347 
4-00 
4-04 
3-93 
3-47 
2*49 
0-51 
Thus a change of two units in the last place of the 6th difference 
has caused a change of 347 in the value of whereas, if it had 
been computed by the method of differences, the change would 
only have been T64, and thus the number which M. Lefort has 
characterised as “ phantasmagorique” has yet to he augmented 
more than two thousand times, and it is possible that this egre- 
giously absurd mode of proceeding may cause an uncertainty of 
three units in the twelfth place ; also it cannot be predicated that 
this actually exemplified error is the maximum one. 
I had treated as a mystery the fact that MM. Letellier et 
