dL df PdL df 
or — — | — | —— — dt 
/ dt dt? dt dt? 
a a 
In either case the integrated parts are equal to O, because at the 
ok df 
beginning and end —— and — are zero. 
2 8 dt? dt? 
In this way we find the relation: 
2E, (haf) Zi En (Lig— Lr). 
In the same way we find the relation: 
> en (fo—fr) = J en (S,—S,). 
By applying the corrections — f, the minimum /s becomes the 
minimum J; = [s—f. 
Es —f= = 6 (en—En) (Sy—fg Sr tf) == 
aa 0 Cp (Sg—S,) — 2 68, (Sy—S,) — 2 6 en (fg fr) in = 6 en (fa—=fr) 
which expression by means of the latter relation may be reduced to: 
Tyo fe ele ape Oe, ff 
For infinitely small values f, the last term in the expression 
; dls 
given above becomes of the order /? so that we find De LA len— en). 
q 
This result enables us to determine the set of small corrections, 
which, when applied to the quantities S, diminish Js by the greatest 
amount. These corrections will be proportional to the abrupt changes 
The variations in the interpolation coefficients g, c, ¢, resulting 
from these corrections are found by repeating the interpolation, 
with this sole difference that for the observed quantities ‚S we sub- 
Ga 
stitute the abrupt changes of Bi 
As a rule a set of corrections of this kind will not show the 
character of the errors of observation and therefore be dissimilar to 
the set of errors which actually exist in the observed quantities S. 
We may also determine a limit which should not be passed in the 
rectification. 
If the quantities f represent the real errors, we have: 
Ig = IH 12 Ey (Af) + 28 & (ff) 
The coefficients / of the interpolation formula between the 
correct quantities S and the errors f being as a rule entirely 
independent, we must assume that in 2 12 L, (f,—/;) the positive 
