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380 TRAVELS
“came its firmeft fupport; inafmuch as the attraction of the
*« Pyrenees, which by their vicinity produced a deviation in the
«¢ plumb-line, was the caufe of the error. But to place ina ftill
“ ftronger light the reafons that militate in tavour of furfaces of
the fecond order, I imagined it would not be deemed foreign
“to our objet, if I fubjoined here fome general reflections con-
«¢ cerning the developement of any functions whatever in feries,
*¢ In this view, let « be any function of », y, z, a, b, &c. the
“¢ queftion is to develope in a given fucceflion in reference to the
* powers of a, b, &c, and u be what we fuppofe w becomes when
© it comprehends a, b, &c = 0.
Farther, let a = U X @ iM x 7A Bio @A, 4 xX &e,
x baa, x aA, Xa bA,, x &c,
x DA, x ab, . x &e;
x BA) 4 x &e,
or the term whofe co-eflicient @”b” is reprefented by A > we then
GP x2
a
“know thatA = ( aaa
Men dd eb
TEES 0a) wero sio
** Now, to fhew the application of it to the prefent queftion,
‘© let us fuppofe that ~ = 0 is the equation which without any
‘“* approximation reprefents the furface of the earth; but fince
* we learn from all the known meafurements of degrees of the
“meridian, that whatever be the figure of the earth, it does net |
“¢ differ
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