TRAVELS 
3^0 
u came its firmeft fupport; inafmuch as the attraXion of the 
s< Pyrenees, which by their vicinity produced a deviation in the 
“ plumb-line, was the caufe of the error. But to place in a ftill 
“ ftronger light the reafons that militate in favour of furfaces of 
ee the fecond order, I imagined it would not be deemed foreign 
to our objeX, if I fubjoined here fome general reflexions con¬ 
s' cerning the developement of any functions whatever in feries. 
« In this view, let u be any funXion of x, y, 2 , 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 u becomes when 
a it comprehends a, b , &c = 0. 
Farther, let a z=. U X a Q X A ^ Q X a 3 A^ Q X &c, 
X b A Q X «Aj j X cfbA^ J X 
X b z A a X ab 2 A. 0 X Sec, 
0.2 1.2 
X b 3 A no X &c, 
0 . o 
fi or the term whofe co-efllcient a n b” is reprefented by A , we then 
,m X n 
a 
u know that A — (---V 
mM K da m .db n ‘ 
1.2.3. .m.1.2.3. ..Ji 
sc Now, to fliew the application of it to the prefent queftion, 
" let us fuppofe that u — 0 is the equation which without any 
u approximation reprefents the furface of the earth ; but ftnee 
we learn from all the known meafurements of degrees of the 
(t meridian, that whatever be the figure of the earth, it does not 
<e differ 
