INTRODUCTION. [ xxxv ] 
Pour q voisin de l’unité, q' très-petit, on emploiera les formules 
( / 4. s. i± \ 
l 9- x = V \217' I * * 4 Ch x' + ‘xq" > Ch 3a:'4- 2 q' ‘ Ch Sx' -\~ ) 
I / i a il \ 
{12) l 9-, x — V (2q n Sh x' — 2r/' 4 Sh 3ar'4- 2q' 4 * Sh5a:' h.. 
& 2 x = V (1 — 2q' Ch2a;'-f- 2Ch4^'— a«/' 9 ChG^'H ...), 
Sr 3 x — V (1 -f-iq' Ch2a:'4- 2çr' 4 Ch4^'+ 2^r' 9 Ch6^7' — ); 
S* (O) == V/V ( 2<7' 4 -f-2^f' 4 +2i7" i + ), 
(*3) { 9-j (o) = y/7 (j— 2(/' +2ÿ' 4 —2(/' 9 H ...), 
s- 3 (°) = s/ï^+^q' + ^q H +ay' 9 •+•... 
Soient, pour abréger, 
JT' X~ Y* X'- 1 
V=\/q.e 2p =\Zÿ.e 2p ' , f — y^L 
V (a:, yi,q) — 1 — 2<7C0S2X Cll2j 4- 2ycos4a: Ch4J —K, 
y {x, yi, </) = 27 sin 2a; Sh2j — 2<7 4 sin4-r Sh4jH ..., 
I £ 
V, (a?, 77, = a? 4 sina? Chj — 2<7 4 sin3a: Ch3jH— ..., 
J. 9 
l'[ (x, j/, <7) = 2<7 4 cosa; Shjr — 2<7 4 cos 3 a: Sh3j-l—.. 
J. â 
y 2 (ar, yi, q) = 2 <7 4 cosar Ch j + 2 y cos 3a: Ch3jr + •.., 
)/' (x, 7/, 7) = 2 y sin a: Shj-l- 2f/ 4 sin 3 a: Sh 3j + ..., 
Y 3 (a:, 77, q) — 1 + iq COS2a; CI12J + 2 y COS 4^' Ch 4/-f-, 
[x, yi, q) = 2qsin2a; Sh 27- 4- 2q 4 sin4.r Sh4r -f- 
On a 
I Or (- y 4.r0 4-3- 1^—7f) _y (J. t y) =s rcos'^7->4(j',Æ.-V, <7')4~ r sin(y, x'i, q'), 
= l"{x,yi, q)——T sin -y-^ 2 (y\ x'i, q') 4* F COS ^7-^(7'', x'i, q'), 
a.(-*+.yH-9-,U—u) _ y q y = r s j n \' { (y,ar'i,q')4-rcos'^y >"(/, a?'i,q'), 
3-, (a:4-j0 — 9-, [x—yi] 
^ {x-ri) + (^,±21) = yy, y, y) = r COS ^7- V (/', x'i,q') — F sin ^7- y {y, ¿7, <7' ), 
9-, J/) —9- 2 (.g+70 _ Y ^ y = r sin V (/, arV, <7' ) 4- F cos ^ V' (/, ar'i, <7' ), 
21 p P 
& -‘ fg ~-Vl± "■■■(•*= y, (,r, j/, <7) = F COS y, (y, x'i, q' ) 4 F sin -y- /3 (/, a:7, <7'), 
9- 3 (-^—jri) — & 3 (- g 4-7 > 0 _ ^