kkB = L (6"y-6y")(6y-6'y)+L'(y"a-ya)(yd-ya)-{-L"(a"6-} -M \(y"a — yd')(a 6' — a'6 ) -j- (yd — y'a )(a'6 — ß ff")]

+ M'l(a”6-a6")(6y -6'y ) + (a&-d6 )(6"y-6y"j]

-f- M”\(6"y —6y")(y d —y a ) -f- (6y — 6'y )(/ '« —y d')\,kkB' = L (6 y —6'y )(6 ''y' r — 6"y , ')-\-B(y d—ya )(/«"— y"d6'-j -M [(yd — ya }(d6" — cd 6') -f- (y d'—y'd')(ci 6’ — d6 )]-\-M'[(a& — a'6 ')(6'y" — 6'y) -|- (d 6" —d' 6")(6 y' — 6'y )]

M"[(6 y’ —6'y )(ya" — y"a") -f- (6'y"—6”y)(yd—ya )],kkB" = L (6'y"-6"y')(6"y -6 y")+L'(y’a"-y" a )(y" a -y a")+Z"(« 0"-\-M ((y a" — y"d~)(d'6—a 6 "') -)- (y"a — yd")(d6" —c/ , 6 >r )]

-)- M' ((a'6" — a"6'^)(6"y — Oy") -)- (d'6 — a6")(6'y" — 6"y)]

+ M"[(dy"-6"y")(y"a-yd") + (6"y-6y")(y'd'-y"d)].

—a6")(a6'—a'6 )

-a'6 )(d6"-d'6")

—d'6")(a"6 —« 6"')

E comparatione aequationum harum cum aequatiouiLus (32) concluditur: si

aequatio ( f ) per substitutionem (S) transit in (gj, banc ipsam (g) per subslitutionem

6" y — 6y", 6y r — 6’y

y"a — ya", yd — y’a

a" 6 — a6", u6' — a’6

\

/kkA, kkA’, kkA"\

(/ ) \kkB, kkB', kkB") ~ L '

quae oritur multiplicando singulos coefficientes parlis prioris aequationis (f) per kk,siue in eandem, in quam (f) transiret per substitutionem

(S')

transire in banc

pi rt p\r t

,b y —6 y ,

1 f ff ff ff

jy a —y a ,

i fpff "p r

'k 6 — a b >

S ’k, 0, 0

0, k, 00 5 0 , k.

patet,

Designata per F' superficie, quam repraesentat aequatio (f ‘\), sponteetiam transire superficiem G per substitutionem (S ) in superfieiem F'.

16.

Per calculum ei, quem art. praec. addigitauimus, haud absimilem, con-iirmari potest, aequationem