38 
Professor Hamitton’s Third Supplement 
in which é, refers only to the four variations és, ér, dv, 8y, and in which we may treat 
the seven variations, dc, 6r, dv, dy, dc, &’, dv’, as independent, if we assign to the 
fourteen multipliers \,,... 
N';, the following values ; 
‘ SOE Ve oaeose oT SW SRS 
SES 8x 8y/ "Sy" Belbe Sx" ] 
X WOT OW OnnO Wee OL O21 Can 
Be! 82°Sy' * Sr Sy’ Su! 8y'82' Sy!” 
\ _ 87 ew éT br 67 ow OW 
“3 ol Seba!) Sr ody See oul, Sean Bet? 
\ OL ow oT OW oT ew T so ; 
Ae ~ be! 8a82' 67 ba6y/ bu! da62" oe da ” 
aT 5W STEW BOW 9,80. (B) 
Shy BOL OM Say ON! Orde” is a 
or ew ar ew | ar ew 80. 
<0 Se) Subel | SieGudy cio, SUSE ee 
WOW OLA oT Sw oT ow 6, Ww 6Q' ; 
“7 8e' 8y 8a! " Sr Bydy' bu Sy8z2' by ’ 
Ay =o 5A — Tae | 
W Ww er 4 . oh 8 
yee we SNe We, OW aXe We: | 
8x 8x 
the values of ),...A; may also be thus expressed, 
éu Suet 62 
Ae ae a MS BD (Qs? Ve | 
Sw! é 6Q 
= F° = (W=T)~ 
: : 20 -. 
w' w 
tS a ergs Genin Bye | 
ow! 6Q 
aa OP 5 J 
if we put for abridgment 
Ph gles Aue . 
Wi, & de! to y 3y- a 9 (D*) 
and consider w’, like W, as a function of o, 7, v, x, 2’, y', 2, which, relatively to 
3, 7, v, is homogeneous of the first dimension. The four last equations (4°) give, 
by addition, after multiplying them respectively, by 80, 8r, dv, dx, 
