
91 
"ATIONS IN THE PAPER ON Vp¢p = 0, &c. 



1 Letters, &e. 
’ (0), 
(¢) 
ge 
I> J22 Is 
Hi,» hy, he 
H 

* Definitions and some Transformations. 

Ap=wa, &.; A’ =a, &e., 
Designating three conditions concerning the roots of [= O, 
yo = pD, Yo = pd’, ' 
Crees Gy Gus Srxrs 1 G5 % || @= Te, shal Fantini Bees 
E = — Sewe’ ,* and particular values, 
W@) = -fTH@+ Py + 2 Ge 
Ig = 9 — me +, &e. | 
GE 
i: 
The variable of 7g, and roots of fg = 0, 
The variable of ¥,(h), and roots of Fr=0, 
po = (G— He + ea, hee 
The variable h = y — m,, and roots of Jh = 0, 
—(')? 5) 
Ay = bh? + P+ Q, 
FAh=WV+Ph+ Q, 

Coefficients in Fe? = ¢& — 3 Myc* + Myc? — : je ae 
Auxiliary scalar factors, 
= : m,, In fg = 9 — mg? + mg — MN, 
ae 2P = Sawa = * + 2(C—?) = P’ + P”, 
== (P= ee {Santa = x? (ee 
= fm, ; 3Q = >Saw%a = S(ne + 206, — 2ee,), 
3Q! = B(Q)e=o = Simm’ + 261) ee 
3Q” = + 3Sewe = — 3c7E }q=a+Q, 
Auxiliaries, RR’, designating 2 planes, cutting [=0 into circular sections, 
fe defined by h, = sh,, h, =shg. 
The usual for scalar, tensor, &c. 
Two scalar factors: Aa + BB + Cy= tp’ 
A‘a+ BB+ Cy =tp 
=iTpTp; @ = (f'9?—4[(e—- oe 
In o®=ua + vB + wy, 
Scalar auxiliaries, 
X= F(M,), Y= FM), 
Carthesian co-ordinates. 
Defined by We = 5Q; We = —5P, 
ee 
A = — 4X3 — 27Y3, 
Where found first. 



f 
Second Part. 
§ 7. 
Second Part, 
§ 7. 
SF. 
$1. 
§ 8. 
Second Part. 
Second Part. 
§ 8. 
§ 11, &e. 
Say 
§ 1, 
§ 4. 
§ 1, 
§ 5. 
TZ) 
ef 
§ 5. 
§ 9. 
Second Part. 
Second Part. 
Second Part. 
$8, &e. 
§ 7. 
§ 10, and Se- 
cond Part. 


* wel = — SahSae, LH = + Bh,S%re’. 


