206 DOC.

10 RESEARCH NOTES

[eq. 10]

*'2

/2

z'2

,

-^

ö

-- -

1

B2

C2

[eq.

11]

[eq.

12]

(u1x

+

v1y

+

w1z)2

+

(u2x

+

v2y

+

w2z)2

+

[eq. 13]

2

2

2

Wj

+

U2

+

«3 =

OCjj Vj

Wl

+

V2W2

+

V3W3

V2

+

V2

+

V2

=

oc22

= 1

X'

Y'

Z'

X

CCi

«2

0C3

y Pi

ß2

p3

z

Yi

Y3

=

a

[13]

12

1

1

1

A

B

c

M3

V1

V2

v3

Wi

W2

w3

[eq.

14] u1u2

+

v1v2

+

w1w2 =

0

2

2

2 1

U\

+

V\

+

*l

= "2

[10]Einstein

symmetrizes

g12g24

to

the

sum

of the

terms

indicated,

the

only

three

terms

nonredundant under the

symmetries

gik = gki

and

gikgmn = gmngik.

[11]Associating

g12

with

s2Q/sX1sX2

etc.,

Einstein forms

[eq.

8], symmetric

in

the coordinate

derivatives, in

accord with the method

of

[p. 3].

[12]Einstein

transforms the

ellipsoid [eq. 9] to

[eq. 10] by

the

orthogonal

transformation

[eq.

11].

The

new

x',

y',

z'

coordinates

are

rescaled

by

multiplication

with

1/A, 1/B,

and

1/C,

respectively, to complete

the transformation of

[eq. 9]

to

the unit

sphere

[eq. 12].

[13]The

coefficients of the total transformation

are u1...w3

and

satisfy

[eq.

13]

identically

("a12"

should

be

"a23")

and

would

satisfy

[eq. 14]

if the

aik

adopt

the values

of

[eq.

10].