( 700 ) 
dr a’ dv : d? 
= 6 an a iat If, on the other hand — is negative, a 
dadv dx* dx dx dv 
ns dw 
is negative and also — . 
de? 
If the whole curve has contracted to a single point, this applies 
also to the two other projections and for this case it is easy to 
express these projections in the value of £, and e, and 7. Then, as was 
Ve nV &, 
found before, «== ——-— , and 1 —#= 
WV UE 
Then the value of 
1 v (n =| is Ve, We, 
. C 1 ee es 
seg or equal to 1+-B, o1 E 1 + n (MEt WVEN 
Both for «,—O and for e,=û is 
Vv 
— is equal to 
poe 1 
v-b (nl? Ve Ve 
bn Wat Ve 
v—b=0, and as we have to do with a point lying on the line 
or 
d : 
i T=0O. A maximum value of v does not occur, but a 
i 
v . . . . . 
maximum value of 5 does. The easiest way to find this is by retaining 
the form: 
v (n —1)? « (1—e@) 
2 eee = bh = : 
b (lr + ne)? 
If v could be maximum, then: 
db dB 
da da als 
b <5 fa OS 
or 
Ld? nr? 
nn 
n—1 [lees oe 0 
1+(n—l)z 1 (n--1)?2(1 - 2) 2e 
[Lt De} 
After reduction we should find „== 0. But the maximum value of 
v ‚dB b il 
=. or of —— = 0 requires nr =d Or ¢ = — =. 
b aL nl 
If for « and 1—az we put the value We, and n/é,, we find as 
Uv 
condition #€,=e,, and so pr, — Pts. Then the value of ; is equal 
fn 1)? : 
to 1+ eine == a ie When n is small, 5 is only little greater 
An An b 
than 1, and so 7’ much smaller than 7. But for very high values 
of n, e.g. about 10, the critical volume can be reached, and so 7’ 
