742 
NATURE 
> 
[JUNE 2, 1923 

An Einstein Paradox. 
Tue following, with amplified details to help 
discussion, is, I trust, a fair statement of the problem 
in Einstein’s ‘‘ Relativity’’ (Methuen). K, K, are 
together, each provided with a clock. The clocks 
agree at noon when K, starts moving in a straight 
line with uniform speed v (estimated in K's units). 
Some time later, a light signal is flashed from a 
point L on the line, ahead of K,, and is seen by K, Kk, 
at times /, t’ on their respective clocks ; KL=% of K’s 
units of space and K,L =#’ of K,’s. Then, according 
to Einstein, 
(1)... #’=(¥—-vt)/ /1—v2/c%, 
(2)... =(t—va/e*)/ /1—v2/c, 
where c= vel. of light im vacuo. 
Since (1) does not contain #’ we shall avoid the 
comparison of clocks by considering that equation 
only. 
Now let us take the case of x’=0; i.e. let the light 
signal be made exactly when K, reaches L. 
Then by (1), ¢=%/v. 
But x/v is the time on K’s clock when K, reaches 
L; to this must be added the time for light to come 
from L. 4 
Therefore true value of ¢=%/uv+42/c. 
Hence (1) appears to be fallacious. 
In that case, also, **— ct? is not equal to #*—c*t’*. 
It is remarkable that Einstein actually considered 
the case of %’=0, but overlooked the interpretation 
of it. 
It may be interesting, possibly instructive, to 
consider how a “‘ Newtonian philosopher ”’ would deal 
with the above problem as soon as he became aware 
that the velocity of light was not negligible. There 
are three cases. 
1. As above—the signal ahead of K and K,, then 
_4—x! x _(c+v)4—cx’ 
oe a , 


t te 
v c cu 
pati” # _(¢+0)%—Cx SS 
v ‘ctv u(cet+v) ’ 
whence 
c 
‘=—_t d #’= é 
t rare w’=(1+0/c)x 
2. The signal from behind K, K,, so that x, x’ are 
negative : 
w—x' | (—#)_(c—v)*e—cx' 


daler riaa okt cv 
, ae , = = , 
pu% Ea | x’) _(c—v)x Cdl 
v c-—u u(e—v) 
equations which, as might be expected, are deducible 
from the previous pair by writing (—c) for c. ’ 
3. The signal from between K, K,; or x positive, 
x’ negative : 
, 
4=— 5 % 
= —— a 
v c 
- / tA 
v c—v’ 
whence no neat results. 
It seems reasonable to conclude that no single pair 
of equations, such as the Lorenz transformation, can 
meet all the cases ! 
R. W. GENESE. 
40 London Road, 
Southborough, Kent. 
NO. 2796, VOL. 111 | 

Longevity in a Fern. 
I wonpDER what is known of the duration of life 
in common herbaceous plants, other than annuals 
and biennials ? The following instance may serve as 
a contribution to the lore of the subject. 5 
About the year 1872 I found on the Mendip Hill 
a mature specimen of that curious sport of the hart’s- 
tongue known as Scolopendrium vulgare var. pevaferum- 
corvnutum, in which the mid-rib and the lamina part 
company at the apex of the frond, the mid-rib 
projecting as a horn, and the lamina forming a 
frilled pocket on the anterior surface. I transferred 
it to my father’s garden in the same neighbourhood, 
where it has flourished ever since, retaining its 
peculiar character. . ; . 
In 1917, as it was in danger of being choked by 
the growth of surrounding shrubs, I transplanted 
it. The stock had twice divided dichotomously, 
forming three crowns, of which one was dead. I 
placed the living ones where they had room to grow, 
and now they are as vigorous, and as young in 
appearance, as the original plant fifty years ago. 
As the plant was of unknown age when fous and 
looks no older after fifty years, its capacity for life 
seems indefinite. F. J. ALLEN. 
Cambridge, May 3. . , 

The Recording Ultramicrometer. 
THE recording ultramicrometer was first very 
briefly described before the Royal Dublin Society 
(Royal Dublin Society, xvi. p. 185, March 1921 ; 
cf. also NATURE, June 23, 1921, vol. 107, p. 523). 
Since its exhibition at the Edinburgh meeting of the 
British Association many short accounts of it have 
appeared in England and abroad. Many corre- 
spondents have requested further information, and, 
as some time may elapse before a full account of my 
investigations in this connexion are published, I 
take this opportunity of giving some practical hints 
to enable others to set up the apparatus. 
In Fig. 1 the three-electrode valve is connected to 
G 

RE0OD yoo. 7000 

Soon, 
Fic. 1.—Diagram of connexions ; B, 4 to 6 volts; V, 30 to 100; E, 1.5 to 6. 
, N, about io cm., flat, 150 turns. 
10-8 amp. per div. 
an oscillation circuit of the ‘‘ Hartley’ type, and in 
the anode circuit a sensitive galvanometer is intro- — 
« 
duced, its terminals being shunted by the “ zero- 
shunt’? E, R. The condenser C, C, of the oscillation — 
circuit is formed by two parallel metal discs (say 
5 cm. diameter). One of these may conveniently 
be adjustable by a fine micrometer screw, so that the 
capacity can be altered by turning the latter. 
acity, it will generally be found that, from a certain 
point, the anode current increases, reaches a maxi- 
mum, and finally rapidly recedes to its original value. 
G, aperiodic galvanometer, — 
As- 
the plates are screwed together, increasing the cap- — 

ah 
4 
3 
q 
