390 
‘the colourless skin and the vivid scarlet of the exposed gills 
makes the appearance of this subterranean visitor striking in the 
‘extreme. It has four long, slender legs, that are gruesomely 
‘human in appearance, and are supplied with feet that are 
startlingly hand-like. The fore feet bear four fingers or toes 
and the rear ones have five, and though the legs are extremely 
slender, they possess a considerable amount of strength. Behind, 
the body terminates in a flattened tail that bears a fin like that 
of an eel. 
In April 1899, two living specimens of this strange being were 
shipped by mail from San Marcos to the head office of the Fish 
‘Commission in Washington. They bore the journey of nearly 
1800 miles, and reached their destination in good condition. 
They excited great interest, and for some time after their arrival 
a wondering group of spectators crowded about the aquarium 
into which they were put. These living specimens corrected 
several errors that had been made from observations of the dead 
bodies only. The legs are used for locomotion, and the animals 
creep along the bottom with a peculiar movement, swinging the 
legs in irregular circles at each step. They climb easily over 
the rocks piled in the aquarium, and hide in the crevices 
‘between them. All efforts to induce them to eat have been 
futile, as has also been the case with blind cave fish in captivity 
and they are either capable of long fasts or live on infusoria in 
ithe water. 
From whence do these strange creatures come? The well is 
sunk in limestone, and that renders it likely that there may be 
some great cavern or subterranean lake communicating with it, 
‘but the rock through which the hole is bored is solid, except 
for a single channel two feet in diameter. The fact that the 
water rises nearly two hundred feet shows it to be under great 
pressure, and altogether this well affords material for study to 
geologists as well as zoologists. 
Washington, D.C. CHARLES MINOR BLACKFORD. 
Palzolithic Implement of Hertfordshire Conglomerate. 
THE rudely-made Palzolithic implement, illustrated to half 
the actual size in the accompanying engraving, is probably 
unique in the highly intractable material from which it is made. 
It was found by me in May last with Palzeolithic implements of 
flint in the Valley of the Ver, Markyate Street, near Dunstable : 
its weight is 1 lb. 640z.—1677 in my collection. Although 
rude, there is no doubt whatever as to its true nature; there isa 
large bulb of percussion on the plain side, as seen in the edge 
Fic. 1.—Palaolithic implement of Hertfordshire Conglomerate. 
One-half actual size. 
view, and the hump-backed front is chipped to a rough cutting 
edge all round, each facet going right through the embedded 
pebbles. Its condition is totally different from a newly-broken 
block of Conglomerate, and indeed of Conglomerate broken in 
Roman times by quern-makers., It is faintly ochreous from 
being long embedded in clay, and sub-lustrous. _Newly-broken 
Conglomerate is in colour a lustreless cold grey. The peculiar 
mature of the material would not admit of finer work : I have 
NO. 1556, VOL. 60] 
NATURE 
[Aucust 24, 1899 
tried hard to flake Conglomerate without the slightest success ; 
it breaks only after the heaviest blows, and then in the most 
erratic manner, the embedded pebbles often flying from the 
matrix. Sir John Evans has seen this example, and agrees with 
my conclusions as above expressed ; he also informs me that 
several years ago he found what appears to be the point of a 
lanceolate implement of the same material and of Palzolithic 
character on the surface of a field near Leverstock Green. 
Dunstable. WorTHINGTON G, SMITH. 
On the Calculation of Differential Coefficients from 
Tables Involving Differences; with an Interpolation- 
Formula. 
(1) In Narure for July 20 (p. 271) Prof. Everett has given 
formulz for calculating first and second differential coefficients 
in terms of differences. The formule can be more simply 
expressed in terms of ‘‘central differences.” Let the values 
of a function #, be given forx=..., —2, —I, 0,1, 2,...3 
then, with the usual notation, 
Aly = 2, — Uy 
Atty = Atty — Arty = tty — 
&e, 
22) + Moy 
Now write 
2(Arly + Au_,) 
A*u_, 
3(A%2e_, + A3z_, 
Atz_, 
&e. 
Then a, 4, co, %-- are the ‘central differences ” of 2. 
Take, for instance, the following table :— , 
y ev A 
47 109°947 13563 
4'8 121510 12780 1217 126 
ae 
a 16 be m5 909 16 I 155 I 
oS ore L/Z50 181 wh ae 
2c 200° j WEDS 2008 m9 Fy 
23 ooreee 2) aoe 213 18 
oe eae 23286 Bae 231 swineg 
= A 2573 5 2 
ae 
Writing y = 5°2+ ‘Ix, and #,;=10%e”, so as to get rid of 
decimals, we have the following values corresponding to 
a—25-2 (4 — 10) tae 
Uo x b5 a) a) & 
181272 181574 1815 1814 15 24 
With this notation, the value of 2, for values of x between — 4 
and + 4 is given by 
oe x(x? — 1) x? (x2 
Ug = Uy + XA 2 by + ( ) @ ( 
Boh (bb) 
This is a well-known formula. Differentiating with regard to 
x, and putting « = 0, we have (writing zw for z,) 
au “7 4 7 
() = & — so + 30% — trav So + 
a. 0 < 
Similarly, differentiating twice, and putting + = 0, 
shes 5 a Pac 
(@) = by ake china skuo + = we nelle) 
ax] o 
“cc 
Prof. Everett’s formula for the ‘‘increase-rate”’ when fifth 
differences are negligible is obtained by taking the first two 
terms of (ii.). 
(2) The advantage of these formule, as Prof. Everett points 
out, is their greater accuracy. The ordinary formula 
A—$A*+ §A* — fA*+ 3A5, 
in the above example, would give for y=5:2 
au 
=181314, 
ax 
while, if the differences were taken backwards, we should get 
Ut 
Bil 181241. 
ax 
