366 
By the calculus of finite differences we obtain : 
3) AGE + eG h)x+ Ace h) +... 
_ ewe te) 
h h 2. 
and 
2 a@ a 2 
Spat t ale M+ Gat Met 7% (#4 2h) (x+h)xt+ ... 
Therefore : 
ha,=Ap for x=0 and h?a,=A*p for x= —h 
By proceeding in the same way we find 4°%a,,=A°d for 
a= —vh and 2a.,=A"p forx=—vh. 
The value of Ap for «= —vh is the number in the column 
for A2’s, which stands in the horizontal line corresponding to 
the stated value of @ (105 in our case), while the value of A*”*1p 
for «= —vh is the number in the next column just below this 
line. The mean of this number and the one above it we have 
before denoted by 77,4, 3 we now add the notation 77, for the 
value of a2%/ for x=—vh. AS myn45 is the difference of the 
two numbers, whose mean is 7#»41, WE CAN Write 72gn4, + 4ov4o 
instead of the value of A*’+19 for x= — vh. 
We have therefore : 
=U 
and 
Aq 41 = (Mov41 + BMorto) 
Substituting these values in the expression for we have: 
x My x(x—h 
P= alm + brn) +2 EM) 
oot 
I x + h)x(x —h) 
a + Ye 
General terms : 
I ade 
a aaeEe 5 (ma0+4 +4mtyv49) (KX+VK) ... ¥... 
A ree ena Moyyo(X+Vh). . 
23 euce 
(x —vh) he 
Pee Oke A) 
(x —(v+1))h-2-2, 
To find the value of ~ we now need only differentiate ac- 
cording to « and make x equal zero. 
Thus we obtain : 
ap Te i I 7 
ae (772, + Bt) = ae aes 4m) + eG Pas a8 
General terms : 
_—1)y 
ee (Mov44 + SMovp0)2° » 3° 
2B nan ou tae 
(-—1)e44 Bkelo 9 
+ Migvitg ai(2 1-1) ae 2 aia nee ne meas 
213 ieee s.2 
or by contracting two consecutive terms : 
eee ae — Tee a2 
do 28 2 5 oh Choe) 
The second differential coefficient is found in a similar way. 
It is only necessary to observe that the second differential co- 
efficient of (w+vh) . .. x. . . («-—vh) vanishes for x=0 
and that of (vw+vh) ... & 6 (~—(v+1)%) is equal to 
Die (0) 2) 22 os Oe 22h-2", Therefore we obtain 
pL =m, — 2 y+ —— eee 22) — eee 
ae? EIS Yio! Bios SX WR a) 
General term : 
2 pe is 
Sp wee 
BA Bg Cha! 9g. al Sap 
Hannover, Technische Hochschule. 
Pror. RunGE’s proof is longer and more difficult than mine ; 
but his result is in simpler shape, and possesses the great merit 
of giving the successive approximations as the terms of a regular 
series. J. D. EVERETT. 
22 Earl’s Court Square, July 28. 
Denes 
C. RUNGE. 
The So-called ‘‘ Thunder”-storm.—Prevalence of 
Anticyclones, 
Ir must have occurred to others besides myself how very 
absurd it is to designate a meteorological phenomenon by the 
least important of its characteristics, viz. the noise it makes. 
We never speak of a hail-storm as a ‘‘ rattle ”-storm, or a shower 
NO. 1555, VOL. 60] 
INCA ORE 
[AucusT 17, 1899. 
of rain as a ‘‘patter”-storm; why then should we call am 
electrical disturbance a ‘*thunder”-storm? Thunder, though 
no doubt terrifying to savages and children and old ladies (one 
or two of whom have, I believe, been killed by the fright of it), 
and though of some interest as an acoustic phenomenon, is 
absolutely the most trivial of the accompaniments of an 
electrical discharge. 
It would seem hopeless to eradicate the childish term entirely 
from popular language, but surely in the scientific reports and 
forecasts issued by the Meteorological Office, and in scientific 
literature generally, the term ‘‘ electric storm ” (or disturbance) 
might replace ‘* thunderstorm.” 
With regard to the late prevalence and persistence of anti- 
cyclonic conditions over the centre and south of our islands, I 
wish to suggest that it may be connected with the unusual ex- 
tension southwards of the Polar ice-pack this summer. I sawit 
stated about a month ago that even Spitsbergen was then sur- 
rounded by ice, most of the fiords being quite inaccessible. When 
I was there in July 1896 we could only just see the blink of the 
pack in the north horizon. 
Now, it is an ascertained and easily intelligible fact that areas. 
of cold (water or ice) on the earth’s surface have a tendency to- 
cause the formation of areas of high pressure or dense air in the 
atmosphere above them. The result would be, not only a pre- 
valence of anticyclones in high latitudes over the North Atlantic, 
but also the persistent extension of the northern edge of the 
great ‘‘Atlantic anticyclone” over the south and centre of 
England (attracted, as it were, by the high pressure in the north) + 
so that cyclones which usually strike the south-west of Ireland or 
the coast of Cornwall have been ‘‘ fended off” to the north of 
Scotland, with the result of heat and drought over England. 
I only put this forward as a suggestion, and I should be glad 
if any of your Icelandic or Norwegian readers would supply 
details of the position of the Polar ice-pack, temperature of the 
sea in the North Atlantic, &c., for I have learnt to mistrust all 
statements appearing in those interesting, and often sensational, 
works of fiction—the daily papers. METEOR, 
August 12. 
Scoring at Rifle Matches, 
WHILE the Bisley meeting is still fresh in the memory of 
those interested in rifle shooting, it seems worth while to call 
attention to the rather unsatisfactory nature of the method of 
scoring now in general use. 
What brings the matter into special prominence is the large 
number of ‘‘ best possibles” always made in recent years. 
With a satisfactory system of scoring such a phrase ought 
only to apply when every shot passes through the same hole in 
the centre of the bull’s-eye. 
The present practice, however, gives the same number of 
marks to shooting of widely differing merit, and this must 
always be the case as long as the result is made to depend on 
the distance of each shot from the centre of the target, irre- 
spective of the distance of the shots from one another (see 
Figs. 1 and 2). 
Fic. 1 Fic. 2. 
Ordinary score 46. 
By moment of inertia 18. 
Ordinary score 46. 
By moment of inertia 24°5. 
The merit of any series of shots really depends on two ele- 
ments, namely, the distance of the average direction of the 
whole series from the centre of the target and the compactness 
with which the individual shots are grouped about that direction. 
The importance to be assigned to each of these elements may 
vary with the object for which the shooting is undertaken, but 
a knowledge of both is essential in estimating its quality. 
If the object be to get all the shot as near the centre of the 
target as may be, the same importance should be attached to. 
close grouping as to the mean direction, as will be shown 
further on. 
