January 21, 1807] 
NATURE 
269 
Every slide and debacle is due to the combined effects of great 
drought succeeded by heavy wet. In the majority of the bogs, 
of any extent, and even in some of very small dimensions, there 
are in parts “shaky bogs.”” Those portions in great drought 
dry and contract, thereby being traversed by fissures, and more or 
_ less broken away from their soles. When the rains descend and 
the floods come, the water first saturates and floats the lower 
portions and afterwards the upper portions. The latter process 
has a peculiar appearance. When a bog is saturated, on its 
highest part there is generally a Loughaun, ze. a pool with- 
out any surface outlet. During a drought the bog about the 
Loughaun sinks, while it often becomes quite dry ; but when the 
rains come, the bog swells just like a dry sponge put in water, 
and rises the Loughaun along with it. When a bog is 
saturated its lower portion is a sea of mud surrounded by a hard 
margin. If this margin in any place gives way there is a 
bursting forth (*‘ debacle”), as in the recent case in Kerry, but 
sometimes the bog will over-swell, as in the case described by 
Molyneux, when the bog will begin ‘‘to walk” on its own 
account, and in its course lift up and carry away the barrier. 
Different slides, such as that near Clara, that near Dunmore, 
and the recent one, were due to the turf-cutters, who weakened 
the barriers. Turf may be cut on two systems—‘‘ Brest banks,” or 
banks opened round the margin of a bog or along a road; and 
banks that are more or less perpendicular to the margin of a bog 
ora bog road. The latter class of banks prevent slides, as they 
act as drains to the mass of the bog; while the Brest banks 
facilitate slides, as possibly may be exemplified this coming 
season, when the Brest banks are being cut. 
Naturally it will be asked why all the bogs are not cut on the 
perpendicular system? The answer to which is, that it has been 
generally adopted in the mountain districts; but in the Low 
Land deep bogs this is nearly impracticable, as it would take 
years before you could run your bank into them, while all the 
time you would be at a dead loss. This, however, is a subject 
outside the present inquiry. 
During my years of tramping the Irish hills, I have seen some 
interesting aspects of bog and drift slides ; but it is unnecessary 
to recapitulate them here, as any one interested can fully read up 
_ the subject in previous publications. 
It may, however, be allowable to point out that the different 
_ writers on the late Kerry debacle, apparently never saw the site 
of a previous debacle, or they would not make the foolish sug- 
_ gestions that have appeared in their writing. 
I visited the Owenmore site about 1875, or about fifty years 
after its occurrence. This is the most disastrous slide on 
record, as it carried away a whole village and its inhabitants, 
also a picket of Highlanders, whose bodies were afterwards 
pinked up in Tullaghan Bay. When I saw it there was nothing 
very remarkable about the bog ; it had a nice hollow in it, with 
a pollagh for snipe and duck ; but if I had not been told to the 
contrary, I would have seen nothing very extraordinary about 
it. Of similarly other sites that I have visited, that in the Joyce 
country is now a heathy hollow, a good place for grouse ; while 
that on the Glencastle Hill slope, when visited ten years after, 
could scarcely be detected, except that at the north end of the 
townland, adjoining the road and Broad Ilaven, there was a 
tumbling up in hummocks, partly drift, partly bog. 
A new gulch, due to a debacle, is hard to cross, if not im- 
passable, for a year or two ; after which time the bog will have 
soaked, and the bog-mould slopes will begin to consolidate and 
grow vegetation ; once they have a sod on them all appearances 
of the debacle rapidly disappear, so much so, that only one 
person out of a hundred, if you undertook to explain to him 
what had formed a gulch in a mountain slope, would believe 
you ; the other ninety-nine would say ‘‘ Hookey Walker !” 
The bog, the site of the recent slide, is not more than 20 or 
30 feet deep; this will contract at each side of the gulch so as 
to leave a hollow not more than from 10 to 15 feet deep, as has 
elsewhere been practically proved. 
G. Henry KINAHAN, 
District Surveyor (Retired), H.M. Geol. Survey. 
On the Goldbach-Euler Theorem concerning Primes. 
I HAVE verified the new law for all the even numbers 
from 2 to 1000, but will not encumber the pages of NATURE 
with the fetails, The approximate formula hazarded for the 
. . / . . . 
number of resolutions of 27 into two primes, viz. f , where 
NO. 1421, VOL. 55| 
i 
wis the number of mid-primes, does not always come near to 
the true value. I have reasons for thinking that when # is 
sufficiently great, may possibly be an inferior limit. The 
generating function 
given in a recent number of NATURE, p. 196, is subject to a 
singular correction when the partible number 27 is the double of 
a prime. In this case, since the development to be squared is 
PR ese eer tg ye ee based Se +, &c., 
the coefficient of 2?” will contain 2u, arising from the combina- 
tion of 0 with 27, which is foreign to the question, and accord- 
ingly the result given by the generating function would be too 
great by 2u. 
This may be provided against by always rejecting the centre 
of the mid-range from the number of mid-primes. The formula 
will then in all cases give twice the number of ways of breaking 
up 27 into two unequal primes. Another method would be to 
take as the generating function not the square of the sum, but 
the product of the fractions — (without casting out 2 when 
=a 
it is a prime), but this method would be inordinately more diffi- 
cult to work with in computing series involving the roots of 
unity than the one chosen, which is in itself a felicitous inven- 
tion.! Whether the method turns out successful or not, it at the 
very least gives an analytical expression for the number of ways 
of conjoining the mid-primes to make up 27 without trial, which 
in itself is a somewhat surprising result. Ifaving lost my pre- 
liminary calculations, it may be some little time before I shall 
be able to say whether the method does or does not contain a 
proof of the new theorem ; but that this can be ascertained, there 
is no manner of doubt. This is the first serious attempt to deal 
with Euler’s theorem, or to bring the question into line with the 
general theory of partitions. 
It is proper to regard the range I to 2-1 as consisting of 
two complementary flank regions, two lateral mid-prime regions, 
and a region reduced to a single term in the middle, as ex.g7. 
LNs An Ole) 7a Oe Og LO MLe 
Or, again, 
AP KG GHlOR YB ten Cp MOR ty hep ee 
And the question of 27 being resoluble into 2 primes breaks up 
into three, viz. whether 27 can be composed with two flank 
primes, two lateral mid-primes, or with the number in the central 
region repeated. : 
Some slight corrections are required in the preceding note in 
Nature. P. 196, 1. 5 of letter, for ‘‘improved method” read 
‘* original method ” ; 1. 7, for ‘‘ demonstration” read ‘* denume- 
ration” ; 1. 24, omit the words ‘‘ with the exception of 27 = 2.” 
Also, p- 197, 1. 3, for ‘‘pe*” read ‘* pet.” 
January I. J. J. SYLVESTER. 
Patterns produced by Charged Conductors on 
Sensitive Plates. 
In the course of a recent X-ray lecture demonstration, I 
accidentally got what is, so far as I know, a novel, and certainly 
an interesting result. Having takena radiograph of three small 
wire skeletons enclosed in cardboard bodies, on the developed 
plate (covered with a plain glass pressed upon the film) being 
put into the lantern, I noticed the precipitated silver particles 
set themselves in certain lines. These radiated normally from 
the skulls and limbs of the figures, and in the more open parts 
of the background set themselves into a key or fret pattern. I 
concluded, on further examination, that this effect was probably 
due to a state of electric strain induced by the Réntgen tube, 
but it was only upon the softening of the gelatine film by the heat 
of the lantern that the particles were set free, so as to obey the 
electric impulse to which they were subjected. _ 
This led me to experiment upon the effect produced by 
charged conductors on sensitive plates, with the final result of 
1 For the generating function we may take any power greater than 
instead of the square, and the coefficient of 2» will then be the number of 
couples making up 2# multiplied by (7* - yur-1, which can be calculated by 
the same method as for the square, but is more difficult and must give rise to 
numerous theorems of great interest, arising from the multiform representa- 
tion of the same quantity. 
