1825.] 
For the Monthly Magazine. 
DeMmonsTRATION of a GEOMETRICAL 
Turorrm. By Mr. T.S. Davies. 
Pror.—Upon either pair of opposite 
sides of a trapezium, as BC, DA, let 
the triangles AFD, BEC be constructed, 
each having its vertex any where in the 
other’s base: then, if the sides of the 
triangles intersect in G and H, and the 
diagonals of the trapezium intersect 
each other in K, the points G, K, H are 
in the same straight line. 
._ Dem.—We shall first consider the 
ease where BC is parallel to AD. 
_ Let the line GK cut the sides in L 
and M; let it also cut EC in H, and 
FD in a point H’, supposed not to 
coincide with H. 
Then, LB: LC:: BG. EH: GE.CH, and 
MD: MA::GF.H’D: AG.HF. 
But, by parallels, 
« LB:LC:;: MD: MA; and hence, 
BG.EH : GE.CH:: GF.H'D: AG. HF. 
Again, we have, by parallels, 
BG :GE:: GF: AG; and hence, 
EH: CH:: DH’: FH’, 
which implies that H’ coincides with H. 
The lines, with the exception of the 
parallelism of BC, AD, being arbitrary, 
we have merely to conceive the figure 
radially projected upon an_ oblique 
plane, when the representation will be 
a trapezium perfectly unlimited in the 
conditions of its structure, and having 
all the coincidences stated in the 
Theorem, Q.E.D. 
Tuts demonstration is, in some points 
of view, simpler than that which is 
employed in the forthcoming “ Studies 
in Plane Geometry,” which is by means 
‘of Lattire’s Harmonical Porism. Every 
method which I haye tried for the solu- 
tion of the General Theorem, by means 
of the Ancient Geometry, has been very 
tedious in affording the required result ; 
and, I think, the one now given will be 
found as simple as any we can hope to 
©: Bristol, June 7, 1825. 
Montuty Mae, No. 41]. 
Geometrical Theorem—Copper Powder Barrels. 
521 
To the. Editor of the Monthly Magazine. 
Sir: 
%7 OUR intelligent correspondent Mr. 
J.G. Tatem has, in: your last 
Number, very feelingly described the 
miserable situation of the crew of a 
ship on fire: and, assuming that their 
energies are materially diminished by 
fear of the gunpowder exploding in the 
magazine, he has recommended it to be 
lined with lead—made water-tight—and 
filled, when necessary, by a pipe leading 
from the forecastle, &c. 
A shorter and more simple remedy 
presents itself, by the adoption of 
Walker’s Copper Powder Barrels. 
It isa fact ascertained beyond con- 
troversy, that guupowder packed in 
these barrels (which are air-tight and 
water-tight) is found to be of. stronger 
proof, after the voyage to India, than it 
was when shipped; while that packed 
in wooden barrels soon becomes dete- 
riorated in quality—and, often, a coagu- 
lated lump—by the absorption of damp. 
T recollect the general practice in the 
East-India Company’s service, of land- 
ing the gunpowder in India or China, 
for the purpose of drying and sifting it, 
by which a considerable quantity: was 
lost, and the remainder, after the voy- 
age, considered unserviceable: conse- 
quently, the saving in gunpowder mate- 
rially lessens the objection made to the 
expense of copper barrels. 
I know the merit of inventing these 
barrels has been the subject of contro- - 
versy between Mr. Walker and the 
Board of Ordnance; but, leaving them 
to settle the question of “ original in- 
vention,” I join with Mr. J, G. Tatem 
in opinion, that every danger to a ship’s 
crew should be to the uttermost les- 
sened—and I hope the subject will meet 
with the attention, not only of the East- 
India Company, but also of the Lords 
of the Admiralty—as I am convineed 
that Copper Powder Barrels (whether 
invented by Walker or Congreve) ought 
to be adopted in both services, to the 
exclusion of wooden barrels.—Your’s, 
&e. A.B. 
=e 
Berore the Revolution of South 
America, the mints of New Granada 
produced—(in piastres at 4s. each) : 
SANTA FE. POPAYAN, 
Piastres. Piastres. 
1801 .... 1,506,356 .... 962,748 . 
1802 .... 1,240,476 .... 962,748 
1803 .... 1,192,791 ...+ 965, 
1804 .,.. 1,274,576 .,.. 663,696 
5,214,199 3,554,878 
3 X THE 
