The Sun.
London, England, 1853-03-18 00:00:00

MISCELLANEOUS.

)0 . 35 Australian Agricult , 103 108
!O 6 Austrlasn.Pcific.lsfail .. ...
.0 5 Australis. Royal Mail, ...
38A,Brit. Americn. Land
3241 Canada
5 Crystal Palace
2 Crystal Pal. of France ...
1 Eastern Steam —
1 Electric. Teleg. of Ir ...
14 Gen. Steam Navigat ...
50 General Screw Steam ...
24 Irish Beetroot Sugar, ~,
all Nat. Pat. Steam Fuel ...
2 Netherlands Land ...
2. Nrth. of Europe Steam ...
all Peninsular & Oriental ...
25 Do. Do. ...
60 Royal Mail Steam.... ..
25' South Austral. Land 50 56
1 Submar. Telegraph...l ... ...
2 Universal Emigration
and Colonisation... ... ...
284 Van Diemen's Land.. 24 —25

- ...

24A 5i 4}

RA f LWA r ACCIDENTS.

TO THE EDITOR OF THE SUN.

SlR,—Allow me to forward for the benefit of your
readers, the probable cause of the accidents which have
taken place lately on two of the principal railway lines in
this country. I enclose the mathematical calculation ;
and for the benefit of your non-algebraic readers the fol-
lowing explanation :—lf the, velocity of any body be infi-
nite, it will describe a circle moving horizontally on an
even plane, but as the speed is decreased the body gradu-
ally recovers its perpendicular ; it is therefore impossible
for a goods train to go round a curve with the same in-
clination as an Express. The permanent way being
necessarily the same for all trains, an express train will
very possibly go over the upper rail, and thereby cause
the accidents which the railway officials and the public
in general are unable to account for.

Let A B be parallel to the axles through the centre of
gravity, and the inclination of the vertical to AB.
CD a section of the rails by a vertical plane through
AB, CB, DA =to the fiat surface of the rails. Sup-
posing no tendency to upset endwise, the reactions of
the rail on the two wheels on one side perpendicular to
the flat surface will be equivalent to single force RI, in
CB, and the similar reactions on the other two wheels to
a single force Rin DA. There will also be a pressure
2

13} i

of the flange of the wheels against the inner side of the
outer rail, and consequently a reaction on the wheels
parallel to the plane of the rails. By these forces the
• carriage is constantly turned in the plane parallel to the
rails, so as to make it follow the curve of the rails. The
single force, therefore, which is equivalent to these
would act parallel to these would act parallel to DC, at
some point a little in advance of D, but as far as the
effect of upsetting the carriage sideways is concerned, it
may be supposed to act at D : let it be Q.
♦—The velocity.
11011 r—The radius of curvature.

The centrifugal force— acts at G in GA.

GA=a, AD=b.

Resolving forces parallel and perpendicular to AB, we

Mv2

W Cos a + Q o.

R + R—W sin A=o.

M being the mass of carriage.
Taking moments about Gin the plane BAD.
Qb (R R) a= o (3)
2 1
from (1) and (3) we obtain
(11v2. —IV cos a) b= (R —R) a.
2 1
When the carriage is on the point of upsetting R=o.
R=W sin a.

MV2

cos a +2- W sin a.
=w (a sin a + b cos a) •

r W n
Ca Si a+ b cos a)

%)(
• - g the force of gravity.

= b
2.._. g (a sin a + b cos a)
Which gives the limiting value of v, and if v be greater
the carriage will upset.

CANTAB.

THE WAR WITH Ave.—The House of Lords has just
ordered a document from the East India House to be
printed respecting the war with Ava. A. return was
called for of the expense of the war. It appears that no
account of the expense already incurred has yet been
received. In the Bengal regular estimate for 1851-52
the war-charges on account of the expedition to Burmah
are assumed to amount that year to 10,00,000 rupees,
and in the Bengal sketch estimate for next year 1852-03,
the amount assumed is 50,00,000 rupees.