80 
MAGAZINE OF SCIENCE AND ART. 
speed of 40 or 50 miles an hour; bat this rate of tra¬ 
velling involves considerable risk, troiu bad joints, and 
from collisions with other trains. In Australia such a 
speed is totally uncalled for, and a speed ot 20. to 25 
miles an hour appears to be the highest velocity re¬ 
quired. 
In thinly populated districts, such as exist at present 
in Australia, single lines of rails, with sidings for trains 
to pass each other at appointed times, appear to be 
am pi V sufficient for all useful purposes, and the advan¬ 
tage of the single line is that of its su'perior economy. 
The necessity for double lines of rails exists only in 
thickly peopled districts, where tho traffic has outgrow n 
the single line ; but where, as in Australia, a moderate 
traffic only rau be expected for the first 10 years, it ap¬ 
pears premature and utiadvisable to expend large sums 
in the formation of double lines, although such, expen¬ 
diture might be justifiable in cases of considerable 
traffic. • • i 
Assuming tho foregoing to be the correct principles 
that should govern the structure of railways in Aus¬ 
tralia, tho next consideration is that ol the gradients, 
and “ gw age," or distance between the rails. 
The gradients must, in fact, govern the power of tho 
engines, their speed in one direction—the size and 
weight of the trains t and it must always be remem¬ 
bered that their operation is a permanent one, which 
nothing ran alter, and the effect of which nothing ran 
diminish. That level aud straight lines are desirable 
for railways, no ono will for a moment dispute; hut 
every advantage has its money value, and there is 
reason to believe that engineers are too apt to incar 
heavy aud sometimes ruinous expenses, in order to 
render their lines mechanically as perfect as possible, 
without duly considering whether the advantages thus 
obtained will compensate for the expenditure required 
to produce them. 
The following Table will serve to illustrate the effects 
of gravity and faction on different kinds of road. The 
amount if friction is that assigned by Mr. de Pambour 
as the result of his experiments on the Liverpool and 
Manchester railway. 
Nature of the Road. 
Friction in 
lbs.perton 
on a level. 
Inclination 
on which the 
gravity be¬ 
comes equal 
to friction. 
On a veil made paved road ... 
On a broken stone surface or 
lbs. 
33 
65 
1 in 68 
I in 34£ 
147 
1 in 15i 
46 
1 in 49 
On a railway . 
8 
1 in 280 
This Table is so simple that it requires no explana¬ 
tion. Some writers, however, assume 9 lbs. per ton as 
the amount of friction on a level railway; and it J lbs. 
per ton, or l-250th part of the load, is the amount ol 
friction and surface resistance, it is demonstrable that 
an inclination which rises 7 feet in a mile, or 0 in , 50, 
will increase the resistance to ihe amount of d lbs. pel- 
ton In like manner, if the incline rise at the rate .ot 
14 feet in a mile, or 1 in 375, three pounds more will 
be added to the resistance. And again—Supposing an 
inclination to rise at the rate of 21 feet m a mile, or 1 
iik250, this would add 9 lbs. to tlie resistance, and, con- 
s^uently, the drawing power must be doubled or made 
equal to 18 lbs. per ton. . . , . , 
From this it is apparent that railroads intended to be 
worked bv locomotive engines ought to be constructed 
so as to be free from any considerable inclinations. In¬ 
deed it may be safely assorted that no gradient exceed¬ 
ing 21 feet in a mile, or 1 in 250, ought to be permitted 
on°a steam railway, for the power of the locomotive en¬ 
gine should not he expended m overcoming the resist 
ance of gravity, or, in other words, in ascending steep 
inclines, and is most beneficially expended wjicn it is 
exclusively employed in overcoming the resistance of 
friction. 
But it has been asserted, on the subject of gradients, 
that on a series of inclinations the power required to 
transport a weight from one end to another is precisely 
the same, whatever inclinations are adopted, provided 
none of them exceed 21 feet in a mile, or 1 in 250, 
which is the limiting slope of a plane on which the 
force of gravity becomes equal to, aud consequently of 
balancing, the retarding force of friction. In order to 
explain this apparently paradoxical result, let us sup¬ 
pose that the railway rises from one. extremity to the 
other bv one continued ascent or inclination of 1 in 250, 
aud that tho road is 100 miles long. Then the resist¬ 
ance or force required to transport a load in ascending 
this incline would he 18 lbs. per ton; hut, on the other 
hand, in descending it the resistance wonld be nothing, 
since the load would move down by its gravity. The 
total power, therefore, requited to transport a ton weight 
from end to end, in both directions, would be a force of 
18 lbs. acting through 100 miles. 
Now, a road of the same length, absolutely level, 
would offei a resistanac of 9 lbs. per ton both ways, and 
the total quantity of pow er necessary to. transport a ton 
from one end to the other, and back again, would bo a 
force of 9 lbs. acting through a distanco of 200 miles. 
It is obvious, therefore, that 18 lbs. acting through 
100 miles is mechanically equivalent to 9 lbs. acting 
through 200 miles. And if we Suppose the law which 
regulates the descent of a weight on a railway to accord 
with that which tlm science of mechanics, establishes— 
namely, that the spaces passed over are directly as the 
squares of the times of descent, we should, on any in¬ 
clined plane, acquire, by tho aid of gravity, an average 
velocity which might he consistent with the speed re¬ 
quired. 
But it is essential to remark that, in tho case of a 
railway, the velocity is by no means increased in that 
ratio. ’ Anil even supposing that this law of mechanics 
were applicable to the case of a weight moving on a 
railway, there exist several-important reasons which 
render it impracticable to take advantage of this law of 
increasing velocity. 
Tho firet and principal of these reasons is founded on 
the necessitv which exists for preserving an equality of 
velocity throughout a line nf railway, whether for goods 
or passengers. It must also be considered that on a 
plane inclining 21 feet in a mile, a certain power must 
be exerted in order to cause the train to move with the 
same speed as on the level; for although, as a direct 
consequence of the law of gravity, it might move, it is 
by no means to he supposed that it would move at any 
Speed at all compatible with that required. Hence a 
power must still be exerted to propel the train with the 
required velocity. 
These remarks render it clear that, in a practical 
point of view, an inclination of 21 feet in a milo is not, 
in fact, that limit at which it is rendered unnecessary 
to exert anv propelling power; and the theory of 
“ compensating gradients” must he considered as. fal¬ 
lacious, as applied to the locomotive engine, for inde¬ 
pendently of the difficulty and disadvantage of making 
it change its energy, and supposing that a. locomotive 
engine could he constructed so as to change its power to 
the extent of double its average force, it must be borne 
in mind that on an acclivity of 21 feet in a mile, it 
would require engines capable of exerting a double 
power, and, therefore, of nearly doable, weight that 
would be required on a level The moving power is 
thus burdened with a load in that additional weight of 
the engine, which is unnecessary save in the ascent of 
that acclivity. The injury arising from this is not only 
the loss of power necessary to move this additional 
weight, but tlie increased weight of the engine produces 
increased wear and tear of the rails, aud of the engine 
itself. Either the danger arising from accidental frac¬ 
tures must be encountered, and the increased wear and 
tear of the road incurred, or rails of greatly increased 
