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A
P R A C T I C A L IN Q U I R Y
INTO THE
LAWS OF EXCAVATION AND EMBANKMENT
UPON
R. A. I L W A Y S.
A -
PRACTICAL INQUIRY
LAWS OF EXCAVATION AND EMBANKMENT
UPON
RAILWAYS;
BEING AN ATTEMPT TO DEVELOPE THE NATURAL CAUSES
WHICH AFFECT THE PROGRESS OF SUCH WORKS,
AND TO POINT OUT THE MEANS BY WHICH THE GREATEST
EXPEDITION AND ECONOMY IN EXECUTION
MAY BE OBTAINED. -
WITH
AN APPENDIX AND PLATES,
ILLUSTRATIVE of THEIR APPLICATION IN
PRACTICE.
****-*. .
’’ wº. .
BY A RESIDENT AssistANT ENGINEER,
- *
| *
* *
e º . \ , ;
Ut varias usus meditando extunderèt artes ; :
Paulatim. - VIRGIL. -
- LONDON :
SAUNDERS AND OTLEY, CONDUIT STREET.
1840.
LONDON :
BLATCH AND LAMPERT, PRINTERs, GROVE PLACE, BROMPTON.
s
TO
CAPTAIN W. S. MOORSOM
ENGINEER IN CHIEF
TO THE
BIRMINGHAM AND GLOUCESTER RAILWAY,
&c. &c.
THE FOLLOWING
I N Q U I R Y
IS DEDICATED,
C O N T E N T S.
PART I.
SECTION 1-Preliminary Remarks
SECT.
SECT.
SECT.
SECT.
SECT.
2.—Statement of the principal experiments, made
with reference to the removal of earth, with com-
mon railway wagons; accompanied by explanatory
observations tº g & *
3.—Analysis of the experiments given in the pre-
vious section e º sº e
4.—Investigation of the fundamental formulae,
with a few practical applications of them
. 5.—Investigation of the formulae of limitation,
and development of the causes which particularly
affect the progress of embankments upon rail-
ways
PART II.
6.—An inquiry into the effects of the lead, show-
ing the alterations necessary in the general ar-
rangements of excavations and embankments
7.—Determination of the amount of friction inci-
dent upon contractor's rails
PAGlº,
1()
20
30
41
56
75
viii CONTENTS.
SECT. 8.—Summary of the principal formulae and facts PAGE .
connected with the removal of materials by
means of wagons and horse power . tº . 103
SECT. 9.-Investigation of the system of removing
soil by means of barrows and human labour . 130
APPENDIX.
Notes, and explanation of technical terms . • . 155
Description of Plates tº g ſº g & . 163
P. R. E. F. A. C. E.
THE inquiry pursued in the following Treatise,
into the laws which govern the process of exca-
Vation and embankment upon railways, was not
originally undertaken by the Author for the pur-
pose of publication; his object, upon commencing
it, being to mature his private judgment in the
estimation of such undertakings generally. Nor
was it for some years after the first investigations
were made for this purpose, that the real impor-
tance of the subject to the engineer—the small
amount of practical knowledge upon it extant,
and the unaccountable mystification or oversight
of it by scientific men, combined with the re-
markable facility and accuracy of the formulae
to be derived from it—suggested to the Author, the
propriety of arranging and selecting, from amongst
B
X PREFACE.
the various desultory papers which he had written,
from time to time, those which seemed more imme-
diately to bear upon the practical results.
All members of the engineering profession
must have been already convinced of the utility
to be derived from an inquiry like the present,
when it can be made practically available; es-
pecially if they have ever been engaged in the
execution of large cuttings and embankments; or
observed the remarkable discrepancies which
exist between the recorded opinions of celebrated
engineers, given before Committees of the House
of Commons, and elsewhere; not only as to the
cost, but as to the mode best adapted, and the
time required for the completion of such works.
But more so, if they have observed, that up
to the present moment, few men, not even con-
tractors, make out their estimates of expenditure
and time upon any fixed principles—the accu-
racy of their estimates, in all cases, being de-
pendent upon the conjectural instinct of the per-
sons who may make them—and that hence, doubt-
less, arose the late disastrous effects upon the
railway system—public confidence being unavoid-
ably forfeited, in consequence of the glaring
discrepancies between the supposed and actual
outlay required for their completion.
These discrepancies have been so various and
frequent, that it would be at present unnecessary,
PREFA CE, xi
and perhaps invidious, to make any allusion to
them; further than what is merely necessary to
point out the advantage that may be derived, from
an experimental inquiry into the causes upon
which they depend; and a clear statement or
analysis, of the means by which they may be in
future obviated, as afforded by the results of such
an inquiry.
That the above object has been wholly at-
tained in the present work, the author will not
take upon himself to determine; but he is led
anxiously to expect, that it presents such a theo-
retical and practical insight into the principles of
railway cuttings and embankments, as will enable
any person, moderately acquainted with the sub-
ject, to avoid making any serious difference be-
tween the estimated and actual cost.
There is no department in the varied range of
engineering practice, which has been so lamentably
neglected as that which is comprised in the pre-
sent treatise; and as no previous author has in-
vestigated it, a more than usual share of indul-
gence is claimed from the reader. A few theo-
retical men have undoubtedly alluded to the
subject; of whom Mahan, an American writer, in
the appendix to his Elementary Treatise upon
Civil Engineering, has given the most comprehen-
sive elucidation that has been hitherto attempted ;
but so practically erroneous and speculative, are
B 2
xii PREFACE,
the mode of investigation adhered to, and the
results arrived at, that it may be considered
worse than nugatory; because all such methods
of treating natural subjects, have a tendency to
pervert the mind of the student from the train of
thought indigenous to them, and the absolute
importance of a personal knowledge of facts, into
an abstract and conventional habit of viewing all
phenomena purely practical—making the pheno-
mena coincide with preconceived theoretical
notions, instead of correcting theory by the phe-
nomena.” Indeed, few writers who have applied
themselves to engineering subjects are free from
this tendency—the Compte de Pambour, perhaps,
alone excepted, whose work upon the Locomotive
Engine is a perfect model of that simplicity and
sound judgment, so desirable in the treatment of
every subject connected with natural philosophy.
If the present inquiry is not altogether as free
from the above-mentioned stricture, as the Author
would wish it to be, he nevertheless entertains a
hope, that merely on that account it will not be
exempt from the approbation of the engineering
profession ; for he is strongly impressed with an
idea, that its appearance was not altogether un-
* It may be as well to state, that these remarks are not
intended to apply, to any other portion of Professor Mahan’s
valuable treatise, than that which treats of earthwork. In
other respects, as an elementary work, it ought to be perused
by every professioual student,
PREFA CE. xiii
called for, if only for the purpose of attracting
more general attention to that department in en-
gineering of which it treats. However, should it
have the eventual effect, of drawing the attention
and talent of men who have more leisure, and
are conversant with the treatment of similar in-
vestigations, one advance, at least, will be made
towards the object which induced the publication,
in the following pages, of the results derived from
a few years of personal experience and close
attention to the subject.
The theory and mode of induction adopted,
will be found as simple, and at the same time as
comprehensive, as the nature of the subject would
admit of ; every endeavour having been made to
exclude what was foreign or only collateral to the
main features of the inquiry, and render the whole
as easy as possible; consistent with a thorough
comprehension of each department, and that mo-
derate acquaintance with the elementary prin-
ciples of science, which almost every individual
interested upon such points has acquired.
With respect to the data upon which the
theory is founded, it may be observed, that they
are common to the observation of every person,
who wishes to give his attention to the several
arrangements connected with the execution of
cuttings and embankments, when worked with a
proper force, and under good management; and,
xiv. PREFACE.
that in such cases, although a slight variation, in
favour of larger results, may occur under particu-
lar circumstances, yet, that the average of the
work done in a given time—a year for instance—
will in no case exceed the results given by the
formulae deduced from this inquiry.
In conclusion, it may be proper to remark, that
the emoluments of the Earthwork Contractor have
not been interfered with in any way; but, on the
contrary, that he is likely to obtain much profit-
able information, by being enabled to render
himself thoroughly conversant in the most im-
portant points connected with his particular
calling, and to manage his works upon fixed
principles, and consequently more economically.
Bredom's Norton,
March 4th, 1840.
A PRACTICAL INQUIRY,
&c.
PART I.
SECTION I.-Preliminary Remarks.
BEING perfectly sensible of the great circum-
spection and clearness, with which all opinions
and theories upon practical subjects ought to be
advanced, especially, when they are for the most
part at variance with preconceived notions upon
them ; we have been induced to commence in
limine, and relate in detail the several circum-
stances by which the following inquiry has been
influenced. We are moreover convinced that,
in doing so, we are doing no more than our duty
towards the reader, when it is considered that the
subject is entirely new ; for there is nothing more
useful, when such is the case, than explaining, as
elaborately as possible, the gradations by which
16 PR'ELIMINARY REMARKS,
conclusions are arrived at, link by link; as it
affords others the opportunity of pursuing similar
investigations with greater facility, by means of
the observations they are enabled to make upon
the points on which the author has, or has not, been
successful in giving a satisfactory elucidation.
With these views, we offer the following pre-
liminary remarks.
The original motive which induced us to under-
take the following investigation, was—as we have
mentioned in the preface—simply, to mature the
judgment in the estimation of cuttings and em-
bankments generally; nor had we, at the time,
the slightest anticipation that the causes of an
effect, comprehending so many various details,
and seemingly so anomalous, could be grasped
and confined within certain rules and modes of
action, either in detail or in the aggregate, as be-
came subsequently evident.
The first and principal department connected
with the execution of earthwork, to which we
directed our attention, was that which comprises
the removal of earth, by means of wagons * drawn
by horses over the common temporary roads
used by contractors; and the second, that which
may be denominated the barrowing system,
or the removal of soil with the common wheel-
barrow.
* Wide Appendix, Note 1.
PRELIMINARY REMARKS. H7
After making several observations in the first
department—for the purpose of obtaining an
average estimate of the quantity of work which a
given force could perform, in a given time, when
applied in the usual manner—and upon comparing
them, it became so evident that the estimates
derived from each set of experiments, varied ac-
cording to the arrangements adopted upon the
particular work to which it referred; that we found
it useless to attempt arriving at any satisfactory
conclusions, without entering into a thorough in-
vestigation of the general principles developed in
the system. For this end, we found it necessary
to undertake a series of observations and experi-
ments upon a much more extended scale than was
originally attempted.
In contemplating the results of these observa-
tions, and endeavouring to arrange them methodi-
cally, much difficulty was experienced, and
dissatisfactory conclusions sometimes arose out of
the same experiments; this led us to suspect that
there was some mode of calculation peculiar to
them, or that some cause, of which we remained
ignorant, affected them; accordingly several addi-
tional sets of experiments were undertaken at
different times, and under various circumstances,
upon the same works, and a closer attention given
to the details; until we found that the main points
18 PRELIMINARY REMARKS.
to be taken into consideration, in order to render
them fit for the application of any mode of cal-
culation, were—the time spent in filling the wagons,
—the rate of speed at which they could be drawn
by the horses, and the time spent in tipping them—
each separately. The results of the experiments
made upon these points, produced the following
conclusions; viz:—that the quantity of work
done in any instance, varied with the rate of speed
at which the wagons were removed from cutting
to embankment, and the number of wagons
which could be tipped or emptied over the head of
the embankment in a given time—the latter bear-
ing a direct proportion to the height and rate of
slope to which the sides of the embankment were
to be finally dressed off; but that the number of
getters and fillerst produced no sensible effect
upon the progress of the work; being limited by
the number of wagons in each set, and these
again by the breadth of the tip or battery-head.
We also perceived that the first of these, or the
time spent while each set of wagons was being
removed from cutting to embankment, could be
calculated for any increase or decrease of lead, by
applying the laws of the arithmetic series, when
once the rate per mile per hour at which the horses
travelled was determined ; and that the latter, or
the number of wagons that could be tipped in a
* Wide Appendix, Note 2.
f Wide Appendix, Note 3. f Wide Appendix, Note 9.
PRELIMINARY REMARKS. 19
given time, was of course variable, inasmuch as the
height and rate of slope, to which the sides of
each embankment were to be finally dressed off,
were variable.
When these conclusions were confirmed by
repeated observations, the experiments hereafter
detailed, and several others, were submitted to a
method of calculation founded upon the principles
of the common arithmetic series; and the results
were found to agree exactly with practice. By
using this method of calculating, it also became
evident, that the quantity of work done, could in
any case be obtained, by merely knowing the
number of wagons used, and the breadth of the
tip ; * provided the wagons were worked with their
proper compliment of men and horses.
The adoption of the arithmetic series—as the
basis of the calculations for finding the number of
wagons that could be removed, from cutting to
the head of an embankment, in a given time—
when the length of the leadt was also given—by
a slight modification, enabled us, subsequently, to
arrive at the formulae for variable leads; which
will be found of great use, in those cases where
the head of an embankment progresses rapidly;
but more particularly, where side-tippingi is re-
sorted to in dressing off slopes, &c.S
As the formulae for calculating the number of
* Wide Appendix, Note 4. + Wide Appendix, Note 5.
t Wide Appendix, Note 6. § Wide Appendix, Note 7.
20 PRELIMINARY REMARKS.
wagons that can be tipped under both these cir-
cumstances, (according with the usual arrange-
ments) have been rendered generally applicable,
the cost per wagon, incident upon any length of
lead—variable or constant—may be easily obtain-
ed; as for this purpose, it is only requisite to know
the rate of wages for a day labourer, and the cost
of maintaining a horse per diem, in the neighbour-
hood of the works;–due allowance being made for
superintendance, and per-centage upon the capi-
tal sunk, in procuring the proper materials for their
execution. It was intended to give detailed
estimates under these heads; but the prices of
labour are so variable in different places, that a
separate estimate would be required for each, in
order to render them useful. This intention was
therefore abandoned; and it is believed, without
affecting the utility of an inquiry relating to the
development of general principles.
The process of induction by which the formulae
above referred to were arrived at, laid open a
much larger field for inquiry than we were ori-
ginally prepared to expect; and indicated that
the system of arrangement hitherto adopted, in
the conveyance department especially, was far
from being perfect. With the prospect of finding
out where the imperfection lay, and the princi-
ples by which it might be corrected, the subse-
quent part of the inquiry was entered upon.—
PRELIMINARY REMARKS. 21
After some consideration, it became obvious that
to effect this purpose, the first point to be deter-
mined, was the number of wagons required for
producing the most effective result upon a given
length of lead: in determining this, little difficulty
was experienced; as it was not found necessary
to enter upon principles of calculation different
from those which were adopted in the first in-
stance; and was so far satisfactory, inasmuch as it
rendered the details of the subject unique in prin-
ciple.
From the process of induction by which this
point was established, we came to a knowledge of
the peculiar fact, that at certain exact periods in
the progress of the works, an increase in the num-
ber of sets of wagons” becomes necessary—the
law of increase also agreeing with that of an
arithmetic series; but leaving a greater common
difference than the former. The periods at which
this increase in the number of sets of wagons be-
comes necessary, will be found to correspond with
every twenty-five chains of increase in the length of
the lead, or distance between the face of the cutting
and the head of the embankment. This curious
fact could never be obtained with sufficient accu-
racy by actual observation; for it branches, as it
were, adventitiously, out of the previous calcula-
tions: a deficiency in the quantity of work done,
* Wide Appendix, Note 8.
22 PRELIMINARY REMARKS.
would certainly be experienced as the lead became
longer; but it is difficult to suppose, that the
cause of such deficiency, or the particular mode in
which it might be remedied, could be discovered
by mere observation, in a case where there are no
palpable appearances to argue from.
Having ascertained the number of sets of
wagons requisite for working any length of lead,
we were led to find the number in each
set, that would ensure the greatest expedition in
tipping, according with the dimensions of the
battery head; and this, it will be seen, depends
upon the time which a single wagon will take,
in being drawn from the siding next the head
of the embankment, backwards and forwards,
including the tipping; and the number of sperms,
or shunt roads, that can be laid abreast of the
embankment.
The results of the formulae we have given,
for determining the two latter quantities—viz. the
number of sets of wagons, and the number of
wagons in each set—show clearly, that the
present system of excavating cuttings and forming
embankments is imperfect, as regards the ar-
rangement of the sets of wagons, and the number
placed in each set; because they prove, that both
vary with the increase or decrease in the length
of the lead, and the breadth of the tip ; whereas
in all works of this description which we have
PRELIMINARY REMARKS, 23
had an opportunity of examining, the number of
sets of wagons were invariably three; and the
number of wagons in each set bore a direct pro-
portion to the area of the face of the cutting; or in
other words, consisted of the greatest number of
wagons that could be filled simultaneously; and
this arrangement has been hitherto sanctioned by
the universal dogma, that “upon the area of
the face of a cutting, or the number of wagons
which can be filled in it together, depends the
facility of working it.”
As subordinate to the foregoing points, we
have given the load proper for an ordinary horse,
expressed in wagons; and in order to establish
this, several experiments were undertaken, to
determine the amount of friction due to the ordi-
nary roads and wagons, made use of by earthwork
contractors. The results of these experiments
have been calculated in the ordinary way, from
the angle of friction.
In conclusion, we have to add, that experi-
ments and formulae have been also given for bar-
row work; but as there is not any material
difference in the nature of the observations, or the
principles upon which they have been treated,
any particular remarks here, upon that portion of
the inquiry, would be superfluous.
Having thus far detailed the principal facts
connected with the inquiry, it remains for us to
24 PRE LIMINARY RE MARKS,
remark, that the reader will find the general theory
to hold good, whether the data, upon which each
formula is founded, exactly coincide with his own
observations or not, with reference to any par-
ticular system of earthwork which he may
examine ; or, in other words, that the formulae
point out the method of arrangement for all
observations of a similar nature, and are univer-
Sally applicable; as, for instance, to experiments
upon carting, or the excavation and conveyance
of earth, for the formation of turnpike roads; in
which cases, although the quantities representing
each factor in the general formula, would con-
siderably differ; yet the laws which they will be
found to obey, are identically the same, and sub-
ject to the same method of calculation—the
difference altogether depending upon the differ-
ence in the amount of friction which exists
between the two modes of transit made use of.
SECTION II.
Statement of the principal earperiments made nith
reference to the removal of earth nith common
railway nagons, accompanied by earplanatory
observations.
Of the several experiments which were made
from time to time, in order to ascertain the effect
EXPERIMENTs, ETC. 25
produced by the common system of arrangement.
upon different works, we have selected those
given in the present section as being the most
correct; having been found to agree best with the
average of the greatest number of experiments
that were undertaken. Indeed the difference be-
tween any two was so trifling, that it would
be prolix, if not useless, to insert them all; be-
sides, the nature and compass of the present trea-
tise did not admit of its being done; and we
were of opinion, that it was requisite to state only
so many of the experiments, as would afford suffi-
cient data to show the accuracy and eatent of the
investigations. However, should any reader not
deem them sufficiently extensive for this purpose,
he cannot ſail in having frequent opportunities, for
procuring similar observations, “ad libitum,” in
his daily practice, or by application to the foremen
of the works he is engaged on.
TABLE 1.
Showing the results of four experiments made
upon the number of wagons tipped, in a given
time, for the repair of the permanent way of the
Great Western Railway, in August, 1838:—
C
EXPERIMIENT'S WITH

EXPERIMENTS UPON THE GREAT WESTERN RAILWAY.
No. of | No. of No. of | No. of | No. of º
Nos. wagons IOCIn horses wagons. hours lead in REMARKs.
working. working-working, tipped. |worked. | Chain.
I 16 48 4 109 8 60 The average time
which elapsed, from
when each set of
2 | 16 || 48 || 4 || 112 || 8 || 60 ºl..."
- til it returned emp-
ty, was 50.50 mi-
3 16 4 8 4 | 1 l 8 6 0 nutes.
In these experiments the horses worked with
apparent ease, when the wagons were once in
motion; nevertheless, it was evident that a greater
load would have distressed them. The material
which was removed was gravel for ballasting the
road; and each wagon, when filled level, contained
fifty-six cubic feet of gravel; and when heaped,
eighty-one cubic feet. In the above experiments
all the wagons were heaped.
From this table we find, that the average work
done by twelve men, and one horse, with four wa-
gons, working for eight hours, was the excavation,
filling, removal, and tipping, or emptying, of
27.66 wagon-loads of gravel, each wagon-load
containing eighty-one cubic feet; besides the
drawing back the empty wagons, after being tip-
ped, to the spot where they had been first filled;
CONTRACTORS’ WAGONS. 27
when the length of the lead, or distance, between
the points where the gravel was excavated and
deposited, was sixty chains, or three-quarters of a
mile. This being the average amount of work
done by forty-eight wagons, twelve horses, and a
hundred and forty-four men, working for eight
hours, as will be seen by an inspection of the table.
TABLE 2.
Showing the results of four experiments, upon
the number of wagon-loads removed to embank-
ment from side cutting, in a given time, upon
the Birmingham and Gloucester Railway, at
Eckington, during the month of November, 1838.



EXPERIMENTS UPON THE BIRMINGHAM AND GLOUCESTER,
RAILWAY, ON THE ECKINGTON EXTENSION CONTRACT.
i... No. of No. of No. of No. of lºſſ.
gons of the
Nos. working_* horses wagons | hours lead in REMARKs.
- in a se. working-working. tipped. |worked. chains.
l 4 12 2 35 8 40
The average #.
2 || 8 || 24 || 4 || 69 || 8 || 40 |V}...”.”;
- ..., : the
tting ed, un-
3 || 4 || 12 || 2 || 34 || 8 || 40 |jº.
ty, was 36 minutes.
4 4 12 2 36 8 40
C 2
28 EXPERIMENTS WITH
These experiments were made during the exca-
vation of the side-cutting, * near the village of
Eckington, on the Birmingham and Gloucester
Railway; contracted for by Mr. Henry Milne of
Worcester, and known as the “First extension
of Eckington contract.” The horses were in high
condition, but could not draw more than two
wagons each ; although, in general, they performed
their work with ease. The road over which the
wagons worked, consisted of the temporary rails
generally used by contractors, laid upon cross
sleepers; and was also level, and in good order.
Each wagon contained 49.28 cubic feet, when
filled level, and when heaped, 65.72 cubic feet.
The material excavated was the blue lias clay,
laminated, and very hard ; and in all the experi-
ments the wagons were heaped.
From this table we find, that upon an average,
two horses, twelve men, and four wagons, exca-
wated, filled, removed to embankment, and tipped
34.80 wagon-loads, besides drawing back the
empty wagons, when the number of hours, actually
worked, consisted of eight, and when the length of
the lead was forty chains, or half a mile; for this is
the average of the quantity of work done—as
shown by examination of the table—in eight hours,
by sixty men and ten horses, with twenty
Wagons.
* Wide Appendix, Note 13.
wº
contRACTORs' wagoNs.
29 .
TABLE 3.
Showing the most correct of a series of expe-
riments, made upon the number of wagon-loads
removed from cutting to embankment, in a given
time, on the Birmingham and Gloucester Rail-
way, at Bredon's Norton; between November
1838, and April 1839.

--
EXPERIMENTS UPON THE BIRMINGHAM AND GLOUCESTER,
RAILWAY, CONTRACT 4. G., AT BREDON'S NORTON.

No. of No. of | No. of | No. of | No. of Length
wagons of the
Nos. workin men horses wagons | hours lead; REMARKs.
§ * g - ead in
in . . working.working. tipped. |worked. chains.
I 12 36 6 131 10 40
2 8 24 4 88 10 40 The average time
which elapsed, from
3 || 8 || 24 || 4 || 86 || 10 | 40 ||...”.
. º UIIl-
4 || 6 || 12 || 3 | 66 | 10 | 40 ||.
5 6 12 3 65 10 40
These experiments were made upon a large
work, near the village of Bredon, on the Birming-
ham and Gloucester Railway; called the “Bre-
don's Norton Portion;” in which, upwards of
240,000 cubic yards of excavation, through the
30 EXPERIMENTS WITH
blue lias clay, was led from cutting to embank-
ment. The contract was taken by Mr. George
Williams, of Birmingham, who had recourse to
all the usual expedients for speedily completing
the work.
The horses were in very good condition, con-
sidering the harassing nature of the work which
they had to perform: in one or two instances,
which came under our observation, when acci-
dents happened to some of the horses, three wa-
gons were attached to a single horse; but so evi-
dent was the distress the animals laboured under
in such cases, that it seemed impossible, if tried,
that they could continue drawing so heavy a load
for more than an hour; and to give motion to
the wagons at starting, it was always found ne-
cessary to apply a lever to the spokes of the
wheels. But when the number of horses bore
the same proportion to the number of wagons, as
that shown by the table, they endured the work
without any visible detriment.
The road, over which the wagons were drawn,
was level, and consisted of the ordinary rails used
by contractors, laid upon cross sleepers;* the
wagons contained the same quantity of materials;
and the lias excavated exhibited the same fea-
tures, as stated under the head of the previous
* Wide Appendix, Note 10.
CONTRACTORs' wa GONs. 3 i
table. The wagons were all heaped in these ex-
periments also.
From this table we perceive that 43.60 wagon-
loads were excavated, filled, removed from cutting
to embankment, and tipped, by two horses, four
wagons, and twelve men—besides the drawing
back of the empty wagons, which had been tipped,
to the spot where they had been previously filled—
when the number of hours actually worked con-
sisted of ten; and when the length of the lead was
forty chains, or half a mile. This being the aver-
age, taken from the quantity of work done by one
hundred and eight men, and twenty horses, with
forty wagons, working for eight hours.
TABLE 4.
Showing the results of a series of experiments,
made in order to find the number of wagons
which could be removed from cutting to embank-
ment, in a given time, on the Birmingham and
Gloucester Railway, upon the second extension
of the Eckington contract, in May 1839.”
* The experiments given in this, and the preceding tables,
refer to a single set of wagons only. There were generally
three sets working per day; so that the results given in the
tables, when multiplied by three, will give the total quantity
of work done. It was impossible to make correct observations
upon three sets of wagons, at the sametime, or we would have
preferred doing so.
ExPERIMENTs witH

ExPERIMENTS UPON THE BIRMINGHAM AND GLOUCESTER
RAILWAY, ON THE SECOND EXTENSION OF ECKING-
TON CONTRACT.
** | No. of No. of | No. of | No. of |**
wagons of the REMARK
Nos. working|_*.* horses wagons hours lead in EMARKS.
in a se. working-working: tipped. |worked. jºins.
l 4 12 2 59 10 20 The average time
W. *
O
2 | 8 24 4 119 || 10 | 20 |M|...”.f.".
º Ul]]-
t CTUITIle (i. eIOlſ)-
3 || 6 18 3 89 || 10 | 20 ||.."...”.
nutes.
4 6 18 3 88 10 20
All things connected with these experiments,
were the same as those mentioned under the
head of the second table; except that the material
excavated was sand, and each wagon when
heaped contained 68.10 cubic feet.
Aecording to this table, the quantity of work
done by two horses, four wagons, and twelve
men, working ten hours upon a quarter of a
mile lead, was equal to 59.16 wagon-loads
excavated, filled, removed to embankment, and
tipped; besides the bringing back of the empty
contRACTORs’ WAGONS. 33
wagons to the filling places: being the average,
taken from the quantity of work performed by
seventy-two men, and twelve horses, with twenty-
four wagons, when working for ten hours; as
shown by an examination of the table.
The experiments upon the Great Western
Railway given in the first table, were inserted in
order that a comparison might be afforded of the
horse power to be deduced from them hereafter,
and that deduced from the experiment we have
made upon the friction, due to the ordinary wagons
and roads used by contractors; for, as we have
deduced the horse power from the amount of
friction incident upon the loads, we considered,
that the deductions arrived at on that head,
would be rendered more conclusive, if corroborated
by similar results upon a railway perfectly
formed ; where the amount of friction is more
accurately and generally known. There was
another inducement also for giving them, viz. to
show by facts, that the opinion of its being an
impossibility to remove from cutting to embank-
ment an equal number of wagon-loads, by the
same force of men and horses in the same time,
and over the same length of lead, whether of stiff
or loose soil—of clay or gravel—is an evident
fallacy, when referred to the mode of excavation
adopted on railways. That the above mentioned
34 EXPERIMENTS WITIT
opinion is incorrect, can be easily proved to the
practical man as follows:—
In the first place, it will be granted by him, that
it is quite as difficult to fill gravel into a wagon,
as clay or chalk, when once it is stocked * or
loosened; and therefore, the only possible way
in which the stiffness of a soil can affect the pro-
gress of any earthwork, is, by its rendering it
necessary to place an eatra getter to every two
wagons; which in itself would be, at farthest, a
question of earpenditure, not of ea pedition. But
that such a necessity never arises, is a point-blank
refutation of the opinion ; for when the soil is so
stiff, as that the usual number of getters are un-
able to loosen it fast enough for the fillers, all
practical men have recourse to blasting with gun-
powder, as in quarrying stone, rather than add
an extra getter; for the plain reason, that they
find it the most expeditious means of loosening a
large quantity of material at once, and also much
cheaper, when the soil will admit of it, than em-
ploying getters at all.
As for ourselves, we never could see the neces-
sity of putting on extra getters; for in general, the
stiffer the soil, the greater is the quantity of it that
can be brought down by the getter at each fall;
as he is enabled to stock much farther in than he
* Wide Appendix, Note 11.
CONTRACTORS’ WAGONS. 35
can do when the stratum is friable. For instance,
stiff clay, or chalk, can be stocked much farther in
than gravel, or sand ; and consequently, a much
larger quantity becomes loosened when the falls
take place; although the frequency of the falls in
the two latter mentioned strata, compensates for,
and renders equal, the effect in both cases; which
would otherwise be different, in consequence of
the difference in the quantity of material that
would have descended at each time, when the
falls occurred. Finally, as regards the compara-
tive facility of tipping; when the bumpers” are
properly secured, against which the wagons are
precipitated at the head of the embankment, no
soil, unless it consists of a perfect puddle, (which
is an unfrequent exception—the pons asinorum of
railway contractors,) will require removal out of
the wagons with the spade. We have made
these preparatory remarks in order to render the
subsequent investigation plainer.
SECTION III.
Analysis of the eaperiments given in the previous
º
section.
From the experiments detailed in the previous
section, we have been enabled to determine the
* Wide Appendix, Note 12.
36 ANALY SIS OF
constants, upon which the fundamental investiga-
tions of the inquiry are founded ; these—as we
have mentioned before — are, the time which
elapses during each trip made by the horses and
wagons, from the face of the cutting—where they
are filled—to the head of the embankment—where
they are tipped—including the drawing back of
the empty wagons into the cutting, and the time
required for filling and tipping the wagons.
From these constants, the total number of wa-
gon-loads that can be removed, from cutting to
embankment, in a given time, by a given force,
and upon a given lead, can be easily obtained;
provided the relation between the time spent in
performing these operations and the length of the
lead, can be arrived at.
In the present section, we have succeeded in
determining the above-mentioned points, as the
following investigation shows.
Since, from the experiments contained in the
first table, we have found that 27.66 wagon-
loads of material were tipped from four wagons,
in eight hours, with their proper complement of
men and horses; we have
gº 27.66
–H–6.91
for the number of trips which the wagons made
—from the face of the cutting loaded to the
head of the embankment, and back from the head
THE EXPERIMENTS. 37
of the embankment empty to the face of the
cutting again—during eight hours ; and further
we have
8 × 60 480
sºmeº = 69.47
6.9 IT 6.91 6
minutes, for the time consumed in each trip ; when
the lead was sixty chains, or three quarters of a
mile in length.
From the second table, we find, that with the
same number of wagons, 34.80 wagon-loads
were tipped over the head of the embankment, by
the same processes as mentioned above ; the
number of hours actually worked being eight;
and the length of the lead forty chains, or quarter
of a mile; hence
34.80
tº = 8.70
4
gives the number of trips made; and again we
have
8 × 60 480
sió-sid=55.17
minutes, for the time spent in each trip, when the
length of the lead was half a mile.
We find, from the results afforded by the third
table of experiments, that 43.60 wagon-loads of
soil, was the number removed from cutting to em-
bankment by means of four wagons, with their
38 A NALY SIS OF
proper complement of men and horses, when
worked for ten hours consecutively, upon a lead
half a mile long; hence
43.60 *
"YY = 10.90
4 0.9
gives the number of trips made during that time,
upon that length of lead ; and
10 × 60 600 = 55.04
IO.90T TO.90
minutes, was the time spent in each trip.
Upon reference to the fourth table, it will be
seen, that 59.16 wagon-loads of material were
removed from cutting to embankment, in ten
hours, upon a length of lead equal to twenty
chains, or quarter of a mile long ; hence we
have
*10–14.79
4
for the number of trips made during that time,
and
10 × 60 600
I.1.79- fº-40.56
minutes, the time elapsed, from when the wagons
left the gullet” loaded, until they returned empty.
Having now found the total number of minutes
spent in each trip, which the wagons made from
* Wide Appendix, Note 14.
THE EXPERIMENTS. 39
the cutting to the head of the embankment loaded,
and back empty, upon different lengths of lead;
the certain portion of that time which it took to
fill, remove to, and from the cutting to the em-
bankment, and that portion of it spent in tipping
them, can be found as follows:—
We have seen, that the sum of the times spent
in the three separate operations of filling, remov-
ing, and tipping the wagons, as deduced from the
second and third tables, where the lengths of the
leads were the same, (being half a mile long),
amounted to 55.17, and 55.04 minutes, respec-
tively; taking the average of these, we have
*** sºlo
or say in round numbers fifty-five minutes, as the
time elapsed during the operations of filling, re-
moving, and tipping, collectively.
The sum of the times required to perform the
same operations, as deduced from the first table,
where the length of the lead is stated to be three
quarters of a mile, amounted to 69.47 minutes;
hence we have
69.47—55= 14.47
minutes, for the difference between the time re-
quired for filling, removing, tipping, and bring-
ing back a set of wagons upon a lead three quar-
ters of a mile long ; and the time required for
filling, removing, tipping, and bringing back a
40 AN AL YSIS OF
set of wagons upon a lead half a mile long. This
difference, viz., 14.47 minutes, is evidently the time
which elapsed, while the horses were drawing the
loaded and empty wagons, backwards and for-
wards over a quarter of a mile; or in fact, the
difference of time answering to the difference in
the lengths of the leads.
Again, we find, from the results of the fourth
table, that 40.56 minutes elapsed, while the wagons
were being filled, removed, tipped, and brought
back, when the length of the lead was one
Quarter of a mile; and hence we have, by a similar
process,
55—40.56= 14.44,
as the number of minutes spent, in drawing the
wagons backwards and forwards over a quarter of
a mile only—exclusive of filling and tipping for
the same reasons as stated above.
As the lead given in the first table was the
longest, and the observations made upon it were
consequently less liable to be affected by any
minute errors, arising from slight interruptions in
the progress of the trains; which may sometimes
happen when the length of the lead does not ex-
ceed a quarter of a mile; we have taken the result
given by the comparison of the first table with
the second and third, viz., 14.47 minutes, as the
constant for the time, in which a train of earth
wagons" can be drawn backwards, and forwards
THE EXPERIMIENTS. 41
upon a lead, the length of which is a quarter of
a mile; by means of horse power, as ordinarily
applied in the execution of earthwork upon rail-
ways. This shows that the average speed of
transit rates at 2.40 miles per hour.
We will now proceed to find the time spent in
tipping each wagon, after having arrived at the
siding, close by the head of the embankment.
Upon reference to the first table, we find, that the
time elapsed, from when the wagons left the place
of excavation loaded, until they returned empty,
(including the tipping), averaged, by actual ob-
servation, fifty minutes and a half, when the lead
was three quarters of a mile long; and as, accord-
ing to the rate of speed established above,
14.47 × 3–43.41
minutes, must have been the time spent in mo-
tion; we have
50.50—43.41=7.09,
the number of minutes required for tipping the
wagons; or, as in such a case as this (where the
wagons were tipped sideways off the permanent
road), any number can be emptied simultaneously,
in the same space of time as a single wagon can be
emptied; we have 7.09 minutes, as the time that is
required for tipping one wagon also.
Upon reference to the second and third tables,
where the lengths of the leads were the same, we
find that the average of the time spent, from when
D
42 AN AI.YSIS OF
the wagons left the gullet loaded, until they re-
turned empty, was thirty-six minutes; and as
the time spent in motion—from what we have
seen before—must have been **-
14.47 × 2–28.94
minutes; we have
36–28.94= 7.06
minutes for the time consumed in tipping the
wagons; or, as the time required for tipping any
set of wagons is the same as the time required
for tipping one—provided it does not numerically
exceed the shunt or sperm roads, which in these
instances they did not—we have 7.06 minutes, for
the time required for tipping a single wagon also.
In the fourth table we find, that twenty-one-and-
a-half minutes elapsed, from the time the wagons
left the cutting loaded, until they returned empty,
the length of the lead being a quarter of a mile :
and as the time spent in motion must have been
14.47
minutes, we have
21.5—14.47 = 7.03
minutes for the time which elapsed while the
wagons were being tipped; or the time that would
have been spent in tipping a single wagon, as
the number of shunt roads were not less than
the number of wagons in each set.
Now, if the average of the results, afforded by
the seventeen experiments given in the tables,
is taken upon this point; it will be seen, that the
THE EXPERIMENTS. 43
time required for tipping any set of wagons—what-
ever may be the number it contains, when the
breadth of the tip is unlimited—or, the time re-
quired for tipping any set of wagons, which does
not numerically eaceed the number of shunt
roads placed on the head of an embankment,
when the breadth of the embankment is limited,
as on railways—as also, the time required for tip-
ping a single wagon, in any case; amounts to 7.07
minutes.
With regard to the time required for filling the
wagons, it is evident, whether a set contains two
or twenty, or any other number—provided each
set is worked with its proper compliment of men—
that the time spent in the operation will be the
same in all cases; because, when a set of wagons
is brought into a cutting, the men appointed for
the purpose commence filling all the wagons
in it at once ; so that, whether a cutting is suffici-
ently extensive to contain a set consisting of two
wagons, or twenty, the time in which every set
can be filled will always amount to the same ;
hence, we have for the time required to fill any
number of wagons, working together in the same
set—from the results of the first table—
69.47—(43.41.--7.09)= 18.97
minutes.
By reference to the results of the second and
third tables—where the time spent in loading, re-
D 2
44 AN AI. Y SIS OF
moving, bringing back, and tipping the wagons,
was fifty-five minutes—we have, by a process
similar to the above,
55—G28.94.--7.06)= 19
minutes, for the time spent in filling the
wagons; or, from what we have said before, that
which would be required for filling any set of
Wagons.
From the results of the fourth table, we find
that the filling and removing backwards and for-
wards, besides the tipping, took 40.56 minutes;
therefore—by the same reasoning as before, and a
similar process—we have,
40.56–014.47.--7.03)= 19.06
minutes, for the time required to fill the wagons;
or the time required for filling any set of wagons
also ; allowing it to consist of any number what-
soever, which the cutting may be extensive
enough to contain.
Taking the average of the results thus arrived
at, we have nineteen minutes, as a constant
quantity; denoting the time which is required for
filling a set of wagons, of whatsoever number it
may consist.
Now, these two quantities being always con-
stant, whatever may be the length of the lead;
their sum, 26.06 minutes, will also become a con-
stänt in every calculation, and will represent the
sum of the times required for filling, and tipping
any single set of wagons. In the method of cal-
2 THE EXPERIMENTS. 45
culation which we have adopted, the quantity
becomes the first term of an arithmetical pro-
gression, by the reduction of which we have
obtained—as will be shown in the following sec-
tion—two general formulae; by means of which,
the number of wagon-loads that can be removed
from cutting to embankment—by a given force,
and in a given time, upon any length of lead,
variable or constant—can be computed; when
the breadth of the head of the embankment is
unlimited, (as in tipping to spoil,”) or when the
number in each set does not exceed the number
of shunt roadst placed at the tip.
SECTION IV.
Investigation of the fundamental formulae, with a
fen, practical applications of them.
It is evident from what has been stated before,
that the results of any calculations, upon the
quantity of material that can be removed in a
given time, (according to the common system,)
must depend entirely upon the length of the
lead—varying when it varies; or, in other words,
that they must vary with the amount of time
required to remove the wagons from cutting to
embankment; because we have seen, that the
* Wide Appendix. Note 15. + Wide Appendix, Note 17.
46 INVESTIGATION OF
time spent in the operations of tipping * and filling
will be always the same, although the length of
the leads may vary ad infinitum. Therefore, if
the rate of speed or progression, at which the
earth can be removed from cutting to embankment,
has once been accurately determined—which it is
believed we have succeeded in doing in the last
section—it is evident we can have recourse to any
theoretical principles which embrace variable
quantities; and which can be successfully applied
to the different lengths of lead which occur, in the
formation of cuttings and embankments.
The principles upon which the formulae in
the present instance are founded, are those which
belong to thearithmetical series; it having appeared
to us to be the most simple, and at the same time so
well adapted for practical purposes, that there was
no sound reason for having recourse to any of the
higher, or more difficult departments of science.
To save the reader the trouble of referring to
works on Algebra, the following compendious
analysis of the formulae which have been made
use of, is given.
In any case where quantities increase, or de-
crease by a constant difference, it is evident that
* It ought to be borne in mind, that what we have said
here, with respect to tipping, holds good, only, when the
breadth of the head of the embankment is unlimited. It will
be shown hereafter, that when the latter is limited, it affects
the quantity of work done, jointly, with the length of the lead.
FUNDAMENTAL FORMULAF, 47
they come under the same form as the common
arithmetical progressions.
1. 2. 3. 4. 5. &c. or H. 3. 5. 7. 9. &c.
Therefore if a, represent the first term in the
series, and b, the quantity by which the terms in-
crease, we shall have :
a, a-H b, a-H2b, a-H3b, &c.,
for the resulting progression.
Or, if a, be the first term, and b, the quantity
by which the consecutive terms decrease, then the
form of the progression becomes
a, a-b, a-2b, a-3b, &c.
The sum of any positive series of this form can
be found by multiplying the sum of the first and
last terms by half the number of terms.
For let a-the first term,
And b-the common difference, or quantity
by which the terms increase or decrease con-
secutively,
Then,
a,-Ha-H b-Ha-H2b-H&c. . . . . . a-H (n—1). b-s,
also,
a-H (n—1). b+a+(n-2). 5-Ha-H (n-3). b + &c.. . . . a =s;
by addition,
2a+(n-1). 6+2a+(n-1). b + &c. to n terms=2 s;
therefore,
{2a+(n-1). b m.–2s;
whence,
s=| 2a+(n-1). º ſº -:
48 INVESTIGATION OF
Or,
s={a-Ha-H (n—1). b). -: o
the sum of the first and last terms, multiplied by
half the number of terms.
If the series be of the decreasing form, b, be-
comes negative, and
S = {a-a-(n-1)} º + e
Upon the principles of these formulae, the sub-
sequent calculations have been arranged; and the
constants have been reduced so as to answer for
computing the effects, at every sixteenth of a mile
difference in the lengths of the leads.
According to this arrangement, the quantity
answering to the first term, (a), is 29.6776 mi-
nutes; viz: the sum of the times required for
filling and tipping the wagons, together with the
time required for drawing them backwards and
forwards upon a lead of five chains, or a sixteenth
of a mile in length; and the common difference
answering to b, for a lead a sixteenth of a mile
long, will be 3.6176 minutes; being deduced from
the constant for the speed of transit given in the
third section; also the number of terms, or the
quantity answering to n, will be
L
T5 2
five chains being the sixteenth of a mile, and L
being the length of the lead in chains.
FUND AMENTAL FORMUL.AE. 49
From the series resulting from the above ar-
rangement, we have been able to give condensed
formulae, by means of which, the number of wa-
gons that can be removed from cutting to em-
bankment, in a given time, and upon any given
length of lead, varying from a sixteenth of a mile
upwards, can be computed as follows.
The expanded form of the series being
a, a +b, a +2b, a-H3b-H&c......... a-H (n—1).b,
we have in figures, in consequence of the above
arrangement,
29.67 +33.29-–36.91 +40.53+ &c.. . . . a+(n-1). 5;
and the last term will be the time required for load-
ing, removing, tipping, and returning to the cutting
with the empty wagons, at any given length of
lead. The last term (l) is
a-H (n—1) b,
or, according to our notation,
(l)=29.67+ (#–1) × 3.6176, or
(l)=.7235 L-H26.06,
the time, in minutes, which will elapse during each
trip. This time, it may be perceived, increases
directly—and the number of trips inversely—as
L
*-
5
Now if t is put for the whole time in minutes
worked, l for the last term in any series, and N
for the total number of wagons working, we shall
50 INVESTIGATION OF
have }=the total number of trips made during
that time; and this multiplied by the number of
wagons working altogether, represented by N.
will give,
/ !
the total number of wagons that can be removed,
from cutting to embankment, in a given time. If
We put its equivalent for l, we get
Nt º-
.7235 L-E26.06T
Hence, the total number of wagons working, and
the time in minutes worked, being given, the to-
tal number of wagon-loads removed from cutting
to embankment, represented in the last formulae
by ar, may be computed by the following practical
R.U.L.E.
Divide the product of the total number of nya-
gons n'orking, and the time in minutes norked, by
the sum of three-quarters the length of the lead,
and the number truenty-sia, and the result mill be
the number of nagon-loads removed from cutting
to embankment. -
When the lead is increasing regularly and ra-
pidly, as is sometimes the case in side-tipping,
and in dressing off slopes, the sum of the se-
FUNDAMENTAL FOR.MUL.AE. 51
ries must be found; this formula, as we have
shown above, is
s={ 2a+(n-1).] 4- #;
and this, divided by the number of terms, (n) will
give the divisor to be used in such case, instead
of the last term (l).
Therefore, using the same notation as before,
the formulae applicable to variable leads will be-
COIſle
*—= –*——w, or
(a+1). n. T y (a+1)T“ ”
2n
Jº — 2 Nt
(a+l)
hence, putting their equivalents for a and l, and
reducing, we have
M t
.3617L-H 27.86
the total number of wagon-loads that can be re-
moved from cutting to embankment, in any given
time, denoted by t, when the length of the lead
varies regularly and rapidly; L being in this for-
mula the longest of the variable leads.
Hence the following practical
RULE.
Divide the product of the total number of nagons
working, and the time in minutes norked, by the
sum of one-third the length of the longest lead,
and the number twenty-eight; the result mill be the
52 INVESTIGATION OF
number of wagon-loads removed from cutting to
embankment, myhen the leads become variable.
In order to shew the application of the formulae,
and the coincidence of their results with those
given by the tables, under similar circumstances,
we have inserted a few practical examples, as fol-
lows.
ExAMPLE 1st.
Let it be required to find the number of wagon-
loads that can be removed from cutting to em-
bankment, by means of four wagons, worked for
eight hours consecutively, with their proper com-
pliment of men and horses, at the usual rate of
speed, when the length of the lead is half a
mile P
In this, and similar cases, where the length of
the lead is constant, the first formula must be re-
ferred to, viz.:
tºº N t
*= .7235L-E26.06
or, as in the present instance,
N=4,
t=8 x 60,
and L=40;
by substituting them for their equivalents in the
above formula, we shall have

4× (8 × 60)
(7255×10) E33.06 −"; *
FUND AMENTAL FORMUL, AE. 53
I920
the number of wagon-loads that could be removed
from cutting to embankment, under the above cir-
cumstances. This result agrees within 10, with
the average of those given by the second table;
where it will be seen that the conditions were si-
milar.
ExAMPLE 2nd.
Let it be required to find the number of wagon-
loads that can be removed from cutting to em-
bankment, by means of four wagons, with their
proper compliment of men and horses, when
worked for ten hours consecutively, at the usual
rate of 2.40 miles per hour; the length of the
lead being a quarter of a mile?
Here, the lead being constant, the first formula
is to be likewise used, viz:
N t = @
.7235L-E26.06 Tº
or, as in the present case,
N=4,
t= 10 × 60,
and L-20 ;
by substituting them in the general formula, we
shall have
54 INVESTIGATION OF

4x (10x60)
**(.7335×20)+26.06;
Or,
=* =59.21
*F10.53
the number of wagon-loads that would be re-
moved from cutting to embankment, under the
above circumstances; which shows only a tri-
fling difference, with the quantity of work done
according to the fourth table, when the length of
the lead was also a quarter of a mile.
Now, in order to show the application of the
second formula, or that for variable leads, we will
suppose the following case.
ExAMPLE 3rd.
Required the number of wagon loads that could
be removed from cutting to embankment, by four
wagons, with their full compliment of men and
horses, when worked for ten hours consecutive-
ly; allowing the leads to vary from a sixteenth to
three quarters of a mile in length P
The leads, in this instance, being variable, the
second formula must be applied ; viz:
Nt - ??
.3617L-E27.86 Tº
or, as in the present case,
FUND AMENTAL FORMUL.A. 55
N=4,
t= 10 × 60,
and L=60,
(for in this formula L represents the longest of the
variable leads); we shall have, by substitution,

4× (10 × 60 E º' -
(.3617 × 60)+27.86 T 2
* _2400 tº
Or, ** 19.563 =48.42;
the number of wagons that could be removed
from cutting to embankment, when the leads vary
within the limits prescribed in the above exam-
ple.
The latter question could also be solved by
means of the formula given for constant leads,
provided the mean of the variable leads was con-
sidered as a constant one; but, in almost every
instance, the mean of the leads would contain a
thirty-second part of a mile, which would render
it necessary to alter the constant decimal multi-
plier in the divisor, in order to suit the more
minute subdivision of the lead.
However, under all circumstances, it has been
considered more suitable to the nature of the ques-
tion, to give a separate formula for each ; espe-
cially as the application in both instances is
equally simple, if any thing, more agreeable
56 INVESTIGATION OF
with practice in the latter; and besides, exhibits a
train of induction more immediately analogous to
that upon which the first formula is founded.
SECTION V.
Containing an investigation of the formulae of
limitation, which develope the causes particularly
affecting the progress of embankment upon
railways.
The results of the general investigations con-
cluded in the previous section, would, of them-
selves, be likely to induce a supposition, to the
effect—that the quantity of material which can be
removed from cutting to embankment in a given
time, is, in all cases as unlimited, as the number of
wagons that can be filled in a cutting, in the same
time. This is true, only, when the breadth of the
tip, or the number of shunt roads that can be
fixed upon the head of an embankment, is, practi-
cally speaking, also unlimited. But this can
seldom be the case upon any description of em-
bankment, and never with respect to a railway
embankment, the instance of a spoil bank being
now and then a solitary exception. Therefore,
although a hundred wagons might be filled in
some cuttings in nineteen minutes, provided each
wagon was worked with its proper complement of
FORMUL.AE OF LIMITATION. 57
fillers and getters; yet, if the number of shunt
roads was so limited by the breadth of the head
of the embankment, as that the number which
could be tipped in the same time did not exceed
eighteen, (which would be the case on an em-
bankment twenty feet high, with slopes of two
to one, as will be seen hereafter); in a very short
time, the roads on the head of the embankment
would become so crowded—with the loaded wagons
which remained untipped at the expiration of
every nineteen minutes—that it would be finally
impossible to tip any at all. Hence, it is evident,
that the number of wagons which can be removed
from cutting to embankment upon railways, must
always depend, upon the number of shunt roads
that can be fixed on the head of an embankment;
or, which is the same in effect, upon the breadth to
which the embankment is limited.
Otherwise, and were it not for the above rea-
son, that the number of shunt roads upon rail-
way embankments is generally limited to sir;
the number of wagon-loads that could be tip-
ped, would be as numerous as the number of
wagons that could be filled in the cutting, from
which the material for forming it is supplied; or,
in other words, the number of wagon-loads tipped,
would bear a direct proportion to the area of the
face of the cutting ; an opinion which, upon a
superficial glance, would appear feasible enough,
E
58 INVESTIGATION OF
and which is, we believe, at present very pre-
valent.
Now, this limit to the number of wagon-loads
that can be tipped in a given time, which we have
referred to above, may be easily determined, gene-
rally, by making use of the constants previously
obtained in the third section.
For there we have seen, that it takes 7.07
minutes to tip a single wagon from one shunt
road; and therefore,
60
7.07
will be the total number of wagon-loads that can
be tipped over the head of an embankment, and off
a single shunt road, in an hour. Hence, putting R
for the number of shunt roads that can be fixed
on the head of an embankment, we have
60
Hºx R=w
Or, a'=8.48 R ;
for the number of wagons which can be tipped off
all the shunt roads in an hour.
According to this, as the number of wagons
which can be tipped, will depend upon the num-
ber of shunt roads that can be fixed, on the
head of the embankment; and, as this again must
depend, upon the breadth of the head of the em-
bankment; it follows, that the broader every em-
FORMUL.AE OF LIMITATION. 59
bankment can be formed, previous to dressing off
the slopes, the greater will be the quantity of
material that can be removed to, it in a given
time.
Now, the breadth to which the head of an em-
bankment can be formed, previous to dressing off
the slopes, will obviously increase, in all cases, with
the height of each embankment, and the rate of
inclination to which the sides are to be finally
dressed off-—for the following reasons.
Almost every material, used in the formation of
embankments, will stand at a slope of one-and-
a-half to one, at least, when first tipped; some
soils may remain only for a week at this rate of
inclination, while others will remain so for months;
and, in many instances, at a much sharper inclina-
tion—according to the state of the weather, and
the nature of the material itself—before it slips, or
collapses finally, into its natural slope. This is a
fact known to every practical man. Therefore, as
the average number of embankments are finally
dressed off, to flatter inclinations than one-and-a-
half to one ; and as, from what we have just
stated, they can be generally run out in the first
formation, at the latter rate of slope; there will be
always an extra width, on both sides of the head of
the embankment, besides the thirty feet to which it
is to be finally dressed off, which can be made
available for fixing shunt roads upon. This extra
E 2
60. INVESTIGATION OF
width, will be always proportional to the difference
between the lengths of the bases of the skypes,
due to an inclination of one-and-a-half to one,
and that to which the embankment is to be finally
formed; and, evidently, depends upon the height
and rate of slope, determined on by the engineer.
For instance,—in the formation of an embank-
ment twenty feet high, and thirty feet wide at
top, with inclinations of two to one on both
sides—we can at first run it out with inclinations
of one-and-a-half to one, as we have stated above;
and consequently, the slopes will stand, at first,
upon only three quarters of the length of the base
upon which they are to stand finally; so that
the embankment will thus have an extra width at
top, on both sides, equal to one quarter the length
of the base, answering to an inclination of two to
one. In the present instance, this extra width
would be ten feet; the height being twenty
feet.
If the reader will take the trouble to refer to
Plate No. 2, Fig. 3; perhaps we may succeed in
giving a clearer elucidation of the point in ques-
tion.
In this figure, a, b, e, f, represents the cross
section of an embankment, as it is to be finally
dressed off; the slopes of which, a, e, and b, f,
we will suppose, for the sake of illustration, to be
tWO to One.
FORMUL.AE OF LIMITATION. 61
Also, c, d, g, h, represents the cross section of
the same embankment, as it can be originally
run out; before the sides are finally dressed off,
—with slopes c, g, and d, h, of one-and-a-half to
one; where c, a, equal to e, g, and b, d, equal to
h, f, represent the whole extra width obtained at
top, that may be made available for placing shunt
roads upon.
In the same manner, if the height of the em-
bankment was thirty feet, and the slopes, to which
it was finally to be dressed off, were two to one
also, we should have the base of each slope sixty
feet long ; and consequently, if it was originally
run out, with slopes of one-and-a-half to one, we
should have an extra width on both sides—in
addition to the thirty feet at top—of fifteen feet; or
a quarter of the length of the base, answering to
an inclination of two to one. Hence; the total
width gained at top during the formation, would
be thirty feet.
From what has been already shewn, it is clearly
evident, that the number of shunt roads which
can be made available on an embankment, or—
which is tantamount in the present case—the
number of wagon-loads which can be tipped
over any embankment, n'hen the breadth of it is
limited, must always depend upon its height, and
the rate of inclination given finally to the slopes.
But to return to the calculation;– since we have
62 INVESTIGATION OF
shown, that the number of wagon-loads which
can be tipped, in an hour, off the head of an
embankment, is expressed by the general formula
a'-8.48 R;
and, as we have seen, that the quantity repre-
sented by R will vary in every instance, according
to the final height and rate of slope peculiar to
each embankment ; we will now proceed to
determine what value is to be ascribed to it, in
those calculations that will be most commonly
required.
For this purpose, let B represent the breadth of
the tip head upon any embankment, and S the
space occupied by a single shunt road; then,
B
s=R
will give the number of shunt roads that can be
fixed. In this expression, S is equal to eight
feet in all cases; so that the numerical relation
which the quantity represented by B, bears to the
height and rate of slope, to which any particular
embankment is to be dressed off, is all that
remains to be found; in order to determine the
quantity represented by R also numerically.
Therefore, as we have shown above, that every
embankment can be originally run out with
slopes of one-and-a-half to one ; it follows, that
tnice the difference between the talus of a slope
FORMUL.AE OF LIMITATION. 63
of such an inclination, and that to which the
embankment is eventually to be formed, added to
thirty feet—the constant width of a finished em-
bankment—will give the total breadth, which can
be rendered available for fixing shunt roads upon
—represented in the latter formula by B. This
difference, in any case, is the ratio which the
bases of the slopes bear to each other; and, with
respect to an embankment with two to one slopes,
is expressed by
r=.5 h 3
h being put for the height of the embankment,
and r for the ratio which exists between the
bases of a slope of two to one, and a slope of one-
and-a-half to one.
Where the slopes are three to one, the expression
becomes
r= 1.5 h.
Where the slopes are four to one, it becomes
r=2.5 h;
and where the slopes are five to one, it becomes
r= 3.5 h;
and so on.
Hence, when an embankment is to be finally
dressed off, to an inclination of two to one at the
sides; we shall have, for the total breadth that can
be made available for fixing shunt roads upon,
B=30+2(.5 h)=30+h.
In an embankment, which is to be finally dressed
64 INVESTIGATION OF
off to an inclination at the sides, of three to one ;
we shall, in a similar way, have
B=30+2(1.5 h)=30+3 h.
If the slopes of the embankment become four to
one, after being finally dressed off; we shall
have
B=30+2(2.5h)=30+5h.
and so on in proportion; so that when we have an
embankment with 2. 3. 4. 5 or 6 to 1. &c., the
corresponding increase in the available width at
top, will be
30–H h, 30+3h, 30+5h, 30+7h, &c.;
where the law of increase is evident.
Consequently, in the expression
B
R=:
S 5
when it refers to an embankment with two to one
slopes, becomes, by substitution,
30–H h
R= ‘’YT “.
8
With reference to an embankment which is to be
finally dressed off to slopes of three to one, it be-
COIſleS
30–4–3h.
R= * 5
and so on, the value of R increasing, according to
the increase in the height of the embankment, and
the length the base of the slopes.
Hence we have the following general expres-
sion, denoting the number of shunt roads that can
FORMUL.AE OF LIMITATION. 65
be fixed on the head of any railway embankment;
Viz ;— b-H2rh
R="##".
b, representing the final breadth at top, to which
any embankment is to be formed; h, the height
of any embankment; and r, the ratio which exists
between the base of a slope of one-and-a-half to
one, and that of the slope to which any particular
embankment is to be finally dressed off.
Now, returning to the general formula, which
shows the number of wagon-loads that can be
tipped over the head of an embankment in an
hour, and substituting in it the equivalent values
of R, we shall have, for an embankment with two
to one slopes—
a' = 8.48 (º) 3
Or, a'= 1.06(30+h).
For an embankment with slopes of three to
one, we shall have
a'-8.48 (30+3h).
8 2
Or, a'- 1.06(30+3h).
Where the slopes of an embankment are four to
one, we shall have, by the same process,
a'-8.48 (º),
Or, a'= 1.06(30+5h);
and so on, with any other rate of slope, to which the
sides of anembankmentare to be dressed off finally.
66 INVESTIGATION OF
These formulae, it will be perceived by the
reader, are applicable to every description of rail-
way embankment, when the height, breadth at
top, and rate of inclination given to the sides, are
once known ; and may be generally represented
by the following formula:—
* a'-1.06 (b+2rh); *
when a represents the number of wagon-loads
that can be tipped over any embankment in an
hour; r, the ratio which exists, between the rate of
slope, at which such an embankment can be at
first run out, and that to which it is to be finally
formed ; and h, the height of it.
For the sake of illustration, we will now pro-
ceed to give a few examples, in finding the num-
ber of wagon-loads which can be tipped over
the head of an embankment in an hour; and first,
* Whether the accuracy of the constant 1.06—which is
derived from the time we have given for the tipping of a wagon
(viz: 7.07 minutes)—is disputed or not, the general form of
this expression holds good. For instance, if we put a, for the
number of wagon-loads that can be tipped in an hour, of a
single shunt road; then, in general terms, the formula will
become (b **). ; and holds equally good, whatever
may be the values of the factors that may be found from ex-
periment. We have mentioned this, merely to show, that
this, and the other formulae, will not be affected in principle ;
in any case where a difference of opinion may arise, as to the
accuracy of the numerical values given to the factors.
FORMUL.AE OF LIMITATION. 67
as we have shown that the results of the calcu-
lations, in every instance, will vary proportionally
with the quantity represented by (b+2rh); in
the general formula,
a'-1.06.(b+2rh);
we will suppose b to be thirty feet—the width at
top given to ordinary railway embankments—the
height (h) to be twenty feet; and the slopes to
incline at the rate of two to One.
Hence, allowing that the embankment can be
originally run out with slopes of one-and-a-half to
one; the above general formula will become
a- 1.06 (30+ 2 × .5 × 20);
Ol', a'=53;
the total number of wagon-loads that could be
tipped, under the above conditions, in an hour.
Again, if it were required to find the number of
shunt roads, that should be fixed on the head of
the embankment, to produce this result; we have
the general formula,
R_*. _b4-2 rh,
TS S ’
which—under the same conditions as we have sup-
posed—will, in the present instance, become
R_**** h).
or R_*.*
—the greatest number of shunt roads that could be
fixed on the head of such an embankment; and
68 INVESTIGATION OF
also, the number necessary to insure fifty-three
wagon-loads being tipped over it in an hour.
Next let us suppose the case of an embank-
ment—fifteen feet high, with slopes of three to
one, and thirty feet wide at top—where it is re-
quired to determine the number of wagon-loads,
that can be tipped over it in an hour.
Here the general formula,
a'-1.06 (b+2 rh),
becomes
a'= 1.06 (30+3 h),
OT a'—1.06 (30+45),=w=79.50
wagon-loads;–the greatest number that could be
tipped off such an embankment, under any cir-
Cumstances.
The formula for finding the number of shunt
roads, that could be fixed upon the head of the
embankment, under similar conditions; or the
number necessary to produce such a result; would
become
30–H3h
8
the greatest number of shunt roads that could be
fixed; which in practice would be reduced to nine.
In some cases the breadth of the embankments
on the Great Western Railway was thirty-eight
feet; so that in these instances, we should have
wº- 1.06 (38+3h);
which—if the other conditions are supposed the
same as those mentioned in the first example above,
R= =9.33,
FORMULAC OF LIMITATION. 69
—would become
a'—1.06 (38+20)=61.48;
—the greatest number of wagons that could be
emptied over the head of the embankmentinan hour.
Also, the general formula
_ (b+2 rh)
R=\ºtº,
—for finding the greatest number of shunt roads
that could be fixed upon such an embankment—
would become
R -º-; 25.
These two latter calculations show, that 8.48
wagon-loads per hour, could be tipped over some
of the embankments upon the Great Western
Railway, more, than the number that could be
tipped over ordinary railway embankments, under
similar circumstances.
Thus it is evident, as we have mentioned before,
that the quantity of material that can be removed
from cutting to embankment upon railways—Or
indeed in any system of earthwork, where the
breadth of the heads of the embankments are
limited—must of necessity depend, upon the
heights and rates of slope to which the embank-
ments are to be finally formed; and moreover,
that the opinion—to the effect, that the size, and
facility of working afforded by a cutting, renders
the expenditure in time and capital comparatively
less—is utterly fallacious.
P A RT II.
SECTION VI.
Containing an inquiry into the effects of the lead,
njith the alterations, necessary in the general sys-
tem of arranging cuttings and embankments,
which are derived from it.
HAVING shewn, in the first part of the inquiry,
the method of determining the greatest number of
shunt roads, that can be fixed upon the head of
any embankment during its formation; when it is
limited, and the dimensions of its limits given;
and also, having given the investigation of the
general formulae, for finding the greatest possible
number of wagon-loads that can be tipped, in an
hour, over such an embankment: we shall now
endeavour to determine the effect upon the pro-
gress of the works, which is caused by the length
of the lead, or distance, between the face of a cut-
ting and the head of the embankment formed
from it; as also, the total number of sets of wagons,
and the number of nagons in each set, that will
EFFECTS OF THE LEAD. 7I
be necessary to produce the greatest effect, with
the greatest possible economy of time and expen-
diture.
It may be frequently observed, that at certain pe-
riods in the progress of every railway embankment,
a deficiency in horses and materials is experienced
by the contractor; and, that an endeavour is made
to compensate for this deficiency, by increasing
the usual rate of speed, at which the horses trans-
port the material from the cutting to embank-
ment. This deficiency, is evidently caused by
the length of the lead, or distance, which the
horses have to travel over, between the cutting and
embankment;-which increases as the work pro-
gresses. For when the lead exceeds a certain length,
the time that elapses while the horses are going
to, and returning from, the tip, will become greater,
than the time required for filling a set of wagons;
so that the wagons cannot be removed and
brought back fast enough, to prevent a certain
portion of time being lost by the fillers and
getters in the cutting.
This loss of time must be a serious item in the
expenditure of the contractor; who may have to
pay, perhaps, a hundred men for a whole
day's work; when, perhaps, five or ten minutes at
the expiration of every nineteen (the time re-
quired for filling a set of wagons,) throughout
the day, are utterly profitless—in consequence of
72 INQUIRY INTO THE
the delay in the arrival of the wagons, as the lead
becomes longer.
Therefore, in order to insure such two impor-
tant components in the arrangement of a work, as
economy and speed, it is well worthy the atten-
tion of practical men, to determine the number of
sets of nagons, and the number of nagons in each
set, which shall be necessary to keep the getters
and fillers in the cutting—as also the men sta-
tioned on the head of the embankment—constantly
employed. To insure this, it is evident, that a
certain proportion—between the length of the lead,
and the number of sets of wagons—must be previ-
ously fixed upon.
This proportion—between the length of the
lead, and the number of sets of wagons rendered
necessary by it—has never been properly defined
in any one instance ; and has been mostly,
altogether overlooked, in the general arrangement;
so that contractors—by not foreseeing the neces-
sity of providing an extra quantity of materials
and horses, as the length of the lead increases,
until it is too late—invariably experience a defici-
ency of the means, required to carry on their works
with that uniform vigour, which they and their
employers were previously led to expect. But,
even allowing that a contractor does apprehend a
deficiency, in horses or materials; which is a very
rare occurrence—he never imagines, that the defi-
EFFECTS OF THE LEAD. 73
ciency will be experienced suddenly; nor more-
over, when it does arise, has he any means of
calculating the extent of it, and the exact extra sup-
ply that will counteract it, so as to ensure his horses
from being over-worked, and himself from unne-
cessary expenditure.
Now to remedy these defects, it is evident, that
the increase in the number of sets of wagons
must take place, at those lengths of the lead, in
drawing any set of wagons over which, the same
time would be spent, as in filling them ; and also,
that the number of wagons in each set, should be
such, as that the time consumed in tipping, and
filling them be the same ; or, as these times are
constant, that the number of wagons in each set,
must vary with the breadth at which the embank-
ment can be run out in the original formation; for
the following reasons.
First,--as each set of wagons is tipped, another
set must be ready at hand to take its place imme-
diately, at the head of the embankment, in order
to prevent the men stationed there losing any
time.
Secondly,–when each set of wagons is filled,
another set of empty ones must be likewise ready
at the face of the cutting.
Now, to effect these arrangements, it is ob-
viously necessary that each set of wagons, should
contain such a number as can be filled and tipped
F
74 INQUIRY INTO THE
in the same time; and also, that the number of
sets be so proportioned to the length of the lead,
as will allow of their following each other in
regular order; from cutting to embankment, at cer-
tain intervals of time, these intervals being deter-
mined by the number of minutes spent in filling
each set separately.
Where this disposition is not adhered to, the
getters and fillers in the cutting must remain idle,
after filling each set; while they await the return
of the set which was being tipped, during the
time they were employed in filling.
The methods by which these arrangements can
be secured, we shall now proceed to investigate.
As the time required for filling any set of
wagons—whether it consists of one or twenty, or
any other ascribable number which a cutting can
contain—will be in all cases nineteen minutes, pro-
vided each set is worked with its proper comple-
ment of getters and fillers; it follows, that when
the lead increases to such a length, as that the
time spent in drawing the wagons over it begins
to exceed nineteen minutes, two additional sets
must be set on, besides the two constantly em-
ployed at the head of the embankment, and the
face of the cutting. These additional sets, being
the two going backwards and forwards between
the cutting and embankment, during the time the
wagons are being filled and tipped; and so ar-
EFFECTS OF THE LEAD. 75
ranged, that they shall arrive at their respective
destinations at the expiration of that time.
The exact length of the lead at which these ad-
ditional sets are required, is every five sixteenths
of a mile. For at the rate of speed we have es-
tablished in the third section—viz. 2.40 miles per
hour—18.05 minutes are spent in drawing the
wagons such a distance; and this period of time
comes nearest to nineteen minutes, the time re-
quired for filling them.
Therefore, if we put L for the length of the
lead in chains, we shall have
L
25-
the number of additional sets of wagons required to
supply any lead in one direction; or the number of
sets travelling constantly between the face of the
cutting, and the head of the embankment. But
while this number of sets is proceeding onnards to-
wards the tip, an equal number must be returning
in the contrary direction : consequently, we have
2L ,
-35°n.
for the number of sets constantly in motion, to
and from the tip and face of the cutting; and this
number, in addition to the two sets that remain
stationary, while all the others are progressing—
one at the tip, and the other at the cutting, for
the purpose of being filled and emptied ;-gives
70),
F 2
7t; INQUIRY INTO THE
#+2=w
for the total number of sets of wagons that must
be constantly at work on any length of lead, in
order to insure the greatest expedition and eco-
nomy.
We may affirm, without fear of contradiction,
that this order in the sets of wagons has never
been exactly adhered to ; both because it was
never accurately defined, and because contractors
Have seldom or never at their disposal, a sufficient
number of wagons to put it into practice, at the
time the emergency occurs. However, the atten-
tive reader will at once perceive, that the foregoing
induction leads to the irresistible conclusion, that
such an order and disposition of the sets of
wagons are palpably indispensable, before it can
be hoped to attain to the two most desirable ob-
jects in the arrangement of all works ;-viz :
economy and expedition.
Only one more point remains for us to investi-
gate, and then the development of the more
prominent features of the inquiry may be con-
sidered as complete. This is, the determination of
the number of wagons of which each set ought to
be composed.
From what has been previously discussed, it is
obvious, that each set must be comprised of such
a number of wagons, as can be tipped and filled
EFFECTS OF THE LEAD. 77
in equal portions of time; otherwise, the order,
and due succession in the progress of each set—
proved to be so indispensable—would be inter-
rupted. Now, the number of wagons in each set,
will depend solely upon the breadth of the head
of the embankment; or—which is the same in
effect—upon the number of shunt roads that can
be fixed on it; because the number that can be
filled in any cutting, will always exceed the
number that can be tipped;” and for this reason,
as we have explained before, cannot in any way
affect either the progress or arrangements of the
works.
Hence, let t, represent the time required for
filling a set of wagons,—t, the time spent in tipp-
ing a single wagon, R, the number of shunt
roads fixed on the head of any embankment—
and, n, the number of wagons contained in each
set; then, in order to prevent more time being
spent in tipping any set of wagons, than in filling
them, we must have,
7?, it
t
r—X R,
t
for the number of wagons in each set; or, as we
* This will hold good in every case, except when the mate-
rial taken out of the cutting is led to spoil; in which instance,
the available breadth of tip, is almost universally unlimited;
and, consequently, the number of wagons that can be tipped,
will be entirely dependant upon the area of the cutting.
78 NUMBER OF WA G ONS
have seen before that the time required to fill a set
of wagons, (t), is nineteen minutes, and the time
for tipping a single wagon (t'), is 7.07 minutes;
we must have,
19
=== XR,
"=Hdi X
Or, m=2.68 R ,
for the number of wagons required in each set,
answering to any breadth on the head of an em-
bankment. Or, if we exclude the constant values
which we have determined for, t, and t, and put
for R, the equivalent which has been given for it—
in terms of the breadth, height, and rate of slope of
an embankment—in section the fifth of the first
part of the inquiry; we shall have,
t b-H2rh)
7) E –F– X (ºr, 5
_bt+2r ht
Or, n=–sp-
for a general expression, denoting the number of
wagons that ought to compose each set, upon every
embankment: where r, represents the ratio be-
tween the basis of a slope of one-and-a-half to
one, and that to which any embankment is to be
dressed off; h, the height of any embankment;
and s, the space occupied by a single shunt road.
By applying the constants we have given, the
formula—when used for finding the number of
IN EACH SET. 79
wagons required in each set, upon any railway
embankment—will become
n=10.09-H.673 r h;
as may be seen, upon reducing the general for-
mula; when the constants previously determined
upon—are substituted for the letters representing
them.
Now, for the sake of illustration, let it be re-
quired to find the number of wagons that each
set of wagons ought to contain ; when referred to
a railway embankment twenty feet high, and with
slopes of two to one. In this instance,
r=.5,
and h-20;
hence,
n = 10.09-H.673 r h,
becomes,
n=10.09-H.673 × .5 × 20 ;
Or, m = 16.82.
In practice, seventeen wagons, would be the num-
ber required in each set, to insure the greatest
possible degree of expedition and economy. If a
lesser number, comprised each set, the progress of
the work would not be so rapid ; and on the
other hand, a greater number would cause a loss
of the men's time, who were at work in the cut-
ting ; because the time spent in tipping, would
exceed the time in filling them, and consequently
a delay would be experienced in the arrival of
80 NUMBER OF WAGONS
the empty sets, after each set was filled in the
cutting; as we have explained at the commence-
ment of this section.
It may be useful to remark, that no alteration
in the contractors' roads will be found necessary,
whenever the alterations we have alluded to, may
be put into practice; with the single exception,
that at every twenty-five chains in length of the
road, a siding” will be required, in length propor-
tional to the number of wagons in each set ; in
order to allow the going and returning sets, to
pass each other.
This alteration, in itself is very simple, although
of great importance. For, as we have mentioned
before, according to the present system of arrange-
ment, three sets of wagons are made to answer
every length of lead, from a sixteenth of a mile to
two miles; and when the lead exceeds twenty-
five chains, the time that it takes to remove the
wagons, from cutting to embankment, and back,
begins to exceed the time required for filling
them : consequently, the getters and fillers lose a
portion of time, after each set leaves the cutting,
proportional to that excess; and this evil becomes
greater as the lead becomes longer; notwithstand-
ing the rude attempts that are sometimes made to
counteract it, such as increasing the speed of the
horses, &c. Moreover, according to the common
system, the greater the number of wagons that
* Wide Appendix, Note 16.
1 N E A C H SET. 81
can be crammed in one set, into a cutting, the
greater, it is supposed, will be the effect; what-
ever the breadth of the head of the embankment
may be: the consequence of which is, that the
head of the embankment is constantly crowded
to inconvenience, with the loaded wagons, which
cannot be tipped fast enough ; and the return
of the empty trains to the cutting, is retarded, far
beyond the proper time for their arrival.
With regard to the first of these our investi-
gations prove—in order to insure a constant
supply of wagons, at the cutting, and tip—it is
necessary, that the number of sets of wagons
should be so proportioned to the length of the
lead, as to form a continuous chain of sets, going
to, and returning from the tip, at certain exact
intervals of time; which intervals are to be deter-
mined by the period required to empty a single set
over the head of the embankment. With respect
to the second point, we have shown, first—that the
number of wagons that can be filled in a cutting,
has no effect whatever, on the progress of the
work; and secondly—that the carrying out of the
opinion, in practice, produces a most injurious
effect; for it confines the limits of the tip, which if
possible ought to be extended ; and is evidently
adopted without any reference whatsoever to the
form or dimensions of the embankments, upon
which, the results of the investigations demonstrate,
that the rapidity of progress must entirely depend.
82 INQUIRY INTO THE
The previous portion of the inquiry also satisfac-
torily illustrates, the hitherto undefinable causes,
which produce the anomalies that so frequently
occur in the progress of cuttings and embank-
ments upon railways; conducted oftentimes by
the same individual, and upon principles of ar-
rangement exactly identical.
Thus, it often occurs, that two embankments
are to be formed immediately contiguous to each
other, out of the same material; nay, out of the
same cutting:—one of them, for instance, may be
twenty feet in height, with slopes of three to one;
the other only fifteen feet in height, and having
slopes of two to one. Under these circumstances,
according to the generally received notions respect-
ing earthwork, the engineer or contractor, would
without hesitation believe, and act upon the be-
lief, that the progress in both would be the same;
especially if both were supplied with material out
of the same cutting. When the works are to be
let, and if the contractors who take them are not
in partnership, it is ten to one, but the engineer
stipulates for—and the contractors bind themselves
to—an equal rate of progress in both cases. The
works subsequently commence—the arrangements
made by each contractor are similar—and we
will suppose, the best which obtain amongst prac-
tical men; but it is found out too late—perhaps
to the utter discomfiture of the engineer's precon-
certed arrangements—and in nine cases out of
EFFECTS OF THE LEAD. 83
ten, to the irretrievable ruin of one, and the cent-
per-centage profit of the other of the contractors—
that the formation of the larger of the two em-
bankments, progresses at the rate of 238,500
wagon-loads per annum; while the formation of
the smaller one, progresses at the rate of only
I 19,250 wagon-loads per annum;-allowing 250
working days in the year, and using the formula
given in the fifth section, of the first portion of
the inquiry.—This may be shewn as follows:—
The formula, which gives the number of wa-
gons that can be tipped over the head of any
embankment in an hour, is
a'= 1.06 (b+2 r h);
and in the larger of the two embankments sup-
posed above, it will become
a'= 1.06 (30+2×30);
Or, a: = 95.40,
the number of wagon-loads that could be tipped
per hour ; hence,
95.40 × 10=954
is the number of wagon-loads that could be
tipped during a day; and this, further multiplied
by two-hundred-and-fifty—the average number
of working-days, computed at ten hours each, in
a single year—will give
954 × 250=238,500
wagon-loads, for the greatest possible number
that can be removed from cutting to embankment
8.4 INQUIRY INTO THE
in a year; when the height of the embankment
is twenty feet, and the slope three to one.
In the case of the smaller embankment, the
formula
a'= 1.06 (b+2rh),
would become
a'-1.06 (30+15);
as the rate of slope is given at two to one; or,
a'=45 × 1.06=47.70.
This, multiplied by ten, for the same reasons
as mentioned in the calculations referring to the
larger embankment, gives
47.70 × 10=477;
and hence, multiplying by two hundred and fifty,
we have
477 × 250= | 19.250
for the greatest number of wagon-loads that could
possibly be tipped, from the smaller embankment,
in one year.
Thus then, we find, that one of the two con-
tractors, is, by a physical impossibility, prevented
from keeping pace with the other, or from ful-
filling his engagement, and the expectations of
the engineers;–what is the consequence?
This—that the opening of that portion of the
railway, comprising the smaller embankment,
—having been promised by the engineer to the
directors, to be the first portion ready, turns out
eventually to be the last :-but the consequences
do not end here ; for, the directors of the rail-
EFFECTS OF THE LEAD. 85
way, (relying upon the authority of the engineer,)
having made a similar promise to the proprietary,
a réaction takes place; the proprietors call the
directors to account;-the directors the engineer;
—and the engineer the delinquent contractor, and
“assistant,” upon whom all the “devilish enginery”
native to arbitrary power is brought to bear. The
contractor is first fined, next foreclosed,” if the
case be one of emergency; and not unfrequently
confined, into the bargain, by his creditors. As for
the unfortunate “assistant,” he is either compelled
to relinquish his office, and ephemeral authority,
to the “mens divinior” of some more fortunate
aspirant; or else he struggles on, “shorn of his
beams,” and anxiously alive to any opportunity
which may offer, in order to recover his “clouded
reputation.”
The individuals who suffer in such a case as
this, may in reality, be persons of good capa-
city, considerable energy, and in every way
meritorious of better deserts; but who, by an
unlucky fatality, were placed under the influence
of circumstances, which neither the science of a
Newton, or the practical experience of a Smeaton,
could control.
All these arbitrary measures, and others of a
* Foreclosing, means, depriving a person of his contract
before it is complete, and stopping the percentage upon any
monies due to him, for work previously done.
86 INQ UIRY INTO THE
\
similar description, which engineers have resorted
to—in many instances, with such fatal effects to the
welfare of contractors—are founded upon no just
principles of theory or practice; and the results of
our inquiry demonstrate that it is equally as absurd
to attempt pushing the progress of any earthwork,
beyond the limits within which it is confined; in
consequence of its peculiar form and dimensions,
by applying any extra force of men or horses; as
it is, to produce a more rapid moral development by
the application of brute force. And the idea, that the
irregularities we have noticed, arise from the incapa-
city, or want of energy, of the persons immediately
connected with the direction of the smaller embank-
ment, we have just proved to be utterly fallacious;
these irregularities being the effect of natural
causes, which are beyond the compass of human
control.
Engineers will at once perceive, from what we
have stated, how much the orderly progress of the
railways under their charge—the fulfilment of their
own expectations, and those of the proprietaries—
depend upon a judicious arrangement of the gene-
ral features of the embankments and cuttings, at
the commencement; and that the arrangement of
their estimates, are not, in all instances, to be pro-
portioned with regard to time, according to that
determined upon for the largest work they may
have to execute; for in many cases the formulae
EFFECT'S OF THE L E AD. 87
shew, that an embankment of comparatively
smaller dimensions, will take the same time for
completion as one of larger. In some instances,
it may take a longer time.
It is to be hoped, if a more intimate knowledge
of the principles upon which railway cuttings and
embankments ought to be conducted—which it is
the object of this treatise to supply—is once con-
firmed and acted upon ; that disappointment, un-
necessary compulsion, and the individual ruin of
contractors, will become much less frequent, than
they have been hitherto.
SECTION VII.
Determining the amount of friction incident upon
Contractors’ rails.
Having thus far conducted the reader through
that portion of the inquiry, which has reference
to the mode of arranging and directing the means
at present available in the formation of cuttings
and embankments; we will now enter upon the
only remaining subject, which appears necessary,
to render the investigation, sui generis, complete;
viz. the determination of the friction incident upon
contractors' rails, and from that, the maximum
load which a horse is capable of removing.
The power which a horse is capable of exerting
88 AM () U NT OF FRICTION
in several ways, has been already experimented
upon, and detailed in various works upon engi-
neering; but we apprehend, that in most of the
deductions upon that head, the difference between
the resistance of the surfaces upon myhich the loads
mere transported, and that upon which the tractive
power travelled, was never sufficiently taken into
consideration; or, in other words, that no dis-
tinction has been made between that portion of
the power which is expended in giving motion to
the body in which it is situated, and that portion
of it which is effective in traction merely ; which
has been determined with respect to the locomotive
engine, as the friction due to the machinery and
the load are separately laid down.
When horse power is made use of in transport-
ing materials upon common roads, the surface
upon which the horse and his load move, opposes
exactly the same amount of resistance to both ;
but when it is used as the motion power upon
canals or railways, especially in the latter, the
amount of resistance to both is materially different.
The surface upon which the load is moved upon
railways, consists of an iron bar, supported
throughout upon cross sleepers; whereas the sur-
face upon which the horse travels, is seldom, if
ever, as uniform or solid as that of the worst
parish road; therefore, it follows, as a necessary
consequence, that the horse is compelled to exert
on CONTRACTORS’ RAILS. 89
a much larger amount of power in moving him-
self, than the load, comparatively speaking.
We have therefore taken this opportunity, of
noting a singular oversight in all the deductions
hitherto made upon the power of horses, and the
application of them to practice. This oversight
consists, in never taking into consideration the va-
rious circumstances under which horse power can
be made available.
For instance, if we assume the constant for
horse power as deduced from observations made
upon it, when applied upon turnpike roads, for
calculating the effect produced by it, upon a rail-
way embankment, during its formation, the result
of such a calculation would be exceedingly er-
roneous. For, in the former, the power expended
by a horse in moving himself, is much less than
that which he exerts in the latter, because the sur-
face which he travels over is harder and more uni-
form ; while on the other hand, the surface over
which the load is drawn in the latter case, opposes
a far greater degree of rigidity than it does in the
former. Hence, it is plain, that the same horse,
in drawing any load over a turnpike road, can
apply a greater portion of his power to it, than he
can when drawing it over contractors' rails, during
the formation of a railway embankment; but ne-
vertheless, that in consequence of the amount of
friction being comparatively smaller in the latter,
G
90 A MOUNT OF FRICTION
as regards the load, he is capable of producing a
greater effect. This distinction, between the fric-
tion due to the tractive power and the load, in dif-
ferent circumstances, we must leave to philosophers
to determine. Our investigations refer only to
that practically developed upon railways.
The mode in which a horse plies himself, in
drawing earth wagons from cutting to embank-
ment, is altogether peculiar; he makes use of his
own weight, in addition to his muscular power,
and lunges, as it were, or hangs against the load;
whereas, in drawing a load over a common road,
the pace at which a horse travels is considerably
faster, and his muscular energy is alone employed;
except during the time he is starting the load from
a state of rest.
Whether these remarks upon the subject in
hand, will explain satisfactorily enough to the
reader, the difference between the results of the
experiments given hereafter, and those stated by
other authors, we must leave entirely to his pri-
vate judgment; merely stating, that from our
experience in such matters, we are led to suppose,
that a horse, by making use of his own weight,
in addition to his muscular energy, is enabled to
produce a much greater effect in drawing heavy
loads at a slow pace, and upon an inferior sur-
face, than he is at a quicker pace, upon a com-
paratively good surface; notwithstanding, that he
ON CONTRACTORs' RAILS. 91
may be compelled to exert a much more consider-
able portion of power, in overcoming his own
friction, (if we may use the term). We are fur-
ther strengthened in this opinion, by the direct
method of experiment we have had recourse to.
In all investigations of this description, it will
be found, that the most correct conclusions are to
be arrived at, by making use of the data afforded
by the established practice, although they may
widely differ with theory or previous opinions.
For neither the one, or the other, can controvert
plain and palpable effects; and it is clear, that
where men's private interests are concerned, they
scarcely ever fail to find out the way of applying
the means in their power to the best advantage.
With this view, we thought fit to ascertain—first
the actual load that was attached to each horse, in
the several instances where we were able to make
satisfactory observations;–(the results of these
we have stated in the second section;)—and se-
condly, to determine the friction per ton, from
direct experiments upon loaded wagons. Then,
having multiplied the constant for the friction per
ton, found thus, into the number of tons contained
in each horse's load; we adopted the result as the
exponent of horse power, when applied in the
particular manner of drawing materials from cut-
ting to embankment upon railways. The dis-
tinction which we have noted before, has not
G 2
92 AMOUNT OF FRICTION
been attempted; for it would be out of place
here, and does not affect calculations, except when
the exponent of horse power belonging to one
mode of application, is applied to another mode,
entirely different. The value which we are about
to give, refers only to the mode of application,
from which the observations have been taken.
The general load, which each horse was found
capable of drawing over contractors' rails, has
been mentioned in wagons, in the explanatory
remarks following each table in the second section,
to which we refer the reader.
The experiments, upon the friction incident
upon contractors’ rails and earth wagons, which
we are about to detail, were made upon an in-
clined plane that was constructed by the con-
tractor, for working the second lift in the cutting
at Bredon's Norton, on the Birmingham and
Gloucester Railway. This incline afforded an
opportunity very rarely to be met with, for ob-
taining an accurate estimate of the amount of
friction per ton, from what is generally known as
the angle of friction.
In December 1839, the inclined plane which
was at first made use of, in the Bredon's Norton
cutting, was taken up, being found insufficient for
the advanced state of the work; and another of
greater inclination was substituted. The sleepers
were well packed, and the rails laid remarkably
on CoNTRACTORs' RAILs. 93
well, for a rough incline, consisting of contractors'
rails. iº
The form of the incline, or rather the longitu-
dinal section of the rails, was favourable; inas-
much, as it was not likely to give a sudden check,
or jolt to the wagons, when entering upon, and
leaving it. The longitudinal section of the plane,
if exaggerated, would present the following ap-
pearance. *.

The incline descended from the face of the cut-
ting, where the wagons were filled, towards the
head of the embankment; and the difference of
level between the top and bottom of the plane—or
between the points where the loaded wagons were
left to their own gravity, and the point where they
came to rest upon the level—was at first nine feet.
It afterwards increased to nine feet six inches.
Experiments were made, while the differences
of level were found to be the same as stated above;
and we have given the particulars of each in the
table hereinafter inserted.
The wagons which were used, were of the same
description as those generally working upon con-
tractors’ rails; and contained each 49.28 cubic
94 AMOUNT OF FRICTION
feet of clay, when filled level, and when heaped
in a conical form, they contained 65.72 cubic feet.
The material with which these wagons were filled,
consisted of blue lias shale; twenty-seven cubic
feet of which, thrown loosely together, as in the
filling of wagons, weighed on an average one
ton; so that the quantity of clay comprising each
wagon-load, was equal to 2.43 tons. Upon
taking the weight of several empty wagons, it
was found, that the average weight of a single
empty wagon, was exactly one ton; consequently,
the weight of each loaded wagon, amounted to
3.43 tons.
The number of wagons with which the experi-
ments were made, consisted in all cases of twelve;
and the formula made use of, for determining the
friction, is the same as that given in the Compte
de Pambour's treatise upon the Locomotive En-
gine, to which we refer the reader for an investi-
gation of it.
The formula is
2.
& F= P a;+a;' '
where F represents the friction due to the whole
ImaSS,
P the gross weight, and
a-Far' the ratio of the friction, or the quantity
which, multiplied into the total number of tons,
on CoNTRACTORs' RAILS. 95
contained in the wagons and their loads, gives
the gross resistance.
The following table, contains the results of
those experiments which we have selected from
several others.

EXPERIMENTS UPON THE FRICTION, DUE TO CONTRACTORS'
RAILS AND WAGONS, ON THE BREDON'S NORTON IN-
CLINED PLANE. MARCH 4, 1839.
ta º tº rº, º *
g s?: $ $3: 5 § $3 E! & .
q-. H cº.: .s a $2 gº 'º - g 8p 3 . ‘5.3 9-4 tº
S 3 || 3: ...? § 3 : . 2 ºf 3 ºf ‘g &# ‘S a;:
à || 3 ### ; ; #. § 3 E. : : 3.2 87.
§§ #3 sp ####: ºf # 2 = a §§ 3.5 REMARKS.
2. g. ; : 33 £3333 & #, 3. * ſº p ..? F;
§ 5 ##| |####| || 3: 5 ° # #3
g) g-4 $4 * > 0)
9-4 %
Theload for each
horse, consisted
of two wagons.
1 792 9.00 12 92198.40 || 88 25.45
of 1,50 wagons.
Theload for each
horse, consisted
of two wagons.
3 || 792 9.50 12 92198.40 83.37 26.86
The load for each
horse, consisted
of 1.50 wagons.
4 || 561 9.00 12 92198.40) 62.33 35.54
l Theload for each
2 660 9.20 12 92198.40 71.75 31.22 {; consisted
The weather, at the time we undertook the first
and third experiments, was fine during several
days previous; and the rails, particularly at the
time the first was made, were in good order.
At the time the second experiment was made,
the rails were moist and dirty ;-or what the
96 AMOUNT OF FRICTION
workmen term, greasy—the surface of the rails
being covered with particles of wet clay, in con-
sequence of a large quantity of rain having fallen
during the previous days; although the weather
was tolerably fine while the experiments were
being made.
The weather was exceedingly wet at the time
the fourth experiment was made, and the stratum
under the sleepers consisted of a perfect puddle;
so much so, that the surfaces of the rails were
coated with an eighth of an inch of Saturated
clay. The friction was so great, when this, and
the second experiment were made, that it required
two horses to draw every three wagons, after de-
scending the plane.
Now in order to show the manner, in which
the formula we have adopted, has been applied;
we have given, as follows, the calculation of the
amount of friction per ton; having assumed the
data, afforded by the first experiment in the
table.
Upon an inspection of the first experiment
mentioned in the table, we find that twelve loaded
wagons, when left to their own gravity at the top
of the incline, ran forward seven hundred and
ninety-two feet, or twelve chains, from the point
where they were first set in motion, until they
came to rest; and that the difference of level be-
ON CONTRACTORS’ RAILS. 97
tween the starting and resting points, was nine
feet. Hence, applying the formula,
2.
– P wº-Faº’
we find,
P=41.16 tons, or
P=9219840lbs. ;
and, 2=9 feet;
also, ac-Ha!-792 feet.
Hence,
— — —”--- -
a-Ha' T. 792 T 88°
the ratio of the friction; and therefore, substi-
tuting these values in the original formula, we
have
I
F= 92198.40 5
X as
Ol' E=1047.70 lbs.,
the gross resistance due to the friction. Hence,
1947.79–25.45lbs.
41.16
is the amount of friction per ton upon the gross
load.
In this manner the value of F has been calcu-
lated in the preceding table, and placed opposite
each experiment.
Several other experiments were made, besides
those given in the table; but they always varied
in result between the first and fourth ;-the ave-
98 AMOUNT OF FRICTION
rage, however, agreeing more nearly with the
first. From the results of the four experiments
detailed in the table, we would prefer adopting
those afforded by the first; viz. 25.45lbs. perton,
as the average amount of friction upon contractors’
rails, during fine weather; and 31.22lbs. per ton,
as the average amount during wet weather, or
when the rails are in bad order for working over.
Our reason for this preference, is, that contrac-
tors' rails are generally fixed very loosely, when
compared with a perfect railway, and are not
adapted for a greater speed than the ordinary rate
which a horse performs in walking ; so that when
wagons are allowed to run down an inclined
plane, constructed with these rails, and in the
usual manner, a considerable jolting and swerving
takes place; resulting jointly, from the inequality
of the levels, and the crookedness of the roads.
On the other hand, when the wagons are drawn
on these rails, at the ordinary rate at which horses
travel—viz. 2.40 miles per hour—and on a level,
the swerving and jolting ceases altogether; and
consequently, the amount of friction is lessened
beyond the amounts mentioned in the table, pro-
vided the roads are laid tolerably level, and the
junctions of the rails are even.
However, when the horses are worked at a
smart trot, the results in the table will apply
exactly, according to the different states of the
ON CONTRACTORs' RAILs. 99
weather; but in consequence of the reasons
stated above—when the ordinary pace is adhered
to—we would recommend the two lowest results;
(for they were obtained when the rails were in
good order, and under circumstances in which
the results were least likely to be affected by the
jolting ;) viz. 25.45lbs. per ton, in fine weather,
and 31.221bs. per ton, when the weather is unſa-
vourable.
Now, comparing the results given in the table
for the value of F, with the values ascribed to it
generally, with reference to a perfect railway; and
also comparing the number of wagons which a
horse is able to draw generally on contractors'
rails, (which consist of two,) with the number
which he is able to draw over a perfect railway,
(which, according to the experiments made upon
the Great Western Railway, we find to be four;)
an estimate of the power which a single horse is ca-
pable of exerting, when employed in the removal
of soil, from cutting to embankment, can be arrived
at—sufficiently accurate, we hope, for our present
purpose; and also an estimate of the number of
wagons of which a fair load for a horse ought to
consist; and finally, the number of horses required
to execute any earthwork, where the length of the
lead is given.
It will be seen, upon reference to the explanatory
remarks under the first table, given in the second
100 AMOUNT OF FRICTION
section, that each of the wagons which were work-
ing upon the Great Western Railway, when the
observations were made, contained eighty-one cubic
feet of gravel—that each empty wagon weighed
1.30 tons—and that one horse drew four of them
up an ascent of four feet, six inches, per mile.
Now, as twenty-three-and-a-half cubic feet of
gravel weigh one ton, and each wagon contained
81 cubic feet, when heaped, (as they were when
the observations were taken,) we have,
81
23.5
tons, for the load of each wagon ; and, adding
1.30 tons, for the weight of the wagon itself, we
have,
= 3.44
3.44-H 1.30=4.47
tons, for the gross weight of one loaded wagon;
hence,
4.47 × 4= 18.96,
say, nineteen—tons was the total weight drawn
by a single horse : therefore, assuming eight
pounds per ton, as the average amount of friction
I
upon a perfect railway, and Hää of the gross
weight, as the quantity due to the resistance of
gravity, upon a gradient rising four feet six inches
per mile ; we shall have
19x8–H36.27 – 188.271bs,
for the power exerted by a singlehorse; or the maxi-
on CoNTRACTORS’ RAILS. 101
mum force which an ordinary horse can apply, in
the usual manner observed upon railways; for four
hours a day upon a permanent road, when the
speed averages at 2.40 miles per hour, without
being over-worked.
This result agrees closely with the estimate of a
horse's power, given in the appendix to Fredgold's
treatise upon cast iron; for, upon reference to that
work, we find, that he estimates it at 187.50lbs.; so
that the difference between the two, amounts only
to .77|bs.
If we return to the experiments made upon the
Bredon's Norton Contract, on contractors' rails;
we shall find, that each wagon contained 65.72
cubic feet of blue lias clay, weighing 2.43 tons,
and that the gross weight of one loaded wagon
amounted to 3.43 tons; also, that one horse drew
two of them on a level for four hours” a day—alter-
mately loaded and empty, (when the weather was
fine) at the rate of 2.40 miles per hour. Hence,
3.43 × 2–6.86 tons,
was the load drawn at each trip, from cutting to
embankment, by each horse; consequently, taking
the friction per ton, in fine weather, upon con-
tractors' rails, at 25.45lbs; we have
25.45× 6.86= 174.68lbs,
for the effective power which each horse exerted.
* This load was drawn by each horse for four hours a day
only, as in the arrangement of the work, loaded and empty
wagons were drawn alternately.
102 A MOUNT OF FRI ("I'ION
When the weather was unfavourable, we find,
upon reference to the table, that the amount of
friction per ton, was 31.221bs.; and consequently,
we have
31.22 X 5.14= 160.47]bs.,
for the value of the power which each horse ex-
erted during four hours each day.
The results of these experiments show, very
clearly, that the oversight which we have noted,
when remarking upon the usual calculations
referring to horse power, does not exist merely
in abstract reasoning, but is fully confirmed by
practical facts ; for we see, that upon a perfect
railway, a horse is capable of exerting an effective
tractive power of 188.271bs.; whereas, upon a
temporary road, consisting of contractors' rails,
laid in the usual manner upon cross sleepers, he
can only exert an effective tractive power,
amounting to 174.68lbs.; and moreover, that upon
the same identical road, when the weather chances
to be wet, he is capable of applying only an
effective tractive power of 160.47lbs.
These differences in the results of experiments,
submitted to a similar method of calculation, and
similarly conducted, are at once sufficient to arrest
the attention of the scientific and practical man ;
and will enable him to detect, at a glance, that the
conventional assumption of 150 lbs., as the aver-
age of effective horse power, is, altogether, an in-
on CONTRACTORS’ RAILs. 103
correct datum for founding general calculations
upon; especially when referring to railways.
They prove, in fact, that for every particular case
in which any power is made available, a definite
distinction ought to be made, in calculations, be-
tween that portion of the power which is expended
in giving motion to the body, in which it is situ-
ated, and that portion of the power which may
be counted effective in the traction of the load,
merely. To obtain such a distinction, it is also
obvious, that separate experiments are necessary,
for every several mode in which the power is
brought to bear.
For instance, in the three experiments which
we have referred to, and from the previous cal-
culations, we find, that
188.27–174.68– 13.59 lbs.
was the value of the extra amount of power
which each horse applied, in moving himself,
when drawing upon contractors' rails during fine
weather, beyond that which it would be necessary
for him to exert upon a perfect railway ; and
again, that
174.68—160.47 = 14.21 lbs.
was the extra amount of power expended
by a single horse in giving motion to him-
selſ, when the weather was wet, beyond that
which he was compelled to exert during fine wea-
ther, upon the same temporary road—the rate of
10 ! AMOUNT OF FRICTION
speed amounting to 2.40 miles per hour, and the
surface worked over being level.
Now, as a perfect railway offers the least possi-
ble resistance of any other surface which we know
of, both to the body in which the tractive power
is situated, and the load it draws; we have as-
sumed the value of the horse power deduced from
it, as the greatest possible which can be effectually
applied under any circumstances, when the horses
work day after day. Hence, taking 188.27 lbs.,
as the maximum effective value of the force that
can be rendered available in traction; we will pro-
ceed to determine the effective power, which a
horse can exert upon contractors' roads, when
worked for eight hours consecutively, at the rate
of 2.40 miles per hour.
First, then, with respect to a perfect railway we
find, that the maximum force of traction exerted
by each horse, amounted to 188.27 lbs; but that
this effort did not continue for more than four
hours, the remainder of the time being spent in
returning with the empty wagons, from the point
where they were tipped, to that where they were
filled.
Hence, having 188.27 lbs., for the value of the
power which a horse exerted, during four hours;
it remains only to find the power which he exert-
ed, in drawing the empty wagons during the re-
maining time; and the mean of the two, will
on contRACTORs' RAILS. 105
give the value of the power, which a horse in si-
milar circumstances can exert constantly; when
worked eight hours a day consecutively, at the
rate of 2.40 miles per hour.
Now we see, upon reference to the first table, in
the second section, that four wagons were affixed
to each horse, and that each wagon weighed 1.30
tons; therefore, the total weight which each horse
drew, during half the time he was in motion,”
amounted to
1.30 × 4=5.20 tons;
and the friction to be overcome in drawing this
load, down a gradent of four feet six inches per
mile, must have been equal to
5.20
5.20x8–Hºa–31.67 lbs.;
the value of the effective force, which the horse
exerted during four out of the eight hours, he was
at work.
Taking the mean of these results, we have
109.97 lbs., for the value of the power exerted
during eight hours, at the rate of 2.40 miles per
hour; which shows, that a horse upon such a sur-
face, can remove 263.61 tons, one mile a day, or
13.73 tons, 19.20 miles a day, when he draws the
same load constantly; but in the particular instance
* The reader should bear in mind, that during half the time a
horse is at work upon Railways, he is employed in drawing
back the empty wagons, from the tip, to the face of the cutting.
H
I ()6 AMOUNT OF FRICTION
of a railway this is impossible; because, from the
necessary order of the works, the same horse is
employed, alternately, in drawing loaded and empty
wagons: consequently, as we perceive upon re-
ference to the third section, that 6.91 trips were
made by each horse, upon a length of three quar-
ters of a mile, with a quantity of material weigh-
ing 18.96 tons; (5.20 tons of which are due to the
weight of the empty wagons) we have
13.76 × 6.91 = 95.08 tons,
for the neight of material which each horse removed
from cutting, to an embankment, three quarters of
a mile distant, in eight hours; which is equal to
71.37 tons of material, moved one mile per day;
and this is the maximum practical effect, that a
single horse can perform upon a perfect railway,
when worked in the particular manner we have
referred to.
By a similar process, we can determine the
actual, and efficient power, (practically speaking),
which a horse can exert upon contractors' rails dur-
ing fine weather; for assuming 188.27 lbs., as
the maximum power which he can apply during
four hours, at 2.40 miles per hour; we find that
upon a temporary road, only 174.68 lbs. of it can
be rendered available for drawing the load, the
remaining 13.59 lbs. being expended in overcom-
ing his own friction—and moreover, that this
power was applied only for four hours; conse-
on contRACTORs' RAILS. 107
'quently, if we take the mean between this, and
the power which he applied in drawing the empty
wagons, during the remainder of the time; we
shall have the value of the power expended, when
we suppose the horse to draw the same load con-
stantly, for eight hours a day, at the rate of 2.40
miles per hour. Therefore, as each horse, when the
weather was fine, drew two wagons, which, when
empty, weighed one ton each, we have
2× 25.45=50.90 lbs.,
for the value of the power he exerted, during four
out of the eight hours; hence, the average power
which he exerted for eight hours consecutively,
amounted to 112.79 lbs. This would be equal
to an effect of 84.67 tons, removed one mile a
day, or 4.41 tons removed 19.20 miles a day, if
the horse drew the same load constantly, upon a
temporary road; but the practical effect produced,
in removing material from cutting to embankment,
would be quite different; for, upon reference to
the third section, we perceive, that 8.70 trips
were made by each horse, over a lead half a mile
in length, and with a load weighing 4.86 tons.”
Hence,
4.86 × 8.70=42.28 tons,
* The actual load drawn by each horse, at each trip, was
6.86 tons; the weight of two wagons and their loads—but as
the wagons weighed two tons, the quantity of material re-
moved by a single horse, from cutting to embankment, at
each trip, amounted only to 4.86 tons; as we have stated above.
H 2
108 AMOUNT OF FRICTION
was the quantity of material removed from cutting
to embankment during eight hours, when the
length of the lead was half a mile; which is equal to
21.14 tons, removed one mile a day, by each horse.
Again, when the weather was wet, we have
seen, that 160.47 lbs. was the value of the power
which each horse was capable of exerting; there-
fore, as this force was exerted for four hours only
out of the eight, which were worked; and as every
empty wagon weighed one ton, and three were
attached to two horses; we shall have
1.5 × 1 = 1.5 tons,
for the weight, which each horse drew during the
remainder of the time; and
1.5 × 31.22=46.83 lbs.,
for the value of the effective power. The mean of
these, gives 103.65 lbs., for the average power of
each horse; which would produce an effect, equal to
63.74 tons of material removed one mile a day,
or 3.32 tons removed 19.20 miles per day, when
the horse is supposed to draw the same load con-
stantly. In the formation of a railway embank-
ment, during wet weather, the practical effect pro-
duced by a single horse, however, would amount
only to 31.66 tons of material, removed from
cutting to embankment, over a lead of half a mile
long ; or 15.83 tons, removed a distance of one
mile.*
* This may be proved, by the same reasoning as that in the
on contRACTORS’ RAILS. 109
The slightest consideration, on the part of the
reader, will show him, that the discrepancy be-
tween the quantity of material which ought to be
removed—judging from the ponyer which the horse
eacerts—and that which he actually removes; arises
from a portion of time and power being non-effect-
ive, while he is drawing empty wagons: and the
quantity of both last, while the horses are being
attached, and detached from their loads.
These calculations show, that the effective force
exerted by each horse, in traction upon a perma-
nent road—when the wagons are moved forwards
and backwards, loaded and empty, alternately—
amounts to 109.97 lbs., if worked at the rate of
2.40 miles per hour. This is equal to an effect
of 263.61 tons, removed one mile per day. They
also show, that the effective power applied in trac-
tion, by a horse on a temporary road, under the
same circumstances, in fine weather, amounts to
112.79 lbs.;* which is equal to an effect (allowing
25.45 lbs. per ton for the friction,) of 84.67 tons
preceding page; relative to the practical effect produced, when
the weather was favourable for working.
* It is singular, that the value of the power, should become
less upon a permanent road, than on a temporary one. But,
perhaps, in calculating the former, no deduction ought to be
made for the effect of gravity, upon so slight an incline as
1 for it is likely, that no effectual assistance was af.
1173.3’ forded by it to the horses; although theory alone
would lead us to suppose there was.
I 10 AMOUNT OF FRICTION
removed one mile a day; but that the practical
results amount (from the peculiar manner in which
horses are worked upon a railway,) only to 71.31
tons, moved one mile a day, in the former instance,
and 21.14 tons in the latter.
The last may be taken as the average practical
effect, produced by a single horse, per diem, on
temporary roads; as contractors seldom work
during wet weather, except in cases of extreme
emergency; and therefore, we have passed over
the calculations made for wet weather.
From the experiments detailed in the previous
part of this section, and the calculations founded
upon them, we have been enabled to calculate the
load proper for each horse, when employed in re-
moving materials, from cutting to embankment,
upon railways; according with the different kinds
of weather during which the experiments were
made: and the method of calculation we have
adopted, is as follows.
Let P, represent the power of a horse—F, the
friction per ton, upon the load which he draws—
and W, the weight of a loaded wagon in tons;
then it follows, that
P
FX W
is the load proper for each horse, expressed in
wagons; and this value of X has been given in the
following table.
=X
on CONTRACTORS’ RAILS.
III

TABLE, GIVING THE LOAD PROPER FOR A SINGLE HORSE,
EXPRESSED IN WAGONS, ACCORDING TO THE STATE OF
THE WEATHER.
Value of Value of Value of Value of State
JF in W in P in P Value | of the REMAwks.
lbs. tons. lbs. FX W. of 2% weather.
188.27 * * *
25.45 3.43 |188.27|25.45×3.43 2.09 || Fine, {*...* *
188.27
| 31.22 || 3.43 |188.27|31.22x3.43 | 1.75 | Fine. {*...*
188.27 & g
26.86 3.43 |188.27|26.06x3.43 2.04 || Fine. {*.
188.27
35.54|| 3,43 |188.27|35.54×3.43 | 1.54|| Wet. |{ºn
In the above table, the weight of each wagon
is taken at 3.43 tons, when loaded; but if wagons,
capable of containing a greater quantity of mate-
rial than those commonly used by contractors,
are at work, the results can be easily arrived at, in
a similar manner to that shown by the formulae
we have previously given, when once the friction
due to them is determined ; which latter will evi-
dently vary, according to the construction and
dimensions of the wheels upon which they are
Supported.
\
I 12 SUMMAR Y GF THE
SECTION VIII.
Containing a summary of the principal formulae
and facts, connected with the removal of mate-
rial by nagons and horse ponyer—as collected
from the foregoing sections—together mith the
conclusion of the inquiry into that department.
Having now investigated every circumstance,
which can affect the formation of cuttings and
embankments upon railways; we will make a
summary of the principal formulae contained in
the previous pages, according to the Order in
which they present themselves, previous to closing
this inquiry; and also some observations, explana-
tory of each, should such appear necessary; to-
gether with a table, showing the number of men,
horses, and wagons, required in different kinds of
weather, and on different lengths of lead, when
the breadth of the head of the embankment af-
fords room, sufficient to allow of six shunt roads
being placed upon it.
1. Upon referring back, we find, that the first for-
mula arrived at was one of a general nature, for
finding the total number of wagons-full that could
be tipped, in a given time, when the length of the
lead and the number of wagons working, are given,
if the breadth of the head of the embankment is
comparatively unlimited; or not narroner, than will
FOREGOING SECTIONS. I 13
allow of such a number of shunt roads being
fixed upon it, as will enable the men stationed
there to tip a set of wagons in the same time, as
the men in the cutting can fill a set, consisting of
the same number.
This formula is
—F Ø
! 5
where N represents the number of wagons work-
ing, t the time in minutes worked, and l the time
which elapses while one set of wagons is being
filled, removed, tipped, and brought back, upon
any length of lead.
This formula is applicable to any mode of
transporting materials on a railway, or elsewhere;
and the only difficulty in rendering it applicable
in any particular case, will be found in determining
a correct value for the denominator (l). This value
will, of course, vary according to the method of
arrangement adopted, and the friction. The
latter must be found by direct experiment, where
it has not been given before; and the formula,
—when referred to the method of arrangement
generally followed in the execution of earthwork
upon railways—becomes, upon reduction,
N t = @
.7235L-E26.06 T’’
where L represents the length of the lead in
chains, and a the number of wagons-full tipped
114 SUMMARY OF THE
over the head of the embankment, in a given time
—denoted by t.
We will give the following instance of its ap-
plication in railway practice.
Suppose a contractor was about to engage to
remove from cutting to a spoil bank (when the
breadth of tip is unconfined) fifty thousand cubic
yards of earth—the length of the lead being half
a mile—and that he wished to calculate the num-
ber of yards he could transport per diem, by
means of fifty wagons, working for ten hours
each day; in order that he might regulate his en-
gagement as to progress, and estimate the proba-
ble expense per yard. By reducing the above
formula, or substituting the constants we have
given, he would have
50 × 660 e
(.7335×40) E33,067"
and upon reduction, the value of a will be found
equal to 600; therefore, if we assume the contents
of each loaded wagons to amount to two-and-a-
half cubic yards, the total number of yards re-
moved in one day would amount to 1500.
Hence,
50.000
#––88;
would be the number of days norked, in which
he could remove the whole quantity.
Having once found the number of working
FOREGOING SECTION. II 5
days, he can easily arrive at the net cost per yard,
by inquiring the average price of labour in the
neighbourhood of the work. If the average
amount of a labourer's wages was three shillings
a day, and the cost of keeping the horses five
shillings per day—materials being at the present
market price—then the cost of the above work
would average at ninepence per cubic yard;
(making allowance for the probable number of
days that will turn out wet, in the ratio of one-
sixth of the time worked, and for contingencies,
&c.)—so that the contractor would be amply re-
munerated for risk and trouble, if he undertook to
perform the work, at the rate of elevenpence per
cubic yard.
2. The next formula which presents itself, is
one of the same nature, but having reference to
variable leads only; and is
2 N #
(a+l)
for general application.
Here, a, represents the time required for loading,
removing, tipping, and returning, with any set of
wagons, upon the shortest lead; and l, the time re-
Eð,
Quired for performing the same operations, upon
the longest of the variable leads.
This formula will be found useful in all cases,
where the lengths of the leads vary, such as in the
trimming of slopes, &c.; but as the same remarks
1 16 SUMMARY OF THE
and illustrations apply to this, as to the preceding
formula, we will pass on to the next: this deter-
mines the limit to which the tipping of wagons is
restricted, when the breadth of the head of the
embankment is limited to a certain number of
feet; or rather, when the breadth of it renders it ne-
cessary to confine the number of wagons in each
set, beyond that which otherwise might be ad-
vantageously worked in the cutting.
3. This formula is
8.48 R=a';
a' being the greatest number of wagons that can
be possibly tipped in an hour, off a given number
of shunt roads, represented by R.; and 8.48 being
the number of minutes required for tipping a sin-
gle wagon off a single shunt road.
This formula affords no particular grounds for
remark.
4. The formula, expressing the number of shunt
roads, which can be fixed upon the head of an
embankment, when the height and rate of slope
to which it is to be dressed off, are given, be-
comes—for a embankment having two to one
slopes—
30+h.
8 5
—for one with slopes of three to one,—
R_*.
R=
For EGOING SECTIONs. I 17
—for one with four to one slopes,
_30+5h.
– sº-
R
—or generally,–
R_(b+2rh).
S
R, representing the number of shunt roads; b, the
breadth of the embankment; r, the ratio between
the bases of a slope of one-and-a-half to one, and
that to which the embankment is to be finally
dressed off; and h, to the height of the embankment.
This formula proves, that the greater the height of
the embankment, and the flatter the inclination of
its sides, the greater will be the number of shunt
roads that can be fixed upon it. This, with regard
to the time in which an earthwork can be completed,
is exceedingly favourable; because it shows that
the magnitude of the work is compensated for, in
most instances, by the greater facility of tipping;
or, in other words, that the larger the embankment,
the greater will be the amount of material removed
from cutting to embankment, in a given time;
and also, in the formation of small embankments,
although they require a lesser quantity of mate-
rial in formation, yet that, upon the whole, they
cannot be finished in much less time than large
OIléS.
5. The next formula, determining the greatest
number of wagons that can be tipped, in a given
1 18 SUMMARY OF THE
time, during the formation of a railway embank-
ment, is one of universal application; for it em-
braces every ascribable breadth of tip, when once
the ratio of the inclinations of the sides of the
embankment is known.
The formula is
a'= 1.06 (b+2rh);
where b and h, represent the final breadth and
height of the embankment respectively; and r,
the ratio between the bases of a slope of one-
and-one-half to one, and that to which the sides
of the embankment are to be eventually formed;
ar, representing the total number of wagons that
can be tipped within an hour.
The modifications of this formula, to suit the in-
clinations given to the sides of railway embank-
ments generally, will be seen upon reference to
the investigations under that head, given in the
fifth section of the first part of the inquiry.
The last factor in this formula evidently increases
with the height, and rate of inclination, given to
the sides of the embankment.
This formula also affords a good opportunity
to the engineer, for finding, approximately, the
ratio between the cross sectional area of any em-
bankment, and the progress which may be ex-
pected in its formation; and hence, a rough esti-
mate of the cost per yard run, if required. This
FOREGOING SEC'PIONS. l 19
is so obvious, that it is unnecessary for us to enter
upon it.
The preceding formulae comprise every point
necessary for calculating the results, which a given
force of men and horses is capable of producing,
in the execution of cuttings and embankments
upon railways, as they are universally applied in
the present day; but the remaining formulae will,
we trust, convince the practical reader, that two
very important and valuable modifications may
be made in the present system, tending towards
the attainment both of expedition and economy.
These modifications consist, in arranging the num-
ber of sets of wagons, and the number of nagons
in each set, in proportion to the available breadth
of the tip, and the length of the lead.
The formula, developing the necessity of keeping
up a certain proportion between the length of the
lead and the number of sets of wagons, is that with
which the investigation contained in the second
part of the inquiry commences; and the result
shows, that at certain lengths of the lead, on all
works, a double set of wagons is required; in
order to ensure a constant supply at the face of
the cutting, and the head of the embankment, and
thereby prevent any waste of time in carrying on
the works. The latter is of constant occurrence, and
altogether unavoidable, in the present system of
arrangement; where three sets, at most, are made
120 SUMMARY OF THE
to answer for every variety in the lengths of the
lead.
\
The formula we refer to, is generally
2 L A//
— `--2=777":
where L, represents the length of the lead; and
n", the number of sets of wagons required for
executing any work, upon a lead answering to the
quantity denoted by L.
This formula proves, that the number of sets of
wagons, does not, in any instance, depend upon
the number that can be filled simultaneously in a
cutting; or upon the area of the face of a cutting;
but, altogether, upon the length of the lead;—and
moreover, that is quite unnecessary, and extrava-
gant, to throw out a long gullet, for the purpose
of working more than one set at a time in it.
Such has been hitherto recommended and adopted,
as a part of the arrangement, especially in shallon,
cuttings ; but, even before we commenced these
investigations, we could never discover any sound
reason for doing so. On the contrary, we always
found that the general attention being employed,
in rendering the greatest possible area of cutting
available for filling the wagons, produced an
effect quite contrary to that anticipated, both at
the face of the cutting. and at the head of the
embankment; in consequence of its being impos-
FOREGOING SECTIONS. 121
sible to tip the wagons as fast as they were filled,
which causes an irregularity and delay, in the ar-
rival of the sets at both places.
The formula which immediately succeeds the
preceding one, determines the number of wagons
that ought to comprise each set; and shows, that
this number must in all instances depend upon
the breadth of the head of the embankment. For
general use, it becomes
n=-|- × R ;
t, representing the time spent in filling a set of
wagons, of whatever number it may consist, t',
the time spent in tipping a single wagon, and R,
the number of shunt roads that can be fixed upon
the head of an embankment. The latter varies
with the height, and rate of slope, given to any
particular embankment; or—which is the same in
effect, as we have seen before—with the available
breadth of the tip ; and consequently, as t, and tº,
are constants; the value of n, or the number of
wagons in each set, must vary also, with the
available breadth which can be procured, for tip-
ping over the head of any embankment.
This proves, that the number of wagons in each
set, instead of being optional—as generally sup-
posed, upon all works—must depend altogether
upon the dimensions of the embankment; and
moreover, that in all cases, where the number of
I
122 SUMMARY OF THE
wagons in each set, requires a greater portion of
time being spent in tipping, than in filling them;
a retardation in the progress of the work, will be
the inevitable consequence in the first place; and,
in the second, that a much greater expenditure
will be incurred—beyond that which would be
necessary, if a due proportion was kept up, be-
tween the number of wagons in each set, and the
breadth of the tip ;-arising from the irregularity in
the returns of the empty sets, which causes a loss
of the men's time in the cutting.
From the manner in which contractors’ roads
are laid, the modifications shown by the first of
these two formulae, may be brought into practice,
simply by increasing the number of sidings, as the
length of the lead increases.
For, with reference to the first modification,
we have seen, that at every twenty-five chains, a
double set of wagons is required, in addition to
those previously at work; one for the up, and the
other for the down line: so that if we suppose the
length of the lead to be one hundred chains, there
must be six sets constantly in motion;–three
loaded, proceeding towards the tip, and three
empty, returning from it; besides two sets sta-
tionary—one at the tip, and another at the cutting:
moreover, that each of the sets in motion, will
follow, and pass each other at certain intervals,
equal to twenty-five chains; hence, each separate
set going to, or returning from the tip, will pass
FOREGOING SECTIONS. 123
three others going a contrary way, at distances
of twenty-five chains. Consequently, as we know
the exact points, at which the sets will pass each
other, the necessity of laying a double line of way
is easily avoided, by inserting a siding at each of
them.
The modification shown by the last formula,
can be put into practice, without rendering it ne-
cessary to make the slightest alteration in the ar-
rangement of any of the other materials, except the
wagons themselves; because all that is wanted to
be known, is the exact breadth of the embank-
ment, which can be made available for fixing
shunt roads upon.
Neither of these arrangements, which the two
latter formulae prove to be so eminently advanta-
geous, and which can be brought into practice so
easily, has ever been attempted as yet. In all the
works, which we have had an opportunity of
examining, we found that the number of sets of
wagons, and the number of wagons in each set,
were merely regulated by the number that could
be filled at a time in the cutting ; and when
filled, that each set was drawn out into a siding,
at the end of the cutting, from whence they were
removed by the horses which came up with the
empty wagons from the tip ; and that, in a similar
manner, the empty wagons were brought from
the head of the embankment to the cutting;
I 2
124 SUMMARY OF THE
whether the length of the lead was one mile or
two miles—variable, or constant. The inferiority
of such a system, when compared with that deve-
loped in the latter formulae, is self-evident. Let
us suppose an instance, where the length of the
lead is an hundred chains. Then, from what we
have seen before, all the wagons in the cutting
could be filled in nineteen minutes, and would be
drawn towards the head of the embankment; but
the set coming from the head of the embankment,
to occupy their places in the cutting, would only
have advanced about half way during that time;
consequently, the getters and fillers in the cutting
must remain idle, for a considerable time, after
the loaded set left, until the empty one arrived.
As the length of the lead increases, this evil
increases; and can in no possible way be per-
fectly avoided, except by such an arrangement of
the sets, and number of wagons in each set, as the
two latter formulae require. With respect to pro-
gress, the evil pointed out is sometimes compen-
sated for, in a great measure, by increasing the
speed of the horses, which is evidently a most ex-
pensive alternative.
From the difficulty of prosecuting works suc-
cessfully, according to the common arrangements,
arises the general disinclination, on the part of
contractors, to undertake any work with a long
lead; unless they receive a price, highly dispro-
portionate to the real difficulty of the case; if the
FOREGOING SECTIONS. 125
method of working, and the principles upon
which it depends, are duly considered. But, on
the other hand, it is evident, that the evils in the
present arrangement must remain for a consider-
able time, until persons duly qualified to conduct
these works upon scientific principles, become
numerous enough. This epoch is far distant; for
it is a labour of many years—and for which few
men are constituted—to become proficient equally
in science and practice ; and in this, as in all
cases of a similar kind, we must be prepared to
witness immense sacrifices, both of power and
money, in the attainment of the ultimate object.
The last subject which we have entered into, is
the friction due to contractors' roads, as now
generally used. In the Compte de Pambour's
treatise upon the Locomotive Engine, a full in-
vestigation has been given of the formula for
finding the value of friction, from what is gene-
rally called the angle of friction: and this we have
adopted, in the investigations under that head; so
that it is unnecessary for us to enter into a de-
monstration of it here. The formula is
F= P : ,
a +a;
P representing the gross weight descending any
plane, and riz the height descended, divided by
the distance between the points, where the load
was first left to its own gravity, at the top of the
126 SUMMARY OF THE
plane, and where it came to rest, after having des-
cended the plane. The values of 2, and a +a',
are to be given in feet.
The experiments give
* as the ratio of the
friction to the load in fine weather, and for
I
77.73
the ratio of the friction to the load in wet wea-
ther.
The great difference of these results, as com-
pared with those already given for Permanent
lines of Railway,” induced us to undertake several
sets of experiments; but none of them differed
materially from those given in the table. How-
ever, although the apparent difference in the
rigidity and evenness, of permanent and contract-
ors’ roads, would not, at first sight, lead us to
suppose, that the amount of friction upon the
latter, was nearly in the ratio of four to one to
that on the former; yet,_if we bear in mind,
that the greatest load which a single horse was
found capable of drawing conveniently, consisted
of two loaded wagons, or 6.86 tons, on con-
tractors' roads, laid level ; and, of four loaded
wagons, or 18.96 tons, on a perfect railway, up
an incline of four feet six inches per mile;—the
* It is scarcely necessary to remind the reader, that the
average amount of friction upon permanent lines of railway,
is 81bs. per ton; or # of the gross weight of the load.
9
FOREGOING SECTIONS. 127
fact of such a large amount of friction between the
two, is satisfactorily evident, from the difference
between the gross loads, which the same power
can draw upon each. Hence, for all practical
purposes, we are confident, that the values we
have determined, for the friction upon contractors'
rails, are sufficiently correct.
From the results of the observations upon the
Great Western Railway, we found that under the
circumstances, it was requisite to apply a force
of 188.271bs., to overcome the friction due to the
load, which each horse was capable of drawing,
when worked each day consecutively for eight
hours ; and we have, under the head of horse
power, stated our reasons for adopting this as the
standard estimate, of the maximum power a single
horse can exert, when employed in removing
soil from cutting to embankment, upon railways,
or any other works under similar circumstances.
This amount seems large; but when it is con-
sidered, that in the particular case of a railway,
although each horse draws nearly seven tons
from cutting to embankment; yet, he draws no
more than about two tons back, from the head of
the embankment to the cutting ;-and conse-
quently, exerts a power of 188.27 lbs., during
only one half of the time he is at work;-the ap-
parent excess, in the value of horse power, which
we have given, will vanish. At all events, our
object upon entering upon this portion of the
128 SUMMARY OF THE
inquiry, was, not to determine the power, which
is due to a horse, working with an uniform load,
for eight hours consecutively; but to determine the
maximum power which he can exert, when worked
for eight hours, day by day, and in the particular
manner, rendered necessary by the mode of forma-
tion peculiar to railways; and having determined
this, to obtain the load proper for a single horse.
The following table gives the number of sets
of wagons, the number of wagons in each set,
the total number of men, and the total number of
horses, which would be required in the formation
of an embankment, of the ordinary width at top,
twenty feet high, and with slopes of two to one;
at any length of lead, varying between 25 and
175 chains ; when the arrangements we have
pointed out, are adopted.
In the formation of this table, three men are
allowed as the full compliment for working each
wagon in the cuttings; two men are allowed for
attendance upon each set of wagons, from the
cutting to the tip, and back; and fifteen men are
allowed for attendance at the tip, keeping the
roads in repair, and turning the switches, &c.
It may be further remarked, that the full com-
pliment of horses is allowed for every set, except
the one supposed to be employed in the cutting.
The set at the head of the embankment is not
excepted; because it will give sufficient employ-
ment to its own compliment of horses, in drawing
FOREGOING SECTIONS.
129
the wagons from the siding, near the head of the
embankment, to the tip head.

TABLE, SHOWING THE QUANTITY OF LABOUR, AND MATERIALS,
REQUISITE FOR WORKING AN EMBANKMENT, 20 FEET HIGH;
witH LEADS WARYING FROM TO 1; OF A MILE, WHEN
THE SLOPES ARE TWO TO ONE.
No. of Total
No. of wagons No. of No. of N.F
Length of lead. sets of . . . men horses wagons REMARKs.
wagons. s. Tequired.required. required
5 º
# miles, or In this table, the
25 chains 4 16.82 69 25.23 67.28 calculations are made
ſº according to the for-
3. º in the 6th
5 & ection, for the num-
# miles, or ; 6 | 16.82 | 73 || 42.05100.92 sº
50 chains. answering to each
lead. The results in
15 l Wagons and horses ap-
& pear very large, when
i; miles, or 8 | 16.82 77 58.87 |134.56 compared with the
75 chains. Common system, where
only three sets are
1. il used º; every varia-
IOOllies, Ol' tion of lead. But
iod chains } 10 16.82 81 75.69 168.20 when the time lost
ſº at º trip, according
to the latter system
1% miles, or is taken into account,
16 5 * it will be found, that
125 º) 12 | 16.82 85 92.51201.84."...”
ranged as in the table,
will eventually re-
14 …; quire less expendi-
#. *} 14 | 16.82 | 89 109.33 235.48 ture, and be finished
CI18,111S, S007.67°.
NoTE.—According to the common system of arrangements,
where three sets of wagons only are used, the force required
at a lead of 1% miles, would be 89 mem, 51 working wagons,
and 34 horses; and so on, in all cases, except where a loco-
motive engine is used instead of horse power.
I 30 SUMMARY OF THE
The foregoing table, as we have previously re-
marked, is calculated for an embankment twenty
feet high, and is given as an illustration of
the principles developed in the inquiry, but
not as a table answering every variety in the
heights of embankment; for the formulae show
that in all cases, the tabular numbers will increase
or decrease, according as the number of shunt
roads, that can be fixed upon the head of the
embankment, increases or decreases. For instance,
in the case of a spoil bank, where the breadth of
the head of the embankment may be (practically
speaking) unlimited, the quantities in the table
would be also unlimited, with respect to the tip;
and would merely depend, upon the number that
could be filled in the cutting, which is the only
case, in which the general opinion—viz. that the
capacity of a cutting limits the progress of the
work—holds true. As this is the most important
peculiarity, developed in the formation of em-
bankments, we would recommend the reader to
give most minute attention to the investigation of
the formulae by which it is proved.
An estimate of the cost per yard, incurred in
excavating, and leading soil to embankment, may
be easily made, by calculating tables similar to
the last, for each particular embankment; and ap-
plying the local value of day labour, and the ex-
pense of keeping horses, to the results.
FOREGOING SECTIONS. 131
Also the exact length of lead, at which a loco-
motive engine may be more profitably employed
than horse power, can be determined in a similar
manner.”
As these estimates must entirely depend upon
the value of wages in the neighbourhood of the
works; and as the price of wages varies consider-
ably in different districts, it would be impertinent
to the nature of the treatise, to attempt entering
upon them. Our object was merely to develope
the theory and practice, upon which railway cut-
tings and embankments ought to be conducted.
SECTION IX.
Containing an investigation of the system of re-
moving soil by means of barron's, and human
labour.
Having, in the preceding pages of this work,
concluded our investigation into the laws which
govern the formation of cuttings and embank-
ments upon railways, when the means of trans-
port employed consist of wagons and horse power;
it remains to give the results of our inquiry into
* Eighteen-pence per mile is the average cost of working a
locomotive engine; so that, by comparing this, with the cost of
horse power, the distance at which it would be most advan-
tageous to employ the former, can be easily determined.
132 INVESTIGATION of
the subordinate system of removing earth, by
means of wheel-barrows and human labour.
Upon commencing a cutting, the first por-
tion of excavation is removed to embankment
by barrow work; and this system is continued
until the lead exceeds one hundred yards, or what
is generally denominated four barrow runs. When
this distance is exceeded, horse power and earth
wagons are resorted to, as being more economical,
and more easily worked in the lower gullet of the
cutting. After the cutting has been extended this
distance, and becomes deeper, that which is called
the second lift,” is commenced; and this, with all
succeeding lifts, is always worked by barrows,
upon stagest or platforms, erected for the purpose.
Wide plate 1, fig. 1, at a, b, and d. In some in-
stances, a third lift is commenced, when the cut-
ting is deep; but in all such cases, the superior
advantages and facility which the adoption of the
inclined plane affords, will, we hope, in a short
time, render such an arrangement obsolete.
Also, in the trimming off of the slopes of em-
bankments, the slipsi and irregularities are re-
moved—the parts which are found deficient, being
supplied from those which are too redundant—by
means of barrow work; and gravel, which has
been led to spoil in the first instance, is always
* Wide Appendix, Note 19. f Wide Appendix, Note 18.
f Wide Appendix, Note 20.
THE BARROWING SYSTEM. 133
removed back upon the balance line of the rail-
way, to supply ballast for the permanent way, in
a similar manner.
These effects, produced by barrow-work, although
partial in comparison to the amount of work done
on a railway, seem, nevertheless, worthy of investi-
gation; as it is desirable that no department should
be left untouched, which can affect the ultimate
object of the inquiry.
In all cases, when barrow-work is adopted, it is
necessary that the following arrangements be ad-
hered to ;-viz., three men must be placed at the
point where the barrows are filled, and one at
every twenty-five yards forwards, to the place
where the barrows are emptied. The three men,
stationed at the point where the barrows are filled,
are employed in filling each barrow as it arrives,
and wheeling it one run,” (twenty-five yards).
The man who wheels it the first run, hands it over
to a man stationed at the end of it, and receives a
returned empty barrow, with which he goes back;
and the loaded barrow, which he has exchanged
for it, is wheeled one run farther by the man he
gave it to; who—at the end of the run next to the
one on which the barrows started originally—re-
ceives also an empty one, and returns to his
former post; and so on in succession.f
* Wide Appendix, Note 22.
t If the reader refers to the third plate, and reads the
description of it given in the Appendix, he will be better able
134 INVESTIGATION OF
The length of the second lift—or the distance
between the points where the barrows are filled,
and where they are emptied into the wagons in
the lower gullet—scarcely, if ever, exceeds two
runs. It is generally equal to the length of one
run. From this arrangement, it is evident, that
there must be as many runners, minus one, (ex-
clusive of the three stationed at each of the filling
points,) and as many barrows, plus one, as there
are barrow-runs emanating consecutively from the
same point; and, that to prevent unnecessary
delay, the time spent in filling an empty barrow,
must be the same, as that required for wheeling a
loaded one the length of one run ; and that
required for returning with an empty barrow the
same distance; both taken together.
This accounts for three men being placed at the
point where each barrow is filled; as two ordinary
men, are able to fill an empty barrow, of the di-
mensions now used; while one man is wheeling
a loaded one forwards, and an empty one back-
wards, a distance of twenty-five yards, upon a
level.
Although the aggregate distance, over which
the barrows are wheeled,—or the distance between
the points, where they are filled and emptied,—be
any distance whatever, these circumstances will
remain the same ; for whether there are more, or
to comprehend what we have endeavoured to explain in the
text, with respect to the order and progression of the barrows.
THE BARROWING SYSTEM. 135
less, barrows in motion, at the same time, the
returns to the point where they are to be filled,
will be made in equal times; though not of the
same individual barrows. Moreover, it is evident,
that the quantity of earth removed in this manner,
in a given time, (which is a circumstance peculiar
to barrowing), depends, neither upon the number
of men—the number of barrows—or the number
of runs; but, solely, upon the number of stages
erected; or, in other words, upon the number of
different points at which the barrows can be filled,
and the number of separate roads* which can be
supplied from each.
In general, three roads may terminate, and be
supplied, from the same point.
In barrowing up the slopes of a cutting to
spoil, or down the slopes of an embankment, in
order to fill up deficiencies at the sides; or, in
fact, in any case, where the number of runs ex-
ceeds one; it is always necessary, to have a
square platform, 6ft. × 6ft., at the termination of
each run ; upon which the barrows going, and
returning, are exchanged, and pass each other.
Having given these preliminary illustrations of
the system, we shall now proceed, to state the
most satisfactory experiments that have been
undertaken in this department, and the deduc-
tions arrived at from them.
The following experiments, were made upon
* Wide Appendix, Note 21.
136 INVESTIGATION OF
the Great Western Railway, in the month of
July 1838; in order to obtain constants, for the
times spent in filling and wheeling a single
barrow, one run; and from these, to calculate the
average quantity of earth that could be removed
per day—according to the barrowing system; and
finally, the expense per cubic yard.
ExPERIMENT 1.
One barrow was filled, wheeled four runs,
emptied, and brought back again, to the point
where it was filled at first; in five minutes, and
thirty-five seconds.
ExPERIMENT 2.
A single barrow was filled in fifty-eight seconds,
—wheeled four runs forwards in two minutes and
thirty-two seconds,-emptied, and brought back
again to the place where it was filled, in two
minutes and a half; making a total for filling,
removing, emptying, and bringing back, of six
minutes.
ExPERIMENT 3.
One barrow was filled,—wheeled four runs,—
emptied, and brought back again, in five minutes
and forty seconds.
ExPERIMENT 4.
Three barrows were filled,—wheeled four runs,
emptied and brought back, in seven minutes and
thirty seconds; but before the third returned, the
barrow that first left the place where they were
THE BARROWING SYSTEM. 137
filled, was loaded a second time, and wheeled the
distance of two runs.
ExPERIMENT 5.
Three barrows were filled,—wheeled,—emptied,
and brought back over four runs, in seven minutes
and ten seconds, following consecutively; but, as
mentioned in the preceding experiment, the first
barrow was filled a second time, and wheeled the
two first runs, before the return of the third.
From these experiments, the two following
tables result.
Table, constructed from the results of the three
first experiments; and showing the mean time
which elapsed, while a single barrow was being
filled, removed, emptied, and brought back, over
four runs.
TABLE, SHOWING THE RESULTS OF THE THREE FIRST
EXPERIMENTS.
gº &D
... a. º. º
& rº * 33.33. ſº t to d :
.# #. ii # # | #.
8 : # £3 #####. §§§ s 3 & REMARKS.
o "E # ‘83 3 & E B 5 #5 ºn Hjá
2, #. ‘s 3 'a, 2 sº 3.c.5 .83
; ... R. Žá 3.53 Å; ă § 3 ãº:
3. # ##### ## #:
tº is š.
l I 4 100 5/.35”
These are the
results of obser-
M // f
2 1 4 100 6.00 5.45 |vations made upon
single barrows.
3 l 4 100 5'.40”


138 INVESTIGATION OF
Here we find, that five minutes and forty-five
seconds, was the mean time spent, in filling, re-
moving, emptying, and returning, with a single
barrow, a distance of one hundred yards.
There were five barrows working consecutively,
while these observations were being made.
Table, constructed from the results of the two
last experiments; and showing the time which
elapsed, while three barrows were being filled, re-
moved, emptied, and brought back, a distance of
four runs. This time includes that for filling and
wheeling the tryo first runs, the barrow which left
the filling place first; together with the filling of
the barrow which left it second.

TABLE, GIVING THE RESULTS OF THE TWO LATTER
EXPERIMENTS.
go 'd •º wº
ta 5:33: 3 tº gº? 3.3
+5 £: on tº 5:33.5 #### §º a
så | # | # ####| ###, #
§§ *::: *** #####| | ######| #### REMARKS.
2: 3 ‘5 5 .# | #####| | ######| ###
; * ; 3.3 ####| | #3; ##" | #3
ź ## #####| | ##### ###
i F #3 #F# 3 # *
|
4 3 4 100 |.. 7.30
- - 7.20%
5 3 4 100 77.10”
- 3rom. this table we perceive, that the mean
time elapsed, from the moment the men com-
THE BARROWING SYSTEM. 139
menced to fill the first of the three barrows, until
the third one returned empty, was seven minutes
and twenty seconds. But it is to be observed,
that before the third returned, the first barrow was
filled a second time, and wheeled tryo runs. Also,
that the barrow which left second, was filled a
second time, before the return of the third. There-
fore, according to the first table, as five minutes
and forty-five seconds must have elapsed, while
the first barrow of the three was being loaded,
removed, emptied, and brought back, over four
runs; and again, as, according to the second table,
the first barrow was filled, and wheeled two runs
a second time, before the third barrow was brought
back empty, at the expiration of seven minutes
and twenty seconds; we shall have,
7' 20"—5'45" = 1' 35",
for the time which elapsed, while the barrow which
first left, was being loaded and wheeled two runs a
second time; and it will be, likewise, the time which
elapsed, from when the men commenced to fill the
first barron, until they commenced to fill the third;
because the time spent in filling the third barrow,
wheeling it four leads, and back, must have been
the same, as the time spent, while similar opera-
tions were being performed with the first. There-
fore, if this portion is taken from the total time
spent, from when the filling of the first barrow
was commenced, until the return of the third one
K 2
140 INVESTIGATION OF
empty; the difference will be the time spent in
filling the first and second barrows. This difference
is 7.20"—5.45"= 1.35";
being the same as the time for filling a single bar-
row, and wheeling it two runs, or backwards and for-
wards one run, as deduced from the results of the
first table. Now, as the times required to fill two
barrows, and to fill and wheel, backwards and
forwards upon one run, a single barrow, are each
equal to 1.35"; it is clear, that if we subtract the
equal times spent in both cases, (viz. while a
barrow was being filled,) that the remaining portion
of time will be equal—or, in fact, that the times re-
quired to fill the remaining barrow in the one case,
and to wheel a barrow backwards and forwards,
on the same run, in the other case, are exactly the
same in amount.
Hence, it is evident, that the size of the barrow
must regulate the length of the runs. For the
arrangements above stated, and what we have ar-
gued from them, show that the length of each
run must be exactly such as will allow of a
barrow being wheeled over it, backwards and
forwards, in the same time as another empty
barrow of similar dimensions can be filled by two
Iſle]].
The size of the barrows at present in general
use upon railways, seems for every purpose the
most convenient; both with reference to the load
THE BARROWING SYSTEM. 141
which a man can wheel, and the length of run
which it requires; each of these barrows, when
heaped, contains about one-tenth of a cubic yard
of soil; and the above induction shows that each
can be filled in
1' 35 //
-ā-- 67”,
nearly, and wheeled backwards and forwards in the
same time, over a length of twenty-five yards.
We will now proceed to detail a set of experi-
ments, conducted in a different manner; in order
to compare their results with those just given.
The following experiments were made upon the
Birmingham and Gloucester Railway, near the
village of Bredon, where a large quantity of bal-
lasting material was “led to deposit,” + during the
formation of the Northway, and Bredon's Norton
COntractS.
ExPERIMENT 1.
Twenty-four barrows were filled, wheeled for-
wards two runs, and tipped, in thirty-eight minutes
and forty-eight seconds; which is the same in
effect, as if they were filled, wheeled forwards
* Soil is said to be “led to deposit,” when it is wheeled out
on either side of the railway, and intended for use at some
future period; in contradistinction to the term “led to spoil.”
Gravel is chiefly run out in this manner; both for the purpose
of expediting the excavation, and that it may be near at hand,
to be used as ballast for the permanent road.
142 INNESTIGATION OF
and backmards, and tipped upon one run, during
the same time.
ExPERIMENT 2.
Eighteen barrows were filled, wheeled forwards
one run, and brought back empty again, in twen-
ty-five minutes, and forty-two seconds.
ExPERIMENT 3.
Eleven barrows were filled, wheeled forward
upon two runs, and emptied, in eighteen minutes;
which is the same in effect, as if they were
filled, wheeled forwards, emptied, and brought
back, upon one run.
From the results of these experiments we can
determine constants, (as regards the time which
elapses while each barrow is being filled, wheeled
forwards, emptied, and wheeled backwards upon
one run,) equally as simple, and as correct—if not
more so—as those obtained from the experiments
previously given.
Now, referring to the first of the latter expe-
riments, we find, that twenty-four barrows were,
in effect, filled, wheeled forwards and backwards,
and emptied, upon one run, in thirty-eight mi-
nutes and forty-eight seconds. Therefore,
38.48"
24 - 137
THE BARROWING SYSTEM. 143
is the period of time which must have elapsed, on
the average, while each of the twenty-four bar-
rows were being filled, wheeled forwards and back-
wards, and emptied; when the distance to which
the soil was removed, was equal to the length of
OIle TUII).
In a similar manner, we find, from the data
afforded by the second experiment, that
29.42,
-Ts-
was the period of time spent, in filling, wheeling
forwards, emptying, and returning, with a single
barrow, over the length of one run. Also, from
the third experiment, it may be perceived, that the
time which elapsed, while each of the eleven bar-
rows was going through the processes of being
filled, removed, emptied, and wheeled back again,
Over One run, was
18'
:- = 1 .. 36” :
11 5
= 1.39"
very nearly. From these experiments, and their
results, we have been enabled to form the follow-
ing table:–
144
INVESTIGATION OF

TABLE, SHOWING THE RESULTS OF THE SECOND SET
OF EXPERIMENTS.
Distance iº
wheeled Time spent | No. of T. #.t
No. of . over, back-| infilling barrows and wheel- Remasks.
experiment. wards and and wheel- working ing one
forwards, ing. barrow
in yards. g
1 50 38/.48’’ 24 1'.37”
2 50 29'.42" 18 I’.39”
3 50 18'. 11 H'.36”
Now, upon taking the mean of the times spent,
in filling, emptying, and wheeling, one barrow
backwards and forwards, the length of one run,
as given in the last and previous tables; we shall
have a correct estimate of the time required, for
filling a single barrow, wheeling it one run,
emptying it, and returning with it, or another
empty barrow, to the filling place. Or, in fact,
an average estimate of the time elapsed, from
when the filling of a barrow commences, until
another returns empty to occupy its place; what-
ever the number of runs may be. For, as we have
shown before, the number of runs will make
no alteration in the periods of time at which the
empty barrows return ; nor in the number of
THE BARROWING SYSTEM. 145
loaded ones which can be emptied in a given
time; provided the number of barrows working,
exceed the number of runs by one; so that if there
were five runs, between the filling and tipping
points, the same number of barrowfulls could be
removed in any given time, as if there was only
one run to be wheeled over ; although the expen-
diture would be much greater, in consequence of
the greater number of materials, and quantity of
labour required in wheeling. Hence, taking the
mean of the results of both tables, we shall have
1.35"
I’.37"
1'. 39"
1'. 36."
4) 5.47"
I’.37” _*
for the mean time which elapsed, while a single
barrow can be filled,—wheeled one run, emp-
tied, and brought back; or in fact, a constant
answering to the interval of time, between the
emptying of each consecutive barrowfull, off each
separate road. Hence it is evident, that if we put
t, for the time in seconds worked,
t
97=w
will be the number of wagons that can be tipped,
off a single road, in any given time. This gives a
146 INVESTIGATION OF
result, of very nearly thirty-seven barrow-loads
per hour, for each separate road. *
Therefore, in any instance, where the number
of separate roads that can be laid, is accurately
determined, we can easily calculate the progress
in any given time, by the formula,
t
97
R representing the number of separate roads
working, and the other letters the same quantities
as before.
Here it may be observed, that the results in any
case, as regards the quantity of earth that can be
removed, by means of barrows, in a given time,
must solely depend upon the number of separate
barrow roads that can be laid in ; and, that the
distance to which the soil is to be removed,—the
number of men employed,—and the quantity of
× R =a';
* From this we can find the number of cubic yards of
material that a railway-labourer can remove in a day; for we
have seen, that two getters can supply each road; therefore,
#=18.5, is the number of barrowfuls answering to the work
of a single man per hour: and supposing, on an average, eight
hours per diem to be actually worked, we shall have 18.5 × 8
=148.0 barrowfuls, for the work performed by a single man
in a day; and allowing ten of these barrows to make up a
14 º
cubic yard, we have iſ a 14.80 cubic yards of material ex-
cavated per * by an ordinary railway labourer.
THE BARROWING SYSTEM. 147
materials required, produce no other effect upon
barrow-work, than increasing, or lessening the ex-
penditure. For although the quantity of materials
and number of men required, to remove soil over a
distance of one hundred yards, will nearly amount
to double that which would be required for a dis-
tance of fifty yards, and consequently increase the
expense, nearly two-fold ; yet, the number of
barrows that could be removed, in both instances,
in a given time, would be exactly the same; pro-
vided the number of roads worked were equal.
As we have seen before, that the barrow, now
in use upon railways, can be wheeled by one man
backwards and forwards twenty-five yards, while
two other men are excavating and filling a quan-
tity of material equal to its load; the number of
runs answering to any distance, between the
filling and emptying points, will be
# × R=r 3
L, being the length between the filling and empty-
ing points, in yards,-R, the number of roads
working-and r, the number of runs required.
From this formula, the quantity of materials
necessary for erecting the stages and roads, (such
as trussels, planks, &c.) for any length, can be
easily calculated.
Again, in order to find the number of barrows
that is required for working any number of roads—
148 INVESTIGATION OF
be their length what it may—it is only necessary
to consider, that the number of barrows required
for each road, must exceed the number of runs in
it by one ; in order to admit of one stationary
barrow being filled, while the others are in motion,
and emptying. Hence, the general expressions
for the number of barrows, will be
{#+1}x R= B.
Or, r—HR-B ;
where B, represents the number of barrows re-
quired, and the others stand for the same quan-
tities as before.
Finally, the number of men required to execute
any quantity of work, will be found by
|## 2} . R=N;
where the letters L, and R, represent the same
quantities as before, and N the number of men
required.
The first of the formulae above given, show, that
the number of separate roads working, solely affect
the number of barrows that can be emptied in a
given time; in a manner exactly similar to that,
in which the number of shunt roads, that can be
fixed upon the head of an embankment, deter-
mines the number of wagons that can be tipped ;
so that the progress in the former, as in the latter,
depends in no wise upon the distance to which
THE BARROWING SYSTEM. 149
the material (whatever it may be,) is to be re-
moved, but upon the number of roads that can be
laid down.
On the other hand, the remaining formulae
demonstrate, that the ultimate cost of removing
material, according to this system, increases pro-
portionally with the distance, over which it is to
be wheeled; for they show, that the number of
men, and the quantity of materials required, (viz.,
planks, barrows, trussels, &c.,) must be increased
after the first run, in direct proportion to the
length, between the points where the barrows are
to be filled, and where they are to be emptied.
Perhaps it may be useful to remark, that in
working the second lift of most cuttings, no more
than six barrow roads can be made available with
advantage; viz: two at the face, and two at each
side of the second lift. But when the system is
adopted, in breaking “the first ground *" in a
cutting, the number of barrowfuls that can be
removed will vary, in all cases, with the magni-
tude of the work. And also, that the quantity
removed in a given time, will be always inva-
riable in working the second lift; for the extent
of it is, practically speaking, the same, in all cut-
tings; and so with respect to the third lift; but
* By breaking the first ground, contractors, and their work-
men, mean the excavation of the first portion of a cutting, pre-
vious to entering upon it with wagons and horses.
150 INVESTIGATION OF
this, as we have mentioned before, is being gradu-
ally superseded by the adoption of the inclined
plane.
These combined results prove, that after the
distance between the points where the material is
excavated, and where it is to be deposited, exceeds
the length of four runs, (one hundred yards,) the
adoption of the barrowing system becomes more
expensive, as a means of transport, than that
afforded by the use of wagons and horse power.
In estimating the expense that would be in-
curred, in the execution of any description of
earthwork by means of barrows and human
labour, we have only to apply the price of wages
and materials, in the neighbourhood of the work,
to the results given by the three last formulae, and
to divide the quantity thus found, by that derived
from the first; and the quotient will be the cost
per barrowfull; or, as on an average, ten loads
of the description of barrow commonly used upon
railways, are contained in a cubic yard; after
multiplying the above quotient by ten, we shall
have the net cost per cubic yard. This will be
found to increase much more rapidly than might
be expected, with the distance between the points
of excavation and deposit.
In order to render this process more adapted
for practical instances, by condensing the previous
formulae, we shall give a general one, showing the
THE BARRow ING SYSTEM. 151
amount for which any work executed upon the
barrowing system, may be contracted for; as fol-
lows. If we represent by r, the wages of one
man per day, together with the per centage upon
it, and the quantity of materials required for a
single run, which the contractor may deem suffi-
cient remuneration for his risk and services; we
shall have
L L L A
=b,
Or,
hence,
l, (3L-H3):r.
T .257 t '
or otherwise,
b_11.64 (Lr--r),
t
the cost per barrow in any case.
Therefore, as ten barrows go to the cubic yard,
on an average,
(3L-H3). r = C:
.0257 t T ~ *
152 INVESTIGATION OF
or otherwise,
C–11.04 (i. r-Er),
1
the cost per cubic yard, for which the contractor
might undertake to execute the work, with rea-
sonable profit.
The results of these investigations into the sys-
tem of barrowing—the reader will observe—show
that no material improvement can be made in it;
nor indeed was it to be expected, as the system is so
simple and free from complication, or the influence
of collateral circumstances. It may be well, how-
ever, to remark, that they prove the length of each
run to be dependant upon the size of the barrows
used, and not constant, as is generally supposed.
Upon attentively considering the results, con-
tained in the two principal departments of this
inquiry, viz: the removal of earth by wagons,
and the removal of it by means of barrows;–it
will be perceived, that both systems—provided
the former is regulated in accordance with the
formulae we have given,_are exactly the same in
principle; or in fact, that the theory we have ad-
vanced with respect to the management of a work,
carried on by means of wagons and horses, has
been already brought into practice in the system
of barrowing. The arrangements in the latter,
THE BARROWING SYSTEMI. 153
being the same as those shown to be most advan-
tageous in the former; and both being evidently
the same in principle, although upon different
scales of magnitude.
It will also be seen, that the principles upon
which former authors attempted to develope the
general laws of excavation and embankment, were
evidently adopted, without any reference to the
practical working of the system ; and, that the
mode of making their observations, (whenever they
were made), was much too isolated, for the pur-
pose of affording an expanded and comprehensive
view of the various agencies—collateral and direct
—which are continually acting, one upon the
other, and by which the ultimate results are col-
lectively influenced. The error into which they
have fallen, seems to have consisted in assuming,
as their constants, quantities in the abstract; or
in observing in detail, instead of the aggregate;
and adopting the results of these separate obser-
vations, as if entirely independent one of the other:
and therefore it is not to be wondered at, that
many matters, essential to the thorough sifting of
the subject, were altogether excluded ; and that
the arguments founded upon these self-begotten
phenomena, led them to a belief, in the inverse
ratio to probability, if not of possibility itself.
Thus, the antecedents being widely unconnected,
and, from their number, subject to frequent error;
J.
I54 THE BARROWING SYSTEM.
the consequents derived from their combination,
turned out utterly fallacious. The method we
have pursued is exactly the reverse: our constants
depend upon observations, made upon the com-
bined effects, produced by the various agencies
in the aggregate; and, by an analysis of these, we
have descended, step by step, to the details; and
not advanced, from the minutiae of detail to ab-
stract generalities, which have no foundation in
truth.
A P P E N D H X.
NoTE 1.
Wagons:—There are various kinds of wagons used upon
Railways, differing both in form and dimensions; but the
best adapted for general purposes, is that delineated in plate
2, fig. 1, which contains, when heaped in a comical form,
3.12 cubic yards. The side-tipping wagon is also of great
use; but the only difference in the construction of the two is,
that the latter extends over the frame, more on one side, than
the other, in order to facilitate the tipping. The former are
always used in front of the tip, as at l, in fig. 1, plate 1;
while the latter are emptied over the sides, to fill up any
slips, or deficiencies that may occur; as represented in figures
5 and 6, plate 1.
The principal object to be attained, in the construction of
earth wagons, is a convenient height. Some are so high
above the rails, that a much greater exertion is required in
filling them, than if they. were lower; but on the other hand,
there is a certain point, beyond which, the height camot be
decreased, without encountering a greater evil, in the diffi-
culty which will be experienced in tipping; especially, when
I, 2
156 APPENDIX.
the material with which they are loaded, is of a loamy and
adhesive nature. The diameter of the wheels should in no
case, be less than two feet six inches; and wheels three feet in
diameter are decidedly to be preferred, if every circumstance
is considered; both with respect to the most convenient
height of the wagons, and the facility with which they can
be drawn by the horses. Oftentimes, when the length of the
lead renders it more economical to work a locomotive engine,
much inconvenience—besides an enormous increase in the
amount of wear and tear—arises from the diameters of the
wheels being too small.
NOTE 2.
Tºpping wagons:—A term used by the workmen, synonymous
with emptying wagons over an embankment. This is dome in
two ways: one, by running each wagon at a smart pace—
say six miles an hour—towards the head of the embankment,
and detaching the horse when within about twenty yards of
it; when the wagon is precipitated, by the velocity it has ac-
quired, against a strong piece of wood, (generally beech or
elm,) 5 feet 6 in. × 9 in. × 12 in., which is fixed on the end
of the embankment. The concussion which the wagon re-
ceives, capsizes the body with its load; as represented in
plate 1, fig. 1, at l. The other method is by simply raising
the body of the wagon off the hinder axle, as shown in plate
1, figs. 4, 5, and 6. This latter method is, however, nearly
obsolete, except where side tipping is carried on. One of the
most important desiderata in the arrangement of a work, is a
good supply of active and intrepid men for attendanee upon
the tip; as upon the efficiency with which that is managed,
will, in a great measure, depend the economy and progress of
the other departments.
APPENDIX. 157
NOTE 3.
Getters and Fillers:—The getters in a cutting, are the men
who use the pickaxe, or loosen the material; so as to render it
smaller, that the fillers may cast it into the empty wagons.
One getter, is generally able to supply two fillers, and one
wagon.
NOTE 4.
Tºp:-This term, as used by the workmen, is synonymous
with the head of the embankment, or place where the wagons
are emptied.
NoTE 5.
Lead:—The distance, between the head of an embank-
ment, and the face of a cutting: which varies of course in
every case, as the work advances.
NOTE 6.
Side tipping:—A term used, when the wagons are emptied
over the sides of an embankment, in contradistinction to
front tipping. See plate l; where front tipping, or tipping
over the head of an embankment, is shown, at l, in fig l;
and in fig 4: and side tipping in figs. 5 and 6.
NOTE 7.
Dressing off slopes:–When an embankment, or cutting, is
first run out, the inclinations given to the sides, are generally
left in a rough state; or at such a rate of inclimation, as the
material will stand at; so that, upon forming the body of the
work, it becomes necessary to fill in, and take off, at several
points along the sides, to give them a uniform appearance.
This operation is called trimming, or dressing off, slopes.
158 A PPE NIDIY.
NOTE 8.
Sets of wagons:—A set of wagons, denominates any num-
ber of wagons which are filled, removed, and emptied
together; and the number of sets, always depends upon the
length of the lead, if the proper system of arrangement is
adhered to; but it generally consists only of three.
^
NOTE 9.
Battery head:—A term sometimes used, especially in the
north, for “tip,” or “head,” of an embankment.
NOTE 10.
Temporary, or contractor's road:—These roads consist,
generally, of fifteen feet iron bars, T shaped, and weighing
on an average 35 lbs. per yard run; which are fixed upon cross
sleepers, 9 in. x 5 in., with double chairs at the end of each
rail, and a half chair at each intermediate sleeper. The form
of the rails, and plan of this description of road, are given in
plate 2; where fig. 5 represents the section of the rail, and
fig. 4 the plan of the road when laid. The dimensions of the
rail, generally used by railway contractors, seem too small; as
a considerable portion of power is wasted in drawing over
them, which might be saved, if rails weighing 40 lbs. to the
yard, were used instead. However, on long embankments,
when it becomes necessary to work a locomotive engine, it is
absolutely necessary, that rails of much greater weight than
those in general use, should be procured.
NOTE 11.
Stocking Earth.-A term used by the workmen, to denote
a mode of excavation, similar to undermining. For instance,
when the soil to be excavated is very stiff, the getters perfo-
rate underneath, until the superincumbent weight falls by its
APPENDIX. 159
own leverage; and then, if the material is very tenacious, they
break it into small lumps, in order that the fillers may be
enabled to cast it into the wagons, or barrows, with the shovel.
The perforations, or channels, made in this method of excava-
tion, are called stocking grips.
NOTE 12.
Bumpers:—The pieces of wood, which are placed on the
head of the embankment, at the termination of each sperm
road, against which the wagons are propelled, when they are to
be tipped. The cross section of a bumper may be seen at m,
Fig. 1, plate l; and a longitudinal section of it at g, Fig. 4.
NOTE: 13.
Side-Cutting:—A term used to represent excavation, be-
yond the boundary line of the railway. This is often resorted
to, when the quantity of material, included between the fences
of a cutting, is insufficient to complete the adjacent embank-
ment. The slopes, given to the sides of these cuttings,
ought never to be less than six to one; in order that the sur-
face may be resoiled, and rendered fit for agriculture or other
purposes, after the quantity of material required, is removed.
As a specimen of these cuttings, we cannot refer the reader
to any better executed, than those upon the Birmingham and
Gloucester Railway, between Cheltenham and the village of
Eckington. In many of these, it is difficult to distinguish
the original, from the made surface; and the ground has been
rendered as eligible for agriculture, as it was before the sub-
soil was removed. It is a question well worthy of every en-
gimeer's attention, as to whether, in many instances, it would
not be more economical to form the embankments chiefly out
of side-cutting: and lead the material in the cuttings to the
nearest spoil bank. The value of the property through
which a railway passes, will, of course, determine this.
160 APPEND IX.
NotE 14.
Gullet:—This represents the furthermost part of the cut-
ting, where the front wagons of each train are filled. It is
sometimes called the lower chamber, when more than one
lift is made. Its dimensions ought to be fifty feet long,
twenty feet broad, and eight feet high; if the extent of the
cutting will allow of them.
The Gullet is that portion of the cutting shown in plate 1,
fig. 2, where the wagons, o, o, o, &c., are situated.
NOTE 15.
Spoil Bank:-In contradistinction to side-cutting, this term
refers to the deposit of material, taken from between the
fences of a railway, when the quantity, or cubical contents in
a cutting, exceed that of the adjacent embankment. These
banks, if properly constructed, may be made as valuable for
agricultural purposes as side cuttings; by resoiling, and trim-
ming the slopes, at an inclimation of six to one.
NOTE 16.
Siding:—A siding is a road run out of the main road, and
joined with it at both ends, as shown in plate 1, fig. 2, at w,
w, &c. The length of a siding, will always bear a certain
proportion to the number of wagons in each set; or, in other
words, to the breadth of the head of an embankment.
NoTE 17.
Sperm, or Shunt Roads:–These are roads, branching out
of the main road, at the face of the cutting, and at the head
of the embankment; they are shown in plate 1, fig. 2, at P,
P, &c. The number of these roads, will always depend upon
the magnitude of the work; and with respect to the head of an
embankment, the greater the number that can be fixed upon
APPENDIX. 161
it, the better; for the more points there are, to tip from simul-
taneously, the faster will be the progress, and the greater the
number of wagons that can be worked in the adjacent cutting,
from which it may be supplied.
NOTE: 18.
Stages:—A term synonymous with barrow runs—a stage
being reckoned twenty-five yards long.
Trussels:—A support for the planks which compose each
road:—a large description of tripod, or stool; as may be seen
in plate 3, at D, D, &c.
NOTE 19.
Second Lift:—The second lift, or chamber, in a cutting, is
that in front of the first, and generally eight feet above it.
This lift, is always worked with barrows; and is of the same
length, but ten feet wider, on each side of the centre line of
cutting, than the first lift. As the inclination given to the
sides of the cutting, in some instances may not allow of this,
it is sometimes narrower.
The second lift is shown in plate 1, fig. 1, immediately
above a, and in the second figure of the same plate is the
plan of it, between the points n, n, &c. and where the wagons,
o, o, &c. are situated.
NOTE: 20.
Slips:—A term used to denote the contraction, subsidence,
or sliding away of the foot of a cutting or embankment; these
accidents are of frequent occurrence, and the only effectual
remedy for them is drainage. They are always removed by
barrow-work, when they take place in the side of an embank-
ment; but with wagons, when they occur in cuttings; and the
excavation, which is thus taken out, is well puddled, and pun-
med, in 18 in. layers; until that part of the slope, where the
I 62 APPENDIX.
slip occurred, is made up in uniformity with the rest of the
cutting or embankment, as the case may be. Piling at the
foot of the slopes, is often resorted to ; but we have never
known it to answer the purpose fully: so that, when once the
fissure appears at the back of a slope, it is, eventually, the best
plan to remove the slip altogether, and pun it in again as
stated above.
NOTE 21.
Barrow-road –This consists of planks, laid at each end on
trussels or tripods, over which the barrows are wheeled; the
planks must be 11 in, broad, and from 2in. to 2% in. deep ;
the length of a road may vary, in executing earthwork upon
railways or canals, within 150 yards; but, in the former in-
stance, it ought not to exceed 100 yards, unless under peculiar
circumstances; such as leading to spoil at a short distance, or
supplying ballast, &c., for the permanent road. The barrow-
road is represented in plate 3, at c, c, &c.
NOTE 22.
Barrow-run :-A term used to signify the length which
each man can wheel a barrow, while one of similar dimensions
can be filled. Several of these runs, may comprise a barrow-
road ; but upon railways, when the small barrow is used, the
length of each run ought to be 25 yards, as one of these bar-
rows can be filled in the same time, that it can be wheeled that
distance.
DESCRIPTION OF THE PLATES.
As there are several technical terms, unavoidably used in
the text ; concerning which, none but men minutely conver-
sant with the mode of excavation and embankment, adopted
upon railways, can obtain any definite ideas, even with the aid
of elaborate descriptions ; it was found necessary, towards a
thorough comprehension of the work, to append a few plates,
and offer such explanations upon them, as were likely to be of
use to the reader.
Description of Plate I.
The first figure in this plate represents the sectional eleva-
tion of the interior of a cutting, and the side view of an em-
bankment, in the manner these works are generally carried on.
The space immediately above a, is that portion of the cutting
called the second lift. This lift is always worked with bar-
rows, and is generally eight feet in height. The barrows,
when filled, and wheeled over the second lift, enter upon the
stages, b, (which are erected over the lower chamber, h,) and
them emptied into the wagons as represented at d : the stages,
upon which the barrows are wheeled, are supported by beams
laid across the lower chamber, as shown in fig. 3. at a.
The space over h, represents the lower lift, gullet, or cham-
ber in a cutting ; into which a certain number of wagons, e, e,
&c., (according to the extent of the cutting) are drawn, and
there filled, partly by men stationed in it, and partly by the
men working in the second lift, a, in the manner stated above:
frepresents a getter in the act of /alling the material, by un-
derstocking it and g, g, fillers, or the men who load the
wagons.
164 APPENDIX.
Immediately above i, may be seen an empty train, returning
towards the gullet after being emptied over the tip ; in order to
take the place of the wagons e, e, &c. and to be filled again.
The wagons under the letter j, are those which having been
filled in the lower gullet, and removed sufficiently near the
tip, are then placed in a siding, and drawn out singly, at the
rate of about five miles an hour, by a horse ; (as shown at k,)
until it comes within twenty yards of the end of the embank-
ment; when the horse is suddenly detached, and the wagon
is precipitated against a piece of wood called the bumper, by
the velocity which it has acquired; and is thus tilted over, off
the hinder axle, as shown at l. Immediately above m, the
bumper, or piece of wood against which each wagon strikes, is
shown ; one of these is placed at the end of every shunt road.
It may be observed, that the road (or surface of the embank-
ment,) is a little inclined towards the tip, upon which the
bumpers are placed. This is done in order to facilitate the
progress of the wagons, after the horses are detached from
them : for when the road is nearly level, it is necessary to
put the horses to a much greater speed, in order to insure the
safe tipping of the wagons ; and in this case, much difficulty
is always experienced in detaching the horse: which often
causes loss of life among the men appointed to the tipping
department.
Description of Fig. 2, Plate I.
In the second figure, a plan of the cutting and embank-
ment, represented by Fig. 1, is given. In this figure, n, n, &c.,
represent the points where each of the barrows, on the second
lift, are filled. These points are commonly called stocking
grips:—o, o, o, &c., represent the empty wagons just returned
from the tip; p, p, &c., are the shunt roads in the cutting
and on the embankment; but those on the embankment are
sometimes in contradistinction called sperms, although in
APPENDIX. 1.65
every respect similar to the ones in the cutting; g, is a wagon
run in on one of the shunt roads, to receive the material
which must be removed, in order to trim off the lower parts
of the slopes to their proper inclination, as the bottom gullet
advances—which is in every respect an arrangement most de-
sirable, as it is a great preventative against slips;–r, represents
a switch, which consists of two railway bars bound together
to the proper guage, (4ft. 8%in.), and moveable at the ex-
tremity nearest to the end of the main road, (as at s, s, &c.);
so that the other extremity may be made to coincide with the
direction of the shunt roads, as shown by the dotted lines at
t, t, &c.; u, u, u, represent the main road, upon which the trains
pass up and down from the cutting towards the tip ; v, v, re-
present the sidings, which the results of our inquiry into the
effects of the lead prove to be necessary, in order to allow
the sets or trains of wagons to pass each other, when the
number of wagons in each set is proportioned to the magni-
tude of the tip-head; w, w, &c. are the filled wagons, which,
after being removed from the cutting sufficiently near the tip,
are placed in a siding close by, and thence drawn one by one,
(as previously explaimed), for the purpose of being tipped ;
w, represents a wagon in the act of being tipped by the force
with which it comes against the bumper, after the horse has
been detached from it.
Description of Fig. 3, Plate I.
This figure shews a section of the cutting through F, G,
when a', aſ, are the sides of the second lift, and 6', the lower
gullet. The indentations, c', c, are the grips formed with the
pickaxe, and continued until the superincumbent mass, d", d",
is completely undermined, and falls down. These grips are
formed for the same purpose as the stocking grips ; and differ
166 APPENDIX.
only inasmuch as the former are perpendicular channels, and
the latter horizontal.
Description of Fig. 4, Plate I.
In this figure, the end view of the tip is represented, where
e', shews a wagon in the position of being tipped;—f, one just
tipped, with the horse attached to draw it back, in order to
make room for another loaded wagon;—and g, the bumper,
against which each wagon is precipitated.
Description of Fig. 5, Plate I.
This figure gives a side view of the embankment, when side
tipping to dress off the slopes, is carried on. It will be ob-
served, that these wagons are not tipped in the same manner
as those used for front tipping, as it is necessary that each
wagon should be lifted off its frame by the workmen, and not
run against a bumper for that purpose, as in front tipping.
Description of Fig. 6, Plate I.
This figure represents the cross section of the embankment,
at H, I, in the former figure, and shows the method in which
the wagons are lifted off their frames. The method of side
tipping, if it could be always adopted, would be much more
advantageous than front tipping; for any number of wagons,
according to the former arrangement, might be emptied simul-
taneously; while, according to the latter, the number that can
be emptied, must, in every case, depend upon the magnitude
of the embankment—or, in other words, upon the number
of shunt or sperm roads that can be fixed upon it.
Plate II. Fig. 1.
This figure represents an earth wagon, drawn to a scale of
twenty feet to an inch. There are various sizes of earth wagons,
APPENDIX. 167
but that given in the plate is the most convenient, and affords
greater advantages for working than any we have met with;
for it combines the advantages of carrying more material at
each trip, and at the same time of allowing as many sperm
--roads being placed on the head of an embankment, as any
other size. Each of these wagons, when heaped in a comical
form, will contain 3.12 cubic yards of loose material; which, in
general, may be reckoned equal to 2% cubic-yards of earth in
its solid state, or previous to its being excavated.
Each of these wagons cost on an average 2622, and contain
24.50 cubic feet of timber.
As follows, we have given the
dimensions of the parts in detail, which may be found useful
to the practical engineer or contractor: —
Dimensions and weights of the timber, and iron-work, in
the description of wagon represented in Plate 2. fig. 1.
Tömöer Work.
Pedestal Frame. ft. in. in. in.
1 Head-piece, elm 5 2 × 10; x 4
2 Elm pedestals, each 5 10 × 9 × 4%
I Fir end-piece 3 5 × 5 × 5%
Body.
2 Bumpers, each. 8 3}× 6 × 5
4 Shoots; three fir, and one elm . 6 4+ x 5 × 5
2 Chocks, elm 2 8 × 6 × 4
1 Head-board, elm . 6 3% x 1.3 × 1%
2 Side-boards, elm 6 8 × 1.3 × 1%
1 Tail-board, elm 6 9% × 1.3 × 1%
8 Bottom-boards in all, elm . 6 6 × 6.6 × 1%
Iron Work.
Cwt. qrs. lbs.
2 Cast-iron tipping blocks 0 2 4
Average of small iron-work . gº . 4 0 0
4 Pedestals º tº tº tº I () 20
2 Pair of wheels, with axles ſº g . 12 0 0
Total 17 2 24
168 APPENDIX.
Plate II, Fig. 2.
Represents the most convenient sized barrow, for exe-
cuting earthwork upon railways. This figure is drawn
to a scale of twenty feet to an inch. When filled well, these
barrows contain 2.70 cubic feet of loose material. The wheels
consist of cast iron, and the sides and bottom of elm board-
ing, one inch thick. The handles are generally made of ash,
well seasoned; and the net cost, when new, averages at seven-
teen shillings apiece.
Plate II, Fig. 3.
This figure represents two cross sections of the same
embankment: —c, b, h, g, the section as it would appear,
when originally run out; and a, b, f, e, the section
according to which it is to be finally formed. Here it will be
seen, that the extra breadths of c, a, and 6, d, are of great
advantage; as by running out an embankment in this manner,
a greater number of sperm roads can be laid on the tip head,
than if the embankment were, at first, formed to its pres-
cribed width, as shewn on the engineer’s sections. The advan-
tage to be derived from this, is more fully discussed in the
fifth section, to which we refer the reader. The areas Ö, d, i,
and a, e, j, (respectively equal to i, f, h, and j, c, g,) are cast
to the bottom of the slope, on each side, and trimmed off to
the regular inclination, to which it is intended the embank-
ment is to be finally formed.
Plate II, Fig. 4.
The fourth figure in this plate, represents the plan
of a contractors' road, as generally laid. At a, and a,
are represented the junction of the rails; where what is termed
a joint chair is made use of, as the best method of fastening
them together, and keeping them in proper guage. At b, b, &c.
APPENDIX. I69
are shown the half chairs, which are fixed on the outside of
the rails, at every intermediate sleeper, between the joint
chairs; in order to keep the rails from being pushed outwards,
by the flanches of the wagon wheels. This is sometimes done
by spiking down the rails on the sleepers; but the use of half
chairs is much more to be preferred. At the joint chairs, the
rails are firmly keyed in the chairs, with iron spikes, as shown
in figure 5, at e :-A, A, A, &c., represent the sleepers,
which consist generally of larch, beech, or other durable tim-
ter. The sleepers are generally laid at distances of two feet
six inches apart; and the rail beds full upon them; but some-
times, they are as much as three feet and more apart: the dis-
tance depending upon the strength of the rail, in all instances.
These roads always rest upon a substratum of gravel, mine
inches, or a foot thick, and the gravel is well rammed under, to
support the sleepers.
Plate II, Fig. 5.
In this figure is represented the cross section of the
rail, generally used upon contractors’ roads. The figure
is drawn to one twelfth of the full size, and shows the
method in which the rail is keyed in the chair, by the small
iron spike or plug, at c. These rails weigh thirty-five pounds
to the yard, and are each fifteen feet long. They cost about
zéll per ton, when bought new. These rails are evidently
unfit for the working of a Locomotive engine; but will answer
well enough, when the work is carried on by means of horses
only; for we have known loads of five tons to pass over them
—when the sleepers were well packed, and two feet six inches
apart—without causing a permanent bend.
M
170 APPENDIX.
Description of Plate 3.
This sketch represents the appearance of the cut-
ting at Bredon, during March 1840, when the slopes were
being trimmed off, and the ballasting of the cutting, for the
permanent way, commenced:—the ballast being procured from
side-cutting. *
In this sketch, A, A, &c., represent the side-cutting from
which the ballast was procured, for laying the permanent way
upon.
At B, are represented the wagons, run in on a shunt off
the main road, into which the gravel is filled out of the bar-
rows. In the near ground, it will be observed that the face
of the side-cutting has receded from the railway considerably;
so that a considerable number of roads was necessary to be
erected, in order to wheel the material from the face, on to
the siding where the wagons are standing. These roads con-
sist of planks, C, C, &c., laid upon upright trussels, D, D, &c.
The figures round about, represent the men in the acts of
getting, filling, and wheeling the material—each of which, it
may be seen, is a separate occupation.
A little beyond, in the distance, at A', may be seem another
party of men, also emptying their barrows into the same train.
Here, the face of the side-cutting being near to the shunt
road, upon which the wagons, B, are standing, a different ar-
rangement of the roads is adopted; for the distance over
which the barrows have to be wheeled, before they can be
emptied over into the wagons, not exceeding the length of one
run, it is only necessary to lay in a number of single roads at
small distances, and parallel to each other; the same barrow
* For this graphic sketch we are indebted to our worthy friend, George
Jackson, Esq., Architect to the Birmingham and Gloucester Railway
Company.
APPEND IX. 171
and its wheeler using the same road constantly. Now, the
arrangement in the foreground, is quite different; for the
length of the road being equal—say to four runs—it is neces-
__sary that a double way should be made, for the empty and
loaded barrows to pass each other; also, that there should be a
small platform at the end of each run, in order to allow of each
loaded, and empty wagon, being exchanged from man to man;
because, as we have previously mentioned, in the ninth section,
the same man does not wheel any of the barrows the whole
length of the road; but only for the length of one run, and
there receives another empty barrow, with which he returns
to have it filled. For instance, on the first run, a man is
represented, at a, wheeling a loaded barrow, with which he
proceeds as far as 6, where another man has just brought back
an empty barrow; both, it will be perceived, are going in a di-
rection towards each other; and where they meet must exchange
the barrows, and return in the contrary direction—one towards
the face of the cutting, with the empty barrow, to have it filled
—and the other, with the loaded one, towards the railway, to
have it emptied;—if the length of the road is equal only to two
runs;—or, when it extends longer, to give it over, at the end
of his run, to another. In this manner each barrow proceeds,
and returns, throughout the time worked.
When the wagons at B, are filled, as we have described,
they are immediately drawn out of the shunt road, and at-
tached to a locomotive on the main line, as may be seen at E;
and conveyed to the place where the material is to be de-
posited. Sometimes, the wagons are removed by horses; but
in any case, where the ballasting of the permanent way is in
operation, it is productive of considerable subsequent injury
to the road, to allow horses to walk over the surface of the
ballasting. In fact, horses should not be allowed to enter
upon a railway, under any pretext, when the use of a locomo-
tive engine can be procured; but this ought to be more espe-
M 2
172 APPENDIX.
cially guarded against, during the period, in which the perma-
ment way is being laid. We have known much trouble and
expence to arise, from inattention to this, upon the opening of
one or two lines.
But to return ; on the opposite side of the railway, at F,
may be seen a party of men, engaged in dressing, or trimming
off the slope; and at the foot of the slope, at G, may also be
seen, a train of wagons placed there, in order to receive the ma-
terial which is removed, in the operation of trimming.—This
is always done with the pickaxe; and to ensure its thorough
performance, it will be found necessary to procure labourers of
considerable experience upon railways, as the work requires
great nicety, and when imperfectly done, cannot fail to offend
the eye, besides reflecting great discredit upon the person who
superintends the setting out of the work.
Having now given such explanations, of the details of
earthwork in general, as are likely to afford the reader of the
foregoing inquiry, all the practical information about it which
it seems possible to communicate upon paper—considering
the number, and magnitude of the natural causes by which it
is affected;—we will conclude, by recommending the general
reader, to make himself personally acquainted, if possible, with
the general appearance and features of any cutting or embank-
ment, which may be in process of execution in his neighbour-
hood, previous to his attempting to master the subject, as it
will much facilitate his entering into the spirit of it. In fact,
we doubt how—without the aid of a model—persons who
have not some slight knowledge of earthwork previously, can
get a thorough insight into that particular portion of the subject,
which refers to the method in which the material is removed from
cutting to embankment ; or in other words, how they can ob-
tain accurate notions of the manmer, and arrangement, accord-
ing to which the trains pass backwards and forwards.—These
remarks likewise apply to barrowing.—But perhaps, (as is not
APPENDIX. 173
unfrequently the case,) the difficulties which the Author had
to encounter, step by step, in exploring the principles of a
department in engineering science, hitherto unattempted (in
a systematic way), may have superinduced a belief, that the
difficulties are of greater magnitude than the real circum-
stances of the case will be found to warrant.—That the reader
may find the latter supposition true, is the anxious wish of
the Author.
THE END.
LONDON :
bi, ATCII AND LAMPERT, PRINTERs, GROVE PLACE, BRom PTON.
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Plate 3 .
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184 O
AS IT APFEARED IN MARCH
|RIEID) (O)Nſ (CU TI'T'][Nſ (G.
SKETCH OF THE B3
Saunders & Otley, Conduit Street.