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UNIVERSITY

ILLINOIS LIBRARY

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vS^

The TECHNOGRAPH

UNIVERSITY OF ILLINOIS.

1890-91.

CONTENTS.

The Schools of Mechanical and Civil Engineering in the University of Illi

Selim II. Peabody ^

The Topographical Survey of the City of St. Louis, Mo. Oliver W. Connet . . . .

1 aces for Cable Roads F. W. Kichart i ;

The Four- Mile Crib of the Chicago Water-Works Simeon C. Co/Ion i -

Notes from Mechanical Engineering Theses

'ck for Everybody—/. O. Baker

(Tubs and Gutters—/''. A'. Williamson

A Remarkable Sink- Hole —A. A. Mather

Rope Driving — F. L. Bunion

Notes on a Railroad Re- Survey — B. A. Wail

Square Drift-Bolts — J. II. Powell and A. E. Harvey

if Brick Pavements— A. D. Thompson .41

Interlocked vs. Unprotected Railroad Grade Crossings — W. M. Hay

Notes on Aluminum and its Alloys—/?. J. Keene

Effect of Counterbalance on Locomotives- S. D. Baivden 51

Prints from Etched Metals— L. W. Peabody

Notes on an Electric Street Railway Plant — W. A. Boyd. .

Lime-Cement Mortar

Railway Transition Curves — Arthur N. Talbot. ...

PRICE 50 CENTS

address, technograph, university or illinois,
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No. 5.

THE TECHNOGRAPH.

Published by the Civil Engineers' Club and the
Mechanical Engineers' Society of the

UNIVERSITY OF ILLINOIS.

CHAMPAiaN, ILLINOIS,

1S90=91.

BLOOMINGTON, ILL.:
Pantagraph Printing and Stationery Company. cu

The Technograph.

No. 5. UNIVERSITY OF ILLINOIS. 1890-91.

THE SCHOOLS OF MECHANICAL AND CIVIL ENGINEER-
ING IN THE UNIVERSITY OF ILLINOIS.
By Selim H. Peabody, LL.D., Regent.

The first movements toward the establishment of schools of
Civil Engineering in America sprang from the demand for compe-
tent engineers of railways consequent upon the rapid development
of that system of transportation in the third decade of this cent-
ury. A second and larger impulse came about thirty years later,
when Congress made its first subsidy for scientific training in the
Land Grant Act of 1862.

The state of Illinois was among the first to move in the found-
ing, under the provisions of this act, of a school of practical and
experimental science, chartered in 1867 and opened to students in
March, 1868. In those days the differentiation between the subjects
of civil and mechanical engineering began to be more fully appre-
ciated, and the institution here begun was one of the earliest to pro-
vide a distinct course of study, with separate equipment in each of
these lines of engineering work. The workshops here erected were
the first distinctively educational shops opened in America, those
at Worcester following soon after. But the Worcester shops were
manufacturing shops, with educational tendencies, rather than shops
purely and simply for instruction. The primary object of the
shops at Champaign has been instruction, with very little consider-
ation of manufacturing results. Dr. Runkle, of the Institute at
Boston, has been called the father of shop-training in America, a
distinction which he surely never claimed for himself. The shops
at Champaign were built, equipped, and opened to students seven
years before the first shop -work was done at the Massachusetts In-
stitute of Technology. A full exhibit from our shops, including a

B THE TECENOORAPH.

line of work analogous to the so-called "Russian" system, a kind
of work practiced here for at least four years previous, was placed
in the Centennial Exposition in Philadelphia in 1876, and a diploma
was awarded to this University therefor. Dr. Runkle's school-shop
in 1877, was no more an innovation or a discovery than is Dr.
Elliot's proposition of to-day that college students of larger
capacity may graduate with a bachelor's degree after three years'
study. The University of Illinois graduates a student when he has
completed his course, and does not ask whether he has occupied
three, four, or five years in so doing.

The shops at Champaign have sent out full lines of its courses
of shop instruction, including blue-print copies of its drawings, and
finished specimens of work, to various institutions scattered from
the Atlantic to the Pacific coasts. It was more complimentary
than ingenuous for the distinguished president of an Eastern Col-
lege, to publish a complete series of fac-similes of our shop-draw-
ings, reduced copies of blue-prints obtained from us, dimensions
and all completely figured, with the statement that the series was
perhaps the most complete extant, but without any credit to the
institution where they originated, or any recognition of indebt-
edness thereto. The University of Illinois has never sought to pro-
tect for herself such products, but has freely distributed them to
all inquirers, but she believes that she may modestly reclaim her
own. She farther confidently claims, that in America there was no
earlier practice in "Manual Training" than hers, and that nowhere
else has that practice been more consistent or more successful.
But this has been restricted to its proper sphere as an incident and
adjunct to other earnest and scholarly culture, and never has been
put forward unduly as a hobby, or a fad.

All our engineering courses begin substantially at the same
point. The entering student is expected to show evidences of fair
previous training, covering the branches taught in primary and
grammar schools, and most of those taught in the High schools.
In particular, he should be well versed in Elementary Algebra, and
in Geometry, both plane and solid. He should have had some
practical contact with elementary science; and because his oppor-
tunities will probably have been better in these subjects, Physics,
Physiology, and Botany are named. The desire is that he shall
have thus acquired some training, some discipline, while the mere
knowledge of facts is deemed of less consequence. It must be
admitted that the ideals are not realized as often as could be wished.

THE TECHNOGRAPH. 7

A good knowledge of the English language is deemed indispensable.
The applicant must not be less than fifteen years of age, and ordi-
narily should have reached eighteen. If to these qualifications
could be added a good practice in drawing, both free-hand and
with instruments, and some careful linguistic culture, the results
would be very advantageous. It is to be hoped that these may be
required at a day not far distant.

The new student is entered at once upon a course of higher
mathematical work, for the double purpose of its exact discipline,
and of its needful facility for solving the multitudinous problems
which occur in the higher departments of his engineering study. It
is meant that he shall acquire the power of sifting matters to their
fundamental principles, and for this purpose the mathematical
training is absolutely indispensable. Parallel with this opens care-
ful training in the exact power of expression in drawing, iu its
mathematical rather than its artistic phase. Parallel, also, comes
the concrete applications of these subjects, in the treatment of
materials, wood, iron, sand, etc., in the shop. In each of these
lines of work, the prime excellence to be sought and inculcated is
precision, exactness, accuracy. Without these, effort is wasted,
and habits worse than useless are inculcated. In the shop, par-
ticularly, is this noticeable. A few enter the shop showing a native
inaptitude for shop methods; but for one such, there are many who
show that for the want of proper training in their preceding work,
stimulated only by that which fond parents suppose to be the cor-
uscation of mechanical genius, or by training inefficiently given in
the early years, before the lad has any real appreciation of earnest
purposes, that which they have learned as to "the use of tools" is
a delusion and a snare; that much pains must be taken to unlearn
bad methods and to erase bad ideas, before good ones can be incul-
cated.

These three, the shop, the drawing room, and the mathematical
class room, lie so at the foundations that they can not be avoided.
To furnish some element of broader culture, at the same time, work
is added in some modern language. So ends the first year's work.

In the second year, the mathematical work proceeds. Physics
comes in as an important theoretical and experimental study. The
differentiation of the departments begins. The civils enter in their
work of surveying in its various phases, including an intimate
acquaintance with the most refined instruments of measurement.
The mechanicals pass from instruction to construction; terms

THE TECHNOGRAPH.

which indicate tendencies rather than differences, since every piece
of work involves both elements. Finished machines begin to show
themselves in the shop, as the results of work that begins in the
designing room, and follows through all the practical departments.

In the third year the schools unite in the investigation of the
problems of mechanics, resistance of materials, hydraulics, etc.;
problems exhaustively discussed by the aid of the mathematical
processes previously mastered. But each school becomes yet more
specialized. The mechanicals discuss the elements of mechanism;
the quality of materials; the combination of machinery. The
civils are busy with the intricacies of construction of railways, and
of municipal improvements.

In the fourth year are reached the higher specialties in each
department. The civil's surveying has developed into the discus-
sion of geodetic problems; their investigation of the material ele-
ments and of mechanical problems, culminates in the designing of
masonry constructions, and in the theoretical and practical investi-
gation of devices for transit over the land, through the air, and
over and under the waters, and the everlasting hills. In like man-
ner the mechanicals are burrowing into the vital constitutions of
motors and appliers of force, and the methods of harnessing the
powers of heat, flowing water, and electric currents, to the service
of men.

In all this, it is hoped that one mistake, a serious one, may be
avoided. These students, ardent, earnest, industrious, successful,
must not come to their graduation with the supposition that they
have mastered the whole of the sciences that pervade their special-
ties. These subjects are broad as the world, and as long as eternity.
Only those principles that are fundamental can be grasped as the
product of study for four brief years, if, indeed, there should be
time and strength for so much as that. The engineer, the mechani-
cian, must be content to be a student during all the years of the
longest life that may be granted for his efforts.

Too many students wish to restrict themselves to those special-
ties in their respective courses which they imagine are of direct and
particular "use." The reason is, that they have a limited, an inade-
quate interpretation of the word "use." Had they the opportunity
to reconstruct man, they would make him only senses, fingers, and
stomach. The University courses have endeavored in some meas-
ure, quite too small, to supplement these vigorous, technical
studies, with others, which may tend toward the humanities, which

THE TECHNOGRAPH. 9

may broaden vision, stimulate aspirations, enlarge conceptions of
life, and capacities for enjoyment. The engineer should not be a
mere machine, typified by his own steam engine, or dynamo, or
theodolite; he should strive to grow into a large-hearted, acute,
brainy, and efficient man. He must not only have great capacities,
but fair means of showing to the world such capacities. He should
be able to write clearly and accurately; to speak forcibly and
effectively; to be a power in the sphere of his action. He has an
account to give, as well for the talents which he may acquire, as
for those which were given him to possess and to enjoy.

In this brief account of the schools of civil and mechanical
engineering, most has been said of the present, the actual. The
possible, in the future, is yet larger and more worthy. The ideals
are not yet realized; there is much to do before they can be real-
ized, requiring combined and persistent effort. The progress made
is but earnest of that which is sought, and for which the aid of
students, instructors, the public, and the state, is invoked.

THE TOPOGRAPHICAL SURVEY OF THE CITY OF
ST. LOUIS, MISSOURI.

By Oliver W. Connet.*

No city contemplating any extensive improvements can afford
to be without a careful topographical survey and an accurate con-
tour map. The survey should cover the whole city, and the map
should be on a large scale and show the streets, alleys, public
grounds, water courses, contours, etc. The information necessary
for the location, plans, and preliminary estimates for sewers, street
improvement, and other public works, can not be obtained so
quickly or at so little cost in any other way; and the study of their
location can not be so general and comprehensive as may be made
from such a map.

This has been recognized in St. Louis, and such a survey is in
progress in this city. The survey was authorized by an ordinance
approved March 21, 1889, and the field wojk was begun in June of
that year. The purpose of the survey, as stated in the ordinance,
is for the perfecting of plans for the drainage of the city, and for
use in locating and opening streets and alleys, and in the establish-

*For three years a member of the class of '87, and at present assistant engineer on the topo-
graphical survey of St. Louis.

10 THE TECHHOGRAPH.

ing of grades for streets and public places. The survey is under
the supervision of the Sewer Commissioner, Mr. Robert E. Mc-
Math, and in direct charge of Mr. B. H. Colby, first assistant
engineer. The force authorized by the ordinance is as follows, viz.:
one first assistant engineer in charge, one precise level man, one
topographer, one draughtsman, three recorders, and as many field
hands as are necessary. The ordinance directs that the survey
shall be begun in that part of the city where least provision is made
for drainage and where the increasing population makes plans for
improvements necessary.

In compliance with this provision the survey was begun in the
central portion of the city west of Grand avenue. Up to the date
of this paper, February i, 189 1, the field work is nearly finished in
the district bounded on the north by Florissant avenue, on the east
by Grand avenue, on the south by Tyler avenue, and on the west
by the City Limits.

The work of the survey may be divided into four heads: Tri-
angulation, Precise Levels, Topography, and Office Work. The
first two are in a sense preliminary to the topography, but of pri-
mary importance as regards the accuracy of the survey.

Triangulation.

The triangulation, which is the basis of the survey, has been
carried forward as the work has progressed. The area covered by
the triangulation is about 30 square miles.

About one half of the stations are marked by limestone monu-
ments 6x6x36 inches, set in the ground. The remainder are on
the roofs of buildings. The system has fifty-four stations, and
sixty-five triangles. The stations are so distributed that they are
on the average less than a mile apart, but the average length of the
sides of the triangles is about one and one half miles. In most
cases the three angles of the triangle have been read by the repeti-
tion method.

The system is based on a line in the trans-continental triangu-
lation of the United States Coast Survey. The line is from a point
on the old stand-pipe to the tip of the dome of the Insane Asylum.
The latitude and longitude of these two points, with the length and
azimuth of the line joining them, were taken from the Coast Survey
reports.

In the report of the Sewer Commissioner for the year 1890,
Mr. Colby gives the following: "The average closure of triangles

THE TECHNOGBAPH. 11

has been a little over four seconds. The angles of each triangle
were summed, and the deficiency or excess from 1800 was divided
equally among the three angles before computing the sides. No
other adjustment has been made, or thought necessary. Several
checks have been made upon length of sides, and discrepancies
have been from i in 80,000 to 1 in 180,000."

It is expected that an ordinance will be passed requiring that
all surveys of streets and subdivisions be connected with the tri-
angulation, and that the true azimuth of all lines be recorded. Such
a requirement is necessary because the present records do not fur-
nish sufficient data to plot the streets on the maps, or retrace the
lines on the ground. In anticipation of this a number of triangula-
tion stations have been connected with, which were not necessary
for the topographical survey.

Precise Levels.

Precise levels have been run on the principal streets west of
Grand avenue. Benches have been established on an average four
to a mile along the lines run. The lines have been so connected
that no point in the district covered is more than one half mile
from a precise bench. There have been 361 benches established,
and the distance run in duplicate is about 92.5 miles. These
benches are to be the standard for all of the departments and for
all elevations in the city. For the convenience of the other depart-
ments and of engineers and surveyors in general, a list of the
benches with their description and elevations is published. The
greater part of the benches are on the stone foundations of bridges
and buildings, but in parts of the city where such marks could not
be had, a burnt tile slab, 4x18x18 inches, with a copper bolt
leaded into the center, was buried to a depth of four feet. The
point is accessible through a tile pipe specially made for the pur-
pose.

The limit of error allowed is 0.0208 feet into the square root of
the distance in miles. In the above mentioned report the follow-
ing figures are given, showing the degree of accuracy with which
the work has been done: "The average closure per mile has been
0.013 feet. The probable error in the determination of a single
mile of the work is 0.001 feet. If the work lay in a continuous
line, the elevation of the last bench, as determined from the first,
would be known within a probable error of 0.066 feet."

12 I III-. TECHNOGRAPH.

Topography.

The value of the survey depends on the amount and reliability
of the information given. To this end every precaution has been
used to secure this result. The best instruments have been pro-
cured, experienced men employed, and the greatest care required.
All possible checks are taken in the field to prevent errors from
creeping into the work.

The stadia has been employed as the best and most rapid
method of locating points and obtaining their elevation. By this
method 300 points may be located in a day. The party is com-
posed of the topographer, one recorder, three stadia-men, and one
general-utility man. The instrument used is a complete Buff &
Berger transit, reading horizontal angles to 10 seconds and vertical
angles to 1 minute. The vertical circle has each quadrant gradu-
ated from o° to 900 so that the angle of depression or elevation
may be read with the telescope direct, or inverted, thus eliminating
errors of adjustment of the vertical circle. The level is attached
to the verniers in such a way that the zeros may be brought into a
horizontal plane without disturbing the leveling screws.

The stadia boards used are 12 feet long, and represent a dis-
tance of 458 meters, or the value of 100 meters is 2.62 feet on the
board. The figures used on the stadia are similar to those used on
the United States Lake Survey. Distances are read in meters, and
elevations are obtained in feet by means of Ockerson & Teeple's
tables. Oak stakes ixixio inches are used for stadia stations,
and are driven nearly flush with the ground.

All lines of stadia courses begin and end on triangulation
stations, or other stadia stations which are in connecting lines.
Both verniers are read to 10 seconds on all stadia courses. In this
way the azimuth is repeatedly checked in the field, and data ob-
tained by which the location of the stations may be checked when
the co-ordinates are computed. The error of closure after making
the known corrections for inclination and graduation of rods, is
about 1 in 800. The average error of closure of azimuth is about
1 minute 5 seconds for each line run, or n seconds per station.
All azimuth readings are with reference to the true meridian.

Elevations are carried by means of distance and vertical angle.
The height of instrument is carefully measured with a rod (gradu-
ated for the purpose), the middle wire is brought to the correspond-
ing point on the board, and the level on the vertical circle is
brought to the center of the tube before the angle is read. It is

THE TECHXOGRAPH.

remarkable with what accuracy elevations may be carried when
these precautions are taken and care is exercised to keep the
instrument in adjustment. The average error of elevations is less
than 0.2 of a foot per mile.

The notes are kept in well bound books, 5x8 inches in size,
made especially for the survey. They contain 100 double pages,
and have the heading of the columns printed on every page, as
shown below:

Left-hand Page.

Object.

Distance.

Vernier A.

Vernier B.

Vertical Angle.

Right-hand Page.

Difference of
Elevation.

Elevation.

Remarks.

The last column is used for descriptions of bench marks, cor-
ner stones, stadia stations, etc., or for sketches.

The area covered (up to the present time) by the topography
is 14,930 acres, or 23^ square miles. The elevations of 54,500
points have been determined, or an average of 3.65 points per acre.

The time occupied in field work is as follows: Triangulation, 62
days; precise levels, 114 days; topography, 248 days; total, 424 days.

Office Work.

The office work consists in reducing the field notes, and plot-
ting. The latitude and longitude of all triangulation stations are
determined to hundredths of a second, and also their linear dis-
tance from the two nearest minutes of latitude and longitude. The
azimuth, and length of the sides of the triangles are computed.

The rectangular co-ordinates of all the stadia stations, with
reference to the nearest 20 seconds of latitude and longitude, are
computed, adjusted, and recorded in a book for that purpose.
This is an important part of the work, as by this means the error
of closure is systematically adjusted, and checks the location of the
stations before the plotting is done. The plotting is done on heavy
mounted egg-shell paper, cut into charts antiquarian size. The
charts are projected by the polyconic method. The tables based
on the development of the Clarke spheroid, published in the report
of the Coast and Geodetic Survey for 1884, are employed. The
scale is 1 in 2,400.

11 /'///•; TECHNOGRAPH.

The charts have the parallels and meridians for every 20 sec-
onds of latitude and longitude on them, and triangulation and
stadia stations are plotted by rectangular co ordinates from them.
Other points are plotted by polar co-ordinates. The streets and
alleys are plotted by means of connections made on the ground
and from data obtained from the street department.

The precise level notes are reduced, and a list of benches, with
elevations and descriptions, prepared for publication in the annual
report of the Sewer Commissioner. The differences of elevation
of the points located by stadia are found by means of Ockerson's
stadia tables, and the elevations determined and recorded in a col-
umn of the field book. In finding the elevation of stakes, the
mean of the differences found by the readings taken in both direc-
tions is used; and the error of closing between benches is divided
equally on the stakes in the line.

All the points taken are plotted, and their elevations written in
small figures on the charts and the contours drawn in. The contour
planes are taken 3 feet apart. The charts are finished in ink. The
elevations of the contours, names of streets, etc., are to be printed
on them by means of a small hand press.

Cost.
The exact cost of the survey can not be given until it is com-
pleted, but some facts concerning the cost of the work, up to the
present time, will be of interest. The total cost of the survey to
February 1, 1891, is $18,827.68. This includes salaries, new instru-
ments, office furniture, transportation, etc. Deducting $1,927.68,
for the value of instruments, etc., on hand, leaves a balance of
$16,900.00 as the actual cost of the survey. The cost of the differ-
ent branches of the work has been as follows:

Triangulation $1,812.00 or 11 per cent.

Precise levels 2,762.00 or 16 "

Topography 6,060.00 or 36 •«

Office work 6,266.06 or 37 "

Total $16,900.00 100 "

The cost of running precise levels has been $30.00 per mile,
run in duplicate. The average cost of the parties, per day, includ-
ing transportation, instruments, etc., is as follows:

Triangulation $29. 25

Precise levels 24.25

Topography 24.50

The average total cost per square mile is $724.50, or a little

over $1.13 per acre.

THE TECHNOGRAPH. 15

GRIP FACES FOR CABLE ROADS.
By F. W. Richart, '91.

One of the heaviest expenses of the cable system of street car
propulsion, is that of renewing cables. Another item of consider-
able expense, is the necessary frequent renewal of grip faces or dies,
as they are usually called. The effect of various materials used for
dies, on the life of the cable, and the relative life of dies made of
these different materials, is a subject which is of considerable impor-
tance to Cable Companies, but has not received much attention in
technical publications.

Very little information could be obtained concesning the earlier
forms of grips. Some of the earlier cable roads in San Francisco
used the Paine grip, which had solid dies, with a pair of carrying
pulleys at each end, forced out beyond the dies by springs, and which
carried the cable, preventing it from rubbing the dies when they
were released. The carrying pulleys are not usually used in more
modern practice. Another form of grip designed to prevent wear
of the cable, consisted of two rectangular steel bars having rounded
ends, each having a dove-tail groove the entire circumference in the
long direction. In these grooves short brass blocks were placed, so
that when the grip was slackened the brass blocks slid round, taking
the wear instead of the cable.

This was once used on the Brooklyn bridge, but was unsatisfac-
tory. The grip used on that bridge at present consists of small
sheaves with grooves facing, which turn when the grip is slack, but
on increasing the pressure the friction becomes sufficient to stop
their turning and move the car. This grip has been used on cable
roads with unsatisfactory results. The tendency is to lengthen the
cable and diminish the diameter. All Kansas City lines use dies
made of the Worrell alloy, which is made of cast-iron and another
metal supposed to be copper. The endurance of the dies is two
weeks on two lines, and is given by two authorities as two weeks and
seven weeks on the third. The one who gives two weeks is probably
the best authority. The Locust Street Line, of St. Louis, use a phos-
phor bronze die, which gives satisfactory results, lasts as long as six
weeks, and wears the cable less than soft (presumably cast) iron.
The Chicago City Railway Co. use a grip die which lasts one month.
The composition is copper 60 lbs., tin 10 lbs., zinc 13 oz., lead 18 oz.

Quite a number of roads have tried cast-iron with unsatisfac-
tory results. It can be used but a short time before renewal is nec-
— 2

THE TECHNOGRAPH.

essary. A silicated iron has been used on one of the Chicago roads,
lasting about five times as long as ordinary cast-iron.

Cast-steel is being used to a considerable extent at present, and
with very satisfactory results. It lasts several times longer than any
of the alloys or cast iron, and, according to Mr. Van Vleck, wears
the cable but a tritle more. The Vogel Cable Construction Co.
state that gripping dies are made of the hardest material possible,
and when the expense is not too great of tool steel.

The conclusions to be drawn from the tables below are not
numerous. We can see that cast-iron does not last any considerable
length of time. Some grades of cast-steel are poor, but good grades
give greater wear than any other material cited. Of alloys, phos-
phor bronze wears longest. The alloy used by the Chicago City
Railway Co. seems to give very good wear, but is evidently expen-
sive. As to the life of cables as effected by different materials used
in the dies, the average life of Kansas City cables from the table is
10.S4 months with dies made of the Worrell alloy, while the Wash-
ington and Georgetown cable has not yet been renewed after eleven
months use, with cast-steel dies. The only difference in the two
cables is in the number of wires, the diameter being the same. The
former has 96 and the latter 1 14 wires in six strands, with hemp core.

e of Grip Dies of Various Mati i;i

Road.

Material.

Chic.

Chicago < ity Ky. . .
1 .ind
.mi Ky

Kans.i

politan.

ble. . .

I .iiir

< ':i~i iron

Silicated iron (spe

cial mixtun
Cast-steel

Len'th

i9» I

20' • J

19"

|i9"
20"

( 'olllj.

el 1

Worrell alloy.

le i

14"

10"

Life.

144 miles. .
225 miles. .

700 miles. .
368 miles. .

2009 miles.

2250 miles.
( >ne month

Two weeks. .

Two weeks [
40 to 50 das j

15 day -

6 weeks

1 i<i ; weeks

Remarks.

Not Chi'go

Co.'s make.
Chicago Cm. S.
Co.'s make.

Have not been re-
moved afte 14 ' j
months' use .

Dies, two

each 7" .

Two authorities.

Made by ( long
den 1 Iraki

L'gtta me'd Irom
scale drawing.

THE TEChXOaitAl'II.

Life ok Cables.

Street.

Kansas City.
E. 5th....
W. 5th....
E. 12th...
W. I2th. ..
W. i8th...
E. i8th...
Westport . ,
Walnut . . .
15th

Holmes .

Main Line. . . ,

Washington . . .

Troost Ave
Washington ....

7th

Chicago

Chi. Cy. Ry. Co

Lgth. cable,

feet. Life cable.

32300-

30500.
14200.
29500.

22000.

33000.

6 months. .

7 months. .
12 months.
7 months. .
7 months. .
18 months.
14 months.
4 months.
15^ mo..

Has been
in 22 mo. .

Speed.

(/i

<T>

miles,
miles,
miles.

miles.

8 months. . 8 miles.

9 months. . 12 miles.
12 months. 9 miles,

On II mo.

40000 mi.

Character
road.

Very

crooked

13 per cent
grade

Very ■
crooked

10 per cent

grades

18.53 Pei"

cent grade

Almost
straight

Remarks.

J Met'p'li'an Line

y Grand Ave Line

K. C. Cable Line
tftt

— ! •"

Business very he'vy

THE FOUR-MILE CRIB OF THE CHICAGO WATER-
WORKS.

By Simeon C. Colton, '85.

Engineer for the Contractors.

This piece of work has received slight notice in engineering
perio dicals, but not by any means such as its prominence warrants.
When this massive steel and timber crib left the Chicago har-
bor, it carried a cargo one half larger than ever floated on the great
lakes, and carried this with a draught of only 14 feet.

The construction of this structure was begun on January 7,
1889, by the FitzSimons & Connell Co., by placing the launching
ways. These ways consisted of nine sets of 12 x 12-inch oak timbers
placed at an incline of three fourths of an inch to a foot to the face
of the dock, which was cut down to a foot above high water. The
ways were covered with 4 x t 2-inch oak, and on these slides was built
the ti mber bottom. For lubricating the ways a mixture of tallow
and graphite was used.

The shoe, 12 inches high, consisted of two parallel timbers
12 x 1 2 -inch pine, and formed a polygon of 24 sides, the greatest diam-
eter being 124 feet. See Fig. 1.

THE TECHSOGRAPH

Fig. i. Four-Mii.k Crib.

THE TECHNOGRAPH. 19

Upon this shoe the timber was laid, upon blocking on the ways,
and firmly bolted with 32-inch round drift bolts, forming a platform
2 feet thick and 125 feet in diameter. All timber in these two courses
was surfaced on four sides to make more compact work and give a
better caulking seam. Upon this bottom a 70-foot circle was struck,
and between the circle and the sides of the polygon (26^ feet) the
timber was carried up 13 feet higher. This ring was planked verti-
cally both outside and inside with 6-inch oak securely drift-bolted
to the pine and thoroughly caulked. The inlet ports to the center
well were placed 5 feet up and were 5 feet square. These ports were
closed by gates and stoppers before the launching of the structure.

With the planking and bottom well caulked, the structure was
ready for the launch, except that the 2 foot bottom would stand
neither the launching strains nor the pressure caused by the dis-
placement. The plan which had been adopted at the outset of the
work was to load the structure to draw 27 feet and keep the interior
well dry, thus this clear space of 70 feet was expected to withstand
a pressure of 1,600 lbs. per square foot, or a total pressure of 3,000
tons. In order to cope with this pressure we placed five Howe trusses
20 feet high within this well, and built the ends fast into the outside
circle of timber. The lower chord, composed of four pieces 5x12,
was securely bolted to another chord underneath the bottom of the
crib. One truss was placed on the center line of the well, and two
others each side, 10 and 22 feet distant. In order to further help
the trusses, a central tower 30 feet high was built of 12x12 timbers
in bents of three, and capped with 14x16 oak. Through the oak
cap, twenty 1^5 -inch round rods were passed, leading down at an
angle of 300 and securely fastened by pins and lugs to the inside
steel cylinder. Notwithstanding these precautions, as well as the
fact that the crib was sunk to a depth of only 25 feet before the
water was allowed to enter the center well, the posts on the tower
were crushed into the caps 1 to 2 inches, and the oak cap was badly
bent.

Upon the fourteenth course of timber in the ring the steel cyl-
inder was started. This cylinder was 124 feet in diameter at the
bottom, and 118 feet at the top, and 30 feet high, and consisted of
plates -vg-inches thick, 4 feet wide, and 16 feet long. Each sheet
butted in the ring, and lapped the rings above and below. Lead
was used in the butted seams to secure a water-tight joint. The
vertical sheets were joined by angles, these same angles receiving
the ends of a bulkhead sheet, -?b -inches thick, 4 feet wide, and 24

THE TECHNOGRAPH.

feet long. The inner cylinder was parallel to, and 27 feet away
from the outside. Thus we have the metal structure, two cylinders
124 feet and 70 feet in diameter, joined by 24 solid bulkheads placed
on radial lines, the whole weighing 430 tons. There were some
96,000 rivets in the work, which fitted so well that no holes required
than a drift to draw them into place. All seams were caulked,
so that the steel work was absolutely tight.

The cylinder was filled with Portland cement concrete, consist-
ing of 1 part cement, 3 parts sand, and 6 parts stone. The stone
was broken to pass a i)4-inch ring. Rubble stone were imbedded in
the concrete, each stone being carefully laid flat and surrounded
with concrete well tamped. The concrete was mixed by a screw
mixer (Caldwell's) mounted on a scow, and was able to turn out
250 cubic yards in 10 hours. All concrete and stone was handled
by a double-ended derrick mounted on a movable platform over
the center well; this derrick being able to reach every point in the
circle of the crib, and was able to lift 15 tons.

When about 1,500 cubic yards of concrete had been placed
aboard, the crib was towed into position a distance of about four
miles. Two tugs towed her about three miles in two hours. Once
started on her journey the water was let into the inner well by
means of valves placed in the sides for that purpose, and after
reaching the site some 200 cords of stone were placed on top of
the iron to secure the structure against damage by storms during
the night. The crib, when sunk, showed about 8 feet above the
water, and up to date has settled about 30 inches into the clay
bottom, leaving the top of the steel 5 feet 6 inches out of the water.

Work was stopped for the season November 5, 1889, with about
one half the pockets filled with concrete. Upon resuming opera-
tions June 11, 1890, it was found that the winter's storms had
caused a slight unevenness in the settlement, but had not damaged
the structure a particle.

Stone setting was commenced July 21, and the masonry por-
tion of the structure was completed September 25, 1S90. In that
time 5,000 cubic yards of concrete had been handled, and about
19,000 cubic feet of granite masonry had been set. This time
includes, of course, all the stormy weather, during which we were
unable to reach the crib, that is, during this period of 64 days we
actually worked only 40 days. The granite masonry was but a fac-
ing on the outer and inner circles, the center being filled with con-
crete. The masonry as completed reached 16 feet above the water,

THE TECHNOGRAPH. 21

but is to be carried higher after the completion of the tunnel. The
stones in the outer circle were bound together by copper clamps 2
inches by 20 inches, weighing 50 pounds each.

The concrete and masonry being finished the derricks were run
to one side over the outer wall, and were used as a hoist during the
sinking of the inlet shaft. The two lower sections of the shaft had
been put in place before the crib was launched, and hence required
only to be cut loose in order to begin the sinking. This was accom-
plished with little difficulty, and we found that there was little or no
leakage through the 3-inch space between the shaft and the bottom
of the crib, the water having been shut off by the settlement of the
crib. Heavy timber guides were placed about the shaft, thus secur-
ing its sinking in a plumb position.

The shaft consisted of thirteen sections of a cast-iron cylinder
10 feet internal diameter and 8 feet high, bolted together by internal
flanges. The cast-iron shaft was underpinned at a depth of 92 feet
below datum by a 12-inch brick shaft to a sump, making the total
height or depth n 1 feet 4 inches to top, and standing n feet 4
inches above city dature (about water's edge).

The material excavated was mostly loam and clay, no pump
being required in the shaft, although we stopped 12 inches above a
water-bearing strata. In fact, water was thrown down the shaft to
wet the miners' spades. About 160 tons of pig-iron was piled upon
the shaft to force it to the required depth, this being nearly 160
pounds per square foot of shaft in the ground.

The inlet gates were placed in the third section from the top,
and are entirely submerged; they are operated from the top by
means of screws. These gates would entirely shut off the water
from the city, should the tunnels ever need repairs. All sliding
parts of the gates are faced with brass in order to avoid rust.

I have mentioned no losses as being sustained by the Fitz-
Simons & Connell Co., during this construction on account of storms,
but they were not a few. We consider ourselves extremely fortu-
nate in being able to say that only one life was lost during the con-
tinuance of the work, and that by drowning. Although the top of
the structure is 16 feet above the water, on several occasions have
the waves gone clear over this wall, throwing solid water into the
inner well.

At the present date the 8-foot tunnel has progressed about 300
feet from the four-mile crib shaft in shore (under another contractor)
and is making good progress daily.

THE '!'/:< HNOGR IPH.

NOTES FROM MECHANICAL ENGINEERING THESES.

Tiik Heating Power oi Illinois Coal.

In the accompanying table is given a summary of the results
of analyses and tests of samples of Illinois coal made by Messrs.
R. B. McConney, '89 (A), and F. H. Clark, *9o (B), together with
the results obtained from samples of Youghiogheny coal which are
inserted for comparison. The samples were, in nearly all cases,
taken from the cars as received in Champaign, the object being to
obtain a fair average sample of the commercial coal in every
instance. The percentage of moisture, volatile matter, fixed carbon,
and ash were determined by the usual laboratory methods. The
heating power was determined by burning samples of the coal in a
water calorimeter of the form described in the American Engineer
for June 12, 1889. In this method 2 grams of pulverized coal are
mixed with say 7.5 grams of potassium chlorate (KC10S) and
2.5 grams of potassium nitrate (KN03). The mixture is placed
in a deep crucible, a fuse is inserted and lighted, and the crucible is
then covered with a cylindrical cup which is perforated near its
edge with many small holes. The crucible and inverted cup are
then placed in a known weight of water at a known temperature.
The gases of combustion given off escape through the small holes
and thence through the surrounding water, the temperature of
which is therefore raised. This rise of temperature is the basis of
the calculation of the heating power. In Mr. McConney's tests
the proportions of coal, potassium chlorate, and potassium nitrate
used were as already given. Mr. Clark found by a special series of
tests that the highest results were obtained with the proportions 2
grams coal; 13.5 grams KC10:!; 4.5 grams KN08, and these
proportions were used in his experiments. In both sets of tests
the method followed was to burn three charges from the same
sample; if the results agreed, the value so found was taken to be
the heating power; if they did not agree, two more charges were
burned and the average of all was taken in Mr. Clark's test as the
heating power; but in Mr. McConney's tests, the results given are
the mean between the value most frequently found in five tests and
the maximum value. The average difference between the highest
and lowest values for any one sample in Mr. Clark's tests is from .5
to .6 of one per cent of the tabulated values.

THE TECHNOGRAPH.

Heating Power of Illinois Coal.

Location of Mine.

LaSalle, LaSalle county

Peru, " "

Bloomington, McLean county.
Oakwood, Vermillion county . .
Fairmount, " " . .

Danville, " " ..

Lincoln, Logan county .

Mt. Pulaski, Logan county .
Niantic, Macon county

Riverton, Sangamon county.

Barclay, " "

Pana, Christian county

Assumption, Christian county.
Mt. Olive, Macoupin county . .

Odin, Marion county .

Kinmundy, Marion county.
Sandoval, " "

Centralia, " "

DuQuoin, Perry county. . . .

Big Muddy, Franklin county.
Carbondale, Jackson county. .
Youghiogheny, Pennsylvania.

.A.
.A.
.A.
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,B..

..A.

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..A.
..B.
..A.
..A.
..B.
..A.

.A.
.A.
.B.
.A.
.B.
.A.
.B.
.B.
.A.
.A.
A.
.B.
.B.
.B.
.A.
.B

■ "3-
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£ <

- o

12,169 39
11,82937

11. 31335
12,528 37

11*431 31
12,285132
12,50643

n.65537

11,272
11,718
11,360
11,529
11,529

".633135
12,096 38
",205135
11,61036
13,06841
",44135
".772 35
",954 33
12,663 4i
11,66434

11.959 35
11,78138
12,17032
12,393 30
12,825 32
12,58233
13,940 33
14.25635

4 43
19 47
99 45
55 46
8 47
35 53
70 45
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9944
3 49
8246

25 47
15 45
39 48
45 44
6746
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7

Tests of a Smoke-Preventing Furnace.

During the winter of 1889-90 tests were made by Messrs. Mc-
Kee and Gilliland ('90), of a steam jet smoke-preventing device as
applied to two of the steam heating boilers at the University of
Illinois. These boilers are of the Root type, each consisting of 100
4-inch tubes 9 feet long, and having 22.5 square feet of grate sur-
face, and are used wholly for steam heating. The returns from the
radiators and coils are connected to traps and thence to a tank
from which the water is fed to the boilers by a steam pump. This
pump is supplied with steam from a small vertical tubular boiler
which also supplied steam to the jets of the smoke preventer at a
gauge pressure at the boiler of from 35 to 40 pounds.

The arrangement for preventing smoke is as follows: Along
each side of the furnace about 9 inches above the grate is a row of

THE TECHXOGEAPH.

openings about ^-inch in diameter and about 6}4 inches from cen-
ter to center. Each is formed by a cast-iron tube set in the brick
work which may be compared to the outer tube of a Bunsen
burner. Air is supplied to what corresponds to the side openings
in a I.unsen burner from the ash pit by passages left in the brick
work, one passage supplying two tubes. At the back end of each
tube is a steam jet of which the opening is about one-sixteenth
inch in diameter, corresponding in position to the gas jet in a Bun-
sen burner, which is supplied with steam by means of a ?4 inch
steam pipe set in the brick work and connected to the small boiler
previously mentioned. This pipe is doubled back and forth in the
bridge wall, the object being to superheat the steam on its way to
the jets.

Five pairs of tests were made in all, three with both main boil-
ers in use, and two with single boilers. For each pair of tests, i. e.,
one with jets in use and one without jets, the times were selected
when the conditions were as nearly identical as possible. In all of
the tests the evaporation in the main boilers was found to be
slightly greater with the jets than without them, the average evap-
oration being increased from 5.16 pounds of water from and at
2120 per pound of coal to 5.31, or about 2.9 per cent. But more
coal was required for the small boiler when the jets were in use, so
that taking the plant as a whole the efficiency with the jets in
operation was found to be about 99 per cent, of that without the
jets. After making allowance for the loss by radiation from the
small boiler and for the steam used by the pump, both being deter-
mined by tests and calculation, it was found that 23.2 pounds of
coal per hour were required to furnish steam to the jets.

As a smoke preventer the arrangement is fairly successful.
The steam supply to the jets for each boiler is controlled by i
inch globe valve. When these valves are opened about two turns,
the smoke issuing from the chimney is reduced to a light cloud
excepting at the time when the furnace doors are opened for firing.
The rate of combustion is ordinarily about 13.5 pounds of coal per
square foot of grate per hour.

THE TECHNOGRAPH. 25

A CLOCK FOR EVERYBODY.

Pbof. Ira O. Baker.

Probably but few, if any, persons living to-day appreciate the
inconvenience in matters involving the time of the day which existed
before the invention, or even the wide distribution, of clocks and
watches. In all countries until a comparatively late date, and in
some even now, the diurnal revolution of the heavens, the rising,
culmination, and setting of the sun and stars were the only means
of telling the time of day. Owing to the cheapness of watches and
clocks, and in no country are they as cheap or as good as in our
own, the ability to tell time by the sun or stars is liable to become a
lost art, if it is not already lost.

One object of this article is to offer a few hints on the deter-
mination of time by simple observations of the heavens; and it will
not have been written in vain if it shall incite even a few to observe
the revolution of the heavens and contemplate the grandeur of the
movements.

THE DAY CLOCK.

"The sun to rule by day." Remember, i, That the meredian is
a circle passing through the north point, the zenith, and the south
point; 2, That the pole is on this meridian at an angle above the
north horizon equal to the latitude of the observer (for a majority
of the readers of this it is a little less than half way up from the
north); 3, That the equator of the heavens is 90 degrees from the
pole, i. e., the equator passes through the east and west points and
crosses the meridian at an angular distance south of the zenith equal
to the latitude — a little more than half way up from the south.

When the sun is on the meridian it is 12 o'clock, noon. Imagine
a line drawn from the east point of the horizon to the north pole,
then when the sun is on this line it is 6 a. m. The straight edge of
a card or pencil held very close to the eye will be of great assist-
ance in tracing this line through the sky. Notice that in the sum-
mer the sun crosses this line long after sunrise, while in the winter
it crosses the line before sunrise. Similarly a line drawn from the
west point to the north pole is the 6 p. m. line. If the sun is half
way between the 6 a. m. line and the meridian, it is 9 o'clock; if
one-third of the way, 8 o'clock, etc., etc.

To those who have not tried it, this will seem like a rough way
of determining the time, but it is astonishing how great accuracy
can be attained by a little practice, particularly when the sun is near

26 THE TECHNOGRAPH.

either 6 o'clock line. Experience seems to show that with a little
practice any bright boy of fifteen can determine time by this method
within fifteen minutes. The method is specially applicable in local-
ities where the cardinal points are accurately marked as, for instance,
in the West where the roads, fences, etc., run north and south, and
east and west.

The time determined as above is apparent solar time, and dif-
fers from the time kept by a good clock. In the words of the house-
hold almanac, "the sun is fast" or "the sun is slow;" that is, time
determined by the sun will be faster or slower than the true time
according as the sun is "fast"' or "slow." The common almanacs
usually contain a column which shows for each day of the year how
much the sun is fast or slow. An examination will show that about
the first of November the sun time is 16 minutes too fast, and that
the difference grows less for nearly two months either way from
that date, when there is practically no difference between the two
kinds of time. About the middle of February sun time is 14 min-
utes too slow, and the difference decreases each way from that date
for about a month and a half, when the two practically agree again.
For any other time of the year, the difference is inappreciable.
Notice that sun time never differs more than about 15 minutes from
the local time.

The time found and corrected as above is local time, and will
differ from railroad time, which most clocks now keep, according as
the observer is east or west of the meridian from which the railroads
count their time. It is not necessary here to explain the method of
making this correction.

THi; NIGHT CLOCK.

"And the stars to rule by night." The ancients seem to have
determined the time during the night by the rising, culmination, and
setting of the various constellations. Euripides, who lived 480-407
B. C, makes the chorus in one of his plays ask the time in this form:

"What is the star now passing?"

And the answer is:

"The Pleiades show themselves in the East;
The eagle soars in the summit of heaven.''

It must have required a prodigious memory to keep in mind the
times of rising of the various constellations, particularly as they
change from day to day.

It is not known that the method described below was used by
the ancients, but it is probable that this and many somewhat similar

THE TECHNO'; RA J '//.

devices were employed to tell the time. It would almost seem that
the Creator, in his sympathy for those who are poor in the things of
this world, has provided them with a clock of unapproachable mag-
nitude, the dial plate of which is studded with jewels, and hung high
in the northern heavens, where it has continued to mark off the
hours with unerring certainty since the beginning of time itself. The
Great Dipper, whose nightly revolutions about the pole has been
observed by all, is the great night clock. An examination of the
accompanying diagram will show how it marks off the hours.

Tothtffat P«*t*r-

At this time of the year (spring), the great dipper is to be found
early in the evening high in the northeast; it moves west as the
hours go by. The diagram represents this constellation when at its
highest point. The dipper is composed of seven bright stars; the

THE TECHNOGBAPH.

two marked i and 2 in the diagram are called the pointers, since
they point nearly toward the north star. The stars of the dipper
correspond to the figures on the clock face. In an ordinary clock
the figures are fixed and the hands are movable; but in our great
star clock the figures (stars) are movable, and the hand (the meri-
dian) is stationary. The heavy lines shown in the diagram are one
hour apart. Then, if the pointers are on the meridian, an hour
thereafter afterwards, a point half-way between stars 3 and 4, will be
on the meridian. The dotted lines indicate the half hours. Notice
the method of numbering these lines. A little study will be required
to fix in mind the positions of the several lines. Notice that there
are two stars in each hour space. The + 2 line is as far beyond
7 as 7 is from 6. Notice that if lines were drawn through stars 4, 5,
6, and 7, they would indicate quarter hours, nearly.

On the 21st of March, when the line marked o coincides with
the meridian, i. e., when the line o points from the zenith to the
north point of the horizon, it is 12 o'clock midnight. This is the
time at which the diagram is set. When the line + 1 comes into
the meridian, it is 1 o'clock; when + 2 is in the meridian, it is 2
o'clock; and when — 1 is in the meridian it is 11 o'clock, etc. If the
dotted line between stars 4 and 5 coincides with the meridian, it is
half past 12 o'clock, etc.

When the line + 2 has passed by the meridian, the time can still
be estimated by imagining a line 4-3 to be placed as far to the right
of +2 as +1 is to the left; but before line +2 has passed very far
by the meridian, the line — 1 or the imaginary one — 2 will have
come into the 6 o'clock line on the west. If the line — 1 coincides
with the west 6 o'clock line, it is 5 a. m. Similarly, if the +2 line
coincides with the 6 o'clock line on the east, it is S o'clock p. m.
Thus between the two 6 o'clock lines and the meridians, it is possible
to determine the time at almost any hour of the night. In the spring
and summer, the 6 o'clock lines and the meridian above the pole
will be used; and in the fall and winter, the 6 o'clock lines and the
meridian below the pole must be employed.

Our great north clock is a sidereal clock; it keeps star time, of
which 366 ! ; days make a year. As compared with common clocks,

us a day in a year; hence, it gains nearly four minutes in a
day, or, to be a little more accurate, it gains each day four minutes
lacking four, seconds, /. <■., 3 min. 56 sec. The two kinds of time
agree on the 21st of March, but for any other time of the year the
star clock is too fast. Suppose that on the 21st of April it is 12

THE TECHXOGRAPH. 2£

o'clock midnight by the north clock, what is the true time? The
21st of April is 30 days after the 21st of March, and hence the star
clock has gained 30 times 4 minutes, which equals 2 hours, or more
exactly the gain is 2 hours lacking 2 minutes; therefore, on the given
date, 12 o'clock by the north clock corresponds to 2 minutes before
10 o'clock p. m.

The computation necessary to correct the north clock is greatly
simplified by noticing that the gain in 3 months is 6 hours. For
example, if on the 21st of June the north clock indicates 12 mid-
night, we know immediately that the clock is 6 hours fast, and that
therefore the true time is 6 p. m. If on the 21st of July the north
clock indicates 6 a. m., we find the true time by remembering that
the star clock was six hours fast on the 21st of June, and that it has
gained 2 hours since, and hence is 8 hours fast; therefore the true
time is 10 p. m. Similarly for other times of the year. With a little
practice these explanations are readily comprehended and easily
remembered. It is astonishing what degree of accuracy can be at-
tained by a little practice.

To those studying astronomy, the north clock affords a simple
and easy method of determining the right ascension of any particu-
lar star, and is, therefore, a great help in finding the objects de-
scribed by the text-books. In times past, the writer's students in
descriptive astronomy reported that this device was very useful to
them for this purpose.

CURBS AND GUTTERS.
F. R. Williamson, '92.

The thickness and depth of curbs, and the form and size of
gutters can not be computed from theoretical considerations, but
must be determined by a careful study of practice. In this article
will be briefly given some results of practice.

Curbs.

The minimum height above the gutter may be put at 3 inches,

while the maximum will depend upon the height of the sidewalk

above the gutter. The depth below the upper surface of the gutter

varies in practice from 10 to 15 inches, but with a concrete founda-

THE TECHNOGRAPH.

tion it may be less. In the ordinary form of curb, the thickness
ranges from 3 to 6 inches, and the lengths most commonly used
range from 2 to 6 feet. For foundation, sand and gravel are largely
used. Concrete is now rapidly gaining favor, as it permits a curb
of much less depth, and at the same time makes a firmer base.
The curb is sometimes set vertically but more generally it is given a
slight batter, in which case the top is usually dressed horizontal
and flush with the sidewalk.

Gutters

On many streets no special form of gutter is used other than
that formed by the curb and the crown of the street, while on
equally as many others some form of gutter is provided. In the
latter case the surface of the gutter may be either flat or slightly
concave. The gutters are generally constructed of the same mate-
rial as the street pavement, but in the case of cobble stone pave-
ments a flat stone 1 foot or more wide is placed in the middle of
the gutter.

Examples.

In the report for 1889 of the Engineering Department of
Washington, D. C, are given the following specifications. For
Standard Granite Curb: Length to be not less than 6 feet, depth
not less than 20 inches nor more than 24 inches, thickness 6 inches,
base must average not less than 6 inches in width. The curb must

•*-«« SLOPE M,

/' 6

Fig. i. Granite Curb. — Washington, D. C.

be dressed ta inches on the face, 3 inches on the back, 6 inches
deep at the joints, and the top beveled '4 inch. For Blue Stone

WILLIAMSON— CURBS AND GUTTERS.

Curb: The specifications are the same as above except that the
length must not be less than 4 feet, nor the thickness less than 5
inches. For Special Granite Curb (Fig. 1): Length not less than
6 feet, thickness 8 inches, depth not less than 8 inches nor more
than 10 inches, dressed on top the full depth of the face, and 3
inches on the back, and the top beveled ^ inch.

In the very valuable series of papers on Municipal Engineer-
ing in Engineering News, Vol. 17, the standard curb and gutter of
Philadelphia is described. See Fig. 2.

\i}SNASHEp PA V/NGt SAND ■; •>'//,

Fig. 2. Curb and Guttkr. — Philadelphia.

The thickness of the curb is 5 inches, depth 20 inches, and
length 6 feet. The gutter is 5 inches deep, except at inlets where it
varies from 7 to 10 inches. The bottom of the gutter consists of a
flat stone about 10 inches wide, and 3 to 5 feet long, laid 5 to 8
inches below the top of the curb.

In Cincinnati, Ohio, one of the standard forms of curbs is 4 to
5 inches thick, not less than 21 inches deep, and 3 feet long;
dressed 10 inches on the ends, 12 inches on the face, and 3 inches
on the back; set on 2 inches of packed sand and gravel, with a
batter of 1^ inches, forming a right angle with the gutter flag.
Stones are placed back of the bottom of each curb to help counter-
act the pressure of the sidewalk. The gutter flags are not less than
3 feet long, about 6 inches thick, and 16 inches wide; are cut on
the side next to the curb, the top hammer dressed, the ends dressed
and squared to make y( inch joints 3 inches deep; and are set
upon a 6-inch bed of gravel. The ordinary depth of gutter is 7
inches.

Through the courtesy of William T. Rossell, Captain of Engi-
neers, U. S. A., I am enabled to give a brief description of the com-
bination curb and gutter used in Washington, D. C.

Fig. 3 shows the general section, and Fig. 4 shows a horizontal
view and a vertical section at hand-hole.

THE TECHNOGRAPH.

WALK

ROADWAY

X' 8"

3. Combination Curb 'and Gutter. — Washington, D. C.

coaichi li BASt 6" THICK

•- it r

Fig. 4. Hand hole in Combination Curt, and Gutter.-
w vshing ton, d. c.

MATHER— SINK-HOLE. 33

The dimensions and general plan are as shown in the cuts.
The combined curb and gutter consists of concrete composed of
one part Portland cement, two parts clean sharp sand, and three
parts clean stone broken to pass a i-inch ring. The exposed sur-
faces of both gutter and curb are coated i^ inches thick with a
mortar composed of three parts granulated granite and two parts
cement. The curb and gutter are sawed, at intervals of 8 or 10
feet, to allow for expansion and contraction and to give the appear-
ance of cut stone. A conduit, 4 by 4 inches, for electrical conduct-
ors is left at the base of the curb if so ordered by the Engineer
Commissioner. Hand-holes, to give access to this conduit, are left
at intervals of about 50 feet.

A REMARKABLE SINK-HOLE.
L!y R. A. Mather, '92.

Sixteen miles west of Chicago on the Chicago, Burlington &
Quincy Railway, there is a remarkable sink-hole. As the east-
bound train passes from a 20-feet cut, a passenger may observe a
small flat, some 15 or 16 feet below grade, 1,000 feet across and
extending half a mile on either side the track. This flat is grown
over with slough grass and cats'-tails, and is partly covered with
water. When the grading for the first two tracks was done several
years ago, trouble was caused by the sinking of the embankment.
Piles were driven but to no avail. The roadbed was completed by
filling in until the embankment stopped sinking.

Last summer when the embankment was being widened for a
third track, it again began to sink, sometimes from 1 to 3 feet in a
night and sinking altogether 40 feet. For two months a large
construction gang worked steadily on the fill without gaining a foot.
The earth under the embankment, instead of becoming more com-
pact was pressed out and up, actually moving the telegraph poles
12 feet farther from the track and raising a ridge 10 feet high. As
there is an end to all things, equilibrium was finally established and
the track brought to grade.

About 95,000 cubic yards of gravel and dirt were required to
fill the sink. The cost of labor and material for the 1,000 feet of
embankment, including the new roadbed and the fill on the old one,
was $10,000, or $10 a linear foot, about seven-tenths of which was.

THE TECHNOGRAPH.

owing to the sink-hole. Trains had to slow up to 4 miles an hour,
which added much to the expense, particularly as some days more
than a hundred trains passed over the road.

No borings were made to determine the strata, which perhaps
was not wise, since a complete knowledge of the ground might have
led to a plan which would have saved considerable expense.

The flat is underlaid by a stratum of Niagara limestone. Al-
though underground caves are often found in strata of rock, yet
this can not explain the sinking, for the roadbed would have sunk
rapidly rather than gradually, had the dome of a cave which sup-
ported it suddenly given away. Besides, this would not explain
why the earth was displaced along the sides of the embankment.
Apparently the roadbed rests upon either a bed of quicksand or a
bed of clay saturated with water. Either material, with bed-rock
under it and a tough crust of earth over it, would have a tendency
to transmit pressure to all confining surfaces. When a load great
enough to exceed its ultimate strength was put upon the crust, it
gave way thus transmitting the pressure to the quicksand or satu-
rated clay below. The sand or clay in turn tiansmitted the force
of the load, as upward pressure, against the under side of the sur-
rounding crust. As the load of the embankment was increased, the
upward pressure against the crust increased until finally the surface
in the neighborhood of the telegraph poles was raised into a ridge.
The quicksand or saturated clay followed the displacement of the
crust, while the embankment followed the displacement of the
quicksand or clay. As more dirt was added to fill the sink, the
load was increased, at last producing such a strain on the ridge
that it cracked open, leaving a gap 2 or 3 feet wide.

ROPE DRIVING.
By F. L. Bunton, '91.

The transmission of power by rope, cotton, hemp, rawhide, or
manilla is fast taking the place of gearing and leather belting for
large powers, and where the distance between the power and the
work is comparatively great.

Cotton rope is the most generally used in England, where it is
said to be the best, but as a greater part of the applications are in
cotton factories its extensive use is readily understood. Hemp,

BUNTON—ROPE DRIVING. 35

rawhide and manilla are used extensively in the United States. The
average duration of manilla rope is about six months. Rawhide is
guaranteed for three years. One drive of ten coils of i^-inch
manilla rope in an electric plant in Chicago was used twelve months
before it broke. A transmission at the Rookery Building, Chicago,
of twenty coils of ^3 -inch rawhide rope, transmitting 225 H. P., was
used two years, and was spliced but once during that time.

Cotton is more extensible than the others; hemp and manilla
are about the same in regard to extensibility and flexibility, while
rawhide does not form to the pully quite so readily nor stretch so
rapidly. When the latter becomes set to the pully it maintains its
original cross-section more nearly than any of the other kinds.
Care should be taken in splicing, long splices being better than short,
as a more uniform cross- section is given to the rope and sudden en-
largements cause abrupt changes in velocity, when passing over the
pulley. The Chicago Link-Belt Machinery Co. make their splices
from twelve to twenty- five feet in length.

Mr. C. W. Hunt* recommends a working-stress of 3V of the
breaking strength, while the Link-Belt Machinery Co., of Chicago,
use 3V of the breaking strength. Mr. W. H. Boothf says 5,000 feet
per minute is the best speed, and Mr. Hunt advises 4,800 feet per
minute. These are both reasonable speeds, but above 6,000 feet
per minute, the loss by centrifugal action is much increased.

In order to show how difficult it is to slip the rope in the
groove, the Chicago Link-Belt Machinery Co. attached a 50-lb.
weight to a ^5 -inch manilla rope, and on a 24-inch pully with a 45-
degree angle in its face, a weight of 350 lbs. at the other end was
necessary in order to slip the rope in the groove. Let T2 = tension
on the driving side, T1 = tension on the following side, Y = co-offi-
cient of friction, and N = arc of contact in fraction of the circum-

T
ference. According to Unwin's formula, log. r,,2 = 2.729 NY, whence

rp J j

log. T2 = log. W = log. 7 = .845098, N = .5, therefore for this case
the co-efficient of friction Y = .619. Ropes do not drive pulleys
by adhesion alone, but it is more by wedging action due to the angle
of the grooves.

Rope is not very expensive, and compares favorably with belt-
ing and gearing. Its noiseless movement, evenness of transmission,

* Transations of A. S. M. E., i£
t American Machinist, 12-8-88.

36 THE TBCHNOGRAPH.

and exact alignment being unnecessary, place it far in advance for
long transmissions.

The following table contains data taken from several rope trans-
missions in Chicago. The horse-power in the table is that which the
plant was transmitting at that time. The values Tt , T, , V, are solved
by Unwin's formulas, previously given. The co-efficient of friction
being .731 in every case and 45-degree angles in all of the grooves.
The first ten transmissions are run by manilla rope, the next five by
rawhide, and No. 16 by cotton rope.

B UNTON—ROPE DRI T rIN( • .

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38 THE TECHSUGRAPH.

NOTES ON A RAILROAD RE-SURVEY.
By B. A. Wait, '92.

The road was one of the main trunk lines across northern Iowa.
The route is for the most part through rolling prairie, and runs
nearly at right angles to the largest streams. The company had
only the location notes, and the object was to get complete notes of
everything on the right-of-way, not only for maps but also for use
in making a number of improvements.

The party consisted of a chief who was also transitman, two
chainmen for track measurements, two chainmen for location of
section corners, levelman, and rodman. In addition, two section-
men were taken off of each successive section, one to drive stakes
and one to dig for corners.

The transit was used only to run in the curves and to take the
angles of the road with the land-lines. The transitman kept the
hand-car just ahead of the chainmen, dropped the stakes, and took
the notes. The chaining was done along the rail except around
curves. The head chainman marked the stakes and laid them over
the chain-marks on the rail. The stakes were driven, by one of the
section-men, seven feet to the right of the center of the track. The
rear-chainman gave the distance out by measuring with a pole from
the edge of the rail. The rear-chainman read all "pluses," and in
running in curves acted as rear-flagman.

The beginning and ending of curves were set by eye by sighting
along the rail for some distance back, except on very light curves,
when they were set with the transit. The transit was set over these
points and the deflections were taken at every 100-ft. station. The
tangent points could be set correctly within five feet by eye, and this
is accurate enough where the back-sights are of considerable length.
This method is shorter than setting them with the transit, unless the
beginning of the curve can be set from the end of the preceding one.

Levels were taken at every station, one on top of the tie and
another on the natural surface. Readings were also taken at the
bottom of all culverts, streams, and cattle-passes. Elevations of high-
water marks were taken whenever possible. Bench-marks were es-
tablished every half-mile. The benches were made by driving
spikes into telegraph poles or signal posts, or they were taken on
some part of the depots or other buildings.

The land-line party measured on all section-lines both ways
from the track to the nearest established corner of that section. If

POWELL— SQUARE DRIFT-BOLTS. 39

a section corner was found within one hundred feet of the track no
measurements were taken on the other side. In many places the
highways had been graded over the corners, and the pick and shovel
carried by the second section-man were necessary. About eighty-
five per cent of the corners looked for were found, and nearly one
half of those were covered. The corners covered over a foot deep
were rarely found. When the corners were found they were always
"tied in" from the sides of the roads or from fence corners. The
head chainman kept the notes. Distances to all streams were re-
corded, as well as the depth of the water and length of the bridge.

A tracing of the plat of every town was made from the records
at the county seat, and enough angles and measurements were taken
to connect the surveys of the road with that of the town. Every-
thing on the right-of-way was located with reference to the track.
The notes of station-ground surveys were recorded in a book for
that purpose. The sketches were made on a scale of fifty or a hun-
dred feet to the inch. The station surveys were made by whichever
party was ahead.

The transit book was one made for that survey. It was 8x9
inches, and on each page was a square divided into quarters to
represent the section and its divisions. The track had been previ-
ously sketched in from an old map. The notes were recorded along
the margin. All chain and transit notes, except station surveys,
were recorded in this book. Streams and hills near the track were
sketched in by the transitman.

The plan of the work kept all the parties together. The method
was easy and expeditious, and all the data necessary was determined
with sufficient accuracy.

SQUARE DRIFT-BOLTS.

By J. H. Powell, '91, and A. E. Harvey, '91.

In No. 4 of the "Selected Papers of the Civil Engineers' Club of
the University of Illinois," John B. Tscharner gives a very thorough
discussion of a series of experiments on the holding power of round
drift-bolts. The writers made a series of experiments with square
bolts to determine the best relation between the diameter of hole
and the size of bolt, and also to determine the relative holding power
of square and round bolts.

THE TECHNOGRAPH.

The experiments were made with the University testing machine.
The bolts were of steel, i-inch square, about 30 inches long, the
ends square except that the sharp edges were hammered down
slightly. The timber used was pine, about such as that used in Mr.
Tscharner's experiments. Holes K»tfi Wj and ■;; inches in diame-
ter were bored as nearly as possible perpendicular to the face and
grain of the timber. The rods were driven with a sledge to a depth
of 6 inches, care being taken to start the rod centrally over the
hole.

As a result of the 20 tests, 5 for each sized hole, the average
holding power was found to be as in Table 1.

Table I.

Si/e of Rod.

Size of Hole.

Holding Power in Pounds.

6 inches Depth.

Per inch of Depth.

I inch square.
1 inch square.
1 inch square.
1 inch square.

j | inches.

] ;"; inches.
\f. inches.
j j inches.

3972
4260
4660
4050

662
710
777
675

From the table we see that a j*-inch hole gives the maximum hold-
ing power.

After the bolts were withdrawn the timber was split and the
condition of the wood surrounding the holes examined, from which
it appeared that in the holes larger than ].j inches, only the corners
of the bolt had held effectively; while in the smaller holes the wood
fibers were so crushed and torn as to largely decrease their power
to hold the bolt.

As compared with Mr. Tscharner's conclusions our experiments
seem to show that for holes of the same size but larger than {?
inches (the size which he found to give a maximum holding power
for 1 -inch round rods), the holding power of the i-inch square
bolt is greater than that of the i-inch round bolt, the quality of the
timber being the same in both cases. (See Table II.)

Table II.

DIAMETEH OF 11' •! K.

Round Rod

375 lbs.
710 lbs.

633 lbs.
777 lbs.

788 lbs.

tare Rod

662 lbs.

675 lbs.

Table II. shows the holding power per inch of depth of a i-inch
round rod and a i-inch square rod in different sized holes. From
the table it is seen that the maximum holding power of the round

THOMPSON— COST OF BRICK PAVEMENT. 41

rod is greater than that of the square rod. Since the cost of boring
and driving is the same in each case, and since the amount of iron
in the round rod is only 0.7854 of that in the square one, we must
decide that round drift-bolts have the advantage over square ones,
both as regards holding power and economy.

COST OF BRICK PAVEMENTS.
By A. D. Thompson, '93.

Brick have been used for paving purposes in this country and
in Europe until brick pavements are no longer an experiment. They
have been tested under all conditions, and have fulfilled the require-
ments of a good pavement far beyond the expectations of engineers.
Because of the cheapness, noiselessness, and durability of brick
pavements, many cities are investigating the merits of this paving
"with a view to adopting it, and there^is a call for data on the subject.
This call has been amply responded to in all cases but the cost.
Since this is a matter of such wide interest, it seems proper that
central Illinois, which may be called the home of brick pavements,
should give some data on this part of the question.

This pavement is laid with one course of brick and with two
courses of brick, the former method being, of course, the cheaper.

In the latter method, the ground is first brought to the required
grade and convexity. Then from three to five inches of gravel or
cinders is placed on this and thoroughly rolled. This is followed by
a course of brick laid flat with their length parallel to the street, all
joints being well broken. One inch of sand comes next, and is fol-
lowed by a course of brick on edge with their length at right angles
to the curbing and with the joints well broken. This course is
tamped and rolled thoroughly, and then fine sand is broomed into
the joints and about one-half inch of sand is left on top.

In the one-course method, the ground is brought to the required
grade and convexity, and is rolled solid. On this is placed from
five to seven inches of gravel tamped and rolled solid. The brick
is then laid on edge in about two inches of clean sand. The length
is laid at right angles to the curbing, all joints being well broken.
After this has been rolled and tamped thoroughly, about one half
inch of sand is broomed into the joints.

42 THE TSCHNOGSAPH.

It is evident that the only ways in which this method differs
from the two-course method are: — ist, one course of brick is done
away with; 2d, more work is necessary in preparing the ground and
in the gravel foundation; and 3d, more gravel is used.

Of course the cost of such work will vary with the conditions
existing at different places, and with the nearness of material, amount
of grading, and cost of labor. Below are the particulars for work
done in Illinois.

In all the cases cited the grading was comparatively light, and
labor cost from $1.25 to Si. 60 per day.

Bloomington was one of the first cities to test this method of
paving, having laid the first in 1874. Since then, about 160,000
square yards have been put down at a cost of about $1.65 per
square yard. The brick used are 2x4x8 inches and cost from
S8.00 to $8.50 per thousand. They are manufactured in the city.
Sand cost 80 cents per cubic yard delivered. Cinders were em-
ployed for a foundation.

Decatur has about 235,000 square yards of brick pavement,
which is the most of any city in central Illinois. It has all been
laid since 1884 at a cost of from $1.34 to £1-50 per square yard.
Two grades of brick were used in the work. The bottom course, or
softer burned brick, are 2.76x4x8 inches and cost S8.00 per thou-
sand; while the top course, or harder burned brick, are 2^x3^x7^
inches and cost $9.00 per thousand. The brick are made in the
city. The sand cost 75 cents and gravel 60 cents per cubic yard.

Champaign laid about 7,000 square yards of brick pavement in
1885 at a total cost of Si. 87 per square yard. Last year 7,000 square
yards were laid at a cost of Si. 57 per square yard. The brick are
2x4x8 inches, of which 120 lay a square yard. They are made in
the city and cost $9.00 per thousand delivered. The contractor
made the following estimate of the cost per square yard, including
profit: Grading, 9 cts, the dirt to be moved not more than 400 ft;
gravel and sand, using gravel for foundation, 15 cts; brick, at S9.00
per thousand, S1.0S; plank curbing, per square yard of pavement, 5
cts; laying and tamping the brick, 15 cts; sundry expenses, 5 cts;
making a total of Si. 57 per square yard.

Springfield has laid about 10,000 square yards within the past
three years, at a cost of from Si. 48 to Si. 62 per square yard.* The
brick used are 2x4x8 inches and cost £9.00 per thousand delivered
on the ground. Sand and gravel cost S1.50 per cubic yard delivered
on cars at Springfield.

HAY-RAILROAD GRADE CROSSINGS. 43

Danville laid about 26,500 square yards of brick pavement last
year, at a cost of $1.45 per square yard. Two kinds of brick were
used promiscuously, — one from Bloomington and the other from
Grape Creek. The Bloomington brick are 2x4x8 inches and cost
from $8.00 to $8.50 per thousand delivered on cars at Bloomington.
The Grape Creek brick are 4x4 x 12 inches.

The only city using the one-course system of brick in central
Illinois is Peoria. Considerable pavement has been laid in that city
at a cost of from $1.50 to $1.70 per square yard. The brick are
4x5x12 inches, and thus by laying only one course the pavement is
five inches deep against six inches where the two-course system is
used with common sized brick. Sand and gravel cost from 75 cts
to 90 cts on the streets.

Steubenville, O., uses only one course of common sized brick,
which has cost from 95 cts to $1.00 per square yard. The one-
course method with common sized brick is well adapted to cities
having light traffic, and is being adopted by many of the smaller cities.

In all of these cases, the first cost, or contract price, has been
given. The cost of repairs has been omitted because whenever any
repairs have been necessary, the cost has been too small to be taken
into consideration.

INTERLOCKED VS. UNPROTECTED RAILROAD GRADE

CROSSINGS.
By W. M. Hay, '91.

The rapid growth of the network of railroads of this country
has been marvelous. As this network becomes more and more in-
terlaced, the number of railroad crossings is greatly increased. This
fact has become a potent and perplexing question, especially to rail-
road managers, who desire to know to what extent they may oppose
a new road from crossing their established lines. When railroad
crossings can not be avoided, the question arises as to what should
be done to reduce their disadvantages to a minimum. It therefore
remains to determine from an economical standpoint whether the
new line shall cross the old one at grade, that is, on a level, or by
an over or an under crossing. If at grade, the question then arises
as to the advisability of establishing an interlocking switch and
signal system at such a crossing, whereby the usual stop may be
avoided.

THE TECHNOGRAPH.

That such problems as the above present themselves for con-
sideration, there is no doubt; yet that they are very frequently
ignored, is proven by the fact that over nine tenths of the crossings
of Illinois are unprotected grade crossings. The remainder of the
crossings either are provided with interlocking and signaling appa-
ratus, or are over or under crossings. An act of the State Legisla-
ture, passed in 1S87, provides that when a system of approved
interlocking switch and signal apparatus shall be constructed and
maintained at any crossing which shall prevent the possibility of
trains colliding, then trains may pass over such crossing without
first coming to a stop. Laws of essentially the same nature have
been passed in many of the states. In the eastern states advantage
of such laws has been taken, and interlocking and signaling devices
are rapidly coming into more general use. The time and expense
involved in stopping trains at unprotected grade crossings, shows
that the day can not be far distant when all railroads will find it to
their interest to provide interlocking devices at such places. These
appliances would afford not only greater safety, higher speed, and
more convenience to the traveling public, but (as is shown farther
on) would also reduce the operating expenses of the road.

As is well known, an interlocked grade crossing is one which is
provided with signals and switches located at certain points near
the crossing and operated by a series of interlocking levers, under
control of an operator, in such a manner that it is impossible,
either through the negligence of the operator or of the inattention
of the engine-man, for two trains to collide at the crossing. The
details of the interlocking and signaling apparatus for a single track
grade crossing, are about as follows: At 300 feet each side of the
crossing on both roads, derail switches are placed, which are ope-
rated by the interlocking levers in a tower at the crossing. To
guard against the accidental opening of each switch when a train is
passing over it, a thin iron bar, about 40 feet long, is hinged to the
outside of the switch rail. This bar, called a detector bar, moves
in a vertical plane and is so hung that it can not be moved length-
wise without being raised. It is so long that it can not be raised
between the trucks of a car, thus making it impossible to move the
switch while a train is passing over it. When the track is clear this
bar is raised by the first movement of the lever which controls the
switch. Near this switch the home signal is located. This signal
is of the semaphore pattern and is placed on the engine-man's side
of the track. The signal-blade is movable about its horizontal

HAY-RAILROAD GRADE CROSSINGS. 45

axis, and usually is painted red on the face farther from the cross-
ing. The distant signal is located 1,200 feet beyond the home sig-
nal and is of similar pattern with the exception that the farther face
of the blade is painted green.

All switches and signals are operated by the series of interlock-
ing levers in the tower at the crossing. These levers are painted
and numbered to correspond to the movements they control. The
levers operating derail switches are painted black, the home signal
levers red, and the distant signal levers green. The connection
between the tower and the derailing switches is generally made by
rods, and with the home and distant signals by wire. For a single
track crossing six levers are generally required, two operating the
four derailing switches, and four operating the four home and the
four distant signals.

The normal position of all signals is at danger with derail
switches open. To allow an approaching train on one road to pass
the crossing, the man in the tower must first close the derail
switches for that road by moving the switch lever operating these
switches. This movement automatically locks the switch and sig-
nal levers of the other road and at the same time unlocks the signal
levers of the first road. The signal man then moves the signal lever
which operates the signals on the side of the approaching train,
which first brings the home and then the distant signal to the safety
position. The approaching train then has a clear track. After the
train has passed, the signal man must first bring the distant and
then the home signal to the danger position, before the derail
switches can again be opened.

If, after the train has procured a clear track, an engine-man ot
an approaching train on the other road should attempt to cross, by
disregarding the danger signals, his train would be derailed at the
derailing switch, and the spirit of the law carried out, which says
that the apparatus shall prevent the possibility of trains colliding
at the crossing. Accidents of this nature have very seldom if ever
occurred, and so far as can be ascertained not an accident has yet
occurred through the fault of the interlocking apparatus.

Next, let the attention of the reader be turned to the expense
of (1) the interlocked grade crossing, and (2) the unprotected grade
crossing.

An interlocked grade crossing similar to that described above
costs about $3,000, including cost of erection. The annual expense
is however of much more importance than the first cost. As the

46 THE TECHNOGBAPR

levers demand constant attendance, the services of two men will be
daily required, whose salaries may be taken at $45 per month each.
This gives as the yearly cost of operation $45 x 12 x 2 = Si,o8o.
The annual cost of repairs, inspection, depreciation, etc., will be
about $120. The annual cost of operation and maintenance then
is 5 1,200. As capital can generally be obtained at 5 per cent inter-
est, the original cost of S3,ooo may be procured at an annual
expense of S3,ooox.o5 = $150. Adding this to the cost of opera-
tion and maintenance we find that an annual outlay of $1,350 will
be required to provide and maintain an interlocking switch and sig-
nal apparatus at a single track crossing.

Next, consider the expense of the unprotected grade crossing
with the usual stopping of trains. Careful estimates make the
expense of stopping a train from 35 to 75 cents, and sometimes
more. Taking 40 cents as an average expense, independent of the
kind and length of train, we find the expense per annum of a daily
train to be $.40 x 365 = $146.00. Considering an average traffic
of 10 daily trains each way for each road, we have $146.00x10x4=
$5,840 as the total annual expense which the crossing brings to the
two roads. This sum does not include the pay of a gateman who
is oftentimes needed at such places.

Comparing the annual expense of interlocked grade crossing
with the above result we find that as far as economical advantages
are concerned the system of interlocking is far superior to the
unprotected grade crossing. The reason then for the scarcity of
interlocking devices is not at first thought so quickly apparent, yet
if we examine into the question we may find several plausible, if
not possible, reasons for this deficiency: 1. The roads may
fail to agree upon what proportion of the annual expense each
should bear, as one road may be benefited more than the other and
yet refuse to pay more than half the expense. 2. The expense of
stopping at a grade crossing is paid in loss of time, discomfort,
wear and tear of the rolling stock, etc., and goes on continually,
draining the resources of the company without notice; while the
expense of interlocking is paid in cash and is thus much more
noticeable. 3. Some roads may be so situated that they can not
afford the additional cash outlay, or may be waiting for more
improvements in interlocking devices. Whatever be the reasons, it
is evident that an interlocking switch and signal apparatus under
the conditions assumed above would more than pay for itself during
the first year of its operation.

KEENE— ALUMINUM AND ITS ALLOYS. 47

NOTES ON ALUMINUM AND ITS ALLOYS.

By E. S. Keene, '90.

The first researches in the preparation of aluminum date back
to 1807, Dut it was not until 1854 that it was produced pure, and its
properties determined. It was then considered one of the precious
metals, and was valued at $240 per pound. Three years later the
cost had been reduced to $32 per pound. A steady decrease has
since continued until to-day, commercially pure aluminum can be
bought for $1 per pound. It is not found in the metallic state, but
occurs chiefly in the form of silicates, and in this form is more widely
distributed than any of the other metals. Its cost is due to the dif-
ficulty in extracting the metal from the ores. In color it is a silvery
white, but after being worked it has a slightly blueish tint.

Lightness is one of the most striking properties of aluminum.
A cubic inch of the metal weighs .09 pounds, while an equal
amount of cast-iron weighs .26 pounds, making aluminum therefore
weigh about one-third as much as cast-iron. The specific gravity
of cast aluminum, as determined by Prof. Stratton is, for 99 per
cent pure, 2.622; for 97^ per cent pure, 2.647; aluminum with 10.6
per cent silicon, 2.645. Deville gave the specific gravity of pure
aluminum as 2.56.

Aluminum is one of the most malleable and ductile of all
metals. It may be hammered into sheets as thin as gold-leaf, or
drawn into the finest wire. Its melting point, as given by different
authorities, is from 1,200 to 1,400 degrees, F. Impurities help to
raise the melting point. It is satisfactorily welded by electricity, but
is very red-short, and will not bear hammering at a high heat. Al-
though it may be rolled cold, aluminum is most malleable at about
300 degrees F. At above 400 degrees F. it becomes red-short.
Cold-rolled, or hammered, it becomes hard, and requires frequent
annealing to keep it from cracking. This is done by heating to
about 800 degrees F., at which temperature a bar of iron will ap-
pear slightly red in the dark. Aluminum at this temperature will
not appear red. This temperature may be determined in a prac-
tical way by drawing a pine stick across the surface, the mark of
which will burn slowly away. After being heated the metal should
be allowed to cool very gradually. Light articles may be annealed
by plunging into water after being heated. Wire may be annealed
by placing it in boiling water and allowing it to cool with water.

-4

Illl. I I.' IIXOGR 1/7/.

Iii experimenting with its effects in cast-iron, J. W. Keep has
found that aluminum turns the combined carbon to graphite, that is,
turns a white iron-gray. It also aids in increasing tensile strength
and aids in obtaining sound castings, which are susceptible of a
high polish and are free from oxidation. The same writer found
that in wroughtiron and steel castings aluminum prevented blow
holes, raised the tensile strength, and doubled the power to resist
shock.

In order to find a better and cheaper substitute for German silver,
which industry in the United States amounts to upwards of $6,000,-
000 annually, Eugene H. Cowles, after experimenting with upwards
of two hundred different mixtures, found that the addition of 1.25
per cent of aluminum to a manganese, copper alloy, converted it
from one of the most refractory of metals in the casting process
into one of superior casting qualities and more non-corrodible in
many instances than either German or nickel silver. This metal he
calls silver bronze, and is composed of manganese 18, aluminum 1.25,
silicon 5, zinc 13, and copper 67.5 per cent. Pure aluminum has
been used for instruments of precision, but only to a limited extent.
The pure metal is scarcely rigid enough, and the makers find that
in working, the metal is apt to tear under the tool, and does not give
clean threads. Tiers Argent, an alloy of 95 parts aluminum and 5
parts of silver, has been used, which gives better results, as, while it
is not much heavier, it is more rigid, harder, and works better under
tools. It withstands the corroding action of the atmosphere nearly
as well as aluminum. An alloy of nickel and aluminum might be
used for such purposes, as a small per cent of nickel hardens alumi-
num without destroying its other properties. As aluminum can be
obtained absolutely free from iron, it can be used to advantage for
apparatus where non- magnetic properties are required.

In the drawing press, as stated by Oberlin Smith, the metal
does not appear to stand as much strain in bending as brass or
"gelding," but in drawing will apparently stand more than either
without annealing. Aluminum, therefore, has the very desirable
property in drawing deep articles, it does not require the frequent
annealings which are required in brass and iron.

Such excessive claims have been made for aluminum that the
public has been led to believe that it might be used for anything,
and that with cheap aluminum all other metals would be superseded.
U though aluminum is a wonderful metal, there is no danger, as has

KEENE— ALUMINUM AND ITS ALLOYS. 49

been said, of its "revolutionizing the world." That it has some
bad qualities is shown by the following statement, made by Alfred
E. Hunt, President of the Pittsburgh Reduction Co., in a lecture
before the Boston Society of Arts: "For many purposes the pure
metal cannot be so advantageously used as that containing three or
four per cent of impurities. The pure metal is very soft and not so
strong as the impure. The thin coat of oxide which it gains on ex-
posure gives it a pewtery appearance which makes it undesirable for
table ware. It becomes pasty as low as 1,000 degrees F., melts at
1,300 degrees F., and loses its tensile strength and much of its rigidity
as low as 400 to 500 degrees. It is inferior to copper as a conductor
of electricity; in fact, it is only half as good. Its lack of rigidity is
an obstacle to its use for many purposes, such as castings. In roll-
ing it, not nearly so much draft can be given in the rolls as in the
case of rolling steel. In cold rolling it requires to be annealed
oftener than steel. Alloys of the metal increase its brittleness more
than they do its hardness. Its tensile strength per square inch is not
greater than that of common cast iron, and only about one-third
that of structural steel, while its compressive strength is less than
one-sixth that of cast-iron. The modulus of elasticity of cast-alum-
inum is about 11,000,000, being only one-half that of cast-iron and
one-third that of steel. Under transverse test, a one inch square
bar of cast iron, four feet, six inches between supports, will sustain
a load of 500 pounds, with a deflection of two inches, while a simi-
lar bar of aluminum would deflect over two inches with a load of
250 pounds."

It combines with iron in all proportions, but none of the alloys
with that metal are valuable except those with very small per cent-
ages of aluminum. The addition of aluminum does not lower the
melting point of steel, as has been claimed, nor does it increase its
fluidity.

Ten per cent aluminum bronze (ten per cent of aluminum with
ninety per cent of copper) has a tensile strength of from 70,000 to
75,000 pounds per square inch in castings. Rolled into plates, the
tensile strength is from 100,000 to 120,000 pounds per square inch.
It is a very close, dense metal of a beautiful yellow color and suscep-
tible of taking a very high polish. Unlike any other varieties of
bronze, which are red-short, it may be worked at a high heat as easily
as wrought-iron. One great advantage it has over other varieties of
bronze or brass is that it is comparatively free from oxidation in the

/ ill. TECHNOGRAPH.

air. In castings it has a specific gravity of about 7.8. Its melting
point is about the same as ordinary brass. Five per cent bronze
has a tensile strength of about 60,000 pounds per square inch. In
seven per cent bronze the tensile strength is from 60,000 to 70,000
pounds per square inch.

The following tables show tests, made by the writer, on cast
aluminum and aluminum bronze. The metal used in the test was
kindly furnished by the Pittsburgh Reduction Co., of Pittsburgh, Pa.
The pieces were ingots, each ingot being cut into two or more test
pieces. The pieces used in the tests for tensile strength were melted
and cast into cylinders for the compression tests.

The flow of the metal under tensile test seems to be very local.
The per cent of elongation reducing rapidly in increasing length
from the point of fracture. Under compression the silicon and 99
per cent pieces kept their cylindrical shape to the point of fracture,
but the 97^ per cent piece, at a load of 30,000 pounds, had become
very much distorted. At 50,000, the 99 per cent piece was flattened
to almost one-third its original length and showed a small crack in
the side. The cracks in all of the pieces were in spiral form.

TENSILE TESTS.

E2.8

0 ff.

3 0

" p

Dimensio
duced
inch

13
ft
►1

cr. a

0 r*

•0 s

3 8

p
p K

c n

0 C-

(113 3
« p »

3 r»

a 3

n 3

2 0

3 -

5'3

ere
p

3- <T

99 per cent, aluminum

.229 x .664

.1825X.515

5820

16180

2 99 per cent. "

.225 x .612

.I73X.548

6500

1 7 140

3 97/4 Per cent. "

.254 x .663'. .232x650

12.2

4540

10660

4 97/4 per cent. "

.256 x .662 .218X.630

14-3

4600

12090

5 Al. with 10 6 silicon . .

.671 x .258 .661.X.248

8.2

18510

.660X.257; .658X.239
.452 diam. .412 diam.

5
i3 3

19130
60210

7 per cent. al. bronze.

33420

7 per cent. al. bronze.

.433 diam.

.398 diam.

15 2

41230

64580

7 per cent. al. bronze.

.446 diam.

.408 diam.

12.4

26700

62350

5 per cent. al. bronze.

.458 diam.

.453 diam.

24300

57716

10 per cent. al. bronze .305 diam.

.288 diam.

19.2

48700

74790

10 per cent. al. bronze .312 diam.

.293 diam.

18.

47600

72820

BAWDEX— COUNTERBALANCE ON LOCOMOTIVES.

COMPRESSION TESTS.

Load, pounds.

99 per cent, alumi-
num.

97j^ per cent, alum-
inum.

Aluminum with 10.6
per cent. Si.

Length x Diameter,
Inches.

1.299 x .965
1.298 x .965
1.298 x .965
1.298 x .965
1.296 x .966
1.294 x .967
1.286 x .970
1.279 x -972
1.267 x .976
1.252 x .983
1.233 x .991
1. 212 x 1. 000
1. 180 x 1. 017
1. 150 x 1.032
1. 1 16 x 1.050
.748 x 1.288

1.548 x .974
1.548 x .974
1.546 x .974
1.545 x .974
1.543 x .9745
1.537 x .976
1.534 x .977
1.529 x .979
1.526 x .981

1. 175 X .983
1. 173 x .983
1. 173 x .983
1. 172 x .983
1. 171 x .9835
1. 171 x .9836
1. 170 x .9838
1. 168 x .984
1. 167 x .984
1. 167 x .9845
1. 165 x .9842
1. 164 x .9844
1. 1626 x .9846
I.I6I4X .986
1. 160 x .9865
1.078 x 1.073

500

1,000

I, coo

2,000

3,000

4,000

5,000

6,000

7,000

8,000

1. 513 x .985

Q.OOO

10,000

1.494 x .992

11,000

12,000

1.458 x 1.007

1. 108 x 1. 187

Failed.

25,000

31,600

40,000 ....

•515x1.55

41,300

Failed.

50,000

.482 x 1. 612

EFFECT OF COUNTERBALANCE ON LOCOMOTIVES.

By S. D. Bawden, '90.

In the locomotive strong forces are at work, necessitating strong
parts to stand the wear and tear of use, and one of the things for
the engineer yet to overcome is the necessity of much weight to
give corresponding strength. The weights thus used in the loco-
motive, and falling within the scope of this paper, may be separated
into two classes — the reciprocating parts and the revolving parts.
Of these, the revolving parts can be easily balanced, by placing
equal weights on the opposite side of the axis of rotation; but the
reciprocating parts vary in velocity, and therefore can be balanced
by a given weight for only one position. It is possible to exactly
balance the reciprocating parts at the dead centers, or at the quar-
ters, or, indeed, at any point in the revolution, but they will not be
balanced for other points. For this reason, with respect to the
reciprocating parts on a locomotive, an approximate counterbal-
ance is used, which gives an excess of weight in some positions,

/•///. TECITNOGRAPJf.

and less than the required amount in others. As the speed of the
locomotive increases, the centrifugal effect of this excess of coun-
terbalance increases, until it may become more than the portion of
the weight of the locomotive assigned to the wheel in question.
The purpose of this paper is to investigate somewhat the rela-
tion of this centrifugal force and the weight of the locomotive as
transmitted through the driving-springs.

In the driving-wheel of the locomotive we have a crank-pin
and its boss, which are eccentric with respect to the axis of revolu-
tion of the wheel. Neglecting the
weight of the rim, spokes, etc., in
Fig. i., let
C = weight of the crank-pin and

boss,
D = distance of center of grav-
ity of C from axis.
Place opposite C a weight (C)
at a distance (D') from the
axis, so that

CD = CD' (i)
Then these weights are in statical balance: i. e., the wheel will be
balanced in any position whatever in which it may be placed about
the axis; and, as can easily be proved, the wheel will be also in run-
ning balance. Stating this as a rule — A running balance is a stati-
cal balance, and vice versa.

Next comes the question, whether, if we consider the weight of
the wheel, its rim, spokes, etc., having the wheel in running and stat-
ical balance, and add an eccentric weight, the weights which have
already been balanced will have any effect upon the new weight.
As shown above, the revolving weights in the locomotive may easily
be balanced but it is the reciprocating weights that cause the diffi-
culty. ( )n account of this, the builders of locomotives have exper-
imented till they should find the proportion of the weights of the
reciprocating parts which, placed opposite the crank-pin, would
give the best effect. In this way they reduce the excess of counter-
balance but do not remove it entirely, and it is this excess which is
considered as an eccentric weight in the following discussion.

With the wheel in statical or running balance, the center of
gravity lies in the axis. With an eccentric load added to the bal-
an< ed load, the center of gravity is moved from the axis to some

JiAWDEN COUNTERBALANCE ON LOCOMOTIVES. 53

point between the eccentric load and the axis. In Fig. 2, let C, C,
D, D', be as in Fig. 1. Added to C and C is the weight of the rim,

spokes, hub, etc. These are all to be considered as balanced, and

fulfilling the conditions of Fig. 1. Then the center of gravity of all

these weights will be at H, the axis of revolution.

Let Wc = the balanced load = C+C'+Rim+etc,

Wj = the eccentric load,

r' = distance of center of gravity of eccentric load from
axis,

r" = distance of new center of gravity, after W^ is added,
from axis.

Then W^W^ weight of the whole wheel. »
r" is found from the relation,

(w^w/y^w^' (2)

W, r'

r"= (3)

W +WX

Let v" = velocity of new center of gravity, as it revolves about
axis, in feet per second,

v' = velocity of W, in feet per second.
W, v'2

Then = F1 = centrifugal force of W, |

gr'

THE TECHNOGRAPB.

WW,

•=Fj = centrifugal force of whole wheel. (5)
gr"
Substituting in (5) the value of r" as found in

(W.+W,)' \

F2= (6)

g W, r'
Let N — the number of revolutions per second,
Then2rr' N = v' and 2wr"N=v" (7)

4r-r'-N-^v'' and 4rrV'-N2=v"2 (8)

Substituting in the second equation of (S) the value of r" as
found in (3),

. , ( W> )

i W„4-W, \

r'2N2=v"2 (9)

rw0+w,-)2

[ y'* («o)

But from (8), 4-V-N2 = v,;,

(W.+W.V

Therefore v,2= J [ v"2 (n)

(. W, )
Substituting the value of v'2 from (n) in (4), we have

(Wo+W,)" v"2
F,= (12)

gW.r'

(Wo+W02 v"2

But from (6) F„= (13)

g W, r'
Therefore Fi=F2 (14)

This proves, then, that an eccentric weight has the same effect
in producing centrifugal force, whether acting alone, or placed in a
balanced wheel.

Since there is an excess of counterbalance in the wheel of the
locomotive, the center of gravity of the wheel will not lie in the
axis, but between the axis and the excess of weight. The centrifu-
gal tendency, then, of the wheel, will be the same, whether we con-
sider the mass of the whole wheel concentrated at the center of
gravity of the wheel, or only the excess of counterbalance concen-
trated at the center of gravity of that excess of weight.

The locomotive driving-wheel is so placed that it can move
vertically, either up or down, but in each case there is a resistance

BA WDEX—COUXTERBALANCE OX LOCOMOTIVES.

to its motion; above, there is the pressure of the weight of the
locomotive, transmitted through the driving-springs; below, there is
the rail. This latter, of course, is to be considered as a continuous
beam, and of so much rigidity that its action may be neglected. It
is true that we should expect, with just as much reason, to find
effects from the excess of counterbalance in other directions than
the vertical, and such effects have been experimented upon by
others, but the scope of this paper is simply to investigate the ver-
tical action of the weights in question.

The motion of the wheel may be compared to that of a body
revolving about an axis, and free to move vertically, up or down,
against resistances. In Fig. 3, let

A=center of gravity of wheel, with mass of wheel concen-
trated there,

////. TBCHNOGRAPff.

I; axis iree to mu\ e vertically against springs 1), K),
k radius of center of gravity of wheel.

In order to simplify the conditions of the problem, we will
consider that the wheel is revolving at a uniform angular velocity,
and also neglect the time that it takes the springs to act.

Let w angle made by K, at any moment, with the horizontal:
as before, let

F=the centrifugal tendency of the wheel, which may be calcu-
lated as in (5).

This force acts in the direction of the radius R, and, since we
assumed that h grows constantly, and the weight of the wheel is
constant, F is a constant force. Then the vertical component of
this force is, in all cases,

F sin h (15)

If a unit force, or load, gives a deflection of the spring = S,
then the total deflection at any moment is equal to the total force
acting times the unit deflection, or

FS sin h (16)

Let this be represented by '<, as shown on the figure, then
r)=FSsinfl 117)

The vertical distance of the center of gravity of the wheel from
the horizontal axis equals

R sin H + .) (18)

Referring to the horizontal and vertical axes as co-ordinate
axes,

y = R sin <-> + » (19)

Substituting from (17),

y=R sin 0 +FS sin 8 (20)

In the same way, the horizontal distance of the same point
from the vertical axis is

x = R cos^ (21)

When tt- 900, the value of F sin H reaches a maximum, and
equals F. At that point, then, the greatest deflection of the springs
will occur, and will equal FS, remembering that we assumed that
the time of action of the springs is nil.

To judge of the time allowed the springs for action, take a
driving-wheel 63 inches in diameter. If the locomotive move at
the rate of 40 miles per hour, it will go 3,520 feet per minute. The
number of revolutions per minute 2134, and each revolution
would take .281 seconds. Hut in half a revolution the force has

BAWDEN COUNTERBALANCE ON LOCOMOTIVES. 57

given the deflection 8 and returned to its normal position, so that
the time taken in deflection and recovery is only .1405 seconds.

Unwin defines a suddenly applied load as a load applied to a
structure with6ut velocity, but at one instant; and such a load, not
exceeding the elastic limit, produces twice the stress of an equal
steady load. The case in hand comes under this definition, since,
when 0=O°, the deflecting force is o, and it increases with the
revolution. In the locomotive, flat laminated springs are used, so
that the formulae for beams apply, and the deflection under the sud-
denly applied load is twice that which would occur under a steady
load, or

5=2'' (22)

in which S1 is the deflection under the same load acting steadily.

As the theoretical curve assumed that the springs took no time
to act, while we should naturally expect them to influence the move-
ment because of the resistance which they offer, it was determined
to investigate their action to some degree.

With this idea in view, a machine as shown in Fig. 4 was con-
structed, having, as in the theoretical machine, a spindle free to move
vertically while revolving, although against the resistance of springs.

The machine consists, essentially, of a wooden frame, braced,
and clamped rigidly to the bed of a lathe. Through the upper and
lower cross-pieces two hollow brass rods are fitted to slide verti-
cally. To these rods is clamped a block, carrying a spindle, which
has at one end a rod which works freely in a slot attached to the
face-plate of the lathe; and on the other end another rod, upon
which is a weight, which may be fastened at any point, in order to
give different radii, and thus different centrifugal forces at the same
speed.

The machine has proved itself, on the whole, not altogether
satisfactory. It was not rigid enough, and for that reason the
curves are not as satisfactory as might be desired. The centrifugal
force of the weight combined with its leverage on the brass rods
tended to bend them, and for that reason, in Fig. 6, the curve,
which should always remain outside of the circle, passes within.
However, the machine served its purpose in so far as it shows that
the springs do retard the maximum, so that, whereas it should be on
the vertical axis, it is carried over, in some cases more than 200.
The pencil point which traced the curves was placed at the center of
gravity of the weight, so that it records the movements of the weight.

Sfl

THE Ti:< IIXOGRAPH.

Fig. 4.

:::30e::d

Scale = — .

IS X i J' « J ® 0

c^:

/ % \

Fig. 4.

The method of obtaining a curve was as follows: A drawing-
board, clamped to the carriage of the lathe, and with a sheet of
paper stretched upon it, was moved up until the pencil point
touched it. Then the lathe was started and the curve traced; and
the number of revolutions per minute counted by means of a speed
indicator. After that, the carriage was run back and the radius of
the center of gravity of the weight measured.

Owing to the fact that the data had to be obtained while other
machines in the shop were being used, the speed of revolution

BA )Vl)EN—COUNTEltliALANCE ON LOCOMOTIVES. 59

varied considerably during the experiments, and in all probability
the speed noted is not exactly the same speed as that at which the
curve was traced.

The springs used were of steel wire, B. & S. Wire Gauge No.
10. Their temper proved unsatisfactory and lacked uniformity.
The weight used was 3.19 pounds. In the machine four springs
were used, two on each brass rod, one above the block, and the
other below, in each case. They were intended to be exactly alike,
and are so considered in the calculations.

To calculate the strength of these springs and the theoretical
deflections under the various loads put upon them, Reauleaux's
formulse for spiral springs may be used, which are as follows:

l=ni/(2 - r)M-(pitch)2 (23)

32 P 1 r8

d= (24)

- GdJ
In the case of this machine the load is distributed between two
springs and is equal to the centrifugal force.

Hence P=^F for each spring. (25)

The data obtained from the machine are as follows:
Outside diameter of coils = f j1
d = .ioi91
Hence 2r=.74l

r=-37'
n = 8
pitch = ^1
Whence ')=. 022366 P (26)

The following table gives the results of the experiments, show-
ing the different loads and the deflections corresponding. The
notation is as follows:

r= distance of center of gravity of the weight from the axis of
revolution, in inches,

N=number of revolutions per minute,

v=velocity of weight, in feet per second, as calculated from
2 -r N

the formula: v=

12x60
F=centrifugal force in pounds, as calculated from (4):

W.va
F=

1 III: YECHNOGRAFH.

TOP

I i,.

BAWDEN— COUNTERBALANCE ON LOCOMOTIVES. 61

P=^F=load on each spring, as in (25),

'1= theoretical deflection of spring in inches, and equals. 022366 P
as in (26),

o0 = observed deflection in inches, as measured on Figures 5
and 6,

n = angle at which maximum occurs, measured to the right of
vertical axis.

The first column gives the number of the curve as given on
the Figures 5 and 6.

Fie. 6.

I III. TECHNOGRAPH.
TABLE OF RESULTS.

So
l

1".

2 41 272

5.720

16 14

807 1P1

■23

21.5°

359 *5*

7 895

20.64

10 32 2\\

19^

4 3" 256

9.629

12 78 .286

17. 5°

5.81 264

1338S

36.66

18.33 4>o

17. 5°

;

05<) 264

'5 183

45 5 s

20.79 465

16°

•

9 254

42.24

21 12 .472

19O

3 '6

440

12 134

55 39

27 69

619

22°

It will be noticed that the deflections, as observed on the
curves, do not correspond to the theoretical deflections. A possi-
ble reason for this, is that the springs for Fig. 6 are a different set
from those used in Fig. 5, and they began to take a set, which
increased with the pressure upon them, until in No. 7 the springs
were about /-,' shorter than when they were put into the machine.
That made about l/A.x of lost motion between the two springs, in
which space the weight had no resistance from the springs.

As has been said before, these sources of error serve to render
the results satisfactory, only in so far as they serve as suggestions
for further investigation.

As the effect of the centrifugal force of the excess of counter-
balance increases with the speed, the lifting effect must increase.
The force exerted in the cylinder by the steam, transmitted through
the rods to the crank-pin of the wheel can be found; and thence
the force tending to rotate the wheel, considered as acting at the
circumference of the wheel, where it rests on the rail. This force
can be found for any point in the revolution, and for the same
point the weight on the rail may be found, this last varying, of
course, with the direction and amount of the centrifugal force.
Thus, having found, for any point in a revolution, the rotative force
at the rail and the weight on the rail, the ratio between them is
easily determined, which we may call the coefficient of slip.

Now, the ratio of the force applied horizontally at the rail,
and which will just produce slipping, to the weight on the rail, is
called the coefficient of friction or adhesion. Values for this co-
efficient are given by Haswell, and vary, according to the condi-
tion of the rail, from .09 to .$$.

Mr. J. N. Rarr discusses in the Railroad Gazette (February 6,
1891, p. <)2), the relations between the co-efficient of slip and the
co-efficient of adhesion, and finds, experimentally, that the former

PEA BODY— PRINTS FROM ETCHED METALS. 63

does exceed the latter at times, and summarizes his conclusions as
follows:

"i. Flat places on driving-wheel tires are not entirely due to
lack of uniformity in the wearing quality of the same.

2. The flat places have a tendency to group themselves where
the co-efficient of slip is the greatest.

3. They vary in depth with the pressure on the rail, and when
the pressure does not exceed 11,000 pounds, the imperceptible slip
produces but little abrasion.

4. Imperceptible slip does not appear at random on any part
of the wheel, but in special localities as fixed by the maximum val-
ues of the co-efficient of slip.

5. The counterbalance should be made as light as possible,
consistent with smooth riding.

6. The weight of the reciprocating parts should be as light as
possible."

These conclusions were drawn from experiments on an engine
going at the rate of 40 miles an hour. Others have called atten-
tion to the fact that these spots have a tendency to group them-
selves at corresponding points on the wheels of a locomotive.

However, the data are so meager that it would be foolish to
state that any given spot was caused by any certain action. But
may it not be assumed in the light of the imperfect experiments
just described, that the centrifugal force of the excess of counter-
balance, taken in connection with the driving-springs of the loco-
motive, has considerable to do with the location of the worn places
in the tires?

PRINTS FROM ETCHED METALS.

By L. \V. Peabody, '91.

The specimen to be etched must present a perfectly smooth
plane surface on the side from which the print is desired. The re-
quisite finish may be secured after the piece leaves the machine by
a careful use of a file and emery paper, care being taken to remove
all file or other tool marks, as these will appear in the prints.

It will be a matter of great convenience to have the side op-
posite the etching surface parallel with it. Yet if the specimen is of
considerable size this is not absolutely necessary, as the uneven side
may be blocked up with wood or other material for the press.
-5

t.i I III. I'ECHNOGSAPU.

However, the former method will be found more satisfactory. When
the surface is sufficiently polished, it should be suspended face
downward in a shallow dish containing the etching fluid; but should
never touch the bottom so as to prevent free access of the acid.
The specimen may be held by any suitable clamp which will over-
lap the edges of the containing vessel thus forming a support.

( Onsiderable range is permissible in the proportions of the
etching tluid. Hither of the following volumetric proportions have
been found good in practice.

H2 S 04 (con.) 3 parts.

H CI " i "

HaO 9 "

H, S04 (con.) i "

11 0 3 "

The length of time that the metal should be immersed is largely
a matter of experience, as the acid acts on no two pieces with the
same rapidity. The operator must examine the specimen from time
to time to determine when the desired end is reached. The metal
must remain in the acid until the etching surface when covered with
printers ink will give a good impression. Practice and judgment
will determine this point.

When the action is complete all acid must be washed from the
specimen and the etched surface dried immediately to prevent
rusting. This may be done by placing in hot water for a short
time, the heat being quite sufficient to dry the surface on removal.

Ordinary printers' ink is used exclusively in making prints.
This should be spread in a thin, even coat over a fiat piece of
marble or glass. A common printer's roller is used to ink the
etched surface. This requires considerable care, as the ink must
be spread evenly over the entire surface. Pass the roller over the
slab and etching alternately for each print. No deviation from this
will insure good results. After the specimen is inked it is ready for
the press. For small and medium sized pieces an ordinary copying
press can be used. Place either a thin piece of soft rubber or a
couple of blotters on a plane, smooth board, and over these a white
sheet of moistened paper. The specimen should now be placed
face downward upon the white paper, and the whole placed in the
press. If the top is parallel with the etched surface, place a sheet
of rubber or blotters on the top and subject to a pressure of about
500 lbs. per square inch. If the top is irregular it may be built up

LiOYD-ELECTRIC S THEE T RA ILWAT PLA N T. 65

and covered with a board, when the sheet of rubber is used as
before.

After use the etching plate should be thoroughly cleaned, dried,
and coated with vaseline to avoid all rusting.

NOTES ON AN ELECTRIC STREET RAILWAY PLANT.
By W. A. Boyd, '91.

Tests were made on an electric street railway plant, consisting
of an 80 horse-power Ideal engine, making 250 revolutions per
minute, driving a United States dynamo of 40,000 Watts capacity.
The method of driving is by friction belts between the pulleys.
The engine pulley is six feet in diameter, and the dynamo pulley
about three feet. Four belts, 4^ inches wide, cover the circum-
ference of the dynamo pulley. These are prevented from coming
off by flanges on the pulley. The pressure between the pulleys is
maintained by a screw on the sliding frame of the dynamo.

This plant furnishes power for about two miles of street car
track between the cities of Champaign and Urbana, 111. Also power
for two small motors and about one hundred incandescent lights.
Ordinarily two motor cars, carrying motors of twenty nominal
horse-power each, are run. For additional traffic trailers and more
motor cars are added.

Ten tests of this plant were made, each test lasting twenty
minutes, this being the length of one complete trip. The tests were
begun when the cars were at the end of the line. Indicator cards
were taken each minute during the test. During this time speed
indicators were run continuously from the engine and dynamo
shafts. The speed of the engine, while taking a card, was read from
a tachometer.

In the morning, between the hours of 9 and 12, the power re-
quired varied from 9.1 to 54.6 horse-power. The average for the
time, while running two cars only, was 20.7 horse-power. In the
afternoon, between the hours of 2 and 5, the power ranged from
1 1.5 to 55.23 horse-power. The average power required during the
time was 21.07 horse-power. The average power required for the
day was 20.88 horse-power.

To determine the frictional loss due to increased pressure on
the bearings, successive positions of the tightener screw were

66 THE TECHNOGRAPB

arranged, advancing the dynamo by ^nds of an inch. Table I.
gives the average of a number of cards taken at these positions.
Of these positions Nos. 1-5 are below the limit for ordinary run-
ning, and No. 10 is above the limit for cool bearings. Table II. gives
another set of values taken at a later time for positions advancing
the dynamo by 64ths of an inch. The positions, 1-4 in the second
set, lie between 6 and 8 in the first set. They show a slight in-
crease in engine friction, but a decided decrease in the total fric-
tion.

To determine the velocity ratio of driver and follower, continu-
ous readings were taken from both while running light. The value
thus obtained was compared with the values for different positions,
obtained when running cars, and the per cent slip calculated for
these positions. These results are given in Table III., together
with the mechanical losses due to friction. An examination of this
table shows that for all powers under 30 horse-power the total sum
of frictional losses and losses due to slip is a minimum for the loose
position; while for powers greater than 30 the most economical
point is at the tighter positions.

In order to obtain the pressure on the bearings in this case, a
lever 48 inches long was bolted to the tightener wheel, and the pull
required read from a spring balance. By several trials the pull re-
quired to move the dynamo on its frame alone was 14 pounds. The
pull required to move the dynamo while in running position was
2oy2 pounds. The mean radius of the screw was .6887 inches, and
the pitch yx of an inch. Using .15 as the co-efficient of friction,
the pressure on the bearings was found to be 2,160 pounds.

As a comparison between this system of driving and driving by
means of belting, a calculation was made taking as an extreme case
the distance between driver and follower equal to one inch. Using
the ordinary formulae ior belting, the pressure on the bearings nec-
essary to transmit the maximum power was found to be S84 pounds.
This gives the pressure on the bearings but little more than two-
fifths of the pressure required by the present method of driving.
The width of the belt taking into consideration centrifugal action
was calculated and found to be ten inches for a one-quarter inch
belt.

These results seem to show that for street railway work, or
where the demands lor power vary so much, the ordinary belt driv-
ing is superior in economy to driving direct by means of friction
pulleys.

LIME-CEMENT MORTAL'.
Table I.

Engine.

Dynamo and Engine Friction.

3-°47

4.318

4-583

4774

4.71

4.871

4.418

5 184

5-705

5-831

6.498

Table II.

Engine.

3-312

Dynamo and Engine Friction.

3-77

4327

4619

4-338

Table III.

Set.

Posi-
tion.

I. H. P.

Eng. friction.

H. P. Trans.

Slip per cent.

Mech. loss
H. P.

2
3
4
5
6

4
4
3
3
2
1

20.036

19875

19.549

19.45

28.92

29.01

3312
3312
3 312
3 312
3-312
3-312

16.724
16.563
16.237
16.138
25.608
25.698

■38

•383

•85

I-387

i-555

3.087

1.522
1.522

1 307
1.307
1. 015

•458

LIME-CEMENT MORTAR.

It is common practice, particularly in the construction of large
buildings, to add hydraulic cement to lime mortar, on the supposi-
tion that the cement gives additional strength. Gen. Gilmore, in
his "Practical Treaties on Limes, Hydraulic Cements, and Mortars,"
says: "Most American cements will sustain, without any great loss
of strength, a dose of lime paste equal to that of the cement paste;
while a dose equal to half to three-quarters of the volume of cement
paste may safely be added to any energetic Rosendale cement, with-
out producing deterioration in the quality of the mortar, to a degree
requiring any serious consideration." In order to test these con-
clusions the four series of experiments described below were made.

For the sake of brevity the conditions common to all the series
are described here once for all.

r,- Till. TECHHOGRAPH.

The lime employed was a good quality of ordinary fat lime.
It was slaked in an earthen jar at least two days before being
used. The proportion of water added to the dry lime in slaking
was a little more than two to one by weight. The lime paste was
kept at a constant consistency by weighing the jar each day and
adding water to make up for the loss by evaporation.

Two kinds of hydraulic cement was tried, a German Portland
and Black Diamond Louisville (Ky.) Rosendale. The usual tests
for soundness showed both cements good in this respect. The
following results were obtained for fineness:

PORTLAND. ROSENDALE.

Retained on a No. 50 sieve 1 per cent. 15 per cent.

Retained on a No. 75 sieve 7 " 9 "

Retained on a No. 100 sieve 7 " 4 "

Passing a No. 100 85 " 72

The following results for tensile strength were obtained from

briquettes stored in air:

Pounds per Square Inch,

portland. rosendale.

When 7 days old 150 75

When 21 days old 300

When 28 days old 320 225

When 70 days old 360 250

The sand used was such as passed a No. 18 sieve and was
caught on a No. 30 sieve, and was therefore practically "standard
sand," as recommended by the committee of the American Society
of Civil Engineers. It was fairly sharp, and contained a large per
cent of silica. It was thorougly washed and dried before being
used.

The mortar in all cases consisted of two volumes of sand to
one of the lime-cement paste. The weight of a unit of volume
of each ingredient was first determined, and the proportions were
then adjusted by weighing. The cement and the sand were thor-
oughly mixed dry, the lime was then added and all well mixed, and
finally enough water was added to bring the mass to a proper con-
sistency. Since lime will not harden under water all the specimens
were stored in the air.

The breaking was done on a home-made cement testing ma-
chine giving results accurate to half pounds for light pulls, anil
correct to two pounds for the greater pulls. The machine was so
arranged as to give a central pull upon the test specimen.

EIDMA NN-LIME- GEM EX T MOR TA li.

COHESIVE STRENGTH OF LIME AND LOUISVILLE CEMENT MORTAR.
By E. C. Eidmann, '91.

The mortar was put into the molds by hand with as nearly the
same pressure as possible, and remained in the molds twenty-two
hours. In determining the strength of a mortar of any particular
age at least five briquettes, representing two or more moldings,
were broken and an average taken.

Figure 1 gives the strength of the different mortars at various
ages. It will be noticed that the strength of some mortars are
shown as being greater than others at a succeeding age. In these
cases the briquettes are of different moldings. Owing to the differ-
ent conditions of the atmosphere and the inexperience of the
experimenter, the moldings might not have been made exactly the
same. In all mortars over seven days old, the 20 per cent cement
and 80 per cent lime mortar is weaker than all lime; but as soon as
more cement is added, say 30 per cent, a greater strength than all
lime is produced.

50[

Fig.

Cohesive Strength of Louisville Cement and Lime
Mortar.

Notice that the 60 per cent mortar is but little, if any, stronger
than that containing only 30 per cent of cement; and hence, if it is
not desirable to use more than 60 per cent of cement, it is not eco-
nomical to use more than 30. Notice that the 30 per cent cement
mortar when four days old is nearly 50 per cent stronger than the
all lime mortar, but that the difference in strength steadily decreases
until at 84 days old the all lime mortar is stronger or at least

70 THE TECHNOGR if II

equally as strong. As in most cases it matters little whether the
strength is obtained in a few days or not, it is best, and by far the
cheapest, to use all lime in these cases rather than put in as high as
even 60 per cent of the cement. According to the diagram the
mortar containing 20 per cent of cement and 80 per cent of lime
is not so strong as all lime.

Concerning the addition of small per cents of lime to cement
mortar the diagram gives no very definite conclusions. Apparently
a small per cent of lime decreases the strength of the mortar in a
greater ratio than the proportion of the lime added; and conse-
quently the addition of small per cents of lime to cement mortar is
not economical, at least as far as the strength is concerned. Of
course the addition of lime to cement mortar will decrease the
activity of the latter, but this phase of the subject is not now under
consideration.

COHESIVE STRENGTH OF PORTLAND CEMENT AND LIME MORTAR-
By Chas. D. Vail, '91.

The briquettes were put into the molds by hand. Although
great care was taken to give them uniform pressure, this must have
been the source of greatest error.

Fig. 2 represents graphically the results obtained from the ex-
periments. All points in the curves of the diagram are the mean
of five briquettes.

In the diagram it will be noticed that the relative proportions
of lime and cement vary regularly, except the 90 per cent and 30 per
cent cement. The first was put in to test the reliability of the claim
that a small per cent of lime in cement mortar does not seriously
injure it. This statement is made by Gen. Gilmore, and appears to
be supported by Mr. Kinkead's experiments.* From Fig. 2 we see
that 20 per cent of lime in cement mortar weakens it, but that with
10 per cent of lime the mortar seems to be fully as strong as 100 per
cent cement mortar.

As to adding cement to lime mortar the experiments show con-
clusively that it is not economical, because the strength is not
noticeably increased until 40 per cent of cement is added.

The conclusions drawn from the experiments are: (1) The ad-
dition of lime to cement mortar, up to 15 per cent, does not injure
the mortar; but with the addition of more than this the strength

1 "Selected Papers of the Civil Engineers' l'm\ crsity of Illinois."

ENO-LIME-CEMENT MORTAK.

+ 7 /f- zi z& *2 se

Cls\e in, tlum

Fig. 2. Cohesive Strength of Portland Cement and Lime

Mortar.

decreases more rapidly than the cost. (2) The addition of cement,
up to 40 per cent, to lime mortar is not wise, because first it does
not noticeably increase the strength, and second it greatly increases
the cost.

ADHESIVE STRENGTH OF LIME AND LOUISVILLE CEMENT

MORTAR.

By F. H. Eno, '91.

The method of making the tests consisted in cementing two

brick together cross-wise, with their broad faces in contact; and

then measuring the force required to pull them apart.

THE TECHNOGBAPH.

Before being used, the brick were immersed in water about 30
minutes, when they were taken out and cemented together immedi-
ately after the water had dripped from their surfaces. The mortar
was carefully put on one brick and the other brick placed cross-
wise on it, and given considerable pressure and at the same time a
twisting motion which helped to exclude the air and make a better
bed for the top brick. The attempt was made to use as nearly as
possible the same pressure a mason would use if laying the brick in
a wall. They were left to set, in the air, under the weight of an
additional brick. As the brick averaged a tritle over 4'j pounds
each this made the weight on the mortar joint about 9 pounds.
The brick were hand-molded and moderately smooth. No appre-
ciable difference in the adhesion of the mortar to the rough and
smooth sides of the brick was detected.

The testing machine was so arranged as to certainly bring the
pull perpendicular to the face of the mortar joint.

Fig. 3 represents graphically the results obtained from this
series of experiments. The numbers on the plotted lines show the
per cent of cement in the cementitious material. The results as
plotted are the mean of at least five experiments. Tests were
made daily for the first seven days; but were not plotted for lack of
room. In all about 800 experiments were made.

Fig. 3.

Adhesive Strength of Louisville Cement \m> Lime

Mortar.

The diagram shows very clearly that to add from 10 to 20 per
cent of lime paste to cement mortar does not materially affect its
ultimate strength. The substitution of 10 per cent lime saves 2.5
per cent of the cost of the original cement, while the substitution

FREDERICKSON—LIUE-Ci:Ui:ST MORTAR. 73

of 20 per cent of lime saves 5.0 per cent; while the cost of the lime
thus substituted is scarcely appreciable. Notice that the addition
of more than 20 per cent of lime paste to cement mortar very
materially reduces the strength. Therefore we draw the conclusion
that it is economical to add not more than 20 per cent of lime paste
to cement mortar. This only partially sustains Gen. Gilmore's
statement referred to in the first paragraph of article (page 67).

An examination of Fig. 3 shows that a mortar containing 20
per cent of cement and 80 per cent lime paste is weaker than an all-
lime mortar. Therefore the substitution of 10 or 20 per cent of
cement in a lime mortar for an equal volume of lime paste de-
creases the strength and at the same time increases the cost. Hence
this practice is decidedly uneconomical — at least as far as strength
is concerned.

With all the mortars, it was found that after having gained
some age the adhesion to the brick was greater than the cohesion
between the particles of the mortar. For example, for the first 7
days, in 73 per cent of the tests the adhesion was weaker than the
cohesion; while for the remaining time, in only 14 per cent of the
tests was the adhesion the weaker.

In conclusion it may be well to state that the results obtained
for the adhesion to the brick and by cohesion in the briquettes can
be compared only relatively, since the mortar was compacted dif-
ferently in the molds than it was between the brick and was subject
to various other differences.

ADHESIVE STRENGTH OF PORTLAND CEMENT AND LIME MORTAR.
By T. H. Frederickson, '91.

The experiments were made with German Portland cement and
lime mortar and brick, in the same manner and subject to the same
conditions as described above by Mr. Eno.

Although the tests were made to obtain the adhesive strength
of the mortar to brick, the mortars consisting of 40, 20, 10, o per
cents of lime and 60, 80, 90, 100 per cents of Portland cement re-
spectively, separated from the brick through failure of adhesion;
while the mortars consisting of 60, 80, 90, 100 per cents of lime
and 40, 20, 10, o per cents of cement respectively gave results for
the cohesive strength (except in first 3 to 7 days, when adhesion
was the greater). Or in other words, with the mortar in which the

THE TECHNOGRAPH.

lime predominates separation is through the failure of cohesion, and
with the mortar in which the cement is in excess the separation is
due to the failure of adhesion.

Fig. 4 shows graphically the relative and absolute strength, at
various ages, of mortars composed of different per cents of lime and
Portland cement.

0-4 7 I* 21 2i 35 « 41 Jb

-Hoe in daus

Fig. .}. Adhesive Strength of Portland Cement and Lime

Mortar.

From the diagram it is seen that the strength of the mortars
containing the 8o, 90, and 100 per cents of the cement are prac-
tically the same, which would seem to show that the addition of a
little lime to cement mortar does not materially decrease the
strength. Notice that the mortar containing only 60 per cent of
cement is considerably weaker than that containing 80 per cent,
which shows that more than 20 per cent of lime causes a consider-
able decrease of strength. A study of the lower portion of the dia-
L'l.im show, that 10 per cent of cement added to lime mortar does
not materially increase its strength.

FREDERICKSON- LIME-CEMENT MORTA R.

Table i was derived from the diagram, and shows approxi-
mately the effect of introducing each additional per cent of cement
into lime-cement mortar. The values for the strength were those of
the 8-16 weeks' tests, when the ultimate strength seems to have
been attained.

TABLE 1.

INCREASE IN COST AND STRENGTH BY SUCCESSIVE ADDITIONS OF
CEMENT TO LIME MORTAR.

100
0

90
10

80
20

60
40

40
60

20
80

2.25
239

■95

10
90

Per cent of cement

100

Successive increase in strength.
Successive increase in cost. . . .

I
I
I

•7
.28

■56
1 . n

1 .21

1.68
•7

1.62

2. 14
•75

2.40

2.49

•97

2.41

2 50

.96

This table shows that all-lime mortar is perhaps the most efficient
mortar, when great strength is not required and water is not encoun-
tered; otherwise the high per cents of cement mortars are unneces-
sary and practically as efficient.

Taking the prices of cement and lime at Chicago, i. e., cement
@ #3.25 per bbl. of 400 lbs., or o 8 cents per lb., and lime @ 60
cents per bbl. of 200 lbs., or 0.3 cents per lb , the relative and abso-
lute cost of equal volumes of cementitious material in the various
mortars is as in Table 2.

TABLE 2.

COST, STRENGTH, AND EFFICIENCY OF THE SEVERAL MORTARS.

ementitious Mater

al.

Mortar.

Composition in
per cents.

*Cost per Cubic Yard of Mortar.

Strength.

O - fD P

Pounds

<" 3 3 £■.

Lime.

Cement.

Lime.

Cement.

Total.

Rel'tive.

p'rsq.in.

Rel'tive.

100

$1 .00

$7.46

$7-46

1 .00

I .OO

. 10

6.81

I .09

.20

6.17

III

.40

4.88

.86

.60

3-58

•85

.80

2.29

.76

.90

1.65

100

1 .00

1 05

*Cost of sand not included.

I III. FECHNOGRAPH.

In a cubic yard of brick masonry, containing 500 brick (8^ x 4
laid with <4 to ; -inch joints, there are 10,000 cubic inches of
mortar. It was found that about 160 pounds of Portland cement
was required to produce this amount of mortar. The cost of the
cement, at 0.8 cents per pound, was $1.28. Had 20 per cent of
lime been used with the cement, a mortar nearly as strong and one
not so apt to set before being used, would have been obtained at a
saving of 25 cents. That is to say, by the addition of 2 or 3 cents
worth of lime 18 cents worth of cement would have been saved.

The additions of small per cents of cements to lime mortar
may slightly quicken the activity, and certainly does cause the
mortar to work better; but we could not, for these reasons alone,
recommend this practice, since, while the cement does add slightly
to the strength, the increased cost is such as to render the practice
unprofitable. Small per cents of lime, up to 25 per cent, may be
added to cement mortar without materially weakening it, while at
the same time considerably diminishing the cost, and also retard-
ing the activity, thereby allowing the mason sufficient time to place
the mortars before it begins to set.

TALBOT— RAILWAY TRANSITION CURVES. 77

RAILWAY TRANSITION CURVES.

By Arthur N. Talbot, Professor of Municipal Engineering.

A transition curve, or easement curve, as it is sometimes called,
is a curve of varying radius used to connect circular curves with
tangents for the purpose of avoiding the shock and disagreeable
lurch of trains, due to the instant change of direction and also to
the sudden change from level to inclined track. The primary object
of the transition curve, then, is to effect smooth riding when the
train is entering or leaving a curve.

The generally accepted requirement for a proper transition
curve is that the degree-of-curve shall increase gradually and uni-
formly from the point of tangent until the degree of the main curve
is reached, and that the super-elevation shall increase uniformly
from zero at the tangent to the full amount at the connection with
the main curve and yet have at any point the appropriate super-
elevation for the curvature. In addition to this, an acceptable
transition curve must be so simple that the field work may be easily
and rapidly done, and should be so flexible that it may be adjusted
to meet the varied requirements of problems in location and con-
struction.

Without attempting to show the necessity or the utility of tran-
sition curves, this paper will consider some forms of such curves,
and especially the transition spiral.

The Transition Spiral.*

The Transition Spiral is a curve whose degree-of-curve increases
directly as the distance along the curve from the point of curvature.

Thus, if the spiral is to change at the rate of io° per ioo feet,
at 10 feet from the beginning of the spiral the curvature will be the
same as that of a i° curve; at 25 feet, as of a 20 30' curve; at 60
feet, as of a 6° curve. Likewise, at 60 feet, the spiral may be com-
pounded with a 6° curve; at 80 feet, with an 8° curve, etc.

This curve fulfills the requirements for a transition curve. Its
curvature increases as the distance measured around the curve.
The formulas for its use are comparatively simple and easy. The
field work and the computations necessary in laying it out and in
connecting it with circular curves are neither long nor complicated,
and are similar to those for simple circular curves. The curve is

*The author desires to express his obligation to Mr. J. K. Rarker, '92, for valuable aid in the
preparation of drawings, the calculation of tables, and the checking of formulas.

7- THE TECHNOGRAPH.

extremely llexible, and may easily be adapted to die requirements
of varieil problems. The rate of change of degree-of-curve may
be made any desirable amount according to the maximum curve
used, or according to the requirements of the ground.

As the derivation of the formulas is somewhat long, their
demonstration will be given first. The explanation and application
of these formulas to the field work and to the computations will be
given separately, a knowledge of the demonstration not being essen
tial to the application.

In Fig. i, AEL is the transition spiral connecting the initial
tangent with the main or circular curve LH. A is the beginning of
the spiral and will be known as P.S., point of spiral. AP is the
prolongation of the initial tangent and will be used as the axis of
X. L is the beginning of the circular curve LH, and will be called
P.C.C., point of circular curve. D is the point where the circular
curve produced backward gives a tangent DN parallel to the tan-
gent AP, and will be called the P.C. of the produced simple curve.
BD is also the offset between the tangent of a curve with a transi-
tion spiral, and a curve without the spiral but having the same
change of direction as the former.

The degree-of-curve of the spiral at any point is the same as
the degree of a simple curve having the same radius of curvature
as the spiral has at that point. The radius of the spiral changes
from infinity at the P.S. to that of the main curve at the P.C.C.
The spiral and a simple curve of the same degree will be tangent
to each other at any given point; i. e., they will have a common
tangent.

The following nomenclature will be used:

R— radius of curvature of the spiral at any point.

Z> — degree-of-curve of the spiral at any point. At the P.C.C,
D becomes the degree of the main curve.

aerate of change of D per station of 100 feet measured on
the curve.

j=length in feet from the P.S. to any point on the spiral.

Z = total length of the spiral measured in stations of 100 feet.

/ total central angle of the whole curve, or twice BCH of Fig.
i,ll being the middle of the circular arc.

J— angle showing the change of direction of the spiral at any
point, and is the angle between the initial tangent and the tangent
to the spiral at the given point. For the whole spiral it is equal to
PTL. The latter is also equal to DCL.

TALBOT— RAILWAY TRANSITION CURVES. 79

9= deflection angle at the P.S., from the initial tangent to any
point on the spiral. For the point L, it is BAL.

0 = deflection angle at any point on the spiral, between the tan-
gent at that point and a chord to any other point. For L, $ is
TLA.

.r=abscissa of any point on the spiral, referred to the P.S. as
the origin and the initial tangent as the axis of X. For the point
L, a:=AM.

^=ordinate of the same point, measured at right angles to the
above axis. For the point L, j=ML.

/ = abscissa of the P.C. of the main curve produced backward;
i. e., of a simple curve without the spiral. For the point D, / = AB.

<?=offset between the initial tangent and the parallel tangent
from the main curve produced backward, or it is the ordinate of the
P.C. of the produced main curve. If D is the P.C, BD is o. It is
also the radial distance between the concentric circles LH and BK.

T= tangent-distance for spiral and main curve = distance
from A to the intersection of tangents.

-£'=external-distance for spiral and main curve.

C=long chord AL of the transition spiral.

The length of the spiral is to be measured along chords around
the curve in the same way that simple curves are usually measured.
The best railroad practice, in the writer's opinion, considers curves
up to a 7° curve as measured with ioo-ft. chords, from 70 to 140 as
measured with 50-ft. chords, and from 14" upwards as measured
with 25 -ft. chords; that is to say, a 70 curve is one in which two 50-
ft. chords together subtend 70 of central angle, a 140 curve one in
which four 25-ft. chords together subtend 14° of central angle. The
advantages of this method are two-fold, — the length of the curve
as measured along the chords more nearly approximates the actual
length of the curve, and the radius of the curve is almost exactly
inversely proportional to the degree-of-curve. The latter consider-
ation is an important one, simplifying many formulas. With this

5 TJ50

definition of degree-of-curve, the formula J?— j) will give no er-
ror greater than 1 in 2000. For a io° curve the error in the radius
is .15 feet, and for a 160 curve .06 feet. The resulting difference in
the alignment or distance for the ordinary length of spiral will be
considerably less than this amount. For the transition spiral, then,
the error either in alignment or distance will be well within the
—6

THE TECHNOGRAPH.

limits of accuracy of the field work, and hence the relation R— j}
will be considered true.

B x T MP

S^--\J0 >

r '_ ... r.T" --V i

Fig. i.

Demonstration of Formulas. — From the definition of the
transition spiral, we have, remembering that the value of a as
defined above requires the length of curve to be measured in 100-
ft. units {stations) instead of feet,

a s
Z)=aL="

IOO

From the calculus the radius of curvature

ds
R= — .
dA

B 7 :i i)

Substituting the expression /?= /} and solving,

a s ds

dJ = .

a Z"

573000

a y

Integrating, J — =

1 146000 1 14.6

Changing J from circular measure to degrees,
d=j£tfZ8,

which is the intrinsic equation of the Transition Spiral.

Since from (1 ) a— — , we also have

D I.

(3)

TALBOT— RAILWAY TRANSITION CURVES. 81

From these equations it will be seen that

(a) the change of direction of the spiral varies as the square
of the length instead of as the first power of the length as in the
simple circular curve, and

(b) that the transition spiral for any angle J will be twice as
long as a simple circular curve.

To find the co-ordinates, x and y, of any point on the spiral,
we have by the calculus dy=ds sin J and dx=ds cos J. Expand-
ing the sine and cosine into an infinite series, substituting for ds its
value in terms of dJ, and integrating, we have

" I07°-5 ( . s " 7 I n ')

y= ] ft* ->*+ J* -etc. - (4)

(«)» I 42 1320 \

1070.5 C 1 , 1 )

)a% j*+ j?_etc. '-

(oj% (_ 10 216 \

x= 1 JX J-+ J?— etc. (- (5)

As J here is measured in circular measure and is only ]/2 when
the angle is 28.°65, these series are rapidly converging, especially
for smaller angles.

Changing the angle J from circular measure to degrees, and
dropping the small terms,

y=.z<)\ a L? — .00000158 as L1 (6)

For values of J less than 150 the last term may be dropped,

and up to 250 the term will be small. D L~ may also be written in

place of a L?. Also

jc=iooZ — .00075 a2 I? (7)

Or jv=iooZ — .00075 D* L6 (8)

The last term in eq. (7) or (8) may be used as a correction to
be subtracted from the length of the curve in feet.

. To find the deflection angle 8 for any point on the spiral, as
BAL for the point L, divide equation (4) by equation (5).

tan 0=^3 J + A J34-15||25_l5, etc. But from the tangent series

for y3j,

tan yi J = yi J -\- ^ J3.-|-7^F J5, etc. Subtracting one from the

other, we get a series which is rapidly decreasing when J is less
than 400. Investigating this difference, remembering that J is in
circular measure, it is found that the error of calling the two equa-
tions equal is less than i' for J = 25° and decreases rapidly below
this. As J will rarely reach 250 and as the resultant error of direc-

////•: TECHNOGRAPH

tion will be corrected at the P.C.C. when J— 9 is turned off, wc

may write D1

' 6 • J ' .,«/ L* '•, — (9)

Between 200 and 40", .000053 J:i (where J is in degrees) will
give the numbers of minutes correction to be subtracted from 'J
to give 9.

To find the tangent at the terminal point of the spiral, L, lay
off a deflection angle from LA equal to J — 9. When J is not over
20", ?jJ, or 2H may be used. This since FLT=PTL= J, and FLA
=PAL=0.

The tangent at any other point on the spiral is found in the
same manner, using the 9 and J for that point.

W A

B' F B

T M

>f^.~

--ij-

Lt*

T^ — ■

• — .!> A

1 A

^& "■

- - _ Dr- -
" -1- -

_^ — -ti^*-^'

1
1

"" ~~ - *-L "^^v

**«.

d|-^--\:

">Jr

//VV

T" "

s;^v

/ \ N
/ v

*&S

<kC

\\Vx

v!H

/c:

V x (TIM

Fig. 2.

At any point on the spiral to find the deflection angle for a sec-
ond point. In Fig. 2, let /,, be the distance from the P.S. to R, and
L the distance from the P.S. to any other point on the spiral, as K.
Let FRN be the tangent at R, and RFM = J, its angle with the ini-
tial tangent. Let KTM=:J be angle of tangent at K with initial
tangent, equal to total change of direction of the spiral up to that
point. KRN = "/^required deflection angle. Then
UK >•-,•,

tan (0+4)= = •

RU x—xx

Substituting for the co-ordinates their values from equations

JS — jia
(4) and (5), and also developing tan '3 . - , into a series, and

TALBOT— RAILWAY TRANSITION CURVES. 83

subtracting the latter from the former, an expression for the differ-
ence will be found, which amounts to but a small fraction of a min-
ute for any value of J up to 350. Hence we may write

<lJjrJl — yi (Jt-f J/7* J '-;-|_J); whence by substitution and reduction,

9—^a Zj (L—L^+Yea (L—Ltf (10)

It will be noticed that the first term is the deflection angle for
a simple curve of the same degree as the spiral at the point R
(called the osculating circle), and of length equal to the distance
between the two points; while the second is the deflection angle at
the P.S. from the initial tangent for an equal length of spiral. If
the second point had been chosen on the side nearer the P.S., the
second term would have an opposite sign from the first. Equation
(10) may then be written with the plus and minus sign.

The spiral then deflects from a circle of the same degree-of-
curye at the same rate that it deflects from the initial tangent.
D'RH, in Fig. 2, represents the circular curve tangent to spiral at
R, the two having the same radius at that point and both being
tangent to FRN. The deflection angles between points on the
spiral and on the circle RH, and also between the spiral and RD'
are the same as for the same length of spiral from A. In the same
way at K, RKT=SKT — SKR, the latter angle being equal to the de-
flection from initial tangent at A for a length of spiral equal to KR.

It may also be readily shown from (2) that the difference in
direction of the two tangents, J — Jlf is the central angle for this
simple curve plus the spiral angle, both for a length equal to the
distance between the two points.

It may also be shown that the distance between a point on the
spiral and on this osculating circle is the same as the ordinate y
from the initial tangent for this length.

To find the offset o. From Fig. 1, BD = BF — DF

= BF— CD vers DCL. But tf=BD, BF=y for end of spiral, DCL
= J for whole spiral, and CD=Z\ Hence, o=y — R vers J. Sub-
stituting for v, R, and J their values in terms of the length of the
whole spiral, and reducing, we have for 0 in feet

^ = .0725 a Z3=.o725 D Z2 (it)

where D and Z refer to the whole length of the spiral.. The other
terms of the series are so small that they may be dropped when J
is less than 300. It will be seen that o is approximately one-fourth
of the ordinate of the P.C.C., which of course should be true if E,
the middle point of the spiral, is opposite D, the P.C.

II! I TECHNOGRAPH.

I'ofindt, or A I!. From Fig. i, AB AM— BM *— FL x—

R sin J. Kxpanding and reducing,

t 50 /.— .000125 ,7 / '
or / 50 /, — .000125 D* L% \

Hence to find /, from one-half the length of the spiral in feet
subtract ,„'„„ of the product of the square of the degree of the main
curve by the cube of the length of the spiral, the latter being ex-
sed in stations of 100 feet.

A comparison of / with the abscissa found by substituting '_■ L
in equation (8) shows that BD cuts the spiral at a point only .00005
D I feet from the middle point of the spiral. This is /„ of the
correction used in equation (12) for finding / from ) j /. . 1 or our
purpose we may say that BD bisects the spiral. It also follows that
the spiral bisects the line BD, since BE= jiy.

If the offset is given. From (1 1) and (3) we have

I =3.7141/ — (13)

J = i.857yV/T (,4)

a= .2691 y (15)

3:, i'-;, and {',-, may be used for these co-efficients with advantage.

To find the tangent-distance 7', consider in Fig. 1 that AB in-
tersects CH, H being the middle of the circular curve, at some
point P outside the diagram. Then AP-AB+BP. BP = BC tan
BCH.

Hence T=t + (R+o) tan ^ I (16)

/ and 0 tan ]{, I may be computed separately and added to the
/found from an ordinary table of tangent-distances.

Fig. 3.

1 6) gives / for the same transition spirals at each end of the
main curve. It may be desirable to make one spiral different from

TALBOT— RAILWAY TRANSITION CURVES. 85

the other. To find an expression for the tangent-distances for this
case, proceed as follows: In Fig. 3, let RS=HD=/7f, BD = <?„ AB =
/„ RT = /2, AE=7'„ TE-- '/'.,, A' -radius of main curve DLKS,
J?+<?2 -radius of HR, and /wangle PER.

Then 7,1=/,+HC— PE, and

Tt- !+(tf+*2) tan y2 r—{o—o.:) cot I (r7)

Similarly, Tz—tr\-(R-\-o^ tan l/j /+(", — o2) cosec /.

When 7 is more than 900, the last term of ( 17) becomes essen-
tially positive.

To find the external- distance, is = H P. In Fig. 1 , H P = K P+ H K.
Hence

E=(R+o) exsec y2I + 0 (18)

To find the long chord, C=AL. In Fig. 1, ML— AL sin MAL,

or C= . Putting this in terms of the length of the curve,

sin 6

C= 100L — (.0004 ar L* or .0004 Z>2Z3), (19)

in which Cis in feet and Z in stations. It will be seen that the last
or correction term is ts of the correction for x as given in equa-
tion (7).

The middle ordinate for any arc is equal to the middle ordinate
for an equal length of circular curVe of the same degree-of-curve
as the spiral at the middle point of the arc considered. This degree-
of-curve is the average of the D's, at the end of the given arc. This
is an approximate formula which is true whether one end of the
chord is at the P.S. or not.

The ordinate for any other point along the chord may be found

as follows. If / is the half arc, /' the distance from the middle

point of the arc to the required chord-ordinate, y the ordinate from

the initial tangent for a distance/ from the P.S., andy the same for

distance /', then the required ordinate from the chord equals the

corresponding ordinate for a circular curve of same degree-of-

/'
curve as middle point of arc, minus or plusy, plus or minus v;

the first sign being used for ordinates on the side of the middle
point away from the P.S. and the second when toward it.

Summary of Principles. — For convenience of reference the
principal formulas will be repeated here.

THE TECHSOGRAPtt.

D^al (0

Dl P (2)

H \J \a I ■ \ D I \-^ (9)

*= \a /,. /— /,,)4-,U (/.— Z,r

= \ D (Z— Zi) ±h (Z>+Z>, ) (Z— A) (IO)

0 -oi'iD /.■ (11)

/— 50/. — .000125 (a* Ls or Dl Z8) (12)

T=f + (R+o) tanj£ I (16)

An inspection of the formulas and demonstrations will show the
following properties of the transition spiral:

1. The degree-of curve D at any point on the spiral equals the
product of the rate of change of D per 100 feet by the distance
from the P.S. expressed in stations of 100 feet. 1 Eq. 1.)

2. The angle J between the initial tangent and the tangent at
any point on the spiral (the change of direction, corresponding to
central angle of circular curves) equals:

(a) One-half the rate a multiplied by the square of the dis-
tance in stations;

(b) One-half the product of the distance in stations by the
degree-of-curve of the spiral at the given point, or one-half of the
angle for a circular curve of this degree-of-curve and of the same
length;

This is true for any point along the spiral. For the terminal
point, D becomes the degree of main curve. For the same angle
J, the spiral is twice as long as a circular curve. (Eq. 2.)

3. The dellection angle <-> at the P.S., from the initial tangent to
any point on the spiral, as PAL in Fig. 1, is ' .; J, or one-sixth of the
product of the rate and the square of the distance from the P.S ex-
pressed in stations. It is also one-third of the dellection angle for
a simple curve of the same degree as the spiral at the given point.
(Eq. 9.)

4 The angle between tangents at any two points on the spiral
is J — J, or the difference between the respective angles of these tan-

r.\Ui<rr-i:.\ll.\\\) TRANSITION CVR] ES -7

gents with the initial tangent. J — Ji = j£<* (/.- — Lf). It is also
one-half of the sum of the central angles of two simple curves of
length equal to the distance between the two points and of degree
equal respectively to the degree-of-curve of the spiral at the two
points. (Eq. 2.)

5. The deflection angle at any point on the spiral from its tan-
gent to the P.S. is J — &\ or when J is less than 200, it is also -\ J =
28. This enables the tangent at any point to be found. (Eqs. 2 and 9.)

6. The deflection angle from a tangent at any point on the
spiral to any other point on the spiral is the sum or difference of 1 1)
the deflection angle for a simple curve of same degree as the spiral
at the given point and of length equal to the distance between the
points, and (2) the spiral deflection angle at the P.S. for a length
equal to the distance between the two points. The latter angle is
plus if the desired point is further from the P.S., and minus it nearer,
than the point from which the deflections are made. See illustrations
under Field Work. (Eq. 10.)

7. The spiral diverges from its osculating circle (circular curve
of same degree) at any point at the same rate that the spiral deflects
from the initial tangent, and the distance between the circle and
spiral is the same as the y for an equal length of spiral.

8. The offset 0 between the initial tangent and the parallel tan-
gent from the main curve produced backward in feet, equals .0725
times the product of the rate by the cube of the length of the whole
spiral in stations, or .0725 times the square of the length of spiral
and the degree of main curve. This ordinate is approximately one-
fourth of the ordinate ^ of the end of the spiral. The spiral bisects
the offset at a point half-way between the P.S., and the P.C.C.
(Eq. 11.)

9. The distance / from the P.S. to this offset is found by sub-
tracting the correction .oooi25tf\Z"' from the half length of the curve
in feet. (Eq. 12.)

10. The long chord is found by subtracting the correction,
.0004 D9LS from the length of the curve in feet. (Eq. 19.)

11. Other properties may be found by ordinary trigonometric
operations.

The Field Work. — Before running the curve, the value of a
must be decided upon. If it is desired to connect a given tangent
with a given curve, the offset 0 between the tangent being known, a
may be calculated from equation (15), page 84. This method of
work may be a great convenience in location. Generally, however,

rill TBCIISOGR 1/7/

lerations of maximum degree-of curve, the length of tangents,
and the speed ol trains will determine the value of a to be used. In
mountainous country, with i<> maximum and low speeds, a change
i in 10 feet («= 10) will be suitable. For high speeds and 6° max-
imum, a - will give an easy-riding curve, and for some locations a
value even lower than i may be desirable. For electric and elevated
roads, values as la: may be necessary. It will be seen that

the curve is applicable to a wide range of work.

If the degree -of-curve at any required point is an integral num-
ber, the principle that the deflection angle is one-third of that for a
simple curve may be used. Thus for a— 10, at 40 feet from the P.S.,
the D of the spiral will be ac. Calculate one-third of the deflection
angle for 40 feet of 4" curve. It may be seen that T'„ of the D gives
the required deflection per foot for the point whose curvature is D.

It desired, the calculations may be made by means of a table as
shown hereafter. Or the powers of /. may be taken from a table of
squares and cubes, the lower decimals dropped, and the multiplica-
tion by the simple factors remaining may be made easily and rapidly.
Thus, when a— 2 to determine w for a point 234 feet (2.34 stations)
from the P.S., find the square of 234 (54756), change the decimal
point so that it will become the square of 2.34 (5.48), and from
equation (9) h ' ,,//, '—'6 x 2 X 5.48=1" 49'. For o and y the
table of cubes may be used in a similar way.

The field work after the P.S. has been determined is similar to
that of circular curves. The deflection angles are turned off by the
transit, and the measurements are made along chords as in laying
out circular curves. Since it is not necessary to make succeeding
chords the same length as the first, the stationing may be kept up,
and the even stations and +5o's put in as usual. Herein is an ad-
vantage over methods requiring a regular length of chord to be put
in. When the transit is moved to a point on the spiral, the tangent
is found by laying off from the chord to the P.S. an angle= J — B.
I 01 usual limits this is also 20. Finally, the circular curve is run in
from the P.C.C., the tangent to the curve first having been found.

If it is necessary to use a transit point on the spiral, the tan-
gent at that point is found as before, and the deflections are calcu-
lated by equation (10) and will equal the deflections for a circular
curve of the same degree as the spiral at the transit-point minus or
plus the spiral deflection angle atthe P.S. — minus if toward, and plus if
from the P.S. -the length used in both cases being the distance from
the transit point to the point to be set.

TALBOT— RAILWA V TRANSITION CURVES.

In running from the P.C.C., to the P.S., use a similar method.
Here D is the degree of main curve. After finding the tangent at
the P.C.C., the following rule may be used: To find the deflection
angle for any point on the spiral at a distance L from the P.C.C.,
calculate the deflection angle for a D° curve and length L, and also
the deflection at the P.S. for a spiral of length L. Subtract the
latter from the former. The remainder will be the required angle.
If the new point is to be used as a transit-point, the new tangent
may be obtained by laying off an angle equal to deflection of circular
curve of length L and of same degree as the spiral at the new
point, plus the spiral deflection for length L.

As an illustration, let the P. S. be at sta. 16 + 21, 17 the new tran-
sit-point, and 17 + 50, the point to be set. Assume a to be 4. Then
the deflection angle at the P.S. for sta. 17 may be found from equa-
tion (9) as follows: Station 17 is 79 feet from the P.S. , and hence L
= .79. 798 = 624i, and .79-' = . 62. Since J& X 60=10, we may get
H in minutes by multiplying a/J by 10. Hence 0=io X 4 X .62 =
25'. J = y2 X 4 X .62 X 60 = 75'. <P - 75' — 25' = 50' With the
transit at 17, a deflection angle of 50' from the line to the P.S. will
give the tangent. The degree-of-curve at 17 is 4 X .79 = 3. °i6, which
has a deflection angle of o'.95 per foot. To get the deflection angle
to set 17 + 50, take deflection angle for 50 feet of 3°.i6 curve =
47^2', and also the deflection angle for 50 feet of spiral = 10'; then
#= 47* + io' = 57', with which 17 + 50 may be set. If the point
were on the side nearer the P.S., as 16 + 50, the deflection angle
would be 47' — 10' = 37'.

To facilitate the computation, a transit-point may be chosen at
a point where the spiral has an even degree-of-curve. For example,
164-96 will be 30 curve, and the circular deflections from this curve
are more easily calculated.

If desired, the spiral may be located by ordinates from the tan-
gent or from a circular curve tangent at any point on the spiral.
Thus, in Fig. 2, the ordinates from AB, from RDl, from RH, and
from KSD, as calculated from equation (6). with L as the distance
from A, R, or K, will give points on the spiral.

To locate the P. S. — If the tangents have been run to an inter-
section, the tangent-distance T may be calculated by equation (15)
and the P. S. measured in.

In case a simple curve has been run without a transition, the
distance of the P. S. back of the P. C. used is t + o tan j4 /, where /

THE TECHXOGRAPlt.

is the angle between the tangents, The new curve will come inside
the old, but will not be exactly parallel to it.

If a simple curve has been run, as DLH in Fig. i, and also a
tangent AB, with an offset #=BD between them, the spiral to con-
nect them may be located by finding a from equation (15), which
js a — .2691 /;:; With this value of a, t may be calculated or
found from the table as explained below. This method is a great
convenience where it is desired on account of the ground to throw
the curve in or out without changing the tangent, or where a similar
change in the tangent is desired without a change in the curve, —
the connection being made by means of a suitable spiral.

To replace a simple cutve by a spiral and new curve, without
varying far from the old line and so keep on the old embankment,
proceed as follows. In Fig. 4, the line TNH is the old curve. It is
desired to throw the track out a distance HK=/, in order to

M P

n u

~~^Z '

U h

G 1

v N '

\Jl

/ x

/ %\

[ \'

\ \

1 /

V \\K^

c /

\ A"

1 •*J/

/
1 /

1 /

*' \ t

1 / --

1 / ,, **

S L

1 / "

1 ^

! 3T'

„ - "c'

c"1-"'"

Fig. 4.

in a spiral by throwing it in at the P. C. P is the intersec-
tion of tangents, which comes outside the diagram. Let Rl be
the radius of 'the old curve, and R of the new. HP — KP=/, or
Rx exsec ]/2 I — (R+o) exsec y2 \—p. Hence

R\ — R~o-\- , from which the degree of the new

exsec T2 /

curve may be found.

TALBOT— It AILWA Y TRANSITION CURVES.

Also AT=AP— TP=/— (R — R— *)tan y2 /=/—/> cot # /,
by which the P. S. may be located. A value of p may be chosen
to cause the least re-lining of track.

Fig. 5.

Covipound Curves. — The spiral may be used to connect curves
of different radii, choosing that part of the spiral having curvature
intermediate between the degrees of the two curves; thus, connect
a 30 and an 8° curve by omitting the spiral up to ^=3° and con-
tinuing until Z>=8°. In Fig. 5, DK is a D\ curve, which it is de-
sired to connect with a D\ curve, the transition to commence at K.
Z>2 is greater than D1. The degree of the spiral at K is A . Sup-
pose the spiral to be run backward from K to a tangent at A. The
continuation of this spiral from K to P, where it becomes a D\ curve,
may be run from K the same as from any point on the spiral ac-
cording to the method before described, and no part of the spiral
from K to A need be located. The length of spiral between K

A— A

and P=r/— ; and the angle between tangents at K and P is

a
Yo, l CA+ £>s), or the average of that for a length / for both curves.
The spiral may also be used to connect two curves having a
given offset between them.

THE TECHNOGR IPH.

I bles. — The computations may be shortened by means of the
following tables. Table I. may be used for any value of a. Table
II. is for a change of io° per ioo feet, and Table III. for 3 | ".

The first column contains the distance in feet from the l\S.;
the second, the degree-of-curve of the spiral; the third, the spiral
angle J, the fourth, the deflection angle <-> from the initial tangent;
the fifth, the offset o of the initial tangent from the main curve pro-
duced backward; the sixth, the ordinate y from the initial tangent
as the axis of X; the seventh, a correction to be subtracted from
the length of the spiral in feet to find x; the eighth, a correction to
be subtracted from half the length of the curve in feet to find /. To
find the long chord c, subtract i of this x correction from the length
of the curve in feet.

To find intermediate values, interpolate by multiplying one
tenth of the difference between consecutive values by the number
of additional units. Thus Table II. gives J for 140 feet as 9°48';
for 150 feet, as nu 15'. One tenth of the difference between these
is 8'. 7. For 146.8 feet, add 6.8X8.7 = 59' to 90 48', giving io° 47'.

This interpolation gives a slight error in J which may be neg-
lected for a less than 8, and may not need considering above that.
To find exact values, deduct the following from the interpolated
quantities: For a length in feet ending with i,.o27'; 25.048'; 3,-063';
4, .072'; 5, .075'; 6, .072'; 7, .063'; 8, .048'; 9, .027'. For other
spirals, multiply these corrections by a. For a— 10, the greatest
error is .75'. This difference arises from the fact that the square of
numbers does not increase uniformly.

Interpolation in the other columns gives accurate results.

Table I. has been carried to several decimal places to permit a
use with any value of a. To do this, multiply the tabulated value
opposite the desired length by the a of the spiral, — except for the
x and / corrections, when the square of a must be used as the mul-
tiplier. Thus, if (1=2, multiply the tabulated J, 9, 0, or y by 2 and
the / and x corrections by 4. This may be utilized when it is
desired to correct a fixed tangent with a given circular curve, since
when a and /. have been found the other quantities may be calcu-
lated by means of this table. A similar table for every foot of
1 would not be very bulky. The value of y obtained in this
way is subject to error when J is more than 16° for large values of a.

The tables are of such size that they may be cut out and in-
serted in the ordinary engineer's field book.

TALBOT— RAILW A Y TRANSITION CURVES.

TABLE I. TRANSITION SPIRAL. a = r.

L-ngth

y
0.000

■XCOR

/COR

O-. I

00''. 3

03 OO1. I

.000

00000

o.ccoo

O .2

01 .2

00 .4

.001

.002

0.3

02 .7

00 .9

.002

.008

O.4

04 .8

01 .6

.005

.019

O.5

07 .5

02 .5

.009

.036

O.6

10.8

0 03 .6

.016

.063

.0001

O.7

14.7

04.9

.025

.100

.0001

0 .8

19 .2

06 .4

•037

• 149

.0002

0.9

24 -3

08.1

■053

.212

.0004

.0001

IOO

I .0

3°-

10 .

•073

.291

.0008

.0001

I .1

36.3

0 12 .1

.097

■387

.0012

.0002

120

I .2

43 -2

14 .4

.126

•503

.0019

.0003

I3°

1 -3

5° -7

16 .9

.160

•639 ;

.0028

.0005

140

1 .4

58.8

19 .6

.199

•798

.0041

.0007

150

1 5

07 .5

22 .5

• 245

•982

.0058

.0010

160

1 .6

16.8

0 25 .6

.298

1. 191 ;

i .0080

.0013

170

1 -7

26 7

28 .9

•357

1.429

.0108

.0018

; 180

1 .8

37 -2

32 -4

■424

1.696

.0144

.0024

; »9°

1 .9

48.3

36.I

•499

1.995

.0189

.0031

2CO

2 .0

CO .

40.

.582

2.327 ;

.0244

.0041

2IO

2 .1

12 .3

0 44.1

0.673

2.690

.031

.0052

220

2 .2

25 .2

48.4

•774

3097 :

•039

.0065

230

2 .3

38.7

52 9

.885

3-538

\ .049

.0082

240

2 .4

52 .8

57-6

1.005

4020

.061

.0101

250

2 -5

07 -5

1 02 .5

1. 136

4-544 !

.074

.0124

26o

2 .6

22 .8

1 07 .6

1 278

5. in

. .090

.015

270

2.7

387

1 12 .9

1 43i

5- 724

.109

.018

28o

2 .8

55 2

1 18.4

1.596

6.383

; 131

.022

29O

2.9

12.3

1 24 .1

1-773

7.091

1 .156

.027

300

3-°

3°.

1 30.

1.963

7.850 ;

.185

.031

3IO

3 -i

48.3

1 36.1

2.166

8.66

.218

.036

320

3 2

07 .2

1 42 .4

2.382

9-53

•255

•043

330

3 -3

26 .7

1 48.9

2.612

10.45

.298

.050

340

3 4

46.8

1 55-6

2.857

11.42

•346

.058

35°

3-5

07.5

2 02 .5

3. 116

12.46

.400

.067

360

3-6

28.8

2 09 .6

3-391

I3-56

.460

.077

37o

3 -7

5°-7

2 16 .9

3.681

14.72

.528

.088

380

3-8

13 .2

2 24.4

3.988

'5-94

•603

.100

390

3 -9

36.3

2 32 .1

4-3"

1723

.686

.114

400

4.0

00 .

2 40 .

4651

1859

•779

.130

410

4 1

24-3

2 48 .1

5.01

20.02

.881

.147

420

4.2

49 2

2 56 .4

538

21.51

■994

.166

430

4-3

U-7

3 04.9

5.78

23.08

1. 118

.186

440

4 4

40 .8

3 13 -6

6.19

24-73

1.254

.209

450

4-5

°7 -5

3 22 .5

2645

1.403

•234

460

4.6

34-8

3 31 -6

7.07

28 24

1.566

.261

470

4-7

02 .7

3 40 9

7-54

30.12

1-743

.291

480

4.8

31 .2

3 5° 4

803

32.07

••937

•323 .

490

4.9

00.3

4 00 .1

8.54

34- 1 1

2.146

•358

500

5.o

3°-

4 10 .

9.07

36-23

2-374

•396

THE TECHNOGBAPH.

TABLE I.— Continued.

Lcngib

50.1

520

5 -2

53°

5 -3

540

5-4

55°

5 -5

560

5.6

^70

5-7

580

5.8

SQO

5-9

600

6.0

610

6.1

620

6.2

630

6-3

640

6.4

650

6-5

130 00'. 3

■3 3« -2

14 02 .7

34-8

14
•5

15
16

16 49

17 24

18 00

18 36.3

19 13 .2

19 5° -7

20 28.8

21 07 .5

40 20l.I

4 3° 4

4 4° 9

4 5i

t; 02

13
24
36

48
00 .

12 .1
24.4

36.9
49.6
02 .5

9-63

38-44

10.20

40.73

10.80

43- 12

11.42

45-59

12.07

48.15

12.74

50.69

1343

53-56

14.14

56.40

14.89

59-34

15.65

62.39

16.44

65-52

17.26

68.77

18.10

72.11

18.97

75-56

19.87

79.11

X COR t COR

2.6 21

437

2.888

482

3-175

53o

3.486

582

3.820

637

4.18 |

697

4.56 1

762

4.98

83'

5-42

905

5-89

984

6.40 I

069

6.94 I

'59

7.51 I

2.S5

8.13 I

358

8.78 I

467

TABLE II. TRANSITION SPIRAL. a=io.

Length
10

1 .00

XCOR

t COR

0.00

2 .

.01

.02

.08

•05

.19

•5

.09

■36

6 .00

.16

■63

O.OI

0.00

7 •

•25

1. 00

.01

8 .

•37

1.49

.02

9 •

•53

2.12

.04

.01

100

10 .

•73

2.91

.08

.01

11 .00

•97

387

.12

.02

120

12 .

1.26

5.02

.19

•03

•30

13 •

1.60

6.38

.28

•05

140

14 .

1.99

7-97

■4i

.07

150

>5 •

«5

2 45

9 79

•58

.10

160

16 .00

2.97

11.87

.80

■ 13

170

'7 •

3-56

14-23

1.08

.18

180

18 .

423

16.87

1.44

.24

190

19.

497

19 81

1.88

•3'

200

20 .

39/2

5-79

23.07

1 2.42

.40

210

21 .00

20 >2

6.70

26.65

1 309

.52

220

22 .

2-4

03 %

7.69

30 58

389

•65

230

23-

8.78

34 86

485

.81

240

24.

34 U

996

39 49

599

1. 00

250

25 •

23 '-•

11.24

44 49

7-33

1.23

TALBOT— RAILWAY TRANSITION CURVES.

TABLE III. TRANSITION SPIRAL. a=J]

Length

a: COR /

COR

00. 201

Oil

o°

00 yi

0.00

0 00

0 00 0

0 .40

°> Vi

.00

.01

1 .00

.01

1 .20

05 Vs

.02

.06

1 .40

oS '3

•03

.12

2 .00

.05

.21

.00 0

2 .20

16 %

.08

■33

2 .40

21 M

.12

•5°

3 °°

.18

•71

IOO

3 -2°

33^

.24

•97

O.OI

3 -40

40 Yi

•32

1.29

.01 0

120

4 .00

.42

1.68

.02

*3°

4 .20

56 M

■53

2- 13

•03

140

4.40

05 M

.67

2.66

.05

150

5 .00

.82

327

.06

160

5 .20

25^

•99

3 97

.09

170

5 -40

36 Yi

1 19

476

.12

180

6 .00

1. 41

565

.16

°3

190

6 .20

ooYi

1.66

665

.21

035

200

6 .40

13 ^

1 94

7-75

•27

°5

210

7 .00

2 24

897

•35

220

7 .20

41 >i

258

10.31

•44

230

7 40

56>^

295

11.77

■54

240

8 .00

335

1338

.67

250

8 .20

28 M

37«

15 11

■83

260

8 .40

45 >3

425

1700

1. 00

270

9 .00

4.76

19 02

1. 21

280

9 .20

2lYi

531

21.20

i-45

290

9 -40

40 Yi

5 9°

23 55

"•73

300

10 .00

6 53

2605

2.05

310

10 .20

20 M

7 20

28 72

2 41

320

10 .40

4154

7 92

3i 57

2.83

330

11 .00

869

34 59 !

3 3o

340

n .20

9 49

378o 1

3.82

350

11 .40

1035

41.19

4.42

360

12 .00

ny2

11 25

44.78

5.08

370

12 .20

zsU

12.21

4856

582

380

12 .40

00 y2

13 22

52 53

6.65 1

39°

13 .00

14 28

5671

7 56 1

400

13 .20

52 M

15-39

61.10

8.58 1

410

13 .40

19 k

16.56

6569

9.69 1

62 ,

420

14 .00

4624

17 79

70.49

10.92 1

430

14 .20

1907

75 5i

12.27 2

440

14.40

43^

20.41

80.74

'3 75 2

450

<5 .00

21.81

86.19

1536 2

-7

M THE TECHNOGRAPH.

The transition spiral was probably first used on the Pan Handle
Railroad in 1SS1, by Mr. Elliot Holbrook. The principal part of
the treatment here given was made before the writer's attention was
called to Mr. Holbrook's use of the curve, and it is believed that
most of the formulas and methods appear here for the first time.
I'.y Mr. Holbrook's method, the deflection angles were always cal-
culated from the co-ordinates, .v and y, — along and tedious pro-
cess, especially if accurate results are obtained; and for a transit-
point on a spiral, the deflection angles were calculated from tan

y—y-

9— •

x — x.

If the properties of the transition spiral were more generally
understood and appreciated, it would be more largelv used.

The Tapering Curve.

The Tapering Curve is a compound curve consisting of a series
of circular curves of the same length, whose degree of-curve in-
creases by some constant difference up to the degree of the main
curve. Thus, if the taper is i° for each 30 feet, the approach from
a tangent to a 6° curve will be made by 30 feet of i° curve, 30 feet
of 20 curve, 30 feet of 30 curve, 30 feet of 40 curve, and 30 feet of
50 curve, after which the 6° curve is run in.

If the degree of the main curve is not a multiple of the com-
mon difference of the tapers, at the end of the last full chord a frac-
tional chord is used, proportional to the difference of the degree of
the main curve and last taper. Thus, for a taper of 2 ° 30' per 30
feet, an 8 ° curve would be reached by 30 feet of 2° 30* and 30 feet
of 5 ° curve, ending with 6 feet of 7 ° 30' curve; since 8° is in ex-
cess of 70 30' by one-fifth of the change 2° 30', one-fifth of a full
chord is used.

In order to run the curve with the transit at the beginning of
the tapering curve or at some corresponding point — thus saving
setting at each P. C. C. — a table giving detlection angles to the
different P. C. C's, is used. The formulas for the calculation of
these tables may be shown as follows:

In Fig. 6, let AKL be a tapering curve composed of a number
ofecpaal arcs, AH, I IK, and ECL, and LS the main curve which pro-
duced backward to D will give a tangent parallel to AP. Denote
the points of compound curve by P. C. C. The following nomen-
clature will be used:

TALBOT-BAILWAY TRANSITION CUIO ES.

-C

. fl.1 v'«

'•a

Fig. 6.

Z?=degree of the main curve, and R its radius.

d= degree of arc of taper of number denoted by subscript.

r = radius, distinguished in the same way.

i = central angle of any arc, distinguished in the same way.

J = sum of the central angles up to a given P. C. C.

0 = deflection angle at P. T. C. to end of any arc.

$ = deflection angle at any P. C. C. to end of any arc.

L = total length of the tapering curve (in stations).

c— length of chord of one curve (in stations).

n = number of the chord considered, counting from the P. T. C.
Other terms are as used in the transition spiral.

Since the degree of the tapers increases in arithmetical pro-
gression,

A — y2n{n-\-\)i. Also, since L-n c, A = y? D L, and hence
the curve will be twice as long as the main curve for the same cen-
tral angle.

To find the deflection angle at the P.T.C.,—

tan 8—-.

The values of the co-ordinates may be shown to be

x=ioo(T [cos J^+cos 2i\-\- +cos ^n2/:] ~c"5> cos }£n2t\.

y=ioo<r S sin l/>rPix. Whence

tan 8-.

sin VztPi

cos y2ni

fill-: TECBNOGRAPW.

The co-ordinates may also be expressed as follows:

x=(rt — r,)sin /,+(>.., — /-3) sin (i,-K..) to n terms.

y—{j\ — r2)vers /j+(r2 — r,) vers (ii+i/; to n terms.

The deflection angle at any P.C.C., between the tangent at that
point and a line to the P.T.C will be J — 9.

The deflection angle to any other P.C.C. may be found from

Ji— 7i

tf= .

x, — x2

It may be shown that

0=y — R vers J.

t—x — R sin J.

7*=/ + (*+*) tan yzi.

E = (R-\- o) exsec y&Z+o.

y
c= .

sin H

From these formulas concise tables may be computed for use
in field work. In case the degree of main curve is not an even
multiple of the constant increase of degree, these formulas will need
modification. The computation is somewhat tedious, and the inter-
polation for partial chords can not be made with accuracy.

Tables IV. and V. give the deflection angles for a change of i°
in 30 feet, and for z° 30' in 30 feet. The columns are headed with
the distances from the P.T.C. To find a deflection angle for the
transit at a given distance from the P.T.C, look down the corres-
ponding column for "transit;" in the same horizontal line with this
and in the column headed with the distance of the required point
from the P.T.C. is the deflection angle. Thus, for a change of i°
in 30 feet, with transit at 1+20, the deflection to o is i°o6', and to
2+10 is 2° 03'. The degree of the next taper, or the degree of the
main curve with which the taper compounds, is also given opposite
P.C.C. 0, t, and J are for the whole tapering curve up to a length
given by the column heading. The degree of main curve divided
by the increase of degree will give one more than the number of
chords to be used.

The field work is similar to that of the transition spiral — except
that a uniform chord length must be used — and need not be de-
scribed. Some inconvenience comes from the necessity of taking
even chords and disregarding the usual station stakes on the taper,

TALBO T-RA IL I \ 'A Y TR A NS1 Tl ON CURV KS. '. M I

Table_IV. i ° Taper for 30 feet.

+3°

+60

+9°

1+20

1+5°

1+80

2-f-IO

2+40

2+70

Transit

o° 09'

0°22'^

o°42'

i°ory2

i°39'

2°l6*><

30 00'

3° 49'^

4° 45'

o°09'

Transit

O 18

0 40^

I 09

1 43K

2 24

3 io#

4 03

5 01^

0 3^

0 18

Transit

0 27

0 58^

1 36'

2 19^

3 09

4 04^

5 06

1 06

0 49^

0 27

Transit

0 36

1 i6y2

2 03

2 SS^

3 54

4 58^

1 52^

1 33

I 07^

0 36

Transit

0 45

1 34J4

2 30

3 3i>2

4 39

2 51

2 28^

2 00

1 25^

0 45

Transit

0 54

1 52^

2 57

4 07^

4 oiy2

3 36

3 04^

2 27

1 43)4

0 54

Transit

1 03

2 io>£

3 24

5.24

4 nH

4 21

3 40J*

2 54

2 OI>£

1 03

Transit

1 12

2 28J4

6 58^

6 27

5 49.^

5 06

4 16/2

3 21

2 19K

1 12

Transit

1 21

8 45

8 io# 7 30

6 43/2

5 5i

4 52^

3 48

2 37J4

1 21

Transit

P.C.C.

2°

3°

4°

5°

6°

7°

8°

9°

IO°

o°i8'

o° 54'

I 48

3 0O

4 30

6 18

8 24

10 48

13 30

0.03

0.14

0.38

0.77

1.36

2.18

3.28

4.69

6-45

15.01

30.01

45 01

60.00

74 99

89.95

1 04 . 90

119.80

134.66

30.00

60.00

90.00

119.99

149.96

179.91

209.81

239 63

26935

Table V. 20 30' Taper for 30 Feet.

+30

-f6o

o°56X

0 45'.

Transit

0 I3K

1 07^

2 29^
2 48M
5 00

7 41X
10 52^

+66

94--0

i° 45'
1 4iX
1 07^

l-f-14

i-f-20

1+5°

1+80

2-f-IO

Transit

o° izy2

1 \%%

1 37>3

2 45

4 19
4 41^
7 °llA
10 04

13 3°)£

0 = 22'^

Transit

0 45

1 02

2 03%

3 32

3 52^
6 11X
9 00
12 19

5°

0 45

0. 10
15.00
30.00

IO°4'23

0 55

0 iVA
Transit

20 35'
2 37
2 09^

2° AW4

2 52>4
2 26X

4° 07J4
4 i8#
4 00

5° 4i'
6 00

5 48^

r 29y2

7 56
7 52^

Transit

1 12

1 30

3 33X

6 07 J<

9 "X

1 12

Transit

I 30

3 »X

5 oVA

7 i8#

Transit
I 52)4
4 i8#
7 15

1 52>4
Transit

2 15

5 °3K

15°
11 15

3-43

74.82

149.76

3 56X
2 15

Transit
2 37^

6 15
4 4i X

2 37K
Transit

P.C.C.

J
0
t

7=30'

2 15

0.40
29.99
60 00

8 =
2 42

o.45
32.24

65-99

IO°

4 3°
0 99

44-97
89.98

12°

6 54
1.67

56-44
"3 94

I2°30'

7 3°
1.97

59 93
119.92

17=30'
15 45
548

89 62

179 43

20 °
21 00

8.20
104.27

208.8

but this is not a very serious drawback. If intermediate points are
desired, a tape maybe stretched along the chord, and the proper or-
dinate taken from tables for the purpose and measured off at the
desired point. Interpolations in the tables will not give accurate
results. 30 feet seems to be preferred for the length of chord, since
it is just the length of a rail, but 50-ft. chords would be more ad-
vantageous in some respects.

The tapering curve was introduced by Mr. William Hood, Chief
Engineer of the Southern Pacific Railway, and has been extensively
-8

THE TKCHNOGRAPH.

used on the Southern Pacific, Northern Pacific, Missouri Pacific, and
other Western roads. It makes a good transition curve, and does
not vary much from the transition spiral. However, it lacks flexi-
bility, this property being secured only by a wide range of tapers,
necessitating many tables.

The Railroad Spiral.

The Railroad Spiral, as developed by Wm. H. Searles, C. E.. is
a multiform compound curve, differing from the tapering curve by
using the central angles of the successive arcs as constant quantities,
and varying the length of arc or chord to secure different spirals.
The first arc has 10' central angle, the second 20', the third 30', and
so on to the end of the transition curve. Mr. Searles has published
a little hand-book of tables and explanations for this curve. Tables
of deflection angles with the transit at any chord point are given.
These deflections are constant whatever the chord length. Thus, the
deflection to the end of the 8th chord is 2 ~~ 07', whether the length of
curve be S x 10 feet or S X 21 feet, and the central angle subtended
will also be the same. However, the degree-of-curve of the arcs
will vary with a change in length of chord. This necessitates a set
of tables giving the degree-of-curve for the last chord in the curve.
As this is not an integral number, the one nearest the degree of the
main curve is chosen. This is allowable, since it consists in com-
pounding the last arc with the main curve. As several chord lengths
with the corresponding number of chords will give about the same
degree-of-curve, a variety of spirals for any main curve is secured.
About sixty tables are given in Searles' "The Railroad Spiral," to
which the student is referred for further information.

The "railroad spiral" approaches very near the true transition
spiral. With the tables given, the calculations and field work are
simple and rapid. Deflections for points between the chord points
are found by interpolating in the tables, but only chord points may
be used as transit-points. An objection has been made that the
degree-of-curve for any chord is not an integral multiple of the
number of the chord. This, however, is not of great importance.

Other Meti;

The Cubic Parabola. — The Cubic Parabola is a curve whose
ordinate from the tangent varies as the cube of the distance from
the P. C, measured along the tangent. Its equation isv =

TALBOT RAILWAY TRANSITION CURVES 101

being a constant. Within a small limit, the degree of curve varies
nearly as the distance along the tangent, and J as the square of this
distance. Hence, within this limit, the curve approaches closely to
the true transition spiral; in fact, all its valuable prope ties for a
railway transition cu"ve are approximations of the transition spiral.
As soon as x differs materially from the length of curve, a correc-
tion has to be made, otherwise the curve must be laid out by ordi-
nates from the tangent, a very objectionable method. The radius
of curvature finally begins to increase. Many attempts have been
made to utilize this curve, but both field work and computations are
too intricate and inconvenient if the curve has any considerable
length, and it has no advantage over the transition spiral.

The Pennsylvania Method. — The Pennsylvania Railroad uses
200 feet of 30' curve at the ends of a simple curve. For sharp curves
100 feet of r curve is put in at either end. The superelevation
begins with zero at the P.C., and increases uniformly to the full
amount at the beginning of the main curve. The claim is made that
in this manner the complete super-elevation is attained while the car
is on a light curve where the wheels keep to the outer rail, and that
the shock incident to gaining the super-elevation while on the tan-
gent is avoided. Of course, the field work is simple. It is claimed
that this method is very efficient, but it is open to criticism.

Methods of Track-men. — When simple curves are left with-
out transition curves, many track-men "ease" the curve by throwing
the P. C. inward a short distance and gradually approaching the
tangent a few rail-lengths away, while the main curve is reached
finally by sharpening the curve for a short distance. Even this is
better than no easement curve.

Another simple method consists in utilizing one of the proper-
ties of the transition spiral. In Fig. 1, page — , let ABK be the
original track line, B being the P. C. At some point in the curve a
convenient distance from the P. C, say 100 feet, throw the track
inward any distance to L. At B, the old P. C, throw the track to
E a distance half as great. Measure back from the P. C. an equal
distance, 100 feet, to A for the beginning of the easement. Between
A and L, line the track by eye. The remainder of the main curve
must then be thrown inward the same distance as at L. On long
curves, the latter work would make the method objectionable.

THE TECHNOGRAPH.

5ION.

\n examination of these methods will show that the transition
spiral possesses the requirement that the degree-of-curve shall in-
crease uniformly along the spiral, and that the tapering curve and
Searles' railroad spiral meet the requirements to a sufficient degree.
The transition spiral and the railroad spiral are extremely flexible,
but the former has been shown to have some advantages over the
latter. An advantage is claimed for the tapering curve that when
30 feet is taken for the chord length the rails when previously bent
will fit the separate arcs; thus, for a change of 2 ° 30' for each 30
feet, the first rail may be bent for a 20 30' curve, the second for a
5 :, the third for a 7 ° 30' curve, etc. As the first joint on the curve
may come a half rail length from the P. T. C, the claim for ac-
curacy is not strictly true, while for fiat tapers it is of little import-
ance. With the spiral, an average curvature for the rail-length may
be chosen. In any event, the lining will easily throw the track to
proper centers.

In the matter of field work and computations, the transition
spiral as outlined in the preceding pages is preferable to either of
the others. It may be used with any main curve, even if of frac-
tional degree; any length of chord may be used in measurement
under the same restrictions as circular curves; and the deflections
and co-ordinates to a point not at the end of the common chord
may be accurately and quickly found. If a more compact form of
table is desired, giving the deflection angles from points on the
spiral, a table of the form and size given for tapering curves on
page 100 may be prepared. The writer believes that the ordinary
transit-man, with a little thought and study, can understand and
use the transition spiral as easily as circular curves, and that the
advantages of this method are such that if they were more generally
known it would be more generally used.

Most of the usual formulas of the various location problems,
like "Required to change the P. C. so that the curve may end in a
parallel tangent," may be used without modification with curves
having transition endings, by simply considering the whole inter-
section angle including the angle in the spirals. This is true when-
ever the same amount of spiral is used with the new curve. If the
degree of-curve changes and with it the length of the spiral, the
difference between the </s in the two cases must be allowed for.
With a littte practice in using such formulas with spirals, the engi-
neer will find no difficulty.

TALBOT— RAILWAY TRANSITION CURVES. 103

The objection is sometimes raised that even if track is laid out
with a carefully fitted spiral there would be no possibility of keeping
it in place by the methods of the ordinary track-man. This iden-
tical objection could be made with the same force against carefully
laid out circular curves, yet no engineer would recommend abolish-
ing that practice. Even if, in re-lining, the transition curve is con-
siderably distorted, it remains an easement, and will be in far better
riding condition than a distorted circular curve. By marking the
P.S. and the P.C.C. with a stake or post, with possibly on long spi-
rals an intermediate point, the track-man will be able to keep the
spiral in as good condition as though it were of uniform curvature.

Properly constructed spirals would frequently allow the use of
sharper curvature — since the riding quality of curves may be the
governing consideration in the selection of a maximum — and thus
make a saving in construction. By fitting curves with proper tran-
sition spirals, roads using sharp curves may partially relieve the ob-
jection of the public to traveling by their routes. The transition
curve has, then, a financial value largely overbalancing its cost. The
adoption of such curves by many of our principal railways proves
their efficiency, and the future will see a much more general adoption.

UNIVERSITY OF ILLINOIS

beaming and Liabor.

THE COLLEGE OF ENGINEERING

Mechanical Engineering, Electrical Engineering,

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and Architecture.

Department is furnished with a large and constantly growing equipment forpracti-
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Fur fnriliiT information ndd

Urbanj, May is, 1801

DR. s. //. PBABODY, Recent,

P. 0., Champaign, II I i no i

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Illustrated Manual and Catalogue sent on Application.

Edge Moor Bridge Works

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Railway Bridges, Viaducts, and Roofs, in Steel and Iron

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Prices Furnished on Application for Material on Contracts.

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FIRE BRICK AND SEWER PIPE

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DEALERS IN ALL KIND.-, OF

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Extract from the report of Capt. James B. Eads, Chief Engineer Illinois and St.

Louis Bridge Co., October, 1870, in regard to a test made of a specimen of

stone from the Grafton quarries. He says:

" It is remarkably strong. Many tests of its comparative strength have been
made in the company's testing machine, where its resistance has, in many instan-
ces, exceeded 17,000 pounds per square inch, which is equal to that of granite.

" A curious fact has been developed by these tests, which is that the modulus
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given weight placed upon a wrought iron column and upon a column of the
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incl s in diameter and eight inches long was shortened under compression in the
the testing machine nearly one-quarter of an inch without fracturing it. When
the strain was removed the piece recovered its, original length."

From the Geological Survey of the State of Illinois. Mr. Peattens analysis of a
specimen of Grafton stone:

Insoluble matter 5.60

Carbonate of lime 47-79

Iron and alumina 1. 40

Carbonate of magnesia 42.86

Water and loss 2.35=100

JAMES BLACK, President, and JOHN S.? ROPER, Secy., St. Louis, Mo.
CHAS. BRAINERD, Superintendent, Grafton, 111.

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