ELECTRIC LIGHTING
AND MISCELLANEOUS APPLICATIONS
OF ELECTRICITY
ELECTRIC LIGHTING
AND MISCELLANEOUS APPLICATIONS
OF ELECTRICITY
A TEXT BOOK FOR
TECHNICAL SCHOOLS AND COLLEGES
BY
WILLIAM SUDDARDS FRANKLIN
¥ork
THE MACMILLAN COMPANY
LONDON : MACMILLAN & CO., LTD.
1912
All rights reserved
COPYRIGHT 1912
BY THE MACMILLAN COMPANY
Set up and electrotyped. Published May, 1912
PRESS OP
THE NEW ERA PRINTING <
LANCASTER. PA.
PREFACE.
This book is intended to be a companion volume to Dynamos
and Motors.
In the preparation of these two volumes especial attention has
been given to the physical principles which underlie operating
engineering, and but little attention has been given to the
principles of design.
April 22, 1912.
242234
TABLE OF CONTENTS.
CHAPTER I.
PAGES
Installation and Operation Costs I- 35
CHAPTER II.
Electric Distribution and Wiring 36- 76
CHAPTER III.
Alternating-current Lines 77- 85
CHAPTER IV.
Photometry 86-125
CHAPTER V.
Electric Lamps, Lamp Shades and Reflectors 126-155
CHAPTER VI.
Interior Illumination 156-170
CHAPTER VII.
Street Illumination 171-183
CHAPTER VIII.
Electrolysis and Batteries 184-225
CHAPTER IX.
Telegraph and Telephone 226-256
APPENDIX A.
Dielectric Stresses 257-276
APPENDIX B.
Problems 277-295
Vll
IMPORTANT INDEXES AND TABLES AND SPECIAL
PUBLICATIONS.
Engineering Index Annual, published by The Engineering Magazine, London.
Science Abstracts, published by E. & F. N. Spon, London, Series A, Physics;
Series B, Electrical Engineering.
Science Abstracts is issued by the Institution of Electrical Engineers of Great
Britain in association with the Physical Society of London, and with the cooper-
ation of the American Physical Society, the American Institute of Electrical En-
gineers, and the Associazione Elettrotecnica Italiana.
Physico-Chemical Tables, by John Castell-Evans, Chas. Griffen & Co., London.
Physikalisch-Chemische Tabellen, by Landolt & Bornstein, Julius Springer, Berlin.
Manufacturers' Bulletins and Circulars contain a great deal of important in*
formation.
ELECTRIC LIGHTING,
CHAPTER I
INSTALLATION AND OPERATION COSTS AND THE SELLING PRICE
OF ELECTRICAL ENERGY.
i. General statement. — From one point of view engineering
is a composite of all the physical sciences, and from another
point of view it is a branch of the science of economics. Any
elementary treatise on engineering should, however, be chiefly
devoted to purely physical problems inasmuch as the student
must become familiar with engineering as a branch of physical
science before he can possibly undertake as a practising engineer
to choose that particular physical solution of an engineering
problem which will best meet the requirements of economy.
The economic problem is in every case to produce satisfactory
results at a minimum of ultimate cost, and this is always a very
complicated problem inasmuch as the cost of erection and main-
tenance of engineering works and the value of the service rendered
thereby are both dependent upon minute variations of local
conditions, they both fluctuate from year to year with the varying
stress of business activity and they both change with every
improvement in industrial processes.
The first estimate of the cost of any engineering undertaking
is usually based upon general statistics of the cost of similar
undertakings, and the final cost is determined by the bids of
contractors who have had some experience in the particular line
of work and whose margin of profit must in general be great
enough to cover the many uncertain items that always appear in
any new undertaking.
2 ELECTRIC LIGHTING.
The following data on the cost of installing and operating
steam and electric plants are averages based upon the record of a
large number of actual cases, and the cost of a given station may
depart considerably from these figures on account of peculiar
local and temporary conditions.
THE STUDENT IS WARNED THAT AVERAGES ARE ALWAYS MIS-
LEADING IN COMPLICATED MATTERS LIKE COSTS, BECAUSE TO TAKE
AN AVERAGE IS TO ELIMINATE EVERY ELEMENT OF DIFFERENCE
BETWEEN INDIVIDUAL CASES, AND THESE DIFFERENCES ARE VERY
GREAT.* THE GENERAL ESTIMATES WHICH ARE GIVEN IN THIS
CHAPTER WILL BE WORSE THAN USELESS IF THE ONE WHO USES
THEM DOES NOT CONSIDER THE PECULIAR FEATURES OF THE PAR-
TICULAR CASE UNDER CONSIDERATION.
2. Cost of steam power. f — The ordinates of the curve A in
* In this connection the student should read R. S. Hale's article "The Real
Theory of Real Rates" in the General Electric Review for April, 1911, Vol. XIV,
pages 157-169.
t The data from which the curves in Figs, i and 2 are plotted are taken from a
paper by William O. Weber, The Engineer (Cleveland), Vol. XI, page 145, February
2, 1903-
Important data on the cost of steam power and on the cost of electrical equip-
ment are given by C. E. Emery, Transactions American Institute of Electrical
Engineers, Vol. XII, pages 358-389, 1895; by H. A. Foster, Transactions American
Institute of Electrical Engineers, Vol. XIV, pages 385-421, 1897; and by R. C. Car-
penter, Electrical World, Vol. XLIII, page 1016, May 28, 1904.
An important paper on the cost of power in very large plants is given by H. G.
Stott, Transactions American Institute of Electrical Engineers, Vol. XXVIII, pages
1479-1502, December, 1909. This paper gives data as to cost of plants and as
to fuel and operation costs, and it includes plants driven by reciprocating steam
engines, by steam turbines and by gas engines.
The cost of power in industrial plants where exhaust steam may be used for
heating is discussed by John C. Parker, Proceedings American Institute of Electrical
Engineers, March, 1911, pages 467-483; and by A. E. Hibner, Proceedings American
Institute of Electrical Engineers, March, 1911, pages 485-503.
The economics of a small producer-gas plant are discussed by F. C. Tyron,
Power (New York), Vol. XXVIII, pages 619-620, April 21, 1908. The economics
of a suction-gas plant are discussed by P. W. Robinson, Electrician (London),
Vol. LXI, pages 898-901, September 25, 1908. A description of the equipment of
a gas-engine electric plant together with data as to operation costs of same is given
by E. B. Latta, Jr., Proceedings American Institute of Electrical Engineers, Vol.
XXIX, pages 475~507» April, 1910.
COSTS AND SELLING PRICE. 3
Fig. I give the approximate total cost per horse- power capacity,
of boiler and engine plants of various sizes, including buildings,
chimneys and all accessories, and the ordinates of curve B give
the approximate coal consumption in pounds per horse-power-
hour.*
The ordinates of the curves C, D, E, F and G in Fig. 2
give the costs per horse-power-year (308 days of 10 hours each)
of the following items :
Curve C. Fixed charges per horse-power-year. This item is
'reckoned at 14 per cent, of the total investment, and it includes
interest at six per cent., depreciation! at 4 per cent., repairs at 2
per cent., insurance and taxes at two per cent.
Curve D. Cost of coal per horse-power-year at $4.00 per ton
of 2,000 pounds.
Curve R. Wages per horse-power-year.
Curve F. Cost of oil and supplies per horse-power-year.
Curve G. Total cost per horse-power-year.
These curves are based on the assumption that engines of the
The cost of water power is discussed in the Mechanical Engineer (Manchester,
England), Vol. XII, page 694, November 21, 1903. The comparative cost of
steam and water power is discussed by H. von Schon, Engineering Magazine
(London), Vol. XXX, pages 35-48, 184-194, 353-380, and 611-622, May to July,
1907. See also W. O. Webber, Engineering Magazine, Vol. XXX, pages 889-893,
September, 1907. A paper on hydro-electric plants by H. L. Doherty together
with a very complete discussion of the subject is given in Transactions American
Institute of Electrical Engineers, Vol, XXVIII. pages 1361-1478, December, 1909.
* The coal consumption in a large steam-turbine power plant is considerably
less than the coal consumption given by the ordinates of curve B in Fig. i, and the
coal consumption in a gas-engine plant is less than the coal consumption in a steam-
turbine plant. See paper by H. G. Stott, Transactions American Institute of
Electrical Engineers, Vol. XXVIII, pages 1479-1502, December, 1909; and a
paper by H. G. Stott and J. S. Pigott, Proceedings American Institute of Electrical
Engineers, Vol. XXIX, pages 1455-1501, September, 1910.
f Depreciation is a very uncertain item. The estimate for the whole plant of 4
per cent, per year is perhaps too low. The depreciation of buildings is less than
4 per cent, and the depreciation of electrical machinery is perhaps more than 4
per cent., but the depreciation of boilers and engines is certainly considerably
greater than 4 per cent, per year.
See paper by Henry Floy for a detailed discussion of depreciation: Proceedings
American Institute of Electrical Engineers, Vol. XXX, pages 1143-1185, June, 1911.
ELECTRIC LIGHTING.
100
|J
s,
i
i
t
100 200 300 40O 500 000
Horse-power of engine.
Fig. 1.
700 boo 900
80
70
6o
40
20
IOO 2OO 3OO 400
Horse-power of engine*
Fig. 2.
COSTS AND SELLING PRICE. 5
smaller sizes are simple non-condensing engines of the Corliss
type, that engines of the medium and larger sizes are simple con-
densing engines, and that the engines of the largest sizes are
compound condensing engines.
The wages in a loo-horse-power plant are taken to be as fol-
lows: An engineer at $2.50 per day and a fireman at $1.50 per
day, which would amount to about $1,200 per year. In a 1,000-
horse-power plant the wages are taken to be as follows: One
engineer at $3.00 per day, one assistant engineer at $2.00 per
day and three men in the boiler room during the day and one
night watchman at $1.50 per day each, and the total amount
would be about $3,500 per year.
The cost of coal per horse-power-year at any given price per
ton may be easily determined from curve D, Fig. 2, the ordinates
of which represent the cost of coal* per horse-power-year at $4.00
per ton, and the total cost per horse-power-year, as given by
curve Gj may be corrected accordingly.
It is important to remember that the cost of power as given by
curve G, Fig. 2, is based on the assumption that the engines
are working at full load for 10 hours per day, 308 days in the year.
When a plant operates at a fraction of its full-load capacity the
cost per horse-power-hour is increased as explained in Art. 4.
3. Cost of electrical power at the switch board. — The ordi-
nates of the curve H, Fig. 3, give the capacities in kilowatts of
electrical equipments corresponding to various horse-power ca-
pacities of engine plants. This curve is not exactly a straight
line inasmuch as the efficiency of a large electric generator is
greater than the efficiency of a small electric generator of the
same design.
The following estimate of the cost of electrical power at the
switch board is based upon the cost of steam power as given in
Figs. I and 2 and upon the assumption that the plant operates
at full load, 10 hours per day for 308 days per year. The ap-
* A good quality of coal giving 14,500 B.T.U. per pound is here referred to.
6 ELECTRIC LIGHTING.
proximate cost of the electrical part* of the equipment in dollars
per kilowatt of station capacity may be obtained by dividing
the ordinate of curve /, Fig. 4, by 0.14. This cost ranges
from about $45.00 per kilowatt for a loo-kilowatt station to about
$35 -00 per kilowatt for a yoo-kilowatt station. The cost of
700
600
500
400
300
200
100
s
x
gene™
^
^
•8
x
1
42
x
X
3
X
x
IT,
X
X
X
•
loo zoo 300 400 500 600 7°o °oo 900
Horse-power of engine,
Fig. 3.
additional labor required by the electrical part of the plant is
about 25 per cent, of the cost of labor for the steam plant alone,
and the additional cost of oil and supplies is about 40 per cent,
of the cost of this item for the steam plant alone.
The curves in Fig. 4 show an approximate analysis of the cost
of electrical power as follows:
Curve / shows the cost of steam power per kilowatt-year of
electrical output (determined from curve G of Fig. 2, using
Fig. 3).
Curve / shows the fixed charges on the electrical equipment
per kilowatt-year. This item is reckoned at 14 per cent, of the
cost of the electrical equipment, and it includes interest at 6
* Not including the distributing system. See Art. 5.
COSTS AND SELLING PRICE. 7
per cent., depreciation 4 per cent., repairs 2 per cent., insurance
I per cent., and taxe$ I per cent.
Curve K shows the cost per kilowatt-year for attendance
(labor) of electrical equipment in "addition to attendance of steam
plant.
Curve L shows the cost per kilowatt-year of oil and supplies
for electrical equipment.
300 400 500 600 7°o
Kilowatts capacity of generator^
Fig. 4.
Curve M shows total cost per kilowatt-year of electrical
output.
Curve N shows the total cost per kilowatt-hour of electrical
output.
4. Load factor and its influence on the cost of power.* — The
discussion of cost of power which is given in the foregoing articles
* A very complete table of costs of electric power at the switchboard showing
a wide range of load factors is given by R. W. Conant, Electrical World, Vol. XXXII,
pages 313-319, September 24, 1898. See also Street Railway Journal, Vol. XVIII,
page 827, December 7, 1901, and Vol. XXV, pages 126-128, January 21, 1905;
and Street Railway Review, Vol. XIII, pages 185-198. April, 1903.
8
ELECTRIC LIGHTING.
is based upon the assumption of continuous operation of a power
plant at full load. As a matter of fact, however, the demand for
power always fluctuates greatly so that a power plant which is
designed to deliver the maximum amount of power demanded
must be operated for a large portion of the time at a fraction of
its rated capacity.
capacity of gas engine plant
capacity of hydraulic plant
capacity of steam engine plant
12 i_ 2 3 4 5 6 7 8 9 10 ii 12 i 23 4 55 7 3 9 "> 11 12
Fig. 5. Winter and summer load curves of lighting plant.
The average load on a plant (in kilowatts) divided by the
capacity of the plant in kilowatts is called the load factor. For
example, a 465-kilowatt plant* operating 14 hours per day 365
days per year delivers a total of 464,000 kilowatt-hours, so that
the average load is
464,000
14X365
= 90.8 kilowatts, and the load
The effect of load factor on the cost of power is discussed by W. M. Archibald,
Electrical World, Vol. XLV, pages 303-305., February, 1905.
A paper by H. G. Stott, Transactions American Institute of Electrical Engineers,
Vol. XXVIII, pages 1479-1502, December, 1909, takes account of the influence
of load factor on the cost of power. The curves given in Fig. 8 are taken from this
paper.
* See page 32.
COSTS AND SELLING PRICE.
90.8
factor is ~~TT or 0.195
• 4
In specifying a load factor it is impor-
tant to give also the average daily run in hours.
Figure 5 shows typical summer and winter load-curves on a
power plant supplying power for lighting; Fig. 6 shows a typical
load-curve on a power plant supplying power for the operation
capacity of gas engine plant
/
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__t- _J~J L_| I I- -j
— capacity of hydraulic
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—•
"-"
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A.M.
hour
P.M.
23456789 10 11 12 i 23455739 10 11 12
Fig. 6. Load curve of plant supplying motors in manufacturing district.
of motors in a manufacturing district; and Fig. 7 shows typical
load-curves on a power plant supplying power to a large city
electric railway system.
The horizontal dotted lines in Figs. 5, 6 and 7 show suitable
power ratings of plants for the respective load curves. A prop-
erly designed steam plant has a very large overload capacity,
a hydraulic plant has a small overload capacity, and a gas-
engine plant has practically no overload capacity. Therefore
the "peak of the load" (maximum load) may be 25 or 30 per
cent, in excess of the rated capacity of a steam plant, not more
than 5 or 10 per cent, in excess of the rated capacity of a hy-
draulic plant, and not at all in excess of the rated capacity of a
10
ELECTRIC LIGHTING.
gas-engine plant. A further consideration which bears upon
the proper rating of a power plant is the probability of excessive
demand for power on special occasions. Thus an excessive de-
mand for power is likely to occur in a street railway system, and
it is for this reason that the rated plant capacities in Fig. 7 are
V
I
a ~
I
•s
1
capacity of gas engine plant
capacity of hydraulic plan
steam engine
\:
June.
noon
plant
P.M.
12 2 4 6 8 10 13 2 46 8 10 12
Fig. 7. Winter and summer load curves of electric railway plant.
larger as compared with the normal peak of the load than in
Figs. 5 and 6.
The load factor on an ordinary electric lighting station may
be as low as 0.15 for a small plant in a small town where there is
but little lighting during the day. If the plant supplies current
for motors during the day to any considerable extent the load
factor may be as large as 0.40. The load factor of a plant which
supplies current for electric railways may be as low as 0.20 or
0.30 when there are but few cars in operation, or as high as 0.40
or 0.50 when many cars are operated. When a single large power
plant supplies power for lighting, for manufacturing and for
COSTS AND SELLING PRICE. II
street railways, the combined demand for power is much more
nearly uniform than /or either kind of service alone, and the
load factor in this case is sometimes as large as 0.60 or even larger.
The influence of load factor on the cost of power is illustrated
by the following example: Consider a 1,000 horse-power electric
light station representing a total investment of $100,000, not
including the distributing system. The fixed charge (interest,
depreciation, repairs, insurance and taxes) is, say, 14 per cent,
on the total investment, or $14,000 per year. If the station were
run at full load day and night the year round, the running ex-
penses would be approximately as follows : (a) wages of one chief
engineer and superintendent at $5.00 per day, two assistant
engineers at $2.50 per day, three helpers in the engine room at
$1.50 per day and six men in the boiler room at $1.50 per day,
making a total of $8,600 per year; (b) coal at 2.5 pounds per
horse-power-hour at $4.00 per ton would amount to about
$43,700 per year; and (c) petty stores would amount to about
$6,500 per year. The total annual expense of $72,800 would be
the cost of approximately 6,000,000 kilowatt-hours, which would
be at the rate of 1.22 cents per kilowatt-hour delivered at the
switchboard.
If the station were run night and day the year around at an
average load equal to 0.25 of its full-load capacity, the running
expenses would be approximately as follows: (a) wages, one
engine room helper and three firemen less than before, would
amount to $5,100 per year; (b) the coal consumption of a 1,000-
horse-power engine running at one quarter load would be about
6 pounds per horse-power-hour, therefore, the cost of coal would
be about $26,200 per year; and (c) petty stores would be about
$5»5oo Per year. The total annual expense of $51,400 would be
the cost of 1,500,000 kilowatt-hours which would be at the rate
of 3.43 cents per kilowatt-hour delivered at the switchboard.
This example illustrates the great importance of load factor
as a condition affecting the cost of power. Certain items of
expense are nearly constant whatever the load on the station may
12
ELECTRIC LIGHTING.
be. The sum of these items (interest, depreciation, taxes and
administrative expenses) is called the fixed charge. When a
station is operated at light load the item of wages may be some-
what reduced especially if the station is shut down during certain
hours each day, also the item of fuel is reduced; but neither is
reduced in proportion to the reduction of load. Therefore the
cost per kilowatt-hour increases greatly with decrease of load
on the station. The following table shows the increasing cost
TABLE SHOWING EFFECT OF LOAD FACTOR ON COST OF POWER.
Costs per kilowatt-hour in cents* (i5o-kilowatt steam plant).
Load-factor.
O.2.
0.4.
0.6.
0.8.
Interest on investment
Depreciation
1.70
I 2O
0.85
o 60
O..S7
O 44,
0.42
O 1"?
Management and taxes
I ^O
O 71?
O ^O
o 40
Repairs
I OO
o c c
o 40
o 30
Fuel
I ^O
I A.O
I ^O
Labor
I ^O
I 20
I OO
Petty stores
o 20
O I r
O IO
o 08
Total cost per kilowatt-hour in cents.
8.60
5-56
4.31
3.63
per kilowatt-hour (delivered to the consumer, see Art. 5) with
decrease of load factor as estimated by B. J. Arnold. | These
figures refer to a power station having a full-load capacity of about
150 kilowatts. Figure 8 shows the influence of load factor (per
cent, load) on the cost of electrical energy as estimated by H. G.
StottJ for a large steam-turbine plant costing $75 per kilowatt of
rated capacity. The ordinates of curve A show the cost of coal
[high grade coal (14,500 B.T.U. per pound) at $3.00 per ton]
and water per kilowatt-hour, the ordinates of curve B show the
total operation cost (coal and water, boiler and engine room
labor, coal and ash handling, oil and engine room supplies)
* Costs in this table include interest, depreciation, repairs, etc., on the dis-
tributing system. See Art. 5.
^Electrical World, Vol. XXIV, pages 104-107 and page 120, August 4 and n,
1894-
J Transactions American Institute of Electrical Engineers, Vol. XXVIII, page
1482, December, 1909.
COSTS AND SELLING PRICE. 13
per kilowatt-hour, the ordinates of curve C show the fixed
charge (interest at 5 per cent., taxes and administrative
expenses I per cent., and depreciation 5 per cent.) per kilowatt-
hour, and the ordinates o.f curve D show the total cost per
kilowatt-hour. Thus at 100 per cent, load factor the cost is
60 „ 8O 100 120 140
percent load
Fig. 8.
half-a-cent per kilowatt-hour, and at 20 per cent, load factor
the cost is 0.97 cent per kilowatt-hour at the switchboard.
Multiplying the tabulated costs in the above table by the
corresponding values of the load factor, one can see the extent
to which the various items of total cost change with the load
on the station, as estimated by B. J. Arnold. Similarly the
ordinates of the various curves in Fig. 8 may be multiplied by
"per cent, load" to give the various items of total cost at dif-
ferent station loads as estimated by H. G. Stott.
5. Cost of electrical energy delivered to the consumer. — The
foregoing articles discuss the cost of electrical energy at the
switchboard. The cost of electrical energy delivered to the
14 ELECTRIC LIGHTING.
consumer is greater than the cost at the switchboard by an
amount sufficient to cover the following items: (a) The interest
on the cost, and depreciation of the distributing system ; (b) the
energy lost in the distributing system ; (c) the interest on the
cost of meters, and depreciation and repair of the meters; and
(d) the cost of reading meters, making out bills and collecting
same.
The cost of the distributing system varies so greatly with local
conditions that it is impossible to give any general estimate.
The cost is especially great where the consumers are scattered
over a large district, or where costly underground distributing
cables are used; and the cost varies greatly with the system of
distribution employed. Thus high -voltage alternating-current
distribution with step-down transformation is much cheaper
than low-voltage direct-current distribution when the consumers
are widely scattered.
Complete statistics of a small municipal electric lighting plant
are given in Art. 15, and some idea of the difference between cost
of electrical energy at switchboard and Cost delivered to the
consumer may be obtained by comparing these statistics with
the cost statistics which are given in Art. 3.
6. Customer's load factors. The diversity factor.*— The aver-
age power delivered to a customer divided by his maximum de-
mand is called his load factor. Thus the general average of 24, 1 77
small living apartments in Chicago was 18.34 kilowatt-hours
monthly consumption (representing an average continuous con-
sumption of 25.5 watts per customer) and an average maximum
demand of 370 watts per customer, so that the average load
factor of these customers was 0.069.
If the load factor of an electric lighting station were as low as
* See a paper by H. G. Gear, Transactions American Institute of Electrical En-
gineers, Vol. XXIX, pages 375~384. March 1910. The examples of customer's
load factors which are given in the text are taken from this paper.
See also a paper which was read by Mr. E. W. Lloyd before the Atlantic City
Convention of the National Electric Light Association, June, 1909. The curves
of Fig. 9 are taken from this paper.
COSTS AND SELLING PRICE. 15
0.069 the cost of electric lighting would be almost prohibitive,
but the load factor of a station is always very much larger than
the average load factor* of the customers, because the maximum
demands of the customers never come at the same time. This
diversity among the customers is a very important element in the
cost of electric lighting.
The combined actual maximum demand of a group of cus-
tomers divided by the sum of their individual maximum demands
is called their diversity factor. The diversity factor is here defined
with respect to a group of customers but it can also be applied to
a group of lamps or a group of feeders as shown in the following
examples.
Diversity factor of a customer's group of lamps. — A customer
has fifty 5O-watt lamps and of course the sum of the individual
maximum demands of the lamps is 2,500 watts ("connected
load"). The customer's maximum demand, however, is 1.5
kilowatts. Therefore the diversity factor* of the customer's
group of lamps is 0.60. The ordinates of the curves in Fig. 9
I
1,
P
5
c
maximum divided by connected lo
W 4» tn O* *J CO ^
1
i
!
Q
1
n
B
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V
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4\
*
d
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§
V
\
>C
—^
•^~—
-\
c
\
\
\
>
*^
/
V-C
s
B
~^r<
L.
V-
/'
\
s
--
-—
-^
^
<-
^
X
A
__
^
\
,
10 20 30 40 50 60 7°
o 90 10
number of 50-watt lamps connected
Fig. 9. Curve A average of 30,729 residences. Curve B average of 5,392 offices.
Curve C average of 9,149 small stores.
* The diversity factor of a customer's group of lamps, namely, the ratio of maxi-
mum demand to connected load is usually called the demand factor of the customer.
16 ELECTRIC LIGHTING.
show the ratio maximum demand to connected load for various
kinds of electric lighting service in Chicago.
Diversity factor of a group of customers. — The sum of the
individual maximum demands of the various customers in
a densely populated residence block in Chicago was 63 kilowatts,
whereas the maximum demand upon the service transformer
which supplies the block was 18 kilowatts. Therefore the diver-
sity factor of the group of customers was 0.286.
Diversity factor of a number of feeders. — The actual maxi-
mum demand upon a particular substation in Chicago was 1,000
kilowatts, and the sum of the maximum loads on. the 10 sets
of feeders which go out from the substation was 1 ,200 kilowatts.
The diversity factor of the group of feeders was therefore 0.833.
7. Analysis of costs of electric service.* — There are three fairly
distinct items of cost of a customer to a central station, and
any equitable schedule of rates for electric service should be
based on a careful consideration of these costs which are as
follows :
(a) Connection cost. — A certain service is rendered to a cus-
tomer in that power from a central station is available for his
use at all times even if he does not actually make use of it.
This service of the central station is usually called "readiness
to serve" and its cost to the central station includes a small
part of the total annual expense of the entire plant and distrib-
uting system. It includes a large part of the interest on the
cost of the customer's wiring connections and meter; and it
includes a large part of the cost of maintaining and reading
* This matter is discussed at some length in the following papers: "Central
Station Charging Systems in Use in the United States," Electrical World and
Engineer, Vol. XL, pages 361-366, September 6, 1902. "Methods of Charging
for Electrical Energy," E. H. Crapper, Electrician (London), Vol. HI, pages
330-332, December 18, 1903. "Method of Charging for Electrical Energy,"
Schofiborn, Electrotechnische Zeitschrift, Vol. XXV, pages 377-378, May 12, 1904.
"Price of Electricity," by R. S. Hale, Superintendent Sales Department, Boston
Edison Company. This paper was read before the New England Section of the
National Electric Light Association on March 16, 1910.
COSTS AND SELLING PRICE. 17
his meter, and a portion of the cost of the station book-keeping.
The cost to the central station of "readiness to serve" is called
connection cost.
(b) Demand cost. — A certain service is rendered to a customer
because of and in proportion to his maximum demand for power.
The cost of this service to the central station is called the cus-
tomer's demand cost. The size of a station (and therefore the
total investment) is determined by the total maximum demand
for power, and therefore interest on investment, taxes, and a
portion of the depreciation should be distributed among the
various customers as a demand charge; but a customer who
never uses power at the time of heavy load (on the peak) may
pay little or nothing for demand.
(c) Consumption cost. — A certain service is rendered to a
customer because of and in proportion to his total energy con-
sumption in kilowatt-hours, and the cost of this service to the
central station is called the customer's consumption cost. The
total consumption cost of all the customers of a station is
approximately equal to the cost of coal plus the cost of labor and
station supplies.
A careful analysis of service costs (electric lighting) has been
made by Mr. S. E. Doane* upon the basis of very full statistics
of 112 central stations in the United States, and the results
are shown in the following table.
* "High Efficiency Lamps and their Effect on the Cost of Light to the Central
Station," a paper read before the St. Louis convention of the National Electric
Light Association, May, 1910.
A very important source of information in matters of operation costs and the
fixing of rates for electrical service is the series of Annual Reports of the Massa-
chusetts Commissioners of Gas and Electric Light.
The Railway Commission of Wisconsin has made a most exhaustive study of
the costs of electric service in their handling of the celebrated case of The State
Journal Printing Company vs. The Madison Gas and Electric Company. The
decision of the Commission was rendered March 8, 1910, and copies of it may be
obtained by addressing the commission. The decision is discussed in some detail
by Mr. Percy. H. Thomas in the Electrical Journal, Vol. VII, pages 560-574, July,
1910.
18
ELECTRIC LIGHTING.
Average of 40
Small Stations
in the West.
Per Cent.
Average of 70
Small Stations
in the East.
Per Cent.
One Large Station
Giving Free
Lamp Renewals.
Per Cent.
Another Large Sta-
tion Giving Free
Lamp Renewals.
Per Cent.
Connection cost .
Demand cost. . . .
Consumption cost
II-S
59-6
28.9
II-3
50.8
37-9
18.0
58.5
23-5
17.7
55-1
27.2
Total
IOO.O
IOO.O
IOO.O
IOO.O
8. The fixing of rates for electric service.* — Inasmuch as the
cost of electrical service may be resolved into connection cost,
demand cost, and consumption cost, therefore the rational
method of charging for the service would be to separate the charge
into three items, namely, (a) a fixed charge per year to cover
connection cost, (6) a yearly charge per kilowatt of maximum
demand, and (c) a charge of so much per kilowatt-hour of con-
sumption. Each of these items should exceed the correspond-
ing cost so as to give a fair margin of profit.
In establishing a schedule of rates, however, a number of
things must be carefully considered, some of which are as follows:
(i) There is a strong popular prejudice against a fixed charge
(connection charge), and therefore this item is seldom or never
included in price schedules; (2) the price schedule must be
arranged to attract business by setting a low price (low margin
of profit) on business that is open to sharp competition; and
(3) a simple price schedule is a practical necessity. There
are three more or less distinct price schedules used by every
central station as follows:
(a) For small residence lighting. A certain fairly high rate,
usually II to 15 cents per killowatt-hour, for energy consump-
tion with a minimum charge which is usually $1.00 per month.
(b) For large consumers whose maximum demands are on
the peak. A charge of, say, $60.00 per year for each kilowatt
* A very good discussion of rates is given by R. S. Hale in the General Electric
Review, Vol. XIV, pages 157-169, April, 1911. The student is likely to get an
altogether erroneous idea of rate making from the foregoing analysis of costs
because the employment of averages tends to obscure the fact that there is an endless
variety of conditions to be met with in electric service. The reading of Mr. Hale's
article is strongly recommended.
COSTS AND SELLING PRICE. 19
of maximum demand, and a low rate, say 2 or 3 cents per kilo-
watt-hour, for energy consumption.
(c) For operating motors off the peak. A consumption
charge of 3 to 8 cents per kilowatt-hour.
Equitable charges for electric service may be realized by
resolving the service into its cost elements ("connection,"
"demand" and "consumption") and charging all classes of
customers at the same rate for each element; or the customers
may be carefully classified on the basis of their "connection,"
"demand" and "consumption" costs, and a certain equitable
rate per kilowatt-hour of consumption may be set for each class.
The following table illustrates the complete equivalence of
the two systems of charging.
Class of Service.
Connected Load
Expressed in
5o-watt Units.
Connection
Charge, Dollars
per Month.
Maximum Demand in
Kilowatts.
A. Domestic (small) . .
B. Domestic (medium)
C. Domestic (large) . .
D. Store lighting
E. Small factory light-
ing
IO
2O
50
80
80
ioo (5 H.P.)
0.50
0-75
I.2S
1.50
1.50
i-75
0.35 at peak
0.50 at peak
i. oo at peak
4.00 at peak
4.00 off peak
5.00 off peak
F. Motor driving
Class of Service.
Desani?Paer vTisAr^e
&« cf l°pS,n
watt on Peak. Kilowatt-hours.
Consumption
Charge. Dollars
per Month, at 3
Cents per
Kilowatt-hour.
Total
Monthly
Charge in
Dollars.
Equivalent
Class Rate in
Cents per
Kilowatt-hour.
^
B.
%.
|
1-65 IS
2-50 35
5.00 80
20.00 360
240
900
0-45
I.OS
2.40
10.80
7.2O
27.00
2.6o
4-30
8.65
22.30
8.70
28.75
17-3
12.3
10.8
6.2
3-6
3-2
An objection .to the charging for electrical service by the
kilowatt-hour of consumption (using classified rates) is that
it places a false premium on the economical use of current by
the customer. Thus a customer might reduce his monthly
bill to one-half by reducing his killowatt-hour consumption to
one-half, whereas his cost to the central station would be reduced
20 ELECTRIC LIGHTING.
but very little if his maximum demand is not reduced in pro-
portion to his kilowatt-hour consumption. The time of day
when a customer economizes is very important to the central
station.
Another objection (which applies during a time when an im-
proved high-efficiency lamp like the tungsten lamp is being
introduced) is that a customer can reduce his kilowatt-hour
consumption to, say, one-third for the same amount of light,
and thus reduce his monthly bill to one- third; whereas his cost
to the central station will not be reduced in the same proportion.
In fact the advent of the tungsten lamp has brought the whole
question of electric service costs into a prominence which it
has not had for years.
9. The meter-rate system and the flat-rate system for sell-
ing electrical service. — A central power station supplies energy
to its customers and it may, therefore, seem that the use of an
energy meter (a watt-hour-meter) would, like the use of a gas
meter, furnish a complete and equitable basis for charging cus-
tomers, but it is not so. In supplying gas for lighting, the large
storage reservoir makes the gas generating plant independent
of the irregular consumption of the gas. In an electric plant,
on the other hand, electrical energy must be generated as used,
except in the few cases where storage batteries can be economi-
cally employed, and, therefore, the capacity of the electric plant
must be sufficient to meet the maximum demand for power.
This matter is discussed in detail in Articles 5 to 8. The selling
of electrical energy by the kilowatt-hour as indicated by the
watt-hour meter is called the meter-rate system.
In the early days of electric lighting the customer paid so
much per month for each lamp installed. This method of
selling electrical service is called the flat-rate system. The flat-
rate system is more satisfactory than the meter-rate system be-
cause it simplifies the station book-keeping and avoids the cost
of installing, maintaining and reading of meters, and it avoids
COSTS AND SELLING PRICE. 21
the consumption of energy in the meter. On the other hand,
the flat-rate system i^ unsatisfactory because under this system
a wasteful customer pays no more than an economical one, and
a dishonest customer can connect lamps in excess of the number
he pays for. These two disadvantages of the flat-rate system
may, however, be overcome to some extent as follows: In the
first place if the customer uses high-efficiency tungsten lamps the
cost of the lamps themselves is an incentive to short hours of
use ; and in the second place the so-called excess indicator can be
used to limit the amount of power delivered to the customer.
The excess indicator is a device essentially like an ordinary bell
or buzzer; the current which is delivered to a customer flows
through the winding of an electromagnet and when the customer
turns on more than a prescribed number of lamps the armature of
the electro-magnet is attracted and the circuit is interrupted
repeatedly, causing the lights to flicker in a manner which makes
them practically useless. The excess indicator is much cheaper
than a watt-hour meter and it needs less attention. Without
doubt the extension of electrical service to great numbers of very
small customers is hampered by the prevailing idea that the
meter-rate system must be used, and the cost of installing, main-
taining and reading meters is probihitive in the case of a very
small customer. The very small customer should be supplied
on the flat-rate system buying his own tungsten lamps and using
them under the control of an excess indicator.
10. The watt-hour meter* is a device for summing up the
total amount of work or energy delivered to a circuit. This
meter is sometimes used on a station switchboard to measure the
energy output of the station. Thus the annual output of the
Wallingford station (464,000 kilowatt-hours, see page 32) was
* A good description of the various types of watt-hour meter is given in The
Watt-hour Meter, by Shepard and Jones, Technical Publishing Company, San Fran-
cisco, California, 1910. This book also contains information relating to the main-
tenance of the meter department of an electric power station.
Everyone who has to do with watt-hour meters should possess a copy of the
Meter Code of the National Electric Light Association.
22 ELECTRIC LIGHTING.
measured by a watt-hour meter in the station. The watt-hour
meter is chiefly used, however, to measure the energy delivered
to a customer.
In the following discussion of the two most important types of
watt-hour meter (the commutator-motor type and the induction-
motor type), it is shown that the speed of the motor spindle is
proportional to the watts delivered to the receiving circuit; that
is to say, the rate at which the spindle turns is proportional to the
rate at which energy is delivered to the receiving circuit; therefore*
the total angle (or number of revolutions) turned by the spindle
is proportional to the total energy delivered, and a revolution
counter may be arranged to indicate the delivered energy in
kilowatt-hours.
ii. The Thomson watt-hour meter is a small electric motor
of the commutator type (without iron) driving a revolution
counter. The field coils BB, Fig. 10, are made of coarse wire
and they are connected in series with the receiving circuit or
"load" so that the total current, i, which is delivered to the
receiving circuit flows through the field coils The armature A
is wound with fine wire and it is connected across the supply
mains in series with a non-inductive resistance R so that a
current equal to e/R flows through the armature, e being the
voltage between the mains. The brushes dd are made of metal
and they rub very lightly on a small commutator e. This com-
mutator has silver bars so as to give good electrical connection
with a minimum of friction. The armature is mounted on a
vertical spindle which rests on a jewel so as to turn with as little
friction as possible, and the opposition to rotation is due to the
* This simple case of integration occurs frequently in mathematical arguments,
and it should be understood perfectly by the student. Thus the rate of change
of one quantity y is proportional to the rate of change of another quantity x\
that is to say, the rate of change of y is k times as great as the rate of change of
x. Therefore, if y and x start from zero together, y must be always k times
as large as x. If one person A saves money 10 times as fast as another person
B, then A will always have ten times as much as B if A and B start from zero
together.
COSTS AND SELLING PRICE.
electromagnetic drag of the permanent magnets MM upon the
copper disk / which is attached to the spindle. The result is
that the speed of the armature and spindle is almost exactly
proportional to the driving torque which is exerted on the
Fig. 10.
armature A by the field coils BB, and this driving torque is
proportional to the product of field current i and armature
current e/R. Therefore the speed is proportional to ei (watts
delivered to the receiving circuit).
The commutator-motor type of watt-hour meter can be used
on direct-current or alternating-current circuits.
The compensation for friction in the Thomson meter. — An auxiliary fine-wire
field coil connected in series with the armature is always provided in the Thomson
meter. The effect of this coil is to give a constant driving torque (supply voltage
assumed to be constant) sufficient to overcome friction. This auxiliary field coil
is called a starting coil and it gives a great increase of accuracy of the meter.
12. The induction watt-hour meter is a small induction
motor driving a revolution counter, and it can be used only on
alternating-current circuits. The essential features of the motor
part of the meter are shown in Fig. n. A thin disk DD of
aluminum or copper is mounted on a spindle and rotates in front
24
ELECTRIC LIGHTING.
of the three lugs BAB of a laminated iron structure as shown.
The lugs BB are wound with coarse wire and this winding (the
current winding) is connected in series with the receiving circuit
so that the current i which is delivered to the receiving circuit
flows through the windings on BB. The magnetic field in front
of the lugs BB is therefore proportional to i. The lug A is
wound with fine copper wire and this winding (the voltage winding}
L 'li \\Laminaied iron\' illl, ''li
" 'liH'!' .li'W.li'.ll'.ll'lli ll
Fig. 11.
is connected directly across the supply mains. If the resistance
of the winding on A is negligible,* then the alternating magnetic
flux through the lug A induces a voltage in the winding A which
balances (and is therefore equal to) the supply voltage e, and
this alternating flux induces a proportional voltage (proportional
* Negligible in comparison with the very large reactance of the coil. It is not
wholly negligible. See discussion of compensation for lag.
COSTS AND SELLING PRICE.
to e) along the dotted lines in the disk (around the bundle of flux
which passes through the disk). This voltage in the disk pro-
duces a current in the disk which is proportional to it and to e
(disk assumed to be non-inductive), and this current as it flows
under the lugs BB is pushed s dewise by the flux with a force
which is proportional to the current in the disk and to the flux
density under the lugs BB. But the current in the disk is
proportional to e, and the flux density under BB is proportional
to i, therefore a driving torque proportional to ei is exerted on
the disk.*
The meter spindle carries a copper diskf similar to / in Fig.
10, which rotates between the poles of permanent magnets like
MM, Fig. 10, and therefore the speed of the meter is proportional
to ei, as in the Thomson meter.
Compensation for friction and lag in the induction meter. { — If the driving torque
of the induction meter were Strictly proportional to the delivered watts, the speed
of the meter spindle would not be
proportional to delivered watts
because of friction. The effect of
friction may be to a great extent
eliminated, however, by means of
a device whereby the voltage
winding (on lug A, Fig. n) alone
produces an amount of torque
sufficient to overcome friction.
This is usually done by placing a
flat short-circuited coil 5 between
the lug A and the disk DD, as
shown in Fig. 12, and adjusting this
coil sidewise until the desired torque
D
voltage coil
direction of
motion of disk
is produced by the voltage coil. Fig. 12.
The coil, 5, is called a shading coil.
In order that the combined action of lugs A and B, Fig. n, may produce
a driving torque which is accurately proportional to the delivered watts, the voltage
induced in the disk by the magnetic flux from lug A must produce a current in
* The flux from lugs B also induces currents in the disk, these currents flow
across the face of lug A, and the flux under lug A pushes widewise on these
currents. It can be easily shown that this torque is also proportional to ei.
t Usually the disk DD, Fig. n, serves also as the damping disk.
% Full details of the compensation of the induction meter may be found on pages
28-38 of Shepard and Jones' The Watt-hour Meter.
26 ELECTRIC LIGHTING.
the disk which is in phase with the voltage across the mains. In fact, however,
the current in the disk is not in phase with the supply voltage for two reasons:
(i) The voltage winding does not have a negligible resistance, and (2) The current
paths in the disk are not non-inductive. The error due to this effect is especially
noticeable when the meter is used to measure energy delivered to a receiving circuit
of low power factor, and this error may be to a great extent eliminated by means
of an auxiliary secondary coil L on lug A, as shown in Fig. 12, this coil being
short circuited through an adjustable resistance R. This auxiliary coil con-
stitutes what is called the lag adjustment of the meter.*
13. The two-rate meter. — One of the most satisfactory
schemes for selling electrical service is to charge at a high rate
per kilowatt-hour during the period of heavy station load (on
the peak) and to charge at a low rate per kilowatt-hour during
the period of light station load (off the peak). To carry this
scheme into effect requires the use of the two-rate meter which is
an ordinary watt-hour meter with two sets of dials and a clock
which throws into gear one set of dials during the period of heavy
station load (between 7 and 10 P.M., for example) and the other
set of dials during the remainder of the 24 hours of each day.
One set of dials thus registers the kilowatt-hours of consumption
on the peak and the other set of dials registers the kilowatt-hours
of consumption off the peak. The practical objection to the
two-rate meter is that a high grade and expensive clock is re-
quired in order that the clock may run for a month without too
great an error.
14. The maximum-demand meter, f — The system of selling
electrical service in which a certain charge per year is made for
each kilowatt of maximum demand and a certain charge per
kilowatt-hour of consumption, requires the use of two distinct
meters, namely, a maximum-demand meter and a watt-hour
meter. The most extensively used maximum-demand meter is
the Wright meter, which is essentially a large thermometer, the
bulb of which is heated by a low-resistance strip of metal through
which the current demanded by the customer flows. A mo-
* The theory of the lag adjustment of the induction watt-hour meter is fully
explained on pages 28-33 °f Shepard and Jones' The Watt-hour Meter.
f See Shepard and Jones' The Watt-hour Meter, pages 100-105.
COSTS AND SELLING PRICE. 27
mentary short circuit does not heat the bulb of the thermometer
perceptibly, but a heavy demand lasting for five or six minutes
heats the bulb up to* a certain temperature, a portion of the
liquid in the bulb flows over into a graduated trap, and the
maximum demand for current is indicated by the amount of
liquid in this trap. After reading, the instrument is tilted so as
to cause the liquid in the trap to flow back into the bulb.
The maximum-demand meter is not as yet extensively used.
A central station using a schedule of rates which involves a
yearly charge for maximum demand* may estimate the maximum
demands of its customers on the basis of statistics such as are
represented in Fig. 9.
15. The Borough Electric Plant of Wallingford, Connecti-
cut.!— The cost of erection of this plant was met by the pro-
ceeds ($56,500.00) from the sale of 2O-year municipal bonds bear-
ing interest at 3^2 Per cent., the face value of the bonds being
$55,000.00. The plant began operating on December 23, 1899.
The station building is of brick and steel construction, 45 feet X
104 feet. At the beginning the plant included the necessary
boilers, a 1 5O-horse-power eng ne belted to a 75-kilowatt alter-
nator, a 225-horse-power engine belted to a i5O-kilowatt alter-
nator, the necessary switchboards and accessory apparatus,
including three constant-current transformers for operating three
arc-lamp circuits for street lighting, and a distributing system
for commercial lighting.
A 45O-horse-power engine and a 24O-kilowatt, 2-phase alter-
nator with additional boilers were installed in 1904. A small
water-power plant with a generator capacity of 120 kilowatts
was installed in 1907. The distributing system (pole lines and
transformers) has been slowly extended year by year as roughly
indicated by the yearly increase of the number of customers (see
Fig. 14, curve G).
* See Art. 8.
t A series of detailed annual reports of this plant and the kind permission of the
manager. Mr. A. L. Pierce, to use them here makes it possible to give a good example
of the economies of a small lighting plant.
28
ELECTRIC LIGHTING.
In 1906 about 45 kilowatts of power were expended for operat-
ing the street lamps (89 enclosed-arc lamps and eight loo-watt
incandescent lamps). In 1907 fifty-eight incandescent lamps
(carbon filament) and one enclosed-arc lamp were added to the
street lighting system which was extended to an adjoining village,
and the total power expended for street lighting was about 50
140
100
80
60
40
20
£
V
At
Y
;
/
H
/
7
E
|
/
?
"fc
K
1
At
p*
Ir
--^
<M
plant \
tega
n operation
\
j
Dece
mbe
r23,
186
9
B
Y
Y
^
^
^
Y^
r-"
B*
) — <
r^
1900 1902 1904 1906 1908 1910
August 1
Fig. 13. Curve A assets. Curve B accumulated depreciation.
kilowatts. In 1910, all but 9 of the enclosed-arc lamps and all
of the carbon-filament lamps were replaced by tungsten lamps,
and the power consumed for lighting was about 40 kilowatts.
The plant was operated only at night (about 14 hours per
day) until 1908, when it was operated about 1 8 hours per day
and in 1909 a continuous day and night service was begun.
The population of Wallingford was about 7,000 in 1900, and
about 5,000 inhabitants were included within the service area of
the plant. In 1910 the distributing system had been extended
COSTS AND SELLING PRICE.
29
to include the adjoining villages of Yalesville and Tracy and
about 10,000 inhabitants were included in the service area of the
plant.
The entire capital invested in the plant has grown out of the
proceeds of the bonds above mentioned, and the net assets of
"§2
a
•c
A
G
'»
U.
10
1901
1903
1905
1907
1909
1911
Fig. 14. Curve C capacity of plant. Curve D connected lighting load.
Curve E connected load of motors and heating apparatus. Curve F annual
output in kilowatt-hours. Curve G number of customers.
the plant have increased to $96,881.00* (on July 31, 1910) al-
though the bond interest of $1,925 per year is paid out of the
earnings of the plant. In judging the financial success of the
* $133,000 assets minus $36,119 of accumulated depreciation as carried forward
on the books.
ELECTRIC LIGHTING.
plant, however, one must remember that it pays no taxes. The
ordinates of curve A, Fig. 13, show the growth of assets year
by year. In reckoning these assets the plant equipment* is
estimated at its first cost, and the assets include an increasing
stock of electric lighting supplies (new), and interest-bearing
loans and bonds. The latter amounted to $13,243.50 on August
35
'5
10
H
JL
A
1901 1903 1905 1907 1909 1911
Fig. 15. Curve H yearly operating expenses. Curve I yearly income.
I, 1910. The ordinates of curve B represent the accumulated
depreciation charge of 5 per cent, per year which a municipal
plant in Connecticut is required by law to carry forward in its
annual reports.
* Permanent equipment, only, is included. Lamps and other materials which
are discarded after short periods of use are not included.
COSTS AND SELLING PRICE. 31
The ordinates of the curves in Fig. 14 show the year by year
growth of the following items:
Curve C shows the plant capacity expressed in 5O-watt units
(lamps) .
Curve D shows the connected lighting load expressed in
5O-watt units (lamps).
Curve E shows the connected load of motors and heating
apparatus expressed in 5O-watt units.
Curve F shows the yearly kilowatt-hours output.
Curve G shows the number of customers.
Fig. 15 shows the year by year growth of the following items:
Curve H shows yearly operating expenses including the cost
of maintaining the fire-alarm system.
Curve / shows yearly income including $500.00 per year paid
by the Borough for the maintenance of the fire-alarm system.
INVESTMENT (1907).
Station building and real estate $12,346.38
Steam equipment 21,435.65
Electric equipment 13,437.04
Line equipment, including street lighting circuits 25,068.29
Transformers 3.523.72
Incandescent lamps 3,520.16
Meters 473-73
Arc lamps and arc lamp supplies 1,008.72
Average amount of coal and supplies on hand 2,500.00
Total capital invested $83,313.69
OPERATING EXPENSES (1907).
Maintenance of lamps* $1,200.51
Trimming and maintaining arc lamps 682.82
Labor and superintending 4,896.93
Coal (at $4.00 per ton) 7,409.72
Oil and waste 147-97
Building and boiler insurance 374-13
Liability insurance 288.00
Office rent 30.00
Plant stationery and incidentals 1,622.13
Total expenses $16,652.21
* Customers are supplied with new lamps as the old ones burn out.
ELECTRIC LIGHTING.
Kilowatt-hours output during the year 464,000
3^2 per cent, interest on in-
vestment .$2,916.00
4 per cent, depreciation on
equipment 2,740.00
Total cost per kilowatt-
hour 0.048
6 per cent, interest on in-
vestment $4,999.00
4 per cent, depreciation on
equipment 2,740.00
i per cent, taxes on $80,000 800.00
Total cost per kilowatt-
hour 0.0543
INCOME (1907).
For street lighting $ 6,513.36
For commercial lighting 21,422.47
For maintenance of fire-alarm system 500.00
Profits in excess of 3)^ Per
cent, interest and 4 per
cent, depreciation $6,118.00
Profits in excess of 6 per cent,
interest and 4 per cent, de-
preciation and i per cent,
taxes $3,245.00
The foregoing tables show the details for the year ending
July 31, 1907. In order to show the important relations between
investment, operating expenses, and income, the newly pur-
chased water-power plant (which was not operated during 1907)
is not included as a part of the investment.
It may seem that the profits should be much greater than
what is indicated in the table in view of the fact that the actual
cost per kilowatt-hour is about 5 cents whereas the lighting rate
is II cents per kilowatt-hour; but the sum of all customers'
meter readings is less than the station output because of dis-
tribution losses, and off-peak service is sold at much less than 1 1
cents per kilowatt-hour.
The cost of maintaining the fire-alarm system cannot be clearly
separated from other items of expense. In fact the charge of
$500 is about equal to the cost, which includes care of fire-alarm
apparatus and lines, and fuel and labor for keeping up steam for
the whistle during the daytime.
The schedule of service rates in force in 1907 was a complicated
mixture of flat rates and meter rates, and a knowledge of this
schedule beyond the mere fact that it represented approximately
a meter rate of 1 1 cents per kilowatt-hour is not necessary to an
understanding of the economies of the plant during 1907.
COSTS AND SELLING PRICE.
33
MISCELLANEOUS ITEMS (1907).
Total station capacity expressed in 5o-watt units (lamps) ..... 9,000
Total connected load (commercial) in 5o-watt units ........... 13,316
Street-lighting load expressed in 5o-watt units (lamps) ........ 1,000
3 street-lighting circuits, aggregate length of in miles ......... 26.5
Length of street covered by 2-wire high-voltage line (primary
circuits) in miles ...................................... 14.4
Length of street covered by 3-wire low-voltage line (secondary
circuits) in miles ....................................... 6.8
Number of transformers in service .......................... 58
Aggregate capacity of transformers in kilowatts .............. 346
Rate charged per year for enclosed-arc street lamps in dollars. . 69.58
Commercial lighting rate per kilowatt-hour in cents .......... n
Plant in operation about 14 hours per day on the average.
V
Aug.
Oct.
Dec. Feb.
Fig. 16.
Apr. June
The ordinates of the curves in Fig. 16 show the average
monthly bills of the customers of the Wallingford station after
meters were installed and the service changed to a meter basis.
4
34
ELECTRIC LIGHTING.
Curve A refers to a group of customers having an average of 50
connected lamps, curve B refers to a group of customers having
an average of 30 connected lamps, and curve C refers to a group
of customers having an average of 20 connected lamps. Indi-
vidual monthly bills depart very widely from the averages shown
in Fig. 1 6, and the ordinates of the curves a, b and c in Fig. 17
show the probable departure* of an individual bill from the mean.
For example, the ordinate of curve a for December is $2.21,
which means that the December bill of any customer taken at
random is as likely to depart ess than $2.21 from the mean as it
is to depart more than $2.21 from the mean for December ($7.18,
see Fig. 16).
* Reckoned exactly as the "probable <yrror of a single observation" is reckoned
in the theory of least squares.
COSTS AND SELLING PRICE. 35
The bills of the lo-lamp customers are not shown in Figs. 16
and 17 because these ^.bills come down very frequently to the
fixed minimum of $1.00 per month. In fact the mean of the
ro-lamp customers is about $1.10 per month in midsummer and
about $1.96 per month in midwinter, and the "probable depar-
ture" of an individual's bill from the mean is about 5 cents in
midsummer and about 18 cents in midwinter.
CHAPTER II.
ELECTRIC DISTRIBUTION AND WIRING.
16. Parallel and series systems of distribution.* — In prac-
tice a large number of receiving units (lamps or motors) are al-
ways operated from a single generator, and it is always desirable
to put any lamp or motor into service or to take any lamp or
motor out of service at will without affecting the other lamps or
motors. The easiest method for doing this is to connect the
lamps and motors in parallel with each other between supply
mains and maintain a constant voltage between the mains. In
this case the receiving units must all be of the same voltage rating,
and a given unit is taken out of service by opening its circuit.
This arrangement constitutes what is called the constant-voltage
system of distribution and it is frequently called the parallel
system of distribution. Another method is to connect the lamps
or motors in series and to maintain a constant current through
the circuit. In this case the receiving units must all be of the
same current rating, and a given unit is taken out of service by
short-circuiting it by means of a by-pass switch. This arrange-
ment constitutes what is called the constant-current system of
distribution and it is frequently called the series system of dis-
tribution.
The constant-voltage system is almost universally used now-
adays both for direct current distribution and for alternating
current distribution. This system is exemplified by great num-
bers of plants for supplying current to lamps and motors in our
cities, by nearly every electric railway installation, and by
numerous installations for the long distance transmission of
power.
* A brief discussion of these two systems (with special reference to the char-
acteristics of the generators) is given in Dynamos and Motors, The MacmiUan Co,
36
ELECTRIC DISTRIBUTION AND WIRING. 37
The constant-current system of supply is advantageous when a
fixed number of widely-distributed lamps, arc or incandescent,
are to be operated ; the lamps are connected in series and supplied
with constant current. This system is exemplified by many
street-lighting installations and by the Thury system* of power
transmission.
Combinations of series and parallel connections, (a) Connections
of series-groups in parallel. — When the voltage of supply in the
constant-voltage method of distribution is greater than can be
conveniently used for operating single lamps, the lamps are
usually arranged in groups, each group consisting of a number of
lamps connected in series, and these groups of lamps are con-
nected in parallel with each other across the mains. This ar-
rangement is exemplified in the lighting of electric cars where the
standard supply voltage is 550 volts and where the lamps for
lighting the cars are usually no-volt lamps connected in series-
groups of 5 lamps each, these groups being connected in parallel
with each other between the trolley and the rail. A similar
arrangement is frequently employed for tungsten lamps, es-
pecially in the case of the low-candle-power tungsten lamps
which are extensively used for decorative and sign lighting.
Thus five 22 -volt tungsten lamps may be connected in a series-
group, and such groups may be connected in parallel with each
other across standard no-volt mains.
(b) Connections of parallel-groups of lamps in series. — In the
early days of electric lighting the constant-current method of
supplying arc lamps for street lighting was quite common. Many
towns which were provided with this series system of distribution
were not provided with any other means for supplying incandes-
cent lamps, and the only feasible method for operating incan-
* The Thury system (direct-current) is a constant-current system of distribution.
It is exemplified by several large, long-distance, power-transmission plants in
Europe. A description of the Thury system is given by Wieshofer in the Zeit-
schrift fur Electrotechnik (Vienna), Vol. XVI, pages 5-10, 1898. See also a paper
by Cuenod and Thury in the Bulletin de la Societete Internationale des Electriciens,
Vol. XVII, pages 9-93, January, 1900.
38 ELECTRIC LIGHTING.
descent lamps was to connect a group of such lamps in parallel
and to connect this group in series in the arc lamp circuit. This
arrangement is now seldom or never used.
Advantages and disadvantages of the connections of series- groups
of lamps in parallel. — In order to understand the advantages of
grouping electric lamps in series one must keep in mind the fact
that the electric lamp is essentially a low-voltage device, so that
if one wishes to use a high-voltage distributing line in order to
reduce* the amount of line copper required, the lamps must be
arranged in series groups in order to adapt them to the high-
voltage supply. The disadvantage of the series grouping of
lamps is that each group must be turned off and on as a unit
unless a special device is used to connect an equivalent resistance
in place of a lamp which is to be turned off.
The grouping of incandescent lamps in series is exemplified
in the use of incandescent lamps for street lighting When such
a group is supplied with constant current (i. e., with a current
which is automatically kept at a constant value regardless of
the number of lamps) then any given lamp is simply short-
circuited by a by-pass connection when for any reason the lamp
is taken out of service. When, however, such a group is con-
nected to a constant voltage supply then when a lamp is broken
or otherwise damaged a by-pass containing a similar auxiliary
Fig. 18.
lamp must be provided. Thus Fig. 18 shows twenty no-volt
lamps connected in series and supplied from 2,2OO-volt mains in
a central station, and Fig. 19 shows how each lamp in Fig. 18
is provided with a by-pass. Each lamp L of the series has
a similar auxiliary lamp A connected in parallel with it, and
the circuit of this auxiliary lamp is broken by a thin piece of
* See Art. 23.
ELECTRIC DISTRIBUTION AND WIRING.
39
paper p between two metal springs SS. If the lamp L hap-
pens to break the full voltage of supply (2,200 volts) is brought
to bear upon the thin paper p, thus puncturing it and estab-
lishing a metal bridge from spring to spring. In this way the
auxiliary lamp A is substituted
for the lamp L. The inspector
on his rounds seeing A burn-
ing knows that a new lamp is
needed in place of L, and when
a new lamp is installed a fresh
bit of paper is placed between
the springs SS. When a con-
stant current is supplied to a series group of lamps, as shown
in Fig. 18, then each lamp has a by-pass as shown in Fig. 19
except that the auxiliary lamp A is not used.
17. The Edison three-wire system of distribution. — Figure
20 shows a number of no-volt lamps connected in series-
groups of two lamps each to 22O-volt mains and supplied with
current from two I lo-volt generators connected in series; and Fig.
21 shows an arrangement which is the same as Fig. 20 except
Fig. 19.
O C
O C
O 0 O C
> C
Q 0 0 6 O O
000000006
Fig. 20.
that a third main CD is added as shown. By placing some of
the lamps of each customer in the A -set and some in the B-set
(see Fig. 21), there will always be nearly the same number of
lamps in each set even when each customer exercises entire
ELECTRIC LIGHTING.
freedom in the turning off and on of single lamps; under these
conditions the middle main need never carry very much current,
and therefore the middle main may be made of comparatively
small wire. In fact the current in the middle main will be a
small current coming into the station when the A -set contains
a few more lamps than the J3-set, or a small current going out
O Q OC
0 C
OO O C
) O O O O O O C
B-set
Fig. 21.
from the station when the 5-set contains a few more lamps
than the A -set. In this arrangement, therefore, most of the
advantage (economy of line copper) due to the use of 220-volt
distribution is realized although no-volt lamps are used. The
arrangement is called the Edison three-wire system of distribution.
In practice the middle main is usually made of the same size
of wire as each outside main but each outside main need be
only one-quarter as heavy* as would be required to supply the
same number of lamps in the simple parallel system using no
volts. Therefore to supply a given number of no-volt lamps
in the Edison three-wire system requires only three eighths as
much copper in the mains as would be required in the simple
parallel system of distribution with the same percentage drop
of voltage.
When the number of lamps in the A -set in Fig. 21 is different
from the number of lamps in the .B-set the system is said to be
unbalanced. When the system is unbalanced the middle main
* See Art. 23, page 57.
ELECTRIC DISTRIBUTION AND WIRING. 41
carries current as above explained, and the voltage drop in the
middle main tends to increase the voltage which acts on one
set of lamps and to decrease the voltage which acts on the other
set of lamps. These voltage relations are clearly represented
100 amperes
L
^ to amperes
5
^ 90 amperes
>J
Fig. 22a.
for a particular case in Figs. 220, and 22b. These figures show
the state of affairs when the A -set of lamps takes 100 amperes
and the £-set takes 90 amperes, each main having 1/20 ohm
too amperes
90 amperes
Fig. 22&.
resistance; the lamps being supposed to be bunched at the ends
of the mains for the sake of simplicity. Electric current may
always be considered as flowing downhill, as it were, so that
the electric level (or potential) is to be thought of as falling off
42 ELECTRIC LIGHTING.
along each main in the direction of the current as indicated
by the fine inclined lines in Fig. 22b. The distances between
the inclined lines at the ends of the mains represent the volt-
ages acting on the two sets of lamps. Thus the voltage b acting
on the A -set is 115 volts — 5 volts — % volt = 109.5 vo'ts, and
the voltage d acting on the J5-set is 115 volts — 4.3/2 volts + J/2
volt =in volts.
1 8. Special three-wire generators and three- wire balancers
for direct-current systems. — The use of two generators as
indicated in Figs. 21 and 22 involves an added expense for
machinery in a generating station and the extensive use of
the Edison three-wire system has given rise to the so-called
three-wire generator which can be used for supplying current
to a three-wire system, and to the so-called three-wire balancer
which enables a single 22O-volt generator of the ordinary type
to supply a no- volt Edison three-wire system.
The double-current generator. — Several types of three-wire
generators have been proposed and used to some extent* but
the machine which is now almost universally used to deliver
direct current to the Edison three-wire system is the synchronous
converter (rotary converter). This machine when engine
driven is called the double-current generator '.f The arrange-
ment of the three-ring double-current generator as a three-
wire direct-current generator is shown in Fig. 23. Three sim-
ilar choke coils (inductance coils) C ', C" and C'" are connected
as shown to the middle main and the other ends a, b and c of
the coils are connected to the alternating-current brushes,
a, b and c, of the machine
The motor-generator balancer. — The two generators shown in
Fig. 21 may be replaced by a single 22O-volt generator of the
ordinary type (having two brushes), and the current which
* The three-wire generator of Dettmar is described in Electrotechnische Zeit-
schrift, Vol. XVIII, pages 55 and 320, 1897.
t The structural features of the double-current generator (rotary converter)
are described in Art. 145 of Dynamos and Motors.
ELECTRIC DISTRIBUTION AND WIRING.
43
flows into or out of the station on the middle main may be
taken care of by a small motor-generator consisting of two
simple shunt-wound clynamos P and Q with their armatures
outside main
110' volts
110 volts
/d.c. brush outside main \___
Fig. 23. Terminals a, b and c connected to brushes a, b and c respectively.
mounted on one shaft and connected electrically as shown in
Fig. 24. Consider the particular case in which the upper main
carries a large outward current of 100 amperes, the middle
main a return current of 10 amperes, and the lower main a return
current of 90 amperes as shown in the figure. Assuming the
efficiency of the motor-generator to be 100 per cent, (for the
100 amperes
10 amperes
go amperes
Fig. 24.
sake of simplicity of statement), the action would then be as
follows: One-half of the current entering the station on the
middle main would flow downhill, as it were, through P to the
negative terminal of the large generator; P would therefore act
44
ELECTRIC LIGHTING.
as a motor, drive Q as a generator, and cause Q to pump the
remainder of the current in the middle main uphill, as it were,
to the positive terminal of the large generator. With outward
current flowing in the middle main Q would operate as a motor
and P would operate as a generator. In order to keep the poten-
tial of the middle main at the proper value so as to divide the
electromotive force of the large generator into two equal parts,
the machines P and Q must have carefully adjusted compound
field windings, or the field rheostat of P or Q must be repeatedly
adjusted as the current in the middle main changes in value.
In the use of a motor-generator balancer it is desirable to keep
the system approximately balanced so as to reduce the duty of
the motor-generator. By carefully grouping the consumers'
lamps and motors, the unbalancing of a 3-wire system may be
usually kept within 8 or 10 per cent, and under these conditions
the rated output capacity of each of the dynamos P and Q in
Fig. 24 would need to be only 8 or 10 per cent, of the rated
output capacity of the main generator.
19. The supply of alternating current to an Edison three-wire
system. — A transformer with a divided secondary coil can
street main
street main
primary coil
m^moo
secondary coils
110 volts
to lamps
110 volts to lamps
Fig. 25.
be used to supply alternating current to an Edison three-wire
system by arranging connections as shown in Fig. 25; or two
independent transformers can be used for the same purpose as
shown in Fig. 26.
ELECTRIC DISTRIBUTION AND WIRING.
45
The Edison three-wire system must not be confused with the
polyphase three-wire system.* The fundamental idea in the
Edison three-wire system is to deliver current to two approxi-
mately similar groups of lamps in series, as explained in Art. 17;
and the fundamental idea of the polyphase system is to deliver
alternating currents from electrically separate alternators over
separate lines to separate receivers.
street main
street main
1100 vol\
|
A
primary
OfYYV^on ]
k^Vxjyyyvy/
[-transformer 1
primary
^-transformer
secondary secondary '
110 volts to lamps
110 volts to lamps
Fig. 26
20. Factors which determine the size of wires in practice.
—There are five conditions which should be considered in select-
ing the sizes of wires for the distribution of electric current,
namely, (a) the wire must have sufficient strength to withstand
the mechanical stresses to which it may be subjected. This
condition applies especially to wires strung on poles, (b) The
wire must be large enough to carry the prescribed current without
becoming so hot as to damage its insulation or ignite adjacent
inflammable material. This condition applies especially to wires
in a building, (c) The wire must be large enough to keep the
variations of voltage at the lamps or other receiving units within
certain limits. This condition applies only to the distributing
wires of a "constant-voltage" system. See Art. 23. (d) The
wire should be large enough so that the annual value of the RI2
losses in the wire are not greater than the interest on the cost
* See Arts, 117-120 of Dynamos and Motors,
46 ELECTRIC LIGHTING.
of the wire. See Art. 26. (e) In extreme cases the size of a
wire may be determined by a consideration of the electric strength
of the air or other insulating substance surrounding the wire
because the ability of an insulating medium to withstand the
electric stress between two wires due to a given voltage between
the wires depends in part upon the size and shape of the wires.
See Art. 27.
Whenever in a given case any one of these conditions demands
a larger wire than would be required by any of the other condi-
tions, the larger wire should be used. Frequently an engineer
is guided by one only of the above conditions in laying out the
preliminary plans for a distributing system. When this is the
case the preliminary plans should be examined carefully to see
that all of the conditions are satisfied before the plans are finally
adopted.
21. Mechanical stresses in aerial wires and their supports.*
Stresses in the supports. — The stresses in the insulator pins,
cross-arms, and poles are: (a) The stresses due to the weight of
the wire plus the weight of an occasional coating of ice; this
weight is to be considered as resting directly upon the insulators
and constituting a force acting vertically downwards. f (b) The
stresses due to the unbalanced tensions! of the wire on the
opposite sides of an insulator. The tensions of the wire on the
opposite sides of an insulator are in nearly every case sensibly
equal in value and unbalancing occurs only where the wire termi-
nates or changes its direction. In the case of a straight pole-line
on a slope the tension of the wire is generally greater on the
down-hill side of the pole, but the unbalanced force is in this case
a force acting vertically downwards, that is, a given insulator
* A discussion of the details of pole-line construction is beyond the scope of this
text. Information concerning these details may be found in Electrical Transmission
of Energy, A. V. Abbott, 1905 edition, Chapter III.
t This force is the sum of the vertical components of the tension of the wire on the
two sides of an insulator.
J Horizontal components of the tensions, inasmuch as vertical components are
considered under (a).
ELECTRIC DISTRIBUTION AND WIRING.
47
supports a large part of the weight of the lower span of wire and
a correspondingly small part of the weight of the upper span of
wire, (c) Stresses due to wind pressure.
(i) The weight of wire and ice produces, in the poles and pins, stresses of simple
compression, which stresses may nearly always be neglected, inasmuch as poles and
pins which are strong enough to withstand the bending stresses to which they are
subjected are not perceptibly affected by these slight stresses of compression.
The weight of wire and ice produces a bending stress in the cross-arms, and the
breadth, b, and depth, d, of the cross-arms must be sufficient to sustain this bending
stress, the length of the cross-arms being determined by the number of wires and
their required distance apart. The simplest case is that shown in Fig. 27, which
Fig. 27.
shows a cross-arm carrying two wires. In this case the dimensions, b, d, and /, as
shown in the figure must satisfy the equation:
6WI
C ..... __„
(i)
in which S is the permissible fiber stress of the cross-arm material in pounds per
square inch at the points, TT, Fig. 27, and W is the total weight in pounds resting
on one pin. The dimensions, b, d, and /, are expressed in inches.
A coating of ice one eighth of an inch thick is seldom exceeded, and it is cheaper
to repair the line after an excessively severe sleet storm than it is to make it strong
enough to sustain much more than one eighth of an inch of ice on the wires.
The permissible values of 5 may be taken from the table of tensile strengths of
timber.
48 ELECTRIC LIGHTING.
(2) The stresses due to unbalanced tensions are the most important stresses to be
considered in pins and poles. Having given the value of the tension and the angle
turned at a corner, the side force, W, Fig. 27, is easily determined, and the dimen-
sions, I' and d' (diameter of pin at base), Fig. 27, must satisfy the equation:
in which S' is the maximum permissible fiber stress in pounds per square inch, W is
the resultant horizontal force in pounds acting on the insulator, and /' and dr are ex-
pressed in inches.
The cross-arms on a corner pole are usually set so as to be parallel to the resultant
force due to wire tensions, and hence, except at the end of a line, this resultant force
does not produce a bending stress in the cross-arms.
The unbalanced tensions of the wires produce bending stresses in the poles; and
the diameter, dr, of the pole at the ground and the height, /', of the pole, both in
inches, must satisfy equation (2), using for W the resultant horizontal force due to
all of the wires. In most cases a corner pole is guyed or braced so that the bending
stress in the pole is to a great extent eliminated.
(3) Stresses due to wind pressure vary with the direction as well as the velocity
of the wind. When the wind blows parallel to the line its effect is slight because the
wires are parallel to the wind. It is considered sufficient in practice to provide the
necessary strength to withstand a side wind giving a maximum pressure of from 20
to 30 pounds per square foot of surface, according to the degree of exposure of the
line. In calculating the force of a side wind on a cylinder like a pole or wire, the
effective exposed area is taken as two thirds of the product of the diameter of the
cylinder times its length.
The effect of a side wind is to produce bending stresses in the insulator pins and
in the poles, and the dimensions of the pin in inches, as shown in Fig. 27, must
satisfy equation (2), where W is the total force of the wind on the wire in pounds,
and S' is the maximum permissible fiber stress in pounds per square inch. Also
the height of V of the pole and its diameter, df, at the ground, both in inchest
must satisfy equation (2), in which case W is the force of the wind on all the
wires plus about half or two thirds of the force of the wind upon the pole and cross-
arms.
In estimating the stresses on pin, cross-arm and pole, due to weight of wire
and ice, or the stresses due to wind pressure on the wires, a length of wire equal
to the distance between adjacent poles must be assumed to be supported by each
insulator.
TENSILE STRENGTH OF TIMBER IN POUNDS PER SQUARE INCH.
Cedar (American) .......................................... 11,000
Chestnut ......................................... 7,000 to 13,000
Cypress .................................................. 6,000
Elm .............................................. 6,000 to 10,000
Oak ...................................................... 10,000
Pitch pine ................................................ 7,600
Yellow pine ....................................... 5,000 to 12,060
ELECTRIC DISTRIBUTION AND WIRING. 49
White pine 8,000
Red wood (California) 11,000
Spruce S.ooo to 10,000
The usual factor of safety being 4 to 6, the permissible fiber stress in pounds per
square inch is from one sixth to one fourth of the values given in this table.
Stresses in the wire. — In stringing a wire on poles two things
in particular should be provided for, namely, (a) an approximate
equality of wire tension on the two sides of each insulator, and
(b) a certain maximum tension in the wire when it is shortened
by the coldest winter weather.
The first condition is desirable not only because it relieves the
pins, cross-arms, and poles from unnecessary stress, but also
because it is difficult to tie a line wire to an insulator so that it
cannot slip lengthwise through the tie, unless the line wire is bent,
which it should not be if it can be avoided. The horizontal com-
ponents of the wire tension can always be made equal on the
two sides of an insulator; but in the case of a pole line on a
grade the vertical component of the wire tension will be somewhat
greater on the down-hill side of an insulator when the horizontal
components are equal.
The second condition is explained in the following discussion.
Pole line on a level. — The calculation of the tension in a span of wire in terms
of length of span, vertical sag at the center of the span, and weight of the wire, or
the calculation of the sag corresponding to a prescribed tension, is based upon the
equation of the curve formed by the wire. When the sag is a small fraction of the
length of the span, say one twentieth or less, the curve formed by the wire is sensibly
a parabola and the working formulae are:
*-S «>
and
s-l + ^
in which T is the tension of the wire in pounds, / is the length of the span in feet, h
is the sag at the center of the span as shown in Fig. 28, 5 is the length in feet of the
wire in a span, and w is the weight of the wire in pounds per foot. Equation (3)
gives the tension of the wire at the center of the span. The tension at the ends of
the span is wh pounds greater than at the center; but this difference amounts to
only 2 per cent, when the sag is one twentieth of the length of the span, and it is
always negligible. The important use of equation (4) is in making allowance for
the effects of changes of temperature,
5
50 ELECTRIC LIGHTING.
Equation (3) when solved for I gives:
8hT'
where Tf represents the maximum safe tension of the wire in pounds, which is equal
to the breaking tension Tj> in pounds divided by the factor of safety. See following
tables.
The spacing of the poles is usually chosen tentatively as the first step in the design
of a pole line. When a great deal depends upon the permanence of a line, as in a
transmission line supplying power to many customers, the poles are placed close
together in order to make the line substantial and in order that the sag may be small
enough to avoid the possibility of the wires swaying into contact. Close spacing is
especially necessary in the case of heavy wires so as to distribute the weight of the
heavy wire over a large number of insulators, the insulator being one of the weakest
elements in the construction. Poles are usually spaced as follows on straight-pole
lines: (a) Heavy power transmission lines about 80 feet, which is the spacing on the
Niagara- Buffalo transmission line; (&) ordinary electric-lighting circuits in city or
suburban districts, from 100 to 125 feet; (c) telegraph and telephone lines 125 to
150 feet. In every case the poles should be placed near together where the pole line
follows a curve, thus making the line turn a very obtuse corner at each pole, in order
to avoid excessive stresses in the supporting structure due to unbalanced tensions
of the wire. Furthermore pole spacing is often determined by surrounding local
conditions such as the presence of obstacles or the recurrence of cross-streets in cities.
The amount of sag in a span of line wire should be small in order to prevent the
swaying of the wire by the wind. This swaying is objectionable because it tends to
break the wire where it is fastened to the insulators and because it is likely to bring
adjacent wires into contact. Once the spacing of the poles is chosen, the minimum
permissible sag is determined as explained in the next paragraph; although the
amount of sag that may be allowed has a great deal to do with the choice of the pole
spacing. Very long spans, such as spans across rivers, have a sag equal to one
twentieth or one thirtieth of the span. In ordinary pole-lines the sag seldom exceeds
one one-hundred-and-fiftieth of the length of span, in coldest weather.
Effects of temperature. — Wires are usually strung on poles during warm weather,
the wire grows shorter as the temperature falls, and the tension of the wire is there-
fore greatly increased during cold winter weather. Hence, it is important to string a
wire with sufficient sag (and a correspondingly low tension) so that the coldest
weather may not increase the tension of the wire beyond the dafe value, T'. Know-
ing the temperature, /, of the wire when it is strung, and the lowest winter temper-
ature, tf, the calculation of the necessary sag h, and tension, T, at temperature,
t, is carried out as follows: Take the values of T' (= Tb divided by the factor of
safety) and w from the following tables, .and from these, together with the chosen
distance, I, between poles, calculate the winter sag, h;, using equation (3), and
calculate the corresponding length of wire, s', in a span using equation (4). Then
calculate the length of the wire at summer temperature, t, by the equation
s =s'(i +P(t - /')]
in which ft is the coefficient of linear expansion of the wire as given in the following
ELECTRIC DISTRIBUTION AND WIRING.
tables. From the value of s, so calculated, the value of the sag, h, at temper-
ature, t, may be calculated from equation (4), and then finally the tension, T,
at summer temperature, t, may be calculated from equation (3).
It is to be noted that as a tine wire cools and shortens, its tension increases, so that
its thermal contraction is accompanied by an elastic elongation due to the increase
of tension; but this effect is generally neglected in practical line calculations, inas-
much as the error is always on the safe side, that is, the actual winter tension is
less than that anticipated in the calculations.
It is to be remembered that equations (3) and (4) are approximate because equa-
tion (3) is based on the assumption that the suspended wire forms a parabolic
curve, and equation (4) is based on the assumption that this parabola is sensibly
a circle.
For very long spans or where the sag is greater than about 0.05 of the length of
span more accurate equations are desirable.*
Pole line on a grade. — It is usual to make the horizontal component of the ten-
sion of the wire the same in value all along a pole line on a grade, so that the actual
tension of the wire is slightly greater on the down-hill side than on the up-hill side of
each pole. The problem of determining the sag corresponding to a given horizontal
tension, and the problem of allowing for the effects of temperature are treated in
the same way as in case of a pole line on a level except that the following equations
are used instead of equations (3) and (4) :
T =
PHw
2Hd
2(H -
(5)
(6)
in which T, I, w, and 5 represent the same quantities as in equations (3) and (4),
d is the difference in level between the ends of the span, and H is the sag of the wire
below the upper end of the span, as shown in Fig. 29.
TENSILE STRENGTHS, WEIGHTS AND COEFFICIENTS OF
EXPANSION OF WIRES.
Tensile Strength
in Pounds per Circular
Mil = a.
Density in Pounds
per Mil-Foot=^.
/3-Coefficient of Linear
Expansion per
Degree F.
Steel
0.0785
2.65 Xio~6
O.OOOOO64
Iron . .
0.0417
2.65 Xio~6
O.OOOOO64
Hard-drawn copper . .
Aluminum
0.0300
O.O2O4
3.03 Xio~6
0.91 Xio~6
O.OOO0094
O.OOOOI28
* Charts for facilitating these accurate calculations of long spans have been
constructed by Mr. Percy H. Thomas. See Proceedings American Institute of
Electrical Engineers, Vol. XXX, pages 1131-1142, June, 1911.
Other important papers on long spans are: W. LeRoy Robertson, Proceedings
American Institute of Electrical Engineers, Vol. XXX, pages 1111-1130, June,
191 1 ; Pender and Thomson, Proceedings American Institute of Electrical Engineers,
52 ELECTRIC LIGHTING.
Usual factor of safety from 2 or 3 in warm climates to 6 or 7 in cold climates.
Factor of safety for aluminum must be larger than for other metals on account of
low elastic limit of aluminum.
Breaking tension of wire Tb = ad2 in pounds.
Weight of wire w = bd? in pounds per foot, where d is the diameter of the wire
in mils.
Length at t° F. = length at *' X [i + P(t - /')]•
For weight of galvanized iron or steel wire add about 6 per cent, to weight of
plain wire.
Derivation of equations (j) to (6). — Consider a wire, Fig. 28, suspended between
two points, p and pr. If the wire is nowhere greatly inclined the actual length
of any element, ab, of the wire is very nearly equal to the horizontal projection,
dx, of the element. Therefore the weight of the element is very nearly equal to
'///////////////^^^^
Fig. 28.
•w dx, w being the weight of the wire per unit length. Furthermore, the horizontal
component of the tension of the wire has necessarily the same value, T, all along
the span of wire.
Consider the element, ab, of the wire of which the coordinates of the end, a, are
x and y, and the coordinates of the end, b, are x + dx and y + dy. Let dyfdx
be the value of the first differential coefficient of y at the end, a, then dy/dx
+<Py /dx- • dx is its value at the end, b. The force, Ta, pulling at the end, a, of
the element is the tension of the wire at a, its horizontal component is T, and its
component vertically downwards is T tan B or Tdy/dx. The force Tb pulling
at the end, b, of the element is the tension of the wire at b, its horizontal component
is T, and its component vertically upwards is T tan 0' or T(dy/dx+d?y/dx* • dx).
Therefore the unbalanced force pulling upwards on the element, ab, is Td*y/dx2 -dx,
Vol. XXX, pages 1370-1416, July, 1911; and F. O. Blackwell, Transactions Inter-
national Electrical Congress, Vol. II, pages 331-347, St. Louis, 1904.
ELECTRIC DISTRIBUTION AND WIRING.
53
and this unbalanced force is equal to the weight of the element, iv • dx, so
that-
* * T0 = w (i)
whence
Ty = i^wx* + ex + c'
but, since y = o and dy/dx = o when x = o, the constants, c and cf, must be
each equal to zero, so that:
w
From Fig. 28 it is evident that y = h when x =1/2; therefore, substituting
these values in equation (ii), we have equation (3).
The second member of equation (4) consists of the first two terms of the infinite
series which expresses the length of the arc of a parabola in terms of its chord, I,
and the distance, h, of the middle of the arc from the chord.
W//////////////////^^^
Fig. 29.
Equations (5) and (6) are derived from equations (3) and (4). Consider a
given span of wire between two poles, A and B, Fig. 29, at a horizontal distance,
/, from each other, d being the difference in level of the tops of the poles, and H
the sag of the wire below the top of pole, A, as shown. The given span, AB, may
be considered as part of a longer span, AC, of which the length is L, as shown in
the figure; and the portion, BD, of the given span may be looked upon as a span
also. Let 5 be the length of wire in the long span, AC, and P the length of
wire in the short span, BD. Then the length of wire in the given span, AB, is,
2 2
Furthermore, applying equations (3) and (4) to the span, AC, we have
m
(iii)
(iv)
and
54 ELECTRIC LIGHTING.
S = L -\ — (v)
Applying equation (4) to the span, BD, gives:
P = (zl — L) -\ — — — (vi)
The equation of the parabolic curve formed by the wire is
y-*j~f.
and at the top of the pole, B, y = H — d, and x = I — L/2, so that:
Equations (5) and (6) are obtained by eliminating L, P and 5 from (iii) and
(iv) by means of equations (v), (vi) and (vii).
22. Safe carrying capacity. — An electric wire rises in tem-
perature until it gives off heat to its surroundings as fast as heat
is generated in it by the current. Therefore, the rise of temper-
ature for a given current (or the current which corresponds to
a prescribed rise of temperature) depends upon the facility with
which the wire gives off heat and this facility varies greatly with
the degree of ventilation in the region in 4 which the wire is
placed and with the nature of the adjacent materials. Thus a
wire entirely covered with a wooden moulding gets hotter than a
wire exposed to the open air, and a wire which lies against a
wooden wall gets hotter than a wire which lies against a stone
wall.
The opposite table gives the safe carrying capacity of wires
according to the National Board of Fire Underwriters. This
table refers to the most unfavorable cases, namely, when wires are
covered with wooden moulding or enclosed in narrow air spaces
inside the walls of building.
23. Voltage drop as a factor determining the size of wires.
— The so called "constant-voltage" system of distribution is gen-
erally used in electric-light and power installations, and the sizes
of distributing wires in such a system are usually determined from
a prescribed allowable voltage drop (loss of voltage between the
ELECTRIC DISTRIBUTION AND WIRING.
55
generator and the lamps). When more and more lamps are put
into service as the darkness of evening comes on the current
flowing over the distributing wires increases and a larger and
larger loss of voltage takes place in the wires causing a decrease
of voltage at the lamps even though the voltage at the generator
be kept at a fixed value. Such variation of voltage at the lamps
causes an undesirable variation of brightness, the various lamps
and motors are not independent of each other, and therefore it is
necessary to provide for small drop of voltage in the distributing
wires so as to obviate large fluctuations of voltage at the lamps.
TABLE OF CARRYING CAPACITIES OF COPPER WIRES.
(From National Electrical Code.)
For insulated aluminum wire the safe carrying capacity is eighty-four per cent,
of that given in the following tables for copper wire with the same kind of insulation.
Brown and
Sharpe Gauge.
Sectional Area in
Circular Mils.
Rubber
Insulation.
Amperes.
Other
Insulation.
Amperes.
Bare Wires in Still Air
for 50° F. Rise of
Temperature.
18
1,624
3
5
6.0
16
2,583
6
8
8-5
14
4,107
12
16
12. 1
12
6,530
17
23
I7-I
IO
10,380
24
32
24-3
8
16,510
33
46
41-5
6
26,350
46
65
58.8
5
33,ioo
54
77
69.7
4
41,740
65
92
83.3
3
52,630
76
no
98.8
2
66,370
90
131
II7.6
I
83,690
107
156
I4O.O
O
105,500
127
185
169.8
oo
133,100
150
220
201.5
ooo
167,800
177
262
240.2
oooo
211,600
2IO
312
286.0
400,000
330
500
463-0
600,000
450
680
631.0
1,000,000
650
I, OOO
922.0
1,500,000
850
1,360
1,250.0
2,000,000
I,05O
1,670
1,550.0
The lower carrying capacities of rubber-covered wires is due to a tendency of
rubber to deteriorate rapidly when warm.
The question of voltage drop is not considered in this table.
Figure 30 represents a central station with a pair of feeders
delivering current to a center of distribution C from which pairs
56 ELECTRIC LIGHTING.
of street mains m, m, m radiate. The points p, p, p are
here called service points, and the wires which lead from the
service points into the houses are called service wires.
Fig. 30.
The loss of voltage in the feeders is usually compensated by
what is called feeder control at the station. This is especially
the case in alternating-current distribution because in this case
feeder control is easily accomplished.* Thus we have constant
voltage at the center of distribution C. The loss of voltage in
the street mains and the loss of voltage in the service wires and
house wires are not compensated, and these voltage losses must
therefore be small because they affect the value of the voltage
at the lamps. A total voltage drop of about five per cent, (two
per cent, in the street mains and three per cent, in the service and
house wires) is frequently allowed, although a greater or less
drop may be advisable if the lamps are very far from or very close
to the center of distribution. ,
There are two causes of voltage drop in distributing wires,
namely, resistance and reactance, f Resistance drop of voltage
occurs in direct-current and alternating-current distribution.
Reactance drop of voltage occurs only n alternating-current
distribution.
The voltage across a group of glow lamps is not appreciably
affected by reactance drop in the service wires if the wires supply
current to glow lamps only. The peculiarity of glow lamps is
that they are non-inductive, and the present discussion refers
* See Art. 193, Dynamos and Motors.
t See Art. 112, Dynamos and Motors.
ELECTRIC DISTRIBUTION AND WIRING. 57
alike to alternating and direct currents when the receiver is non-
inductive, that is, when the receiver has unity power factor.*
The resistance drop of voltage along a distributing line is equal
to RI volts, where R is the resistance of the line (both wires)
in ohms and J is the current in amperes which flows out in one
wire and back in the other.
The resistance in ohms of the two wires (copper) of a line is
given by the equation
R = io.S~ (7)
in which / is the length of the line in feet (2l is the length of the
two wires), and d is the diameter of the wire in mils. One mil is
equal to o.ooi inch.
The weight W in pounds of 2/ feet of copper wire d mils in
diameter is given by the equation
W = 0.00000303 X 2ld? (8)
Proposition. — The weight in pounds of the wire required
to transmit a given amount of power with a given percentage
loss of voltage is proportional to /2/E2, where / is the distance
from the generator to the lamps and E is the voltage of the
generator.
Proof. — Let P be the power in watts to be delivered by the
generator and let p be the percentage loss of voltage (actual loss
of voltage equals pE/ioo) . Then P/E is the curent in the line
in amperes, and R X P/E is the loss of voltage in the line.
Therefore
loo E
Eliminating d2 between equations (7) and (8) we get R in
terms of W and /; then substituting this value of R inequation
(i) and solving for W we have
P/2
TF= 0.01 308 j (9)
*See Dynamos and Motors, Art. 49.
58 ELECTRIC LIGHTING.
Inasmuch as the weight of the copper is inversely propor-
tional to E2, according to equation (9), it is evident that a very
great saving in copper may be effected by using high voltage.
The permissible voltage at the lamps is limited, however, (a)
by the fact that incandescent lamps cannot be made to operate
satisfactorily at voltages higher than about 220 volts, and (b)
by the danger that is involved in the use of high voltages.
The saving in copper by the use of high voltage, combined
with the practical necessity of low- voltage delivery, has led to the
use of the Edison three-wire system as explained in Art. 17.
In the alternating-current system of distribution power can be
transmitted at any desired high voltage and cheaply and effi-
ciently transformed near the place of consumption to any desired
low voltage. Therefore the alternating-current system permits
of very great economy of copper in the transmission lines and does
not involve any of the difficulties or dangers incident to the
utilization of high voltages at lamps and motors.
When the voltage-drop in a transmission line is not limited
by the necessity of maintaining an approximately constant vol-
tage at the lamps, or other receiving units, the size of wire should
be determined on the basis of economic considerations as ex-
plained in Art. 26; and it is to be particularly noted that the weight
of copper, demanded by economic considerations, for the delivery
of a given amount of power is not proportional to 12/E2 but to I IE.
24. Wiring calculations for a motor or for a concentrated
group of lamps. — Two important cases arise in the laying out
of wiring plans in a constant-voltage system, namely, (a) the
case in which current is delivered at one point to a motor or
to a group of lamps, constituting what is called a concentrated
load; and (b) the case in which current is delivered to a scattered
group of lamps or motors, constituting what is called a distributed
load.
The problem of determining the size of wire required to deliver
a specified amount of power P (in watts) to a concentrated load
ELECTRIC DISTRIBUTION AND WIRING. 59
at a specified voltage E (at the lamps) with a specified drop of
voltage D in the line is solved as follows :
(a) The current I is equal to P/E. Sometimes the current
is given directly, as when a given number of half -ampere lamps,
for example, are to be supplied.
(b) The given voltage drop D is equal to RI, so that, /
being known, the resistance R of the line (both wires) may be
determined.
(c) Knowing the length 2/ of the wire and its resistance R,
its diameter d in mils may be calculated with the help of equa-
tion (7).
The final result (current being given) is expressed by the
equation
2 1. 611
^ = -JP (10)
in which d2 is the sectional area in circular mils of copper wires
required to deliver / amperes to a group of lamps distant / feet
from the center of distribution, D is the voltage drop, and E is
the voltage at the lamps.
Note i. — In laying out the wiring for a house much time is
saved by using wiring charts which give at a glance the solution
of equation (10) for any particular case.
Note 2. — Equation (10) is frequently used to determine ap-
proximately the size of wires required to deliver a specified current
to a distributed load. In this case I is the distance from the
center of distribution to the middle point of the distributed load
and D is the allowable voltage drop. See rule 2 on page 62.
25. Wiring calculations for distributed loads. — When a
group of widely distributed lamps is supplied with current by
one pair of service wires, or when a group of widely distributed
customers is supplied by one pair of street mains, we have what
is called a distributed load. The problem of determining the
size of street mains to supply a number of scattered customers is
the same as the problem of determining the size of service wires
60 ELECTRIC LIGHTING.
to supply a number of scattered lamps. In the first case the
voltage-drop between the center of distribution and the various
service points is the important thing, and in the second case the
voltage-drop between the service point and the individual lamps
is the important thing.
In a distributed load two kinds of variation of voltage occur,
namely, (a) the variation of voltage from lamp to lamp when the
number of lamps in operation is fixed, and (b) the variation of
voltage at any given lamp as the number of lamps in operation
is increased or decreased.
Concerning the first type of variation it may be stated in gen-
eral that the lamp voltage is less and less the more remote the
lamp is from the service point, the most remote lamp having
always the lowest voltage.
Concerning the second type of variation it may be stated in
general that the voltage at every lamp falls off to some extent
when additional lamps are turned on, and rises when lamps
already in operation are turned off. The range of variation in
voltage at a given lamp is from a lowest value ^when all the lamps
are in operation, to a value very nearly equal to the voltage at the
service point, when the given lamp, only, is in operation. There-
fore, the lamp that is most remote from the service point is subject
to the greatest range of variation of voltage as other lamps are
turned on and off.
There are two clearly defined cases that arise in the laying out
of wires for distributed loads, namely, Case /, in which the lamps
supplied by a given pair of service wires are turned on and off sepa-
rately, and Case 77, in which all of the lamps supplied by a given
pair of service wires are turned on and off together. In the first
case the wiring must be laid out so as to keep the voltage varia-
tions of both types (a) and (b) within certain limits; and in the
second case the wiring may be laid out with reference to the
limitation of voltage variations of the first type only, that is, varia-
tions of voltage from lamp to lamp, inasmuch as voltage varia-
tions of the second type (b) do not exist in Case II.
ELECTRIC DISTRIBUTION AND WIRING. 6l
Case I. — An example of a distributed load is shown in Fig.
31 . When all of the lamps are in operation the end lamp, L, has
the lowest voltage at any lamp in the group, and the voltage at
this lamp varies through the greatest range when other lamps are
turned off and on. Therefore, if the voltage at the end lamp is
4
Supply wains
Fig. 31.
to be kept within, say, three volts of its normal value (which
is the value when all the lamps are in operation) then the voltage-
drop in the wires must not exceed three volts when all the lamps
are in operation.
To secure a specified drop out to the end lamp, L, when all
the lamps are in operation, with the minimum weight of copper
in the wires, the sectional area of each portion, a, b, c and d,
Fig. 3 1, of the wires must be* proportional to the square root
of the current in that portion. f Thus, if each lamp in Fig. 31
takes the same amount of current, then the current values in
the portions a, b, c and d, are as 4 : 3 : 2 : I, and the sec-
tional areas of the respective portions of the wires should be as
1/4 : V $ : 1/2 : i/i in order to give a minimum voltage-drop at
the end lamp, L, with a given amount of copper, or to give a
* It should be kept in mind that the fundamental condition here is a minimum
amount of copper for a given voltage-drop. A minimum amount of copper for
given watts lost in the line requires the sectional area of the wires to be proportional
to the current at each point; that is, the number of circular mils per ampere must
be the same throughout the system to give a minimum amount of copper for a
given loss of power in watts. See Art. 26.
t The general proof of this proposition involves the highly elaborate methods of
the calculus of variations and therefore the proof of the proposition is not given here.
62 ELECTRIC LIGHTING.
minimum amount of copper for a specified voltage-drop at the
end lamp, L.
In laying out street mains to supply a group of scattered cus-
tomers it is generally advisable, on account of the large amount
of copper involved, to taper the mains in steps in going farther
and farther from the center of distribution; but, as a rule, the
successive steps should be made longer than the distance between
adjacent customers, in order to avoid an excessive number of
joints in the mains.
In laying out service wires to supply current to a scattered
group of lamps, it is generally not advisable to taper the wires in
steps, because the amount of copper involved. may not be large;
whereas the expense of making many joints, together with the
expense of inserting fusible cut-outs at each point where wires of
unequal size are joined, as required by the insurance rules, may
be considerable.
Rule i. — When it is desired to reduce the size of a pair of
street mains (or service wires) in steps so as to secure the greatest
economy of copper, the size of each portion of the mains is deter-
mined as follows. Having given the total drop to be allowed out
to the end of the line, calculate the factor 5 from the equation:
2 X 10.8 X (a VTi + b V^. + c Vis + >••)
total drop in volts
in which a, 6, c • - - are the lengths in feet of the respective
portions of the pair of mains, and iit i^, i3 • • • are the currents in
amperes in the respective portions. The sectional areas of the
various portions of the mains in circular mils are then equal to
sVii, $V**t sVis, • - • respectively.
Rule 2. — When service wires of uniform size are to be used
for supplying current to a scattered group of lamps, the size of
the wire to give a prescribed drop may be determined as follows :
Estimate the distance, L, of the "center of gravity" of the group
of lamps by the formula:
i' + 1" + 1'" + ...
j_j — - — —
n
ELECTRIC DISTRIBUTION AND WIRING.
where I', I", I'", etc., are the distances in feet of the individual
lamps* from which the service point and n is the total number of
lamps in the group. ^ Then calculate the size of the wire that
would be required to supply the n lamps as a concentrated group
at the prescribed total drop and at the distance L from the
service point.
Case II. — When the lamps of a group are always turned on
and off together the variation of voltage from lamp to lamp can
of course be kept within bounds by limiting the voltage-drop
between the service point and the end lamp of the group as in
Case I. In fact a group of lamps which is to be operated as a
unit is generally wired according to rules I and 2 of Case I ; but
a special wiring scheme, called the return-loop scheme, f may be
used to eliminate voltage variations of the first type (see page
60) in a group of lamps
that is operated as a
unit, whatever the total
voltage-drop may be.
The fundamental idea
of thereturn-loopscheme
may be seen with the
help of Fig. 32. The
current in the wire, ab,
at any point, p, is pro-
portional to the distance,
pb, the lamps being assumed to be uniformly distributed ; and the
current at any point, pf, in the wire, cd, is proportional to the dis-
tance p'd. If the wires, ab and cd, are tapered so as to have sec-
tional areas proportional to thecurrent ateach point, then the value
of Ri is the same in both wires between any pair of lamps ; but
Ri is a drop of voltage in a given direction along one wire and a
* If the lamps are arranged in subgroups it is easier to take /' as the product of
the distance of the first subgroup times the number of lamps in that subgroup,
I" as the product of the distance of the second subgroup times the number of lamps
in that subgroup, and so on.
t Sometimes called the anti-parallel scheme.
A
Fig. 32.
64 ELECTRIC LIGHTING.
rise of voltage in the same direction along the other wire, there-
fore the lamp voltage is constant throughout the group of lamps,
whatever the total voltage-drop between the service point and
the lamps may be.
The use of tapered wires is of course impracticable and the
return loop scheme is always carried out either with wires tapered
in steps or with wires of uniform size, usually the latter. Under
such conditions the voltage
varies to some extent from
lamp to lamp but the range
of this variation is very
much less than the total
drop.
The return-loop scheme
of wiring evidently requires
three wires of a given
Fig 33 length instead of two, and
therefore it requires much
more copper than the simple parallel wiring scheme for the
same total voltage-drop. The advantage* of the return loop
scheme however is that a very large voltage-drop is permissible.*
See page 63.
The return-loop scheme is usually employed in the wiring of
churches, lecture halls and theaters, where the lamps are either
all in use or all out of use, or where the lamps in certain groups
are either all in use or all out of use.
In many cases the lamps in a group are arranged in a circular
or reentrant row. In such a case the return-loop scheme is
carried out as shown in Fig. 33, or as shown in Fig. 34.
Return-loop scheme with wires of uniform size. — When the
wires used in the return-loop scheme are of uniform size (not
tapered) the middle lamp, p, Fig. 35, has the lowest voltage of
any lamp in the group, and the size of the wires, efab and gcd, is
usually determined with reference to the voltage-drop between
* The limit should be determined by Kelvin's law, as explained in Art. 26.
ELECTRIC DISTRIBUTION AND WIRING.
the service point, eg, and the middle lamp, p. Let / be the
total current delivered to the group of lamps, and let the lamps
be assumed to be u/iiformly distributed as shown in Fig. 35;
Fig. 34.
then the current in the element, Ax, is I(X — x)/Xt and the
voltage-drop in the element, Ax, is p-Ax times I(X — x)/X,
where p is the resistance per unit length of the wire, cd. There-
fore the voltage-drop along cd from c to the middle lamp is:
r
s*x
Jx=0
- X)dx = ySPxi
Also the voltage-drop along ab from a to the middle lamp is
so that the total drop between the service point, eg, and
Fig. 35.
the middle lamp, p, is 7(r' + r"), where r' is the resistance of
gc plus the resistance of efa , and r" is equal to %pX, where
pX is the resistance of one of the wires, ab or cd, Fig. 35.
6
66
ELECTRIC LIGHTING.
Rule 3. — To give a prescribed voltage-drop between the ser-
vice point and the middle lamp of a row, which is connected
according to the return-loop scheme, make the wire of such size
that the total current delivered to the group of lamps would give
the prescribed drop over a length /' + /" of the wire, where I' is
the sum of the distances, gc and efa, in Fig. 35, and I" is three
fourths of the distance ab.
Modifications of Cases I and II. — Every practical case of
wiring in the constant-voltage system of distribution can be
treated as a slight modification of Cases I and II above described.
Thus Fig. 36 shows two groups of lamps each exactly like the
WWW
WWW
Fig. 36.
Fig. 37.
single group in Fig. 31 ; and Fig. 37 shows a combination of Figs.
31 and 32, that is, the portion, pa, of the group of lamps in
Fig. 37 is arranged in conformity with Fig. 31 and the portion,
pb, is arranged in accordance with the return loop scheme.
26. The economic balance between loss of power and the cost
of copper in the distribution of electric current.— The original
ELECTRIC DISTRIBUTION AND WIRING. 67
cost of erection of a distributing line consists of two nearly inde-
pendent parts, namely (a) the cost of the copper and (b) the cost
of poles, cross-arms, p^ins and insulators and the cost of erection.
That is to say, even if one were to double the size of wires to be
used the cost of item (b) would not be increased to any consider-
able extent. The disadvantage of using large wires lies, there-
fore, almost wholly in the annual "charge," including interest on
the cost of the wire, depreciation of the wire, and taxes thereon.
The advantage* of using large wires, on the other hand, lies in
the decreased loss of power in the wires. Therefore, the most
economical size of wire is that for which the additional annual
"charge" on a larger wire would exceed the annual value of the
power saved by the use of the larger wire, or, in other words, the
most economical size of wire is that for which the sum of the
annual "charge" on the total copper plus the annual value of the
power lost in the wires is a minimum.
The economic balance between loss of power and cost of copper
always leads to a definite number of circular mils of sectional
area of wire per ampere of current, without regard to the voltage
or to the distance of transmission.
Electric power is to be supplied for h hours each year to a
customer. The cost of power at the switchboard is p dollars per
kilowatt-hour, the cost of copper is c dollars per pound, and the
interest charge on invested capital (including a small percentage
to cover the depreciation of copper wires and taxes) is t per cent,
per annum. It is required to find the sectional area of the cop-
per wire in circular mils per ampere of current on the condition
that any increase in the amount of copper would effect a saving
of power of which the annual value would be less than the interest
on the cost of the additional copper. Let 2/ be the length of
the wire in feet (equal to twice the length of the line) , s its sec-
tional area in circular mils, R its resistance in ohms, W its
* It is to be kept in mind that we are not here considering the fact that in the
constant- voltage system the wires must be large enough to limit the voltage-drop,
as explained on pages 54-66.
68 ELECTRIC LIGHTING.
weight in pounds, and / the current in amperes. Then R =
10.8 X 2l/s so that the lost power in kilowatts is — '- --- J2,
1,000 ^
and the annual loss of energy is --- Ph kilowatt-hours, of
i ,000 «y
which the value at p dollars per kilowatt-hour is — - — Pph
dollars per year. On the other hand W = 0.00000303 X 2ls
pounds, of which the cost is o.ooooo6o6/sc dollars, the interest
on this cost is o.ooooooo6o6/sc/ dollars per year, and the
quantity to be made a minimum by choosing s is
1,0005
+ o.ooooooo6o6/sc/. Differentiating this expression with respect
to 5 and placing the differential coefficient equal to zero gives:
— - — ^ • Pph + o.ooooooo6o6/c/ = o
1 ,00052
from which / cancels out, and we find :
pt
f
ct
s (
- — circular mils per ampere = 597 Af
j. »
or
IM
(n)
The meanings of the symbols, s, /, h, p, c and t, are specified
above. When the delivered current, I, is not constant, the
average value of the current must not be used, but the square-
root-of-the-average-value-of-the-square should be used in equa-
tion (n).
Example I. — The cost of power at the switchboard of an
electric-power station is 1.6 cents per kilowatt-hour (p = 0.016),
the interest on invested capital is 5 per cent., and the annual
depreciation and taxes is three per cent. (/ = 8), the cost of cop-
per wire is 1 6 cents per pound (c = 0.16), and a current of 200
amperes is delivered to a customer for 1,000 hours each year.
Considerations of economy would lead, under these conditions,
ELECTRIC DISTRIBUTION AND WIRING. 69
to the use of transmission wires 650 mils in diameter, whatever
the distance of the customer from the station may be.
If the distance from the station to the consumer is 538 feet,
then the total length of wire is 1 ,076 feet, its resistance is 0.0275
ohm, and the voltage-drop with 200 amperes is 5.5 volts. That
is, if current is to be supplied to the customer at 1 10 volts, the
size of wire required on the basis of a 5 per cent, drop of voltage
is the same as the size of the wire required to give an economic
balance between the loss of power and the cost of copper under
the specified conditions. If the distance is greater than 538 feet,
then considerations of economy would give a smaller wire than
would be required by a 5 per cent, drop in voltage; and, if the
distance is less than 538 feet, then considerations of economy
would give a larger wire than would be required by a 5 per cent,
drop in voltage.
Example 2. — Cost of power, rate of interest and cost of cop-
per being the same as in example I, it is required to find the
most economical size of wire for carrying 100 amperes for 400
hours each year and 300 amperes for 600 hours. The average
square of the current is
(ioo2 X 400) + (3002 X 600)
177 - = 58, ooo amperes-squared
and the square-root-of-average-square is 241 amperes. There-
fore using h = 400 + 600 hours and / = 241 amperes in equa-
tion (n), we have 5 = 509,200 circular mils, or the diameter of
the wire must be 713 mils.
Kelvin's law. — Dependence of total weight of copper on voltage
of delivery and distance of customer from station. — A given amount
of power, P, is to be delivered to a customer at a distance, /,
from the station and at a voltage, E. The current is P/E so
that from equation (10) we have:
• 597£ N^F
70 ELECTRIC LIGHTING.
which, substituted in the formula W = 0.00000303 X 2/5,
gives :
W = 0.0036I8P- (12)
which shows that the amount of copper required by economic
considerations is proportional to the distance, /, and inversely
proportional to the voltage of delivery.
It is important to note the difference between equations (9)
and (12). To deliver a specified amount of power requires a
weight of copper which is proportional to /2/£2 when the per-
centage voltage drop is fixed whereas it requires a weight of
copper proportional to l/E if maximum economy is the ruling
condition.
Limitations of Kelvin's law. — The economic balance between
the loss of power in transmission wires and the cost of copper
was first pointed put by Lord Kelvin, and the condition ex-
pressed by equation (12) is sometimes called Kelvin's law of
economy.* In the derivation of equation (12) it was assumed,
first, that the cost of poles, cross-arms and 'pins, and the cost
of erection of the pole line are the same whatever the size of
the wire may be, and second, that the cost of the wire is so much
per pound irrespective of size. The first assumption is approxi-
mately true only for wires of moderate weight. For very heavy
wires the supporting structure must be very strong and there-
fore expensive. The second assumption is approximately
true only for bare wires. For insulated wires the cost per
pound varies considerably with the size of the wire.
27. Corona formation as a factor determining the size of
wires. — When the voltagef between two line wires is increased
more and more a point is ultimately reached where the air in
* A very full discussion of Kelvin's law is given by Dr. F. A. C. Perrine in his
book entitled Conductors for Electric Distribution, pages 161-178 (D. Van Nostrand,
1903)-
t This article refers to alternating voltages. Direct voltages exceeding a few
thousand volts never occur in ordinary engineering practice.
ELECTRIC DISTRIBUTION AND WIRING. Ji
the neighborhood of the wires breaks down and we have what
is called the corona, a faint bluish glow surrounding the wires.
A sufficiently high ^voltage causes the complete break-down of
the air insulation and the formation of an electric arc from
wire to wire.
The corona may be easily shown as follows: Two very fine
wires (line wires) are supported on glass rods at a distance of
6 or 8 inches apart in a very dark room, and the wires are con-
nected to the secondary of a good-sized induction coil the
primary of which is connected to alternating current supply
mains. A much smaller induction coil will suffice if its primary
is excited by direct current using a Wehnelt interrupter.
By using two pairs of "line wires," one pair much finer than
the other, and connecting both pairs to the induction coil simul-
taneously it can be shown that the corona starts on the finer
wires more easily (at a lower voltage) than on the coarser wires.
Indeed the approximate voltage E required to start an electrical
breakdown of the air between two line wires is:
/ 2S\
E = 150^ • logio 1 -7- I (13)
in which d is the diameter of the line wires in mils, and S is the
distance of the wires apart center to center in mils. Thus
about 55,000 volts is required to start the corona on wires
125 mils in diameter and 4 feet apart center to center; and about
3,000 volts is required to start the corona on wires 6 mils in
diameter and 6 inches apart center to center. In the case of
very fine wires, however, the corona is limited to the region
very near to the wires unless the voltage greatly exceeds the
corona-starting voltage.
The only cases in practice where corona formation occurs
is near the very high-voltage terminals of transformers and
on very high-voltage transmission lines, and in such cases d
and 5 are both made large enough to give a corona-starting
voltage about two times as great as the voltage which is used.
ELECTRIC LIGHTING.
Thus half -inch line wires would have to be 25 inches apart
center to center to require a corona-starting voltage of 150,000
volts, and therefore half -inch wires 25 inches apart would be
suitable for about 75,000 volts;* or if the distance apart of
the wires is fixed at 25 inches it would not be allowable to use
wires much smaller than 500 mils in diameter on a 75,ooo-volt
transmission line.
A very full discussion of electrical stresses and a derivation of
equation (13) are given in Appendix A.
28. Pole line insulation. — When the voltage between two
line wires is distinctly less than that required to cause an elec-
trical break-down of the air in the neighborhood of the wires,
the leakage of current through the air from wire to wire is entirely
negligible; the only appreciable leakage of current is at the
supporting insulators and through branches of trees and other
objects which happen to touch the wires.
If the insulators are made of glass or
thoroughly vitrified porcelain the leakage of
the current through the .material of the in-
sulator is always negligible, unless the insula-
tor is ruptured, but the leakage of current
over the surface of the insulator may be con-
siderable. This leakage over the surface of
an insulator is reduced to a minimum by
designing the insulator so that the leakage
path measured along the surface (see dotted
line in Fig. 38) may be as long as possible
and so that a portion of the surface may be shielded from rain or
mist. This is accomplished by making a series of deep grooves
around the bottom of the insulator as shown by the dotted lines
at the base of the insulator in Fig. 27. Figure 38 shows a typical
high-voltage insulator. This type of insulator is deficient in
* An alternating voltage of 75,000 effective value has a maximum value of about
105,000 volts on the peak of the wave so that a corona-starting voltage of 150,000
volts on a 7 5,000- volt transmission line would mean a "factor of safety" of about 3/2.
Fig. 38.
ELECTRIC DISTRIBUTION AND WIRING. 73
mechanical strength and a more recent type called a strain in-
sulator is shown in Fig. 39. The strain insulator is used as
a link in a chain which supports the
transmission wire as shown in Fig. 40.
The strength of an insulator to with-
stand high voltage without rupture has
Fig. 39.
nothing directly to do with its insula-
tion resistance, in the same way, that the strength of a porous
earthenware jar to withstand hydraulic pressure without bursting
has nothing directly to do with the facility with which the porous
walls of the jar permit the water to flow through them. There-
fore the most important test of a high-voltage insulator is the
break-down test. In this test the insulator pin and a wire tied
around the insulator are connected to the secondary of a high-
voltage testing transformer and the voltage is raised to the
desired value. In testing a lot of insulators
which are to be used the test voltage is run
up to I Y% or 2 times the voltage which the
insulators are to stand in service.
Wires on pole lines are provided with insu-
lating covering only when it is desired to re-
duce the risk of accidental momentary contacts.
Thus the moderately high -voltage lines (2,200
to 5,000 volts) which supply arc lamps on
city streets usually have insulating covering.
The wires of high-voltage transmission lines
Fig. 40.
are always bare because any ordinary insu-
lating covering would be entirely inadequate.
29. Insulation of underground, house and station wires.
— In the installation of underground, house and station wires,
two things are kept in view, namely, (a) the insulation of the
wires and (b) the protection of the wires from mechanical injury.
It is especially important to use an absolutely waterproof insula-
tion such as rubber or lead encased fiber; and the most satis-
74 ELECTRIC LIGHTING.
factory mechanical protection is that which is afforded by an iron
pipe or by a vitrified clay conduit laid in concrete or built in
the floor and walls of a building.
30. National Electrical Code. — Rules governing the installa-
tion of electrical apparatus of all kinds have been formulated
by a national conference* with the object of minimizing fire risks
and risks of personal injury. These rules are published in
convenient form -and sold at a nominal price by the National
Board of Fire Underwriters! under the title "The National
Electrical Code."
The rules and requirements which constitute the National
Electrical Code are classified in the 1911 edition as follows:
Class A . Rules applying to stations and dynamo rooms.
Class B. Rules applying to outside work.
Class C. Rules applying to inside work (wiring and lamp and
motor installations).
Class D. Rules applying to fittings, materials and details of
construction.
Class E. Miscellaneous. Rules applying to telephone and
telegraph, fire and burglar alarms, etc.
Class F. Marine work.
Classes A, B, C and E are issued in one volume for general
distribution, and Classes D and F are issued in another volume
which may be obtained from the National Board by any one
interested in the special rules contained therein. Contractors
and station managers are specially interested in the list of
* The following is a list of the Associations composing this National Conference:
American Institute of Architects, American Institute of Electrical Engineers,
American Society of Mechanical Engineers, American Institute of Mining Engi-
neers, American Street Railway Association, Associated Factory Mutual Fire
Insurance Companies, Association of Edison Illuminating Companies, International
Association of Fire Engineers, International Association of Municipal Electricians,
National Board of Fire Underwriters, National Electric Light Association, National
Electrical Contractors' Association and Underwriters' National Electric Association.
A brief history of the development of the National Electrical Code is given by
C. E. Skinner, Electric Journal, Vol. II, pages 262-265, January. 1906.
t General agency, 34 Nassau St., New York City.
ELECTRIC DISTRIBUTION AND WIRING.
75
"approved" fittings which is issued semi-annually by the Na-
tional Board for general distribution.
WEIGHTS AND RESISTANCES OF COPPER WIRE.
Brown and Sharpe Gauge.
Gauge
Num-
bers.
Diameters
in Mils = d.
Areas in Cir-
cular Mils
= ^3.
Weights.
Resistances per 1,000 Feet in
International Ohms.
Per i. ooo
Feet.
Per Mile.
At 60° F.
At 75° F.
oooo
ooo
oo
0
I
460
410
365
325
289
2II,6OO
168,100
133,225
105,625
83,521
64I
509
403
320
253
3,382
2,687
2,129
1,688
i,335
.04811
.06056
.07642
.09639
.1219
.04966
.06251
.07887
.09948
.1258
2
3
4
6
258
229
204
182
162
66,564
52'!4!
41,616
33,124
26,244
202
'59
126
100
79
1,064
838
665
529
419
.1529
.1941
.2446
.3074
.3879
•1579
.2004
.2525
.3172
.4004
9
10
II
144
128
II4
102
91
20,736
16,384
12,996
10,404
8,281
63
50
39
32
25
33i
262
208
166
132
.491
.6214
.7834
.9785
1.229
.5067
.6413
.8085
1. 01
1.269
12
13
14
15
16
Si
72
64
57
5i
6,56i
5,184
4,096
3,249
2,601
20
15.7
12.4
9.8
7-9
105
83
65
52
42
1-552
1.964
2.485
3-133
3-9H
1.601
2.027
2.565
3-234
4.04
17'
18
19
20
21
45
$
Si
2,025
i, 600
1,296
1,024
812.3
6.1
4.8
3-9
3-i
2-5
i526
20.7
16.4
13
5.028
6.363
7-855
9-942
12.53
5.189
6.567
8.108
10.26
12.94
22
23
24
3
25-3
22.6
20.1
17.9
15-9
640.1
510.8
404
320.4
252.8
1.9
1-5
1.2
•97
•77
IO.2
8.2
6.5
5-i »
4
15-9
'9-93
25.2
31-77
40.27
16.41
20.57
26.01
32.79
41.56
27
28
29
30
31
14.2
12.6
"•3
IO
8.9
2OI.6
158.8
127.7
100
79.2
.61
.48
•39
•3
.24
32
2-5
2
1.6
1.27
5°- 49
64.13
79.73
101.8
128.5
52.11
66.18
82.29
105.1
132.7
32
33
34
\
8
7i
6.3
5.6
5
64
50-4
39.7
31.4
25
.19
•15
.12
•095
.076
i. 02
.81
•63
• 5
•4
I59-I
202
256.5
324.6
407.2
164.2
208.4
264.7
335-1
420.3
76 ELECTRIC LIGHTING.
This table is based on a resistance of 10.51 ohms per mil-foot at 75° F., a temper-
ature coefficient of resistance of 0.0022 per degree Fahrenheit, and a density of
3.03 X io~6 pound per mil-foot, or 555 pounds per cubic foot.
According to the Report of the Standardization Committee of the American
Institute of Electrical Engineers* it is commercially feasible to supply annealed
copper for electric wires and cables having a resistance not greater than 102 per
cent, of the "annealed copper standard," and hard-drawn copper having a resist-
ance not exceeding 105 per cent, of the "annealed copper standard." The an-
nealed copper standard is 10.36 ohms per mil-foot at 20° C.
Aluminum. — Resistances in above table are to be multiplied by 1.61 for alumi-
num wire.
Weights in above table are to be multiplied by 0.30 for aluminum wire.
Iron and Steel. — Resistances in above table are to be multiplied by about 7 for
iron and steel wires.
Weights in above table are to be multiplied by 0.876 for iron and steel wires.
IMPORTANT BOOKS ON WIRING.
National Electrical Code, National Board of Fire Underwriters.
Standard Tables for Electric Wiremen, C. P. Poole, McGraw-Hill Book Co.
Electric Light Wiring, C. E. Knox, McGraw-Hill Book Co.
Conductors for Electrical Distribution, F. A. C. Perrine.
Electrical Transmission of Energy, A. V. Abbott, Van Nostrand. This book con-
tains a very full discussion of pole lines and of underground conduits and cables.
* Paragraph 260 of Rules as adopted on June 27, 1911. See Proceedings of
Institute for August, 1911, page 1942.
CHAPTER III.
ALTERNATING-CURRENT LINES.
31. Direct-current and alternating-current calculations com-
pared.— Kelvin's law of economy (see Art. 26) applies without
distinction to direct current and to alternating current when the
value of the current is given. If an amount of power P is to be
delivered at voltage E, the current is equal to P/E in the case
of direct-current transmission, but the current is equal to P/(pE)
in the case of alternating-current transmission, where p is the
power factor of the receiver.
When the size of wires is to be determined on the basis of a
prescribed voltage drop (see Arts. 23-25) then alternating-cur-
rent calculations differ from direct-current calculations, although
the direct-current method (which refers only to resistance drop of
voltage) is approximately correct for alterating-current wiring when
the power factor of the receiver is nearly unity.
This chapter refers to alternating-current wiring calculations on
the basis of a prescribed voltage drop but when the power factor of
the receiver is not equal to unity.
The methods of this chapter give very accurate results for
transmission distances up to ten or twenty miles at the usual
alternating-current frequencies, but they give only approximate
results for very long transmission lines.
On a very long transmission line the effects of line capacity
must be taken into account in precise calculations.* The effect
of line capacity is primarily to cause a difference between the
current which flows into the line at the generator end and the
current which flows out of the line at the receiver end. This
* The simplest rigorous discussion of the alternating-current transmission-line
problem is that which is given in Chapter V (pages 116-153) of Electric Waves, by
W. S. Franklin, The Macmillan Co., 1909. This discussion is easily followed
because the geometric and physical features of the problem are kept in view, and
77
78 ELECTRIC LIGHTING.
difference is called the charging current of the line. The effects
of capacity are ignored in this chapter.
32. Resistance drop and reactance drop on a line.* — Figure
41 is a clock diagram in which the line 01 represents the current
flowing through the transmission line and through the receiving
circuit, and the line E\ represents the voltage across the receiving
circuit, 6 being the phase difference between EI and / as
shown. Let r be the resistance and x the reactance of the line.
Then rl is the resistance drop on the line and it is in phase with /
(parallel to I in the clock diagram), and xl is the reactance
drop on the line and it is 90° ahead of / in phase. The generator
voltage EQ is equal to the vector sum of EI, rl and xl.
The numerical difference between £0 and EI is usually called
simply the line drop. It is evident from Fig. 41 that the line
drop is a complicated function of /, 0, EI, r and x.
33. Line resistance. — The resistance of a wire for alternating
current is in nearly all practical cases sensibly equal to the resist-
ance of the same wire for direct current. When the wire is very
large, however, or when the frequency is very high, the alternating
because the solution is expressed in terms of familiar exponential functions. These
exponential functions (as they appear in the solution of this problem) are the so-
called hyperbolic sines and cosines; but it is distinctly misleading to call them such,
because to do so is to convey the impression that the mathematics of the problem
involves something which is entirely unfamiliar and new, which is distinctly not
the case; and every table of logarithms is in effect a table of hyperbolic sines and
cosines provided one ignores these names and looks at the simple facts.
* This matter is discussed in Dynamos and Motors, Art. 112. A general state-
ment is repeated here for the sake of clearness.
ALTERNATING CURRENT LINES.
79
current flows chiefly through the surface layers of the wire, and
the resistance of the wire is very perceptibly larger for alternating
current than for direct current. This effect is called the skin
effect*
34. Line reactance. — The reactance of a transmission line
(outgoing and returning wires side by side) depends upon the size
of the wires and upon their distance apart center to center, and
it is proportional to the length of the line and to the frequency.!
RESISTANCE AND REACTANCE OF ONE MILE OF WIRE
OF TRANSMISSION LINE).
MILE
Reactance in Ohms.
Size of
Wire B.
Resist-
At 60 Cycles per Sec.
At 125 Cycles per Sec.
&S.
Gauc*e
Ohms.
Wires
Wires
Wires
Wires
Wires
Wires
\-7<XUgC.
12 Inches
18 Inches «
24 Inches
12 Inches
18 Inches
24 Inches
Apart.
Apart.
Apart.
Apart.
Apart.
Apart.
oooo
•259
.508
•557
•591
.06
•17
1.23
ooo
.324
•523
•573
.607
.09
.20
1.26
oo
.412
•534
.588
.618
.12
•23
.29
o
.519
•550
.603
.633
•IS
.26
•32
i
•655
.565
.614
.648
.18
.28
•35
2
.826
• 580
.629
.663
.21
.31
•38
3
1.041
•591
.644
.674
.24
•34
.41
4
1-313
.606
.656
.690
.26
•37
•44
5
1.656
.620
.670
.704
•30
.40
•47
6
2.088
.633
.685
.720
•32
•43
•49
7
2.633
.647
.700
•730
•35
.46
•52
8
3-320
.662
.712
.742
•38
.48
•55
9
4,186
•677
.727
.761
.41
•51
•58
10
5.280
.688
.742
.776
.44
•54
.62
The following table gives the resistance and reactance per half
mile of transmission line, using copper wires.
35. Calculation of a single-phase transmission line to give a
specified line drop.J — A single-phase transmission line is to
* See Ernest Merritt, Physical Review, Vol. V, pages 47-60, July, 1897.
f Derivations of the formulas for line reactance and line capacity are given in
Electric Waves, by W. S. Franklin, Appendix A.
J A good discussion of the exact theory of line drop on a long alternating-current
transmission line is given on pages 141-153 of Franklin's Electric Waves. The
Macmillan Company, 1909.
A series of papers on the exact calculation of alternating-current transmission
line problems, by W. F. Miller, is given in the General Electric Review, Vol. XIII,
80 ELECTRIC LIGHTING.
deliver a prescribed amount of power P at a prescribed electro-
motive force EI to a receiving circuit of which the power factor,
cos 0, is given; the line drop, frequency, length of time, and dis-
tance apart of wires being given.
The generator voltage Eo is equal to the sum (numerical sum)
of EI and line drop.
The full load current / is found from the relation EI/ cos 0
equals P.
The component of EI parallel to / is EI cos 0, and the com-
ponent of EI perpendicular to / is EI sin 6.
By treating the problem first as a direct-current problem, the
approximate resistance r' of the line is found from the relation
r'l equals line drop. From this approximate resistance and the
known length of the line, the approximate size of the wire and
the line reactance x may be found from the table ; and since the
line reactance varies but little with the size of the wire, the value
of x need not be further approximated.
The component of Eo parallel to / is EI cos 6 + rl, where r
is the true resistance of the line, and the component of E0 per-
pendicular to / is EI sin 8 + xl. Therefore
E02 = (Ei cos 0 + rl)2 + (Ei sin 6 + xl)2
or
l/Eo2 - (Ei sin 6 + xl)2 - El cos 0
r = - —f~ (0
From this equation the true line resistance r may be found
and thence the correct size of wire.
Example:
Ei = 20,000 volts.
P = i ,000 kilowatts.
cos 0 = 0.85 = power factor of receiving circuit.
Eo = 23,000 volts, or line drop = 3,000 volts.
frequency = 60 cycles per second.
pages 177-181, 220-227, 264-267, and 326-330, April to July, 1910. These papers
refer especially to three-phase lines. A table of hyperbolic functions is published
in a supplement to the General Electric Review for May, 1910.
ALTERNATING CURRENT LINES.
8l
distance = 30 miles.
distance apart of wires = 1 8 inches.
From these data we find :
* •
/ = 58.8 amperes.
r1 = 51 ohms.
Therefore, from the table we find that, approximately, a No. 2
B. & S. wire is required so that x = 37.7 ohms.
Furthermore,
EI cos B = 17,000 volts
EI sin 6 + xl = 12,700 volts
and from equation (i) we find
r = 37-3 ohms
from which the correct size of wire is found to be, approximately,
a No. I B. & S.
36. Calculation of double line for two-phase transmission (four
wires). — In this case each line is calculated to deliver half the
prescribed power. Thus, if it is desired to deliver 1,000 kilo-
watts at 20,000 volts two-phase, at a frequency of 60, line drop
of 3,000 volts, etc., then each line is calculated as a single-phase
line to deliver 500 kilowatts at 3,000 volts line drop.
37. Calculation of a three-wire transmission line for three-
phase currents. — The calculation will be carried out for the case
in which both the genera-
tor and the receiver are Y-
connected as shown in Fig.
42. If it is desired to state
the problem by specifying
the voltage between mains at
generator and at receiver,
and current in each main, the specified voltage between mains may
be divided by 1/3 to give the values of E0 and EI in Fig. 42.
Let cos B be the power factor of each receiving circuit, P
the total power to be delivered, EI the electromotive force be-
7
•receiver
|*
i
3
Fig. 42.
82
ELECTRIC LIGHTING.
wire
tween the terminals of each receiving circuit, and E0 the elec-
tromotive force of each armature winding on the generator; all
prescribed (see Fig. 42). Then
P = 3Ei I cos e
from which the full-load line current / may be calculated.
The numerical difference E0 — EI is the electromotive force
drop in one wire. Therefore, looking upon the problem as one
in direct currents, we have E0 — EI = r'l, where r' is the ap-
proximate resistance of one wire. From this the approximate
size, of the wire may be found from the table.
Consider one of the wires, say
wire number 2. The other two
wires together constitute the re-
turn circuit for this wire, and,
the three wires being arranged
as indicated in Fig. 43, the dis-
tance from wire number 2 to each
of the other wires is equal to d,
which is given. Find the reac-
tance x of a pair of wires at
the prescribed distance apart
center to center, from the above
table.
The component of E\ parallel
to I is EI cos 9, and the component of EI perpendicular to
I is EI sin 6.
The resistance drop in one main is rl and the reactance drop
in one main is %xl, the former being parallel to / and the
latter being perpendicular to I. Then the components of E0
are EI cos 6 + rl, and EI sin 9 + ^xl, respectively, so that
E02 = (Ei cos 0 + rl)2 + (Ei sin 9 +
whence
Fig. 43.
l/E02 - (Ei sin 9 + Y2xl)2 - EI cos 0
(i)
ALTERNATING CURRENT LINES. 83
which gives the true resistance r of one wire from which the
correct size of wire is easily found.
Example. — The electromotive force between mains at the
receiving station is to be 20,000 volts. Therefore, the electro-
motive force between terminals of Y-connected receiving circuits
would be
EI = 20,000 -f- 1/3 = 1 1 ,550 volts (see Fig. 42)
The electromotive force between mains at the generating sta-
tion is to be 23,000 volts. Therefore,
Eo = 23,000 volts -7- 1/3 = 13,280 volts (see Fig. 42)
Further specifications: P = 1,000 kilowatts, cos 6 = 0.85,
frequency = 60 cycles per second, distance = 30 miles, distance
apart of wires = 21 inches.
From these data we find / = 34 amperes, and r' = 50.9 ohms.
Therefore, approximately, a number 5 wire is required. The
reactance x of a 3O-mile double line of number 5 wires, 21 inches
apart center to center, at 60 cycles per second, is
x = 41.2 ohms
which substituted in equation (i) gives
r = 46.5 ohms
so that a wire between number 4 and number 5 would give the
prescribed line drop.
38. Line interference. — An alternating-current transmission
line induces an alternating current in any adjacent line; this is
called line interference. Line interference depends upon three
distinct effects as follows: (a) Magnetic induction. The alter-
nating-current line acts like the primary of an induction coil
and an adjacent telephone line, for example, like the secondary
of the induction coil, or in other words, the magnetic action of
the alternating current induces an alternating electromotive force
in an adjacent line, (b) Electrostatic induction. The alternat-
ing-current transmission wires are repeatedly charged first in one
sense and then in the opposite sense with the reversals of the
84 ELECTRIC LIGHTING.
alternating electromotive force, a repeatedly reversed charge is
produced on the wires of an adjacent line by influence and the
flow of this charge into and out of the adjacent line produces an
alternating current in the adjacent line, (c) Leakage. If the
alternating-current line is not thoroughly insulated from the
Fig. 44.
adjacent line more or less current leaks across from one to the
other.
Line interference is seldom a serious matter, except in the case
of a telephone line exposed to the influence of an alternating-
current transmission line, and in such a case the interference
may be obviated (a) by what is called transposition of wires of
one of the lines thus tending to eliminate magnetic and electro-
top view
tide view
Fig. 45.
static induction, and (b) by thorough insulation, thus tending
to eliminate leakage.*
* See a paper by P. M. Lincoln, Transactions of the American Institute of Electrical
Engineers, Vol. XXI, pages 245-251, and a paper by F. F. Fowle, Transactions
of the American Institute of Electrical Engineers, Vol. XXIII, pages 659-689.
The important part of this latter paper is included in pages 674-687.
TRANSMISSION LINES.
85
Figure 44 shows the essential features of a transposed single-
phase (two-wire) transmission line. Any two successive sections
or loops of the line *may be looked upon as complete circuits
around which the current flows in opposite directions and across
which the voltage is reversed so that the magnetic actions of
two successive sections of the transposed line on an adjacent
(untransposed) line are opposite to each other, and the electro-
static actions of two successive sections of the transposed line
on an adjacent line are opposite to each other.
Line interference between an alternating current line and a
telephone line may be eliminated by the transposition of wires
of the transmission line or by the transposition of wires of the
telephone line. It is more usual to transpose the wires of the
Fig. 46.
telephone line. Figure 45 shows the method of transposing a
telephone line. Three cross-arms are attached to the pole at
which the transposition is to be made, and upon the middle arm
a "two-story" insulator is placed so as to bring one of the wires
above the other at the crossing point as indicated in the figure.
Long distance alternating-current transmission lines are al-
ways transposed so as to minimize interference with adjacent
lines of all kinds. Thus Fig. 46 shows a cross-over or transposi-
tion on a three-wire three-phase line.
CHAPTER IV.
PHOTOMETRY AND ILLUMINATION.
39. Radiant heat. Light. — The radiation from a hot body
may be resolved into simple component parts, each of which is a
train of ether waves of definite wave-length. All of these com-
ponent parts of the total radiation have one common property,
namely, they generate heat in a body which absorbs them.
Therefore every portion of the radiation from a hot body is
properly called radiant heat. The intensity of a beam of radiant
heat is measured by the heat it delivers per second to an ab-
sorbing body. Thus, the radiant heat emitted by a standard
candle represents a flow of about 450 ergs of energy per second
across one square centimeter of area at a distance of one meter
from the candle.
Radiant heat of which the wave-length lies between 39 and 75
millionths of a centimeter affects the optic nerves and gives rise
to sensations of light. Therefore radiant heat of which the wave-
length lies between these limits is called light. These limits,
which are called the limits of the visible spectrum, are not
sharply defined, but vary considerably with the intensity of the
radiation and with the degree of fatigue of the optic nerves, and
they vary greatly with different persons.
40. The physical intensity of a beam of light is measured by
its perfectly definite thermal effect, that is, by the heat energy it
delivers per second to an absorbing body. Thus, those parts
of the radiation of a standard candle which lie within the visible
spectrum represent the flow of about 9.3 ergs per second across
an area of one square centimeter at a distance of one meter from
the candle. Comparing this with the flow of energy which is
represented by the total radiation from a standard candle (450
ergs per second across an area of one square centimeter at a
86
PHOTOMETRY AND ILLUMINATION. 87
distance of one meter from the candle) , it follows that only about
two per cent, of the energy radiated by the standard candle lies
within the visible spectrum, that is, only about two per cent, of
the radiation from the standard candle is light. Full sunlight
represents a flow of about two million ergs (or 0.2 of a watt) per
second across one square centimeter. About one third or one
half of this energy is absorbed by the atmosphere. The lumi-
nous part of the sun's rays represents about four hundred thou-
sand ergs per second, or 0.04 of a watt per square centimeter.
41. The luminous intensity of a beam of light is presumably
measured by the intensity of the light sensation it can produce,
but the intensity of the light sensation which is produced by a
given beam of light is extremely indefinite. A given beam of
light entering the eye may produce a strong or weak sensation,
depending upon various individual peculiarities of the person
and on the degree of fatigue of the retina; and the vividness of
the sensation depends upon the extent to which it is enhanced
by attention. Our sensations are not quantitative in the physical
meaning of that term; in fact, they enable us merely to dis-
tinguish objects, to judge whether things are alike or unlike, and
the certainty and precision with which we can do this is exempli-
fied in every outward aspect of our daily life. The ratio of the
lumionus intensities of two beams of light is measured by using a
device to alter, in a known ratio, the physical intensity of one beam
until it gives, as nearly as one can judge, a degree of illumination
on a screen which is equal to (like) the illumination produced by
the other beam. Such a device is called a photometer. * The
Bunsen photometer is described in Art. 57.
42. Simple photometry and spectrophotometry. — The measure-
ment of the light emitted by a lamp is called photometry. This
measurement is always made by comparing the beam of light
* A very complete and interesting discussion of Photometric Devices is given
by C. H. Sharp, on pages 411-506 of Vol. I of the Johns Hopkins University Lec-
tures on Illuminating Engineering, The Johns Hopkins Press, 1911,
88 FTECTRIC LIGHTING.
from a given lamp with the beam of light from a standard lamp
as explained in Article 41.
The comparison of the total light in a beam from a given lamp
with the total light in a beam from a standard lamp is called
simple photometry; whereas the comparison, wave-length by wave-
length, throughout the spectrum, is called spectrophotometry *
The fundamental difficulty in simple photometry is that dif-
ferent lamps usually show differences of color, and these differ-
ences of color do not disappear when the attempt is made to
adjust a photometer so that two lamps give equal (like) illumina-
tion on a screen. This difficulty is overcome to some extent
by the use of the flicker photometer which is described in
Art. 61.
43. Standard lamps. The fundamental light units. — The
British standard candle is a sperm candle made according to exact
specifications.! When this candle burns 120 grains of sperm
per hour it is a standard candle, and the actual candle-power
during a given test is taken to be a 1 120 where a is the number
of grains of sperm actually burned per hour during the test.
The Hefner lamp, { so called from its inventor, is a lamp which
burns pure amyl acetate ; the wick and its containing tube are of
prescribed dimensions, and the wick is turned up to give a flame
of prescribed height.
The Vernon-Har court pentane lamp\ is a lamp which burns the
vapor of pentane. A stream of air flows through a chamber con-
taining pentane, the air becomes saturated with pentane vapor,
* Some examples of the results of spectrometrical measurements are given in
Fig. 79.
t See American Gas Light Journal, Vol. LX, page 41, 1894.
J A full discussion of the Hefner lamp may be found in Photometrical Measure-
ments by Wilbur M. Stine, The Macmillan Co., 1904. In particular, see the dis-
cussion of Influence of Atmospheric Moisture, Influence of Carbon Dioxide, In-
fluence of Atmospheric Pressure, and Influence of Atmospheric Temperature on
the brightness of the Hefner lamp on pages 153-157.
§The pentane lamp is described on pages 132-134 of Wilbur M. Stine's
Photometrical Measurements. Pentane is one of the more volatile constituents of
gasolene.
PHOTOMETRY AND ILLUMINATION. 89
and this mixture of pentane vapor and air is burned in an Argand *
burner of prescribed dimensions.
The Carcel lamp is 2tn Argand burner of prescribed dimensions
burning rape-seed oil. This lamp has been extensively used as
a standard lamp in France.
Light units. — The intensity of the horizontal beam of light
from a Hefner lamp is called a hefner-unit or a hefner. If a
lamp were to give one hefner-unit of light intensity in every
direction, the amount of light, or the so-called flux of light emitted
by the lamp would be what is called one spherical-hefner.
The candle, or candle-unit, or candle-power, as it is variously
called, is a beam of light of which the intensity is i.n hefner-
units ; that is to say, a horizontal beam from a Hefner lamp has an
intensity of 0.90 candle-power. This is the definition of the
candle-power which is used by the United States Bureau of
Standards, and the candle-power so defined is called the inter-
national candle to distinguish it from the old British Standard
Candle which is now obsolete.
A lamp which would give one candle-unit of intensity in every
direction would emit one spherical-candle of light flux.
For most photometric work nothing is better as a working
standard than a properly aged and standardized incandescent lamp.
Such lamps can be obtained from the United States Bureau of
Standards with certificates specifying their candle-power in a
prescribed direction when operated with a prescribed voltage
between their terminals.
44. Conical intensity and sectional intensity of a beam of light.
— The expression, intensity of a beam of light, which is used in the
above definitions of the hefner-unit and candle-unit, refers to the
amount of light in a unit-sized cone of rays. This conical
intensity, which it may be called for brevity, is expressed in
* The Argand burner is a type of burner in which a supply of air is admitted
to the interior of a flame, as in[the familiar student lamp. See article Argand burner
in any good encyclopaedia.
90 ELECTRIC LIGHTING.
Hefners or candles; and it is independent of distance, since the
light in a given cone of rays always remains in that cone.*
The intensity of a beam of light may also refer to the amount
of light per unit sectional area of the beam. This sectional inten-
sity, which it may be called for brevity, decreases as the square
of the distance from the lamp increases, as explained in Art. 48.
45. Intrinsic brilliancy of a lamp. — The candle-power of a
lamp in a given direction divided by the luminous area f of the
lamp is called the intrinsic brilliancy of the lamp.
Examples. — The intrinsic brilliancy of the crater of a powerful
carbon-arc lamp approaches two hundred thousand candles per
square inch. The tungsten-filament lamp has an intrinsic bril-
liancy of about one thousand candles per square inch. The
carbon-filament lamp has an intrinsic brilliancy of about three
hundred candles per square inch. A kerosene lamp flame has
an intrinsic brilliancy of from four to eight candles per square
inch.
A lamp of great intrinsic brilliancy is very painful to look at,
and such a lamp should always be surrounded by a diffusing
globe or shade so as to hide the luminous surface of the lamp
itself. Thus, an arc lamp when used indoors is always provided
with a diffusing globe, and the tungsten lamp should always have
a diffusing globe or shade when it is used for interior lighting.
46. Unit of spherical angle. Definition of the lumen. — To
understand the relationship of the various light units one must
understand what is called solid or spherical angle. Consider a
cone and a sphere with its center at the apex of the cone. Let
A be the area of the spherical surface which is inside the cone,
* It is assumed in these fundamental definitions that the light source is very
small in size; it requires a very elaborate discussion to establish the fundamental
ideas of photometry if this assumption is not made.
Some matters relating to light sources which are not negligibly small are dis-
cussed in Arts. 50 and 56. A good example of the application of the fundamental
ideas of photometry to large luminous sources is the paper, "Geometrical Theory
of Radiating Surfaces with Discussion of Light Tubes," by E. P. Hyde, Bulletin
of the Bureau of Standards, Vol. Ill, pages 81-104, 1907.
t Projected area at right angles to the given direction.
PHOTOMETRY AND ILLUMINATION. 91
and let r be the radius of the sphere. Then the ratio A/r2
measures what is called the spherical angle of the cone.* Thus
one unit of spherical angle is subtended by one square meter
of the surface of a sphere of one meter radius, or by one square
foot of a sphere of one foot radius and the complete surface of a
sphere represents \-w units of spherical angle. In the following
discussion one unit of spherical angle is called a unit-cone.
Imagine a lamp which gives an intensity of one candle-power
in every direction. The amount of light, or light flux, passing
out from such a lamp in one unit-cone is called the lumen of light
flux. Such a lamp would emit one spherical-candle of light flux,
inasmuch as the conical intensity is assumed to be one candle-
power in every direction; but the whole spherical surface repre-
sents 4?r unit-cones, each of which contains one lumen of light;
therefore there are 4?r lumens of light flux in one spherical-candle.
47. Sectional intensity of a beam of light. Definition of the
foot-candle. Definition of the lux. — Imagine a lamp which gives
out one candle-power in every direction, and consider a sphere
of one foot radius with its center at the lamp. One square foot
of the surface of this sphere is contained inside of a unit-cone, and
such a unit-cone contains one lumen of light flux. Therefore
one lumen of light flux passes through each square foot of the
surface of the sphere; that is, the light which radiates from the
given lamp has a sectional intensity of one lumen per square
foot at a, distance of one foot from the lamp. This sectional
intensity is sometimes called the foot-candle. That is to say,
the foot-candle is the sectional intensity of a one-candle-power
beam at a distance of one foot from the lamp.
The meter-candle is the sectional intensity of a one-candle-
power beam at a distance of one meter from the lamp. The
meter-candle is one lumen per square meter and it is sometimes
called the lux.
* To express the value of a spherical angle as the quotient of the spherical area
divided by square of spherical radius is analogous to the method of expressing a
plane angle as the quotient of the arc of a circle divided by the radius.
92 ELECTRIC LIGHTING.
One foot-candle is equal to 10.75 meter-candles or luxes.
The relation between the various light units may be kept in
mind most easily with the help of Fig. 47.
sphere
one foot radius
one lumen
of light
Fig. 47.
48. The law of inverse squares. — It is evident that the sec-
tional intensity of a beam of light from a lamp decreases with
increasing distance from the lamp. Indeed the sectional in-
tensity of a beam from a lamp is given by the equation
(14)
in which C is the conical intensity of the beam in candle-power,
and I is the sectional intensity of the beam in foot-candles at
a distance of d feet from the lamp. This is evident when we
consider that the amount of light in a cone of rays remains
constant, whereas the sectional area of the cone increases as
the square of the distance from the apex of the cone.
Equation (14) expresses what is called the laiv of inverse squares.
This law applies strictly to the light which comes from a very
PHOTOMETRY AND ILLUMINATION.
93
small portion of the luminous surface of a lamp, a point source
as it is called. The law is approximately true, however, for
a whole lamp at distances which are large compared with the
size of the luminous surface of the lamp. For example, con-
sider the light which is given off by a brightly illuminated flat
disk of paper. The sectional intensities of this light at points on
the axis of the disk at different distances from the disk are ex-
hibited in the accompanying table. The heavy-faced num-
bers show what the sectional intensities would be according
to the law of inverse squares, and the light-faced figures show
the actual intensities.
PAPER DISK 2 FEET IN DIAMETER.
Distances from Disk in Feet.
5
10
20
40
80
160
Sectional intensities according to
the law of inverse squares
Actual sectional intensities
1024
984.6
256
253.5
64
63.84
16
15-99
3.9992
I
0.99996
The error of the law of inverse squares does not exceed two-
tenths of one per cent, for distances exceeding ten times the maxi-
mum dimension of the luminous surface of the lamp. See Art. 50.
49. To find the relation between the intrinsic brilliancy and the lumens of
light emitted per square foot of a flat diffusing surface of plaster or uncalendered
paper. — Consider a small element AA of the plaster surface, and let Cn be the
candle-power of the beam which is given off by the element normally. Then
C»/AA( = B) is the intrinsic brilliancy of the plaster surface according to Art. 45.
The candle power of the normal beam is therefore Cn = B • AA and the candle-
power of the oblique beam b, Fig. 48, is equal to Cn cos 6 according to Lambert's
cosine law (see Art. 53). Therefore we have:
Cb = B cos 0 . AA (i)
in which Cb is the candle-power of the oblique beam 6 in Fig. 48, B is the in-
trinsic brilliancy of the plaster surface, AA is the area of the plaster surface, and
0 is the angle shown in the figure.
Consider the zone zz of the reference sphere, the zone extending entirely
around the "pole" p. The area of this zone is nrr sin 0 X r • A0, the sectional
intensity of the beam b at zz is equal to C&/r2 according to equation (14), and the
amount of light passing through the zone zz is equal to the product of the area of
zz and the sectional intensity of b. Therefore we have
94
ELECTRIC LIGHTING.
sin 0 cos 0 • A0
in which AL is the amount of light in lumens passing through 22.
To find the total amount of light
L emitted by the element of plaster
surface, equation (ii) must be inte-
grated between the limits 0 = o to
0 = 90°, which gives:
sphere of
radius r
whence
B =
• AA
L
(iii)
(iv)
That is, the intrinsic brilliancy of a
flat diffusing surface of plaster or un-
calendered paper is equal to the lu-
mens of light emitted per unit area
(L/AA) divided by TT.
50. Given a flat circular disk of
plaster or uncalendered paper of
which the intrinsic brilliancy is B,
to find the amount of light falling on
unit area at a point p in the axis of
the disk as shown in Fig. 49. — Con-
sider the beam of light which reaches
p from a small element e of the cir-
cular strip 55 of the plaster disk DD.
The conical intensity of this beam is
given by equation (i), where AA is the
area of the element e; and the sectional intensity of the beam at p is found by di-
viding Cb by the square of the distance ep which is (JR2 + P2)- Therefore, multi-
plying this sectional intensity by the projected value of the unit of area at p
(namely unit of area X cos 0), we find the amount of light falling upon the unit
of area at p from the element e. But every element of the circular strip 55 sends
the same amount of light to the unit of area at p, and therefore the total amount
of light AL received by the unit of area at p from the entire circular strip 55 is
Fig. 48.
AL = B X 2trp . Ap X
R*
X cos* B
but
cos 0 '= • , — ~»
so that equation (v) becomes:
= 2irBR*
p.Ap
(v)
(iv)
and the total amount of light falling on unit of area at p from the entire disk DD
is found by integrating equation (vi), from p = o to p — r, that is,
PHOTOMETRY AND ILLUMINATION.
95
2TTBR2
or
c*
irBr*
p.dp
R*
(vii)
(viii)
And of course the lumens of light received by the unit of area at p, in Fig. 49,
is the intensity of illumination of the unit of area by the light from the plaster or
paper disk. The actual sectional intensities which are given in the table in Art.
48 were calculated from equation (viii) , using r = one foot, and using for R the
series of values 5 feet, 10 feet, 20 feet, 40 feet, etc.
front view
side view
51. The intensity of illumination of a surface depends upon
the amount of light falling upon one unit of area of the surface.
Therefore, intensity of illumination is expressed in terms of
the same unit as sectional intensity of a beam of light. Thus
an intensity of illumination of one lux, or one meter-candle,
is one lumen of light falling an each square meter; it is the
intensity of illumination produced by a standard candle at a
distance of one meter. The foot-candle is the intensity of illu-
mination at a distance of one foot from a standard candle;
it is equal to one lumen per square foot.
Examples. — The light from a lo-candle-power lamp falls
perpendicularly upon a sheet of paper at a distance of two feet
from the lamp. Substituting C = 10 and d = 2, in equation
(14) we find the value of 7 to be 2.5 foot-candles.
52. Oblique illumination of a flat surface. — When a beam of
light falls obliquely upon a flat surface as shown in Fig. 50, the
96
ELECTRIC LIGHTING.
light is spread over an area greater than the sectional area of
the beam in the ratio acjab, and therefore the intensity of illu-
mination of the surface is less than the sectional intensity of
the beam in the ratio ab/ac.
That is to say, the intensity
of illumination of the surface
is equal to / cos 6 where /
is the sectional intensity of the
beam and 6 is the angle shown
in Fig. 50.
Let C be the conical inten-
sity of the beam bb from a
lamp as shown in Fig. 51,
and let us consider the inten-
sity of illumination In on a
surface normal to the beam at p, the intensity of illumi-
nation JA on a horizontal surface at p, and the intensity of
illumination Iv on a vertical surface at p. The sectional in-
tensity of the beam at p is C/d? according to equation (14),
Fig. 50.
Fig. 51.
and, since the normal intensity of illumination produced by
a beam is equal to the sectional intensity of the beam, therefore
we have
C
In d?
(15*)
PHOTOMETRY AND ILLUMINATION 97
Furthermore from the above discussion of Fig. 50 we have
(i6a)
C
= -^ • cos
Iv = - • sin 0
(I7a)
where 6 is the angle shown in Figs. 50 and 51.
In many cases the height H of the lamp above the illuminated
plane qp and the angle 6 are given to find /„, IH and Iv.
In such cases more convenient equations can be obtained by
substituting d = H/cos 0 in the above equations giving
cos^
and
C
-^> • cos3 0
c
Iv = -=p, • sin 0 cos2
(166)
(176)
from lamp
53. Regular reflection and diffuse reflection. Lambert's
cosine law. — The reflection from a polished surface like a mirror
is called regular reflection. The
reflection from a rough surface
like plaster or uncalendered paper,
is called diffuse reflection.
Most surfaces show both regular
reflection and diffuse reflection.
Thus everyone is familiar with the
unpleasant shining reflection from the page of a book when it
is viewed as shown in Fig. 52. A scraped plaster surface has
no perceptible regular reflection. The following statements refer
to such a surface.
Proposition (a). — The apparent brightness of an illuminated
plaster surface is independent of its distance from the observer's
8
page of book
Fig. 52.
98 ELECTRIC LIGHTING.
eye. This may be understood from the following argument.
If the distance of the illuminated surface from the eye is doubled
then, according to the law of inverse squares,* one quarter as
much light enters the eye from the surface (size of pupil remain-
„ - - ~*i normal to
plaster surface
one square foot of/
^plaster surface]
Fig. 53.
ing unchanged), but the image of the illuminated sufrace on
the retina is reduced to one quarter of its original area, so
that one quarter as much light falls on one quarter as large a
spot on the retina, and therefore the intensity of illumination of
the retina is unchanged.
Proposition (6). — Surfaces like rough plaster and uncalendered
paper, which diffuse light very completely, have an apparent bright-
ness which remains the same as they are viewed more and more
obliquely. This is an observed fact, and an important conse-
quence of it is as follows. Consider one square foot of an illumi-
nated plaster surface which is viewed obliquely as shown in
Fig- 53> so that the projected area pp of the plaster surface is re-
duced, say, to one half of a square foot. Then the area of the
image on the retina is one half as great as it would be if the
plaster surface were turned at right angles to the line of vision
(the distance of the eye from plaster surface remaining un-
changed). But to make the plaster surface appear of the same
brightness in Fig. 53 with the image on the retina reduced to
half-size (in area), one half as much light must enter the eye.
* The law of inverse squares is true for a small portion of an illuminated surface.
PHOTOMETRY AND ILLUMINATION. 99
That is to say, when an illuminated diffusing surface is viewed
obliquely so that the apparent area of the surface is reduced say
to one half, then tha amount of light which enters the eye from
the surface is reduced to one half also. In general the apparent
area of a flat surface is reduced in the ratio I : cos 0, where 0
is the angle shown in Fig. 53. Therefore the intensity* of the
light given off in the direction ab, Fig. 53, is less than the
intensity* of the light given off in the direction cd in the ratio
I : cos 6. This relation is called Lambert's cosine law.
Consider the light emitted by an element A^4 of an illuminated
surface, the element being so small that it may be considered as
a point source of light. Then the I
j
candle power of the light beam
emitted normally to the element \
is B • AA , where B is the intrinsic 0 \ j v
1 M«. r 1 r \ Q y normal to
brilliancy of the surface, and the Xt'"" *"v Poster surface
candle power of the beam bb, in
Fig. 54, is j5-cos 6-kA.
54. Absorption of light by il-
luminated surfaces. — An abso-
lutely white surface would be a
surface which would reflect (dif-
fusely) all of the light falling upon Fig 54
it. Consider a surface which re-
flects, say, 0.6 of the light which falls upon it and which absorbs
the remaining 0.4 of the light. The fraction 0.6 is called the re-
flection coefficient of the surface, and the fraction 0.4 is called
the absorption coefficient of the surface. The reflection coeffi-
cient of a rough surface is sometimes called the albedo of the
surface.
55. Change of conical intensity by lenses. When the light
source is very small. — Light from a small source A passes
through a lens and is brought to a focus at B, as shown in Fig.
* Conical intensity; or sectional intensity at a given distance from the plaster
surface; see following paragraph.
100
ELECTRIC LIGHTING.
COEFFICIENTS OF REFLECTION* OF WALL PAPERS.
Material.
Coefficients of Re-
flection.
Coefficients of Ab-
sorption.
White blotting paper
o 82
o 18
^Vhite cartridge paper .
o 80
Ordinary foolscap paper
0.70
o 10
Chrome yellow paper
o 62
o 38
Orange paper
O ^O
o 50
Yellow wall paper .
O.4O
o 60
Yellow painted wall
O.4O
o 60
Light pink paper
o.^?6
o 64
Yellow cardboard
o.^o
o 70
Light blue cardboard
0.25
0.75
Brown cardboard
O.2O
0.80
Yellow painted wall (dirty)
Emerald green paper.
O.2O
0.18
0.80
0.82
Dark brown paper
0.13
0.87
Vermilion paper
Bluish green paper
Cobalt blue paper
0.12
0.12
O.I 2
0.88
0.88
0.88
Black paper
O.OS
0.95
Ultamarine blue paper
Black velvet
0-035
O.OO4
0.965
0.996
55. Beyond the focus B the light spreads out again in a conical
beam gg as shown in the figure. It is evident that the conical
intensity of the beam gg is the same as the conical intensity of
lens
Fig. 55.
the beam ff because the total amount of light is the same in
both beams and both cones are of the same size. Let C be the
conical intensity of the beam ee, and C' the conical intensity
of the beam ff (or of the beam gg). Then
* Taken from the Standard Handbook for Electrical Engineers, section 12, para-
graph 37, by Louis Bell.
PHOTOMETRY AND ILLUMINATION.
101
C"
(18)
in which a and b are the distances indicated in the figure. This
equation is based on the assumption that no light is lost in
passing through the lens. Let S be the area of the lens. Imag-
ine a sphere of radius a with its center at A, and a sphere of
radius b with its center at B. The portions of these spherical
surfaces which are included within the cones ee and ff are
approximately equal in area to S. Therefore the spherical angle
of the cone ee is equal to 5/a2 and the spherical angle of the
cone ff is equal to S/62. Let L be the amount of light-flux
in the cone ee, then the conical intensity of the beam ee is
equal to L divided by S/a2, and the conical intensity of the
beam // is equal to L divided by S/b2. That is, C = La?/S
and C' = Lb2/S, whence equation (18) follows at once.
'
K •
Fig. 56.
The action of a concave mirror is the same as the action of a
converging lens in altering the conical intensity of a beam of
light.
The above discussion applies also to Fig. 56 in which the light
source A is inside of the principal focus F.
If the distance a in Fig. 55 is equal to the focal length of the
lens, then the emergent beam ff is a. beam of parallel rays, or,
in other words, the distance b is infinity. Thus, Fig. 57 shows
a very small light source placed at the principal focus of a con-
verging lens. In this ideal case (ideal in that the source is as-
IO2
ELECTRIC LIGHTING.
sumed to be a point) the beam ff is a beam of parallel rays, and
the conical intensity of the beam ff is infinitely greater than the
conical intensity of the beam ee, according to equation (18).
lens
b (= infinity)
1 focal length*
of lens
Fig. 57.
But there is no such thing physically as a point source, and when
an actual light source is placed at the principal focus of a lens
or concave mirror, the size of the light source must be taken into
consideration in the discussion of the action of the lens or mirror,
as in the following article.
56. The searchlight. — The searchlight consists of a lamp placed
at the principal focus of a lens or concave mirror. The action
tens
*--*--<
side view
front view of screen
Fig. 58.
of the searchlight is shown in Fig. 58, in which the luminous source
is a gas flame. The light from each point p of the flame is con-
verted into a beam of parallel rays by the lens as shown in the figure.
Therefore the light from each point of the source illuminates a
PHOTOMETRY AND ILLUMINATION.
103
circular spot ss on a distant screen, and the diameter of this
spot is equal to the diameter of the lens. The illuminated field
on the distant scree A consists of a central portion UU which is
uniformly illuminated (if the flame is uniformly bright), and a
fringe PP which shades off gradually to complete darkness as
shown in the figure. In fact the illuminated field produced
by a searchlight is an inverted blurred image of the source, as
may be understood by a careful study of Fig. 58. Thus, one
sees a large inverted blurred image of the acetylene flame of an
automobile searchlight when the searchlight beam falls on a flat
surface like the side of a house.
When the light source is uniformly bright, then the beam from a
searchlight has a definite conical intensity at a great distance
from the lamp, as may be understood from the following con-
siderations. If the screen in Fig. 58 is at a very great distance
from a searchlight, the diameter of 55 becomes negligible in
comparison with the di-
ameter of the illuminated
field, or, in other words,
the fringe of the illumi-
nated field becomes neg-
ligible. That is to say,
all of the light in the
searchlight beam may be
thought of as being con-
tained within the cone
rr, and consequently the
searchlight beam may be
thought of as having a
definite conical intensity.
To determine the conical intensity of the beam of a searchlight,
consider a source AA, Fig. 59, placed at the principal focus of a
lens as shown. The light which falls upon the lens is contained
within the cone ee, and the searchlight beam at a great distance
from the lens is contained in the cone rr as above explained.
Fig. 59.
104 ELECTRIC LIGHTING.
Therefore, assuming that no light is lost in the lens, the conical
intensity of the searchlight beam is greater than the conical
intensity of the beam from the lamp in the inverse ratio of the
spherical angles of the two cones ee and rr in Fig. 59. Let s
be the area of the luminous surface of the lamp AA in Fig. 59,
and let 5 be the area of the lens. Then the spherical angle of
the cone rr is sensibly equal to s/f, and the spherical angle of
the cone ee is sensibly equal to 5//2. Multiplying the conical
intensity of the beam ee by the spherical angle of the cone ee
gives the number of lumens of light that strike the lens. Ignoring
loss of light, this is the amount of light in the cone rr, and it
may be divided by the spherical angle of the cone rr to give the
conical intensity of the searchlight beam.
In the above discussion the lens or mirror is supposed to be
entirely free from the error called spherical aberration. This is
never the case in practice, especially with a lens or mirror whose
diameter is large as compared with its focal length. The effect
of spherical aberration is to cause more blurring on a distant
screen than is represented in Fig. 58 and to cause a slightly in-
creased divergence of the searchlight beam.
As before stated, it is proper to speak of the candle-power
(conical intensity) of a searchlight beam when the lamp presents
a uniformly brilliant surface and when the searchlight beam is
considered only at great distances from the search lamp. The
effect of spherical aberration is to make it more generally per-
missible to speak of the candle-power of a searchlight beam,
because the blurring due to spherical aberration tends to make
the central portion of the field in Fig. 58 uniformly illuminated
even when the lamp does not present a uniformly illuminated
surface. This is especially the case in a searchlight using a closely
coiled tungsten-filament lamp. The illuminated field on a dis-
tant screen is of course a blurred image of the filament, and it
is not permissible to speak of the candle-power of the searchlight
beam unless the blurring is sufficient to obliterate every trace
of this image of the filament.
PHOTOMETRY AND ILLUMINATION.
105
When a lamp having a small straight filament is used in a
searchlight, then to confine the searchlight beam to the smallest
possible cone, it is best to arrange the filament in the axis of the
lens or mirror as shown in Fig. 60. Thus the light from the
lens
b 'focal
, plane
Fig. 60a.
Fig. 60&.
small straight filament cd, in Fig. 60, may be thought of as
coming from a circular spot ab on the focal plane, and ab is
much shorter than cd, if the focal length of the lens is large as
compared with its diameter.
When the diameter of the lens or mirror is large as compared
with its focal length, as shown in Fig. 61, then the only feasible
Fig. 6ia
Fig. 61&.
method of finding the best position of the lamp filament is by
trial ; it is not feasible to calculate the relative advantages of the
two positions shown in Fig. 6ia and Fig. 6ib.
57. The Bunsen photometer. — The most extensively used
device for comparing the conical intensities of the light from two
lamps is the Bunsen photometer. A given lamp and a standard
lamp are placed at the ends of a horizontal bar, and a screen
(see Fig. 62) of thin paper is moved along the bar until the two
io6
ELECTRIC LIGHTING.
sides of the screen are equally illuminated by the two lamps.
Equal intensities of illumination on the two sides of the screen
indicate equal sectional intensities (at the screen) of the beams
from the two lamps. Let C and C' be the conical intensities of
the beams from the two lamps as shown in Fig. 62. Then the
standard
lamp
screen
given
lamp
JL.
Fig. 62.
sectional intensity at the screen of the beam from the standard
lamp is C/d2, and the sectional intensity at the screen of the
beam from the given lamp is C'/d , according to equation (14),
and since these sectional intensities are equal, as above explained,
we have
C C
7/2
or
C
C'
(19)
from which the ratio of the conical intensities may be calculated
when d and df have been observed.
An irregular grease spot on the thin paper screen enables one
to judge better when the illumination is the same on the two
sides of the screen. This spot should be made with clean paraf-
fine, and the excess of paraffine should be drawn out of the screen
by placing it between folds of absorbent paper and applying a
hot flat-iron. To facilitate the seeing of both faces of the screen
simultaneously two mirrors are usually placed as shown in Fig.
63-
In judging the equality of illumination on the two sides of the
PHOTOMETRY AND ILLUMINATION.
107
Bunsen photometer screen, one eye only should be used. In
using both eyes, one unconsciously looks at one side of the screen
with one eye and aUthe other side of the screen with the other
eye, and the difference between the two eyes leads to a constant
error of setting.
With extremely dim lamps (or with bright lamps at great
distances from the screen of the Bunsen photometer) the accuracy
mirror
mirror
tight -
from
standard
lamp -
^
/ I ~~~^3
\ \
\ X
' I -
\
screen •< —
\
\
7/ ^=
\
\
k
/ -« —
4
\ 1
\ I
\ / lines of vision
\ 1
\l
light
from
given
lamp
Fig. 63.
of setting is very low ; a number of settings taken under such con-
ditions may deviate from each other by several per cent. With
increasing intensity of illumination on the screen the accuracy
of setting increases and reaches about one half of one per cent,
when the intensity of illumination on the screen is about one
foot-candle or more.*
FECHNER'S RATIO. — Given a surface with intensity of illumination / and let
A7 be the added illumination which is barely perceptible to the eye. The ratio
A7/7 is called Fechner's ratio. Thus defined this ratio is approximately equal to
the percentage accuracy of setting of a Bunsen photometer.
* The limit of accuracy of the setting of a Bunsen photometer is about two
tenths of one per cent., and the error which is introduced by the inaccuracy of
the law of inverse squares should be considerably less than two tenths of one
per cent. Therefore the maximum dimension of the luminous surface of a
lamp should not exceed about one twentieth of the distance of the lamp from
the photometer screen. See Art. 48.
io8
ELECTRIC LIGHTING.
The Bunsen photometer screen, together with the two mirrors
which are shown in Fig. 63 is usually mounted in a box which is
called a screen box or sight box. An extensively used substitute
for the Bunsen sight box is the Lummer-Brodhun sight box in
which an optical device (a prism-set) is used for showing portions
of the two sides of a white opaque screen side by side in the
same field of view. Two forms of the Lummer-Brodhun prism-
set are described in Arts. 63 and 65.
58. Distribution of light around a lamp. — In defining the
spherical-candle the idea of uniformity of distribution of light
Fig. 64.
around a lamp was introduced for the sake of simplicity. In
fact, however, no lamp gives complete uniformity of distribution
of light, but the conical intensity (candle-power) is always greater
in certain directions and less in other directions. Thus curve B,
Fig. 64, shows the distribution of light around a tungsten lamp,
and curves E, I and F show the distribution of candle-power
PHOTOMETRY AND ILLUMINATION.
109
around the same lamp when it is equipped with "extensive,"
"intensive" and "focusing" prismatic glass reflectors respec-
tively.* Figure 65 sjiows the distribution of light around an
ordinary carbon-filament lamp without a shade. In these figures
the conical intensity (candle-power) in each direction is repre-
sented to scale by the length of the radius vector of the curve.
— — ^^
— — — 16.0! Horizontal —
Fig. 65.
The distribution of candle-power about a lamp, which, like a
carbon-filament lamp, can be held in any position, may be
determined by mounting the lamp in a universal holder at one
end of the photometer bar, turning it step by step in various
positions and taking the photometer reading for each position.
In some cases a lamp is symmetrical with respect to an axis
so that a complete knowledge of the distribution of candle-power
about the lamp may be obtained by determining the candle-
power in different directions in a single plane which contains the
axis of symmetry of the lamp.
In many cases, a lamp is approximately symmetrical with
respect to an axis, so that the slight variations of candle-power
* These reflectors are described in Articles 73 and 75.
no
ELECTRIC LIGHTING.
around the axis of approximate symmetry are .of no importance.
In such a case the lack of symmetry may be averaged out, as it
were, by rotating the lamp at a speed of three or four revolutions
per second about its axis of approximate symmetry while the
photometer readings are being taken. The data for Figs. 64 and
65 were obtained in this way. The vertical dotted line in Fig.
65 is the axis of approximate symmetry, and the lamp (with
its shade) was rotated about this axis while the various readings
were taken.
In the case of a lamp which must be held in a fixed position,
such as an arc lamp, a gas lamp, or a kerosene lamp, one or more
mirrors are used to reflect the different beams from the lamp
along the photometer bar. Thus Fig. 66 shows three mirrors
•counterpoise
open wheel
axis of
photometer
Fig. 66.
arranged to reflect the light from a fixed lamp along a pho-
tometer bar. The three mirrors are suspended in a rigid frame
which may be rotated about the axis of the photometer as
indicated in the figure. The figure shows the mirrors in the
position to reflect the downward beam from the lamp along the
photometer bar.
The mirrors shown in Fig. 66 must be large enough so that,
with the eye placed at the photometer screen, one can see the
PHOTOMETRY AND ILLUMINATION. Ill
entire luminous surface of the lamp including the globe or shade;
and in using equation (19) the distance of the lamp from the
photometer screen must be taken as the sum of the distances
/, g, h and i in Fig. 66.
The mirrors in Fig. 66 reflect only a certain fractional part
of the light from the lamp, and therefore the photometer reading
must be multiplied by a correction factor when the mirrors are
used. This correction factor may be found by observing the
photometer readings corresponding to a certain beam from the
lamp (a) with the mirrors, and (b) without the mirrors, making due
allowance for the effective distance from the lamp to screen in
each case.
If it is feasible the lamp should be rotated steadily about the
vertical axis in Fig. 66 while the photometer readings are being
taken.
Distribution of light around a very fine straight filament. — In the ordinary
tungsten lamp the light is emitted by a number of nearly straight parallel tungsten
wires, and the distribution of light is very nearly of the kind one would get from a
single straight filament.
Let C be the candle-power of the equatorial beam as shown in Fig. 67. If
the filament is very fine and if it radiates light like a perfectly diffusing surface
(an illu/ninated surface of plaster for example), then, according to Lambert's
cosine law, the candle-power of the beam b is:
b = C cos 6 (i)
The sectional intensity of the beam b at the surface of the reference sphere is
6/r2, according to equation (14) ; the area of the zone zz of the reference sphere is
2irr cos & X r • A0; and the amount of light in lumens which passes through the zone
zz is the product of the sectional intensity &/r2 and the area of the zone. There-
fore
AL = 27TC COS2 0 . A0 (ii)
whence
L = 2TC I " cos2 0 . d6 = 7r*C (iii)
in which L is the total amount of light in lumens emitted by the filament.
To find the mean spherical candle-power of the filament, divide L by the spherical
angle corresponding to the entire reference sphere, namely, 4-0". This gives
Mean spherical ) _ ir
candle-power of the filament j ~~ 4
112
ELECTRIC LIGHTING.
Now the equatorial candle-power, C, corresponds to what is usually called the
mean horizontal candle-power, and the factor by which the mean horizontal candle-
power of a lamp must be multiplied to give the mean spherical candle-power is
called the spherical reduction factor of the lamp. Therefore the spherical reduction
factor of a lamp which has a fine straight filament is T/4 or 0.7854.
/^ pole
/ (reference
U sphere
ft radius r
i
Fig. 67.
Fig. 68.
The candle-power distribution curve of a very fine straight filament is made
up of two circles having the filament as their common tangent, as shown in Fig. 68,
and the diameter of each circle is the equatorial candle-power, C. The radius of
the dotted circle in Fig. 68 is equal to Tr/4 X C and it represents the mean spherical
candle power of the filament.
The candle-power distribution curve of an ordinary tungsten lamp without a
shade is shown by the curve BB in Fig. 64, and it is very similar to the two full-
line circles in Fig. 68. The spherical reduction factor of an ordinary tungsten
lamp should be nearly equal to w/4. In fact the spherical reduction factor of such
a lamp is about 0.79.
59. Measurement of total light flux from a lamp. — If a lamp
were to emit light of the same conical intensity (same candle-
power) in all directions, then the candle-power in any direction
as measured by a Bunsen photometer would be numerically equal
to the total amount of light expressed in spherical-candles, and
multiplying by 4?r would reduce to lumens. In general, how-
ever, light is emitted by a lamp unequally in different directions,
and the amount of light emitted by a lamp is determined by
measuring the candle-power in every direction and taking the
average. This average is the amount of light in spherical-
candles; to reduce to lumens multiply by 471-.
PHOTOMETRY AND ILLUMINATION.
If the average is to be calculated simply by adding and dividing
then the directions in which the separate readings are taken
must be distributed uniformly over the surface of a sphere with
its center at the lamp. This sphere is called the reference sphere
for the sake of brevity. If the readings are not so distributed,
then each reading must be multiplied by the spherical area which
may be properly assigned to it, and the sum of such products must
be divided by the total area of the sphere to give the correct average.
When a lamp can be rotated at a speed
of three or four revolutions per second
about its axis of approximate symmetry,
the total light flux from the lamp may
be determined by taking readings of can-
dle-power in different directions in one
plane only, namely, a plane which in-
cludes the axis of rotation. Thus the
lamp L in Fig. 69 would be rotated about
the vertical axis PQ, and the conical
intensities Ci, C-2, Cs, Q, etc., at equal
angular distances would be measured.
On account of the rotation of the lamp
each setting of the photometer gives the
average candle-power along a parallel of latitude, as it were.
Each of the readings C\, Cz, C3, Ci, etc., represents, therefore, the
candle-power over a zone of the reference sphere. Consequently
the readings must be multiplied by the areas of the respective
zones, and the sum of these products must be divided by the
total area of the reference sphere to get the correct average
candle-power in all directions, the mean spherical candle-power
as it is called.
This calculation may be easily understood with the help of
Fig. 70 in which ccc is a given candle-power curve, the curve
shown in Fig. 65 for example. Consider the candle-power which
is represented by the radius vector Oa. This candle-power may
be thought of as referring to the zone zz of the reference sphere.
9
Fig. 69.
114
ELECTRIC LIGHTING.
Taking the diameter DD of the reference sphere as representing
the total area of the sphere then the height h of the zone zz
represents the area of the zone.* Therefore the product Oa X h
is the product, candle-power Oa X area of the corresponding zone,
and the sum of all such products has to be divided by the diameter
DD of the reference sphere to give the mean spherical candle-
power of the lamp.
It is especially to be noted that the area enclosed by a candle-
power distribution curve is not a measure of the total amount of
reference
sphere
IS
light emitted by a lamp. Thus each of the four candle-power
distribution curves in Fig. 64 represents approximately the same
total amount of light, indeed each of the curves EE, II and FF
represents only about 88 per cent, as much light as curve BB.
60. Rousseau's diagram. — When the observed candle-powers
of a lamp correspond to zones of the reference sphere as above
* That is, the rule for finding the area of a spherical zone is to multiply the entire
area of the sphere (47rr2) by h/D, where h is the altitude of the zone and D
is the diameter of the sphere.
PHOTOMETRY AND ILLUMINATION. 115
explained, then the multiplication of each candle-power by the
area of the corresponding zone, the adding of these products
together, and the dividing of the total sum by the area of the
reference sphere may be done graphically. The most familiar
graphical method is due to Rousseau, and the drawing which is
necessary to carry it out is called Rousseau's diagram.
The curve ccc, Fig. 71, is the given candle-power curve (like
Fig. 65, for example). Construct another curve c'c'c' ', Fig. 72,
such that each abscissa O'a' is equal to the corresponding radius
•
FIG. 71.
Fig. 72.
vector Oa. The candle-power Oa multiplied by the area of
the corresponding zone* is evidently the same thing as O'a'
multiplied by h, and this product is equal to the shaded area in
Fig. 72. Consequently, the sum of all such products is equal to
the total area between the curve c'c'c' and the axis D'D'.
Therefore this area can be measured by a planimeter and divided
by the distance D'D' (the diameter of the reference sphere) to
give the true mean spherical candle-power of the lamp.
* See discussion of Fig. 70 in Art. 59.
n6
ELECTRIC LIGHTING.
Other graphical methods have been proposed for the determina-
tion of mean candle-power by Kennelly* and by Wohlauer.f
61. The flicker photometer. — The flicker photometer is a
device for eliminating, to some extent, the error in the setting
of a photometer which is due to differences in color of the lamps
which are being compared. The following is the principle upon
which the elimination of color error is based. When one looks
at a thing such as a photometer screen one has a sensation of
light from_
standard ££
lamp
light from
_r^.±: m given
lamp
brightness and a sensation of color. Both of these sensations
persist for an appreciable interval of time after stimulation
ceases, but the sensation of color persists much longer than the
sensation of brightness. Therefore if the two sides of the pho-
tometer screen are brought into the same field of view in rapid
succession (with high frequency of interchange), the color sensa-
* See Electrical World, March 28, 1908.
t See Illuminating Engineering, Vol. Ill, page 655.
PHOTOMETRY AND ILLUMINATION. 117
tion produced by the two sides of the screen and also the brightness
sensation produced by the two sides of the screen will both become
perfectly steady (devoid of flicker), whereas a much lower fre-
quency of interchange will suffice to give a steady color sensation
but leave a flickering sensation of brightness unless the two sides
of the screen have the same brightness. Therefore if we use a
frequency of interchange just sufficient to give a steady color
sensation, the two sides of the photometer screen can be brought
to equality of brightness by adjusting the photometer until the
brightness-flicker disappears. The various flicker photometers
differ in the arrangement used for bringing about the rapid inter-
change of the two sides of the photometer screen in the same
field of view, and the most satisfactory device is perhaps that
due to Marten.* The two faces of a prism of white plaster S,
Fig. 73, are illuminated by the standard lamp and a given lamp
respectively. The eye is focused upon one of the illuminated
faces of the plaster prism by means of the lens LL, and the thin
glass prism P which is carried in a rotating holder HH directs
one's vision to one face and then to the other face of the plaster
prism in rapid succession. This arrangement constitutes a sight
box, and it is used on a photometer bar in the same way as the
Bunsen sight box, as explained in Art. 57.
Another form of flicker sight-box which is quite satisfactory is
that of Simmance and Abady.f
62. The complete photometer; laboratory type. — The photom-
eter consists of a sight-box moving along a track or bar, and
the lamps to be compared are placed at the ends of this bar.
The sight-box may be of the Bunsen type as described in Art.
57, or of the Lummer-Brodhun type as described in Arts. 63 and
65, or a sight-box of the flicker- type may be used as described in
Art. 61. Usually the photometer setting is made by moving the
* This flicker photometer is manufactured by Schmidt and Haensch, of Berlin.
t The Simmance-Abady flicker sight-box is described on pages 491-492 of Vol.
I, Johns Hopkins University Lectures on Illuminating Engineering, Johns Hopkins
Press, 1911.
118 ELECTRIC LIGHTING.
sight-box along the photometer bar, but sometimes it is more
convenient to make the setting by moving the standard lamp
as in the Sharp-Millar portable photometer (see Art. 63).
The essential features of the laboratory type of photometer
are shown in Fig. 74. Dead black surfaces BB are placed back
top view of photometer
D\ sight box \D \D \D
standard lamp
tgioen lamp O
Fig. 74.
of each lamp, and a series of black diaphragms DD are placed
so as to shield the photometer screen and the observer's eyes
from all stray light. Freshly brushed black velvet is the best
material to use for these diaphragms and for the back pieces BB.
The law of inverse squares is assumed in the use of a photom-
eter, as explained in Art. 57, and therefore the distance from the
photometer screen to either lamp should never be less than about
20 times the maximum dimension of the luminous surface of the
lamp. A lo-foot photometer bar is therefore suitable for use
with ordinary bare incandescent lamps, but when a lamp has a
large shade the bar should be much longer because the shade is,
in effect, the luminous source. The short distance between the
standard lamp and the photometer screen in the Sharp-Millar
photometer (see next article) is permissible because of the small
size of the standard lamp.
It is best to set up the photometer in a dark room with dead
black walls, but if the back curtains BB and the diaphragms DD
are properly arranged the photometer room may be dimly lighted
without interfering with accurate photometric work.
Tables should be arranged at the ends of the photometer bar
PHOTOMETRY AND ILLUMINATION. 119
for the gas or electric meters and other accessory apparatus, such
as pressure regulators (for gas) and rheostats and switches (for
electric current). „
A single photometer setting is apt to be considerably in error,
and therefore a number of settings is taken whenever possible.
The taking of a set of readings is greatly facilitated by placing
a strip of paper on the photometer bar and marking the succes-
sive positions of the photometer screen for a series of readings;
this marking may be done very quickly by a pencil point which
is carried by a flat spring attached to the sight-box of the
photometer.
A photometer for incandescent lamp tests is usually provided
with a universal rotating holder so that the lamp under test can
be kept rotating and the axis of rotation can be given any desired
position.
It is important to use a storage battery7 for supplying current
to electric lamps under test because other sources of supply are
usually subject to sudden changes of voltage. When a storage
battery is not available the standard lamp and the lamp under
test should both be operated from the same mains so that both
lamps may be affected to approximately the same degree by
voltage variation.
63. The portable photometer and illuminometer. — The most
extensively used portable photometer is perhaps the Weber
photometer * The essential features of this instrument are em-
bodied in the more recent and improved portable photometer of
Sharp and Millar, and it is therefore sufficient to explain the
construction and use of the Sharp-Millar instrument which can
be used for measuring the candle-power of any lamp in service
or for the measurement of the intensity of illumination at any
point on a street or in a room. The essential features of the
Sharp-Millar photometer are shown in Figs. 75 and 76.
The observer's eye is focused on the diagonal plane ffoia.
* See Industrial Photometry, pages 85-91. Palaz (translated by G. W. and M.
R. Patterson), Van Nostrand, 1894.
120
ELECTRIC LIGHTING.
Lummer-Brodhun prism set L-B, and this diagonal plane is the
field of view of the observer. Through the center of the field of
view (where the prisms are in contact) the observer sees the dif-
fusing plate DD in Fig. 75, or the translucent milk-glass plate
-light from test lamp
comparison
lamp
Fig. 75.
SfSr in Fig. 76; and through the edge portions of the field of
view (where the prisms are not in contact) the observer sees the
translucent milk-glass plate 55 which is illuminated by the
comparison lamp (standard lamp) in the instrument.
light from all parts of rowf
comparison
lamp
To set the photometer the comparison lamp is moved towards
or away from 55 until the central and edge portions of the
field of view are equally bright, and the reading of the instrument
is the distance of the comparison lamp from 55. To interpret
the reading of the instrument calibration is necessary as follows :
PHOTOMETRY AND ILLUMINATION. 121
(a) Calibration for candle-power. — A series of lamps of known
candle-powers are placed in succession at a chosen distance d
from DD (in place of the test lamp in Fig. 75), the corresponding
readings of the photometer are taken, and a curve is plotted
showing readings as abscissas and candle-powers as ordinates.
Then if the lamp to be tested is at a distance dr from DD, the
candle-power of the lamp is (d'/d)2 times the candle-power
which is given by the curve.
(b) Calibration for intensities of illumination on S'S'. — A lamp
of known candle-power is placed at a series of measured distances
from S'S' in Fig. 76, thus producing known intensities of
illumination upon S'S' ; the corresponding readings of the pho-
tometer are taken; and a curve is plotted showing readings as
abscissas and foot-candles as ordinates. Then to determine the
intensity of illumination of, say, a horizontal surface at a given
point in a room, the photometer is set up with the plate S'S'
at the given point and horizontal, the photometer reading is
taken, and the desired value of the intensity of illumination is
found from the curve.
The commercial form of the Sharp-Millar photometer is usually
provided with a direct-reading scale, but it should be occasionally
calibrated as above explained.
The comparison lamp is a very small tungsten lamp which has
been thoroughly aged before it is mounted in the instrument,
and the voltage between the terminals of the comparison lamp is
kept at a prescribed value.
The Sharp-Millar photometer as furnished by the manufac-
turers* is provided with a smokefglass plate which can be placed
at p if very dim illumination is to be measured or at p' if very
bright illumination is to be measured. This smoke-glass is
usually adjusted by the manufacturers so that when used at p
the photometer reading (in case the photometer is direct reading)
must be divided by 10, and when used at p' the photometer
reading must be multiplied by 10.
* Foote, Pierson & Co., of New York City.
122
ELECTRIC LIGHTING.
Figure 77 shows the arrangement of the Sharp-Millar photom-
eter. The containing box is blackened inside, and a series of
diaphragms like DD, Fig. 74, are arranged between the com-
parison lamp L and the translucent screen 55. The elbow
tube T can be turned so that its end E points in any desired
direction. The translucent plate S'S' is placed over the end E,
and DM is a plate of which one face is ground milk-glass for
diffusion, and the other face is a thin plate of clear polished
glass backed with silver (a mirror). The mirror face is used in
Fig. 76 and the ground milk-glass face is used in Fig. 75.
* side view
part section
top view
section
H
Fig. 77.
An interesting use of the Sharp-Millar photometer is to turn
the mirror face of DM outward as in Fig. 76, remove the milk-
glass plate S'S' so as to leave the end E of the elbow tube open,
and direct the open end of the elbow tube towards a piece of
uncalendered white paper which faces a lamp to be tested. The
photometer reading is taken for a lamp of known candle-power
at distance d from the paper screen, and then the candle-power
of any given lamp is (df /d)2 times the photometer reading
(photometer thought of as being direct reading for the sake of
simplicity of statement), where d' is the distance of the given
lamp from the paper screen. This result is independent of the
distance of the piece of white paper from the instrument, and if
PHOTOMETRY AND ILLUMINATION.
123
the paper is free from gloss the result is independent of obliquity
of vision of the white paper as seen from the end of the elbow
tube of the instrument. The piece of white paper must face the
lamp to be tested and it must be large enough to completely fill the
central part of the observer's field of view (where the Lummer-
Brodhun prisms are in contact in Fig. 76). This use of the
Sharp-Millar photometer furnishes a striking illustration of the
two propositions (a) and (b) in Art. 53.
64. The globe photometer of Ulbricht.* — Several types of
photometer for determining the mean spherical candle-power of
a lamp by a single setting of the photometer have been devised.
The most notable are perhaps the integrating photometers of
C. P. Matthews,! but the Ulbricht globe photometer is the most
convenient in use. The ar-
rangement of this photometer
is shown in Fig. 78; A A and
BB are two hemispheres on
wheel-bases so that they can
be easily moved apart. The
interior of these hemispheres is
painted with a dead -white paint
(a white paint free from gloss) 4
The lamp to be tested and a
' ' comparison lamp ' 'of which the
mean spherical candle-power Fi 78
has been previously determined
are hung in the sphere as shown in the figure. A small milk-glass
diffusing window S'S' is placed in one side of the sphere and
* The globe photometer is fully described and the results of a thorough inves-
tigation of its reliability are given by L. Bloch in Electrotechnische Zeitschrift,
pages 1047-1052 and 1074-1078, November 16 and 23, 1905. See also a paper
on the Ulbricht integrating sphere by C. H. Sharp, Johns Hopkins University,
Lectures on Illuminating Engineering, Vol. I, pages 481-485, Baltimore, 1911.
f See Transactions of the American Institue of Electrical Engineers, Vol. XVIII,
pages 677-697, 1901; and Vol. XX, pages 59-70, 1902.
J The most satisfactory paint is barium sulphate in zapon lacquer.
124
ELECTRIC LIGHTING.
shaded from the direct light of the lamps by two white card-
board screens kk. The milk-glass diffusing window S'S' is the
illumination plate of a Sharp-Millar photometer (the same as
S'S' in Fig. 76). The photometer reading is taken with the
"comparison lamp" in place. This lamp is then extinguished,
the lamp to be tested is lighted, and the photometer reading is
again taken. Multiplying the known mean spherical candle-
1.8
1.6
1.4
0.8
0.6
0.4
D
\ cave length
0.5
0.7
Fig. 79.
CC, carbon-filament lamp; TTt tungsten-filament lamp ; A A, carbon-arc lamp;
DD, daylight.
power of the "comparison lamp" by the ratio of the two pho-
tometer readings gives the mean spherical candle-power of the
lamp under test. In this statement the photometer is assumed
to be direct reading.
PHOTOMETRY AND ILLUMINATION.
125
65. The spectrophotometer is a combination of a spectroscope and a photom-
eter arranged for comparing the intensities of two beams of light, wave-length by
wave-length. Figure 79 ^shows the results of a spectroscopic comparison of the
light from a carbon-filament lamp (curve C), the light from a tungsten-filament
lamp (curve T), and the light from the crater of a carbon-arc lamp (curve A), each
with daylight (curve D}. The meaning of these curves is as follows: For the same
intensity at the sodium line (wave-length 0.589 millionth of a meter), the light from
the carbon-filament glow lamp is 1.93 times as bright as daylight in the extreme
red and 0.36 as bright as daylight in the extreme violet; for the same brightness at
the sodium line, the light from the hot carbon tips of the carbon-arc lamp is 1.2
times as bright as daylight in the extreme red and 0.45 as bright as daylight in
the extreme violet
One of the best forms of spectrophotometer is the spectrophotometer of Lummer
and Brodhun, the essential features of which are shown in Fig. 80, in which L-B
is a Lummer- Brodhun prism-set. The observer's eye, placed at the narrow slit
Fig. 80.
E, looks through the lens TT and the glass prism P and is focused on the diagonal
face ff of the Lummer- Brodhun set so that this diagonal face is the observer's
field of view. The observer sees the central portion of the field of view illuminated
by light of one wave-length from the diffusing plate G, whereas the edge por-
tions of the field of view are illuminated by light of the same wave-length from
the diffusing plate F. The two diffusing plates F and G are illuminated by
the comparison lamp and the test lamp, respectively, and the distances D and Df
are adjusted until the observer's field of view is uniformly illuminated. Then the
ratio of brightness of the two lamps for the given wave-length is equal to the ratio
of the squares of the distances D and Df. In some forms of the Lummer-Brodhun
spectrophotometer, the observer's field of view is brought to uniform intensity
qf illumination by adjusting the widths of the two slits 5 and •$'..
CHAPTER V.
anode
ELECTRIC LAMPS. LAMP SHADES AND REFLECTORS.
66. The electric arc. The arc lamp. — When two carbon or
metal rods are connected to supply mains, brought into contact*
and then separated, the current flows across the gap between the
ends of the rods producing what is called an electric arc. Thus
Fig. 8 1 shows the appearance of a direct-current arc between
carbon rods. The direc-
tion of flow of the current
is indicated by the arrow.
The column of hot conduct-
ing vapor is called the arc
stream, and the carbon or
metal rods are called the
electrode's (anode and cath-
ode), as shown in Fig. 81.
The arc between pure
carbon electrodes is called
the carbon arc, and an arc
lamp in which pure carbon
electrodes are used is called
a carbon-arc lamp. Nearly
all of the light of a carbon-
arc lamp comes from the
hot tips of the carbons, in-
deed the greater portion of
the light comes from the slightly concave end of the anode car-
bon. The arc stream gives off a pale violet light.
The arc between metal electrodes or between electrodes con-
taining metallic oxides or salts is called the luminous arc, because
* A rheostat must be included in the circuit.
126
cathode
Fig. 81.
LAMPS, LAMP SHADES AND REFLECTORS.
127
the arc stream itself gives off a great deal of light. In this case
the electrodes are not intensely heated and they do not give off
any appreciable amount of light. An arc lamp in which a
luminous arc is used is called a luminous-arc lamp. The luminous
arc stream gives off a smoke or cloud of condensed metal oxide,
and a flow of air must be maintained through the arc chamber
of a luminous-arc lamp to carry away this oxide. Otherwise an
Q 4 8 i* i<5 20 24,
Fig. 82.
Curve a refers to arc 2.76 inches long.
" 6 ' 2.36 "
" c " " " 1.97 "
" d " " " 1.58 "
" e ' 1.18 "
" / ' 0.79 "
" g " " " 0.39 "
opaque deposit would form on the inner walls of the enclosing
glass globe.
The electric arc between pure carbon rods or between carbon
rods impregnated with metallic salts can be maintained by direct
current or by alternating current; but it is not practicable to
maintain an alternating-current arc when either of the electrodes
is of metal. Apparently the cathode of an arc must be at a
128
ELECTRIC LIGHTING.
line wire
temperature sufficiently high to vaporize the cathode material,
and with a massive metal electrode the heat is taken away so
rapidly that the necessary rise of temperature is not produced
unless a very large current is used.*
An important property of the electric arc is that the voltage
across the arc decreases with increasing current, as shown by the
curves in Fig. 82. Consequently it is necessary to place resist-
ance in series with an arc lamp which is connected across constant-
voltage supply mains. Without this resistance the current
would increase indefinitely and the arc would constitute a short
circuit of the system. This resistance is called a ballast resistance,
and the loss of energy in the ballast resistance is usually about
30 per cent, of the total energy delivered by the supply mains.
In an alternating-current
arc lamp a choke coil (an
inductance) can be used as
a ballast. In a direct-cur-
rent arc lamp a resistance
must .be used as ballast.
When arc lamps are con-
nected in series to a con-
stant-current supply, no
ballast is necessary.
An important part of an
arc lamp is the mechanism for automatically moving the elec-
trodes so as to keep the arc steady. Thus Fig. 83 shows
the essential features of an arc-lamp mechanism for lamps
which are to be connected in series. A very small portion of
the current flows through a shunt coil B without passing
through the arc, and the remainder of the current flows through
the coil A and thence through the arc. An iron rod AB pass-
ing loosely into the coils A and B is attached to one end of
* For a discussion of the physics of the electric arc see C. P. Steinmetz, Trans-
actions of International Electrical Congress, Vol. II, pages 710-730, St. Louis, 1904.
Also see W. R. Whitney, Transactions of American Electrochemical Society, Vol,
YII, pages 291-299, 1905.
Fig. 83.
LAMPS, LAMP SHADES AND REFLECTORS. 129
a lever which is pivoted at its center, and the other end of
the lever is provided with a clutch c through which a smooth
brass rod bb passes, This brass rod supports one of the carbon
electrodes, and the clutch is so constructed that it releases the
rod bb when the iron rod AB is raised, thus allowing the carbons
to come together. Each of the coils A and B acts to pull the
rod AB into itself, and a spring which is attached to the lever
is adjusted so that when the arc is burning properly the combined
action of this spring and the two coils A and B holds the lever
in such a position that the clutch clasps the brass rod bb. As
the arc continues to burn the carbons are slowly consumed,
causing the gap between the carbon tips to widen. This increases
the voltage across the arc and causes a greater portion of the
current to flow through the shunt coil B, which pulls up on the
iron rod AB, moves the lever, lowers the carbon and ultimately
releases the clutch so as to allow the rod bb to fall. The carbons
usually come too near together when the clutch c is thus re-
leased, but the current in coil B is thereby greatly reduced so
that the current in coil A quickly pulls the lever down and sepa-
rates the carbons to the desired extent.
67. Carbon-arc lamps. The open-arc lamp and the enclosed-
arc lamp. — In the oldest form of arc lamp the carbons are exposed
to the open air or surrounded by a glass globe through which the
air circulates freely. This type of lamp is called the open-arc
lamp. The carbons in this type of lamp are consumed rapidly
by the oxygen of the air, and the lamp must be trimmed, that
is, the carbons must be renewed, about once in 12 hours.
In the endosed-arc lamp the ends of the carbon rods project
into a small glass bulb which is very nearly air-tight. In this
type of lamp the carbons last about 150 hours.
The carbon-arc lamp operates satisfactorily on direct-current
circuits or on alternating-current circuits. The mechanism is,
however, slightly different in the two cases so that an arc lamp
which has been designed especially for direct current will not
operate satisfactorily with alternating current.
10
130 ELECTRIC LIGHTING.
The carbon-arc lamp is rapidly going out of use. Tungsten
lamps are much better and cheaper where small units are needed,
and luminous-arc lamps and mercury-vapor lamps are much
more efficient where large units are needed.
68. Luminous-arc lamps. The magnetite-arc lamp and the
flame-arc lamp. — In the magnetite-arc lamp the anode is a
short rod of copper as shown in Fig. 84,* and the cathode is
composed of a mixture of iron oxide (mag-
1 copper netite), titanium oxide and chromium ox-
anode '
-f ide. The copper anode remains relatively
—
t arc stream cool and wears away with extreme slowness.
— The end of the cathode is heated to a mod-
magnetite , , . . , ,
cathode erately high temperature during the opera-
tion of the lamp, and the oxides are slowly
vaporized producing an intensely luminous
Fig. 84. arc* The copper anode lasts five thousand
hours or more, and the rod of magnetite
lasts about one hundred and fifty hours. The light emitted
by the lamp is a brilliant white. It is not feasible to operate
the magnetite-arc lamp by alternating current.
In the flame-arc lamp carbon rods are used as electrodes, and
these carbon rods are impregnated with metallic salts. In the
familiar flame-arc lamp, which gives an extremely brilliant yellow
light, the carbons are impregnated with calcium fluoride
The flame arc gives off a cloud of oxide, and it is impracticable
to enclose the flame arc in a small bulb such as is used in the
enclosed carbon-arc lamp. Therefore when the flame-arc lamp
was first brought out the arc was not enclosed and the carbons
burned away rapidly. Consequently very long carbons were
required for a 1 2-hour run, and the use of long carbons led to the
arrangement shown in Fig. 85. This type is called the short-
* Figure 84 shows the arrangement of the electrodes in the General Electric
Company's lamp. In the Westinghouse magnetite-arc lamp the magnetite cathode
is above and the anode is below.
LAMPS, LAMP SHADES AND REFLECTORS. 131
burning inclined-carbon flame-arc lamp. It is now practically
obsolete. The objection to this type of flame-arc lamp is the
cost of the frequent^trimming.
carbon rod
oxide )
deposit
carbon rod
porcelain
arc stream
Fig. 85.
A satisfactory enclosed flame-arc lamp was placed on the
market in 1911, the cloud of oxide from the arc stream being
carried by a natural draft into a condensing chamber where the
oxide is deposited, and the clear cooled air retuns to the arc
chamber, but no fresh air has access to the arc chamber. In the
enclosed flame-arc lamp the carbon electrodes are placed ver-
tically one over the other as in the ordinary carbon-arc lamp,
and the electrodes last about 100 hours.
The flame-arc lamp can be operated either by direct current
or by alternating current.
69. The mercury- vapor lamp. — In 1860 it was known that a
steady and brilliantly luminous effect could be obtained by
passing an electric current through a glass tube containing mer-
cury vapor, and in 1881 the proposal was made to utilize this
effect in an electric lamp. In the early attempts to produce a
132
ELECTRIC LIGHTING.
practicable mercury-vapor lamp the necessary cooling of the
vapor tube was accomplished by the circulation of water, and it
was not until Peter Cooper Hewitt (about 1898) designed a
vapor tube with enlarged condensing chambers (which, indeed,
do not need to be very large on a long tube) that the mercury-
vapor lamp became a success.
The essential features of the Cooper-Hewitt lamp are shown
in Fig. 86. A long glass tube with a bulb on each end is provided
supply mains
switch
j j OCVtt'Vf*
' ^— ww^mooQ^
anode
Hg
cathode
Fig. 86.
with sealed-in lead-wires one of which connects with an electrode
(the anode) of iron or graphite and the other connects with a pool
of mercury (the cathode). The air is removed from the tube
by an air pump.
To start the lamp the tube is brought into a horizontal position
so that a thread of mercury bridges across from electrode to
electrode, the tube is then brought back to an inclined position
and when the thread of mercury breaks the current continues to
flow through the mercury vapor.* A ballast resistance R is
necessary, and an inductance (a choke coil) L is used to prevent
the stoppage of current by a momentary drop of the supply
voltage.
The type of lamp which is started by tilting is provided with
a mechanism in which an electromagnet automatically tilts
* A momentary high voltage produced by a spark-coil is sometimes used for
starting the flow of current through the mercury-vapor lamp.
LAMPS, LAMP SHADES AND REFLECTORS. 133
the tube and brings it back to the running position when the
control switch is closed. A general view of a Cooper-Hewitt
lamp of this type,* with its in verted- trough reflector is shown
in Fig. 87. The ballast and the
tilting mechanism are contained
in the sheet-metal case above the
lamp tube.
The simple form of Cooper-
Hewitt lamp cannot be operated
by alternating current. The alter-
nating-current lamp has two an-
odes and its connections are similar
to the connections of the mercury- Fig. 87.
vapor rectifier.*
The light of the Cooper-Hewitt lamp is intensely green and
it is entirely unsatisfactory where objects must be seen in their
natural colors as by day-light. When color values are not
important, for example in shops and draughting rooms, the
lamp is quite satisfactory.
The Quartz lamp is a mercury-vapor lamp, with a containing
tube made of fused silica or quartz. It differs from the Cooper-
Hewitt lamp in that a greater amount of energy can be delivered
to a small tube. The tube becomes red-hot during the opera-
tion of the lamp and the enclosed vapor gives an extremely bril-
liant light. The light from the quartz lamp contains a small
amount of red, and the light is therefore of a more pleasing
quality than the light of the Cooper-Hewitt lamp.
70. The glow lamp. — The most extensively used type of
electric lamp is the familiar incandescent lamp or glow lampt
in which a fine filament of carbon or metal is heated to incan-
descence by the electric current. The filament is enclosed in
a glass bulb from which the air is exhausted, the object being
to protect the filament from the oxygen of the air and to elim-
* See Dynamos and Motors, Chapter XIII.
134 ELECTRIC LIGHTING.
inate the great cooling effect which exists when the filament is
surrounded by gas of any kind.
There are five important kinds of glow lamps as follows:
(a) The old style carbon-filament lamp.
(b) The "metalized" carbon-filament lamp which differs from
the old style in that the carbon filament is heated to an extremely
high temperature in an electric furnace before it is mounted
in the lamp.
(c) The tantalum lamp in which the filament is a fine wire of
metallic tantalum.
(d) The tungsten lamp in which the filament is a fine wire of
metallic tungsten. The tungsten lamp is sometimes called the
mazda lamp.
(e) The Nernst lamp in which the glower is a small rod of
porcelain-like material.*
The carbon-filament lamp (old style and metalized) and the
tungsten lamp are by far the most important.
The carbon-filament lamp stands rough handling without
breakage of the filament and it is cheap; but^it is not very effi-
cient. The tungsten lamp on the other hand is more fragile
* An interesting article on carbon-filament lamp manufacture by M. K. Eyre
'£ given in The Electrical World, pages 9-13, January 5, 1895.
The "metalizing" process of carbon-filament manufacture is described by J. W.
Howell in the Transactions of the American Institute of Electrical Engineers, Vol.
XXIV, pages 839-849, June, 1905.
A discussion of the tantalum-filament glow lamp is given by Bolton and Feuer-
lein, Electrotechnische Zeitschrift, Vol. XXVI, pages 105-108, January, 1905.
" New Types of Incandescent Lamps," a discussion of the early process of
tungsten filament manufacture and a discussion of the characteristics of metal
filament lamps, by C. H. Sharp, Transactions of the American Institute of Electrical
Engineers, Vol. XXV, pages 815-864, November, 1906.
The manufacture of malleable tungsten which can be drawn into fine wire is
described by W. C. Coolidge, Transactions of the American Institute of Electrical
Engineers, Vol. XXIX, pages 961-965, May, 1910.
The Nernst lamp is described by A. J. Wurts in the Transactions of the American
Institute of Electrical Engineers, Vol. XVIII, pages 545-58?. 1901.
The process of manufacture of the Nernst lamp is described in The Electrical
World and Engineer, Vol. XLIII, pages 981-985, May 21, 1904.
LAMPS, LAMP SHADES AND REFLECTORS.
COST OF LIGHTING BY GLOW LAMPS
(Energy at ip cents per kilowatt-hour.)
B
•sju33 ni
OOO'I JOJ S^AVOU
•3"M" dmBHT DUB
O\ O 10 O OO 00 O
t^* o\ co O ^t~ ^sh t^
* The words cancf/e and candle-power signify mean horizontal candle-power.
f Prices of lamps are net prices, March, 1912, on $300 contract.
Old style carbon lamps and tantalum lamps are practically obsolete and they are therefore omitted from this table.
Candle-hours during life is found by multiplying initial candle-power by hours total life by deterioration factor.
This table refers to what is called "top efficiency." See page 139.
0
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136 ELECTRIC LIGHTING.
and it is more expensive than the carbon-filament lamp, but
it is much more efficient.
A comparison of costs of carbon, tantalum and tungsten
lamps is shown in the accompanying table, energy cost being 10
cents per kilowatt-hour.
It is not strictly correct to compare a carbon lamp with a tungsten lamp on the
basis of mean horizontal candle-power as is done in this table because the mean
spherical candle-power of the regular type of carbon lamp is about 0.85 of its mean
horizontal candle-power whereas the mean spherical candle power of a regular
type of tungsten lamp is only about 0.79 of its mean horizontal candle-power. The
correct basis of comparison is the total amount of light emitted; to reduce the values
in columns 9, 10 and n to this correct basis the tungsten costs should be multiplied
by 0.85/0.79.
An important matter which is shown very clearly in this
table is that more than nine-tenths of the cost of lighting by glow
lamps is for energy, and less than one-tenth of the cost is for lamp
renewals. The users of electric light hesitate, however, to pur-
chase a high-priced tungsten lamp when they can get a low-
priced carbon lamp or when their contract with the lighting
company calls for free renewals of their carbon lamps. This
is a very short-sighted policy because the higher-priced tungsten
lamp has a longer life than the carbon lamp and this longer
life alone makes up for a large part of the greater cost, but
especially because the saving in energy-cost which can be
realized by the high-priced tungsten lamp may be ten or twenty
times the cost of the lamp.
A given glow lamp is usually rated by the manufacturers
for a specified supply voltage as explained below, but the lamp
can, of course, be o erated at a higher or lower voltage. The
effect of a higher voltage is to give a greatly increased candle-
power, an increased power consumption (watts), a decreased
watts-per-candle, and a shortened life. A low power consump-
tion in watts per candle is, of course, desirable because it saves
in the cost of energy, but a short life is undesirable because
short life involves high renewal cost. It is therefore important
to make a proper compromise between these two items of cost
LAMPS, LAMP SHADES AND REFLECTORS.
137
so as to obtain a minimum total cost. This matter is shown
by the curves in Fig. 88. The pairs of curves At B, Ct D and
E refer to energy c^osts
of 2,4, 6, 8 and 10 cents
per kilowatt-hour re-
spectively. These curves
refer to an 8o-candle-
power tungsten lamp.
The abscissas represent
watts per candle, and
the ordinates -represent
the costs for 1 ,000 hours'
use of an 8o-candle-power
lamp of the following
items: (a) energy cost,
(b) renewal cost, and (c)
total cost. The wavy
line connects the mini-
mum points of the total
cost curves. Thus when
energy costs i o cents per
kilowatt-hour a tungsten
lamp of the size specified
gives light at a minimum
total cost when operated
so as to consume about
I.I watts per mean horizontal candle-power.
The cost of energy per kilowatt-hour in a large manufacturing
plant is usually less than two cents and sometimes less than one
cent. It is therefore important to consider total costs of lighting
by glow lamps (lamp renewal cost plus energy cost) when the
rate per kilowatt-hour is less than 2 cents. These costs are
shown by the ordinates of the curves in Fig. 89. These curves
show that the tungsten lamp is cheaper than the carbon-filament
lamp down to an energy rate of about 0.2 cent per kilowatt-hour.
1.2 __,
watts per candle
Fig. 88.
138
ELECTRIC LIGHTING.
The carbon-filament lamp is properly used where it is sub-
jected to rough handling or where it is used only a very small
portion of the time. Thus the drop-lamp which a machinist
uses about a lathe or boring-mill and the lamps one uses in a
cellar or closet should be carbon-filament lamps.
rate per kilowat-hour in cents
Glow lamp ratings* — To rate a thing like a glow lamp is to
specify the conditions under which it is to be used, and the
results to be obtained by its use. Manufacturers usually rate
a glow lamp in terms of the voltage for which the lamp is to be
used. Thus a no- volt lamp is one that is designed to operate
from no-volt mains. In addition to its voltage rating, it is
necessary to specify the approximate candle-power of the lamp
* See Circular No. 13 of the U. S. Bureau of Staudards for standard specifications
for the purchase of incandescent electric lamps.
The Electrical Testing Laboratories, 8oth Street and East End Avenue, N. V.
City, have unsurpassed facilities for testing lamps for purchasers.
LAMPS, LAMP SHADES AND REFLECTORS.
139
or to specify the approximate power consumption of the lamp
in watts at its rated voltage. Carbon-filament lamps are usually
rated in candle-powe/,* and tungsten lamps are usually rated
in terms of their power consumption. Thus we speak of a
i6-candle-power carbon-filament lamp or of a loo-watt tungsten
lamp.
The three-efficiency scheme of rating tungsten lamps. — From Fig.
88 it is evident that it is sometimes economical to burn tungsten
lamps at low watts-per-candle and sometimes economical to
burn tungsten lamps at high watts-per-candle. Therefore, manu-
facturers offer the purchaser a choice of watts-per-candle in lamps
of any given voltage and power rating. Three efficiencies are
offered in regular lamps; namely, "top efficiency," "middle
efficiency" and "bottom efficiency" as shown in the following
table. If a lamp user pays a high rate per kilowatt-hour for his
energy, he should order "top efficiency" lamps, and if he pays a
low rate per kilowatt-hour for his energy, he should order "bot-
tom efficiency" lamps.
LIFE AND EFFICIENCY TABLE FOR REGULAR TUNGSTEN LAMPS'
Size of
Top Efficiency.
Middle Efficiency.
Bottom Efficiency.
Lamp in
Watts.
Watts per
Candle.*
Life in
Hours.
Watts per
Candle.
Life in
Hours.
Watts per
Candle.
Life in
Hours.
25
I-3I
,OOO
1-37
,300
•43
,7OO
40
1.23
,OOO
1.28
,3OO
•33
,70O
60
I.I8
,OOO
1.23
,300
.28
,7OO
IOO
I.I8
,000
1.23
,300
.28
,7OO
150
1.18
,000
1.23
,300
.28
,7OO
250
1. 13
,OOO
1.18
,300
•23
,700
Candle-power ratings of glow lamps. — It is the universal practice
to rate a glow lamp by giving its mean hori ?0ntal candle-power.
*Mean horizontal candle-power.
140
ELECTRIC LIGHTING.
The mean horizontal candle-power, however, is not an exact
measure of the amount of light emitted by a lamp ; the amount of
light emitted must be expressed in spherical-candles or in lumens.
The factor by which the mean horizontal candle-power of a lamp
must be multiplied to give its mean spherical candle-power is
called the spherical reduction factor of the lamp. The spherical
reduction factor of the regular carbon-filament lamp is about
0.85, and the spherical reduction factor of the regular tungsten
lamp is about 0.79. To reduce mean spherical candle-power to
lumens multiply by 471-.
Variations of candle-power and watts due to variation of voltage.
— Glow lamps are generally supplied with current from "constant
voltage" mains, but the supply voltage always varies irregularly
irtn
/
/
/
;/
/
/
//
140
120
IOO
80
60
c/
/ .
/
/,
/ f
'TU
C.*
l^
z
//
'/
1
/
y//
K.
Ta
I
/
<//:
y
-
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/
8
A
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S
g
*
s
S
'/
To
-^
s*
f
Tu.
^
s'/
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,>•
•^x
' /
r
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M.
^
/
'
oer
cen
t V
Oltf
88 9a 96 100 104 108 112 u
Fig. 90.
through a range of one or two per cent, (indeed the variation of
voltage is much more than one or two per cent, when a central
station is poorly designed or carelessly operaced), and all of the
connected lamps fluctuate in candle-power as the supply voltage
rises and falls. This fluctuation of candle-power is very un-
pleasant, and metal-rilament glow lamps have an advantage over
LAMPS, LAMP SHADES AND REFLECTORS.
carbon-filament lamps in that the variation of candle-power due
to a given variation of voltage is less for metal-filament lamps
than for carbon-filament lamps. The ordinates of the curves
in Figs. 90 and 91 show candle-powers and watts for various
Ta
Tu
-CM.
percent volt
C.M
Ta
Tu
92 90
Fig. 91.
values of voltage (abscissas). The normal value of each item
(voltage, candle-power and watts) is taken as 100 so that the
departures from the normal values may be read off directly in
per cent. Thus a two per cent, increase of voltage (100 to 102
in Fig. 90) causes a 12 per cent, increase of candle-power of an
old style carbon-filament lamp (curve C), a 10 per cent, increase
of candle-power of a metalized carbon-filament lamp (curve CM ) .
and a 7 per cent, increase of candle-power of a tungsten lamp
(curve Tu) .
Slow deterioration of glow lamps in service. — A glow-lamp fila-
ment is always operated at a temperature which causes a slow
change of the filament and an ultimate deterioration of the lamp.
This deterioration is chiefly of two kinds, namely, (a) an increase
of resistance of the filament which causes a decrease of power
consumption and a very considerable decrease of candle-power,
and (b) a blackening of the lamp bulb which involves a very
great loss of light. If a lamp is used long enough the filament is
weakened until it breaks.
It is usually advisable to use a tungsten lamp until the filament
142
ELECTRIC LIGHTING.
breaks. Occasionally, however, the bulb of a tungsten lamp
blackens and such a lamp should be discarded when the blacken-
ing causes a serious loss of light.
A carbon-filament lamp should, as a rule, not be used until
the filament breaks, it is cheaper to throw away an old carbon-
filament lamp and buy a new one than it is to use the old lamp
at a greatly decreased efficiency (increased watts-per-candle) .
A carbon-filament glow lamp is usually considered to have reached
the end of its useful life when its candle-power falls to 80 per
cent, of its initial value.
The curves in Fig. 92* show the change of candle-power of
various kinds of glow lamps with age; C, CM, Ta and Tu
1 14°
P-
— f-
\ r
\J
'a
^ —
\
\
c I0°
e, 80
N
.
1 —
Tut
r^
^
V
^
— -
^
.
T^
^_^
• .
—
—
—
-—-
—
— -
— — .
L'.
M.
"~^-»
- ^
^
---
_^_
3 3 4 56 789
Jiundreds of hours
Fig. 92.
refer to carbon, "metalized" carbon, tantulum and tungsten,
respectively.
In estimating the cost of lighting it is important to estimate
the illuminating power of a lamp on the basis of its average
candle-power during its life. Thus the average candle-power of a
tungsten lamp during its life is from 0.90 to 0.95 of its candle-
power when new. See page 149.
Regular lamps and special lamps. — Great numbers of glow
lamps are used, in the ordinary constant-voltage system, for
* These curves are taken from Wickenden's Illumination and Photometry'
The tungsten lamp curve refers, apparently, to an old-style tungsten lamp. More
recent deterioration curves, and a discussion of the important subject of deterio-
ration are given by Sydney W. Ashe, Transactions of the Illuminating Engineering
Society, Vol. VI, pages 503-570, June, 1911.
LAMPS, LAMP SHADES AND REFLECTORS.
143
lighting houses of all kinds, and these lamps are made of standard
form so as to fit standard forms of sockets and shades. Such
lamps are called regular lamps. Glow lamps for street lighting,
sign lighting, and car lighting, are called special
lamps. Very small lamps for batteries are called
miniature lamps.
Figure 93 shows the special form of tungsten
lamp which is used when a large number of lamps
are connected in series for street lighting. These
lamps have a heavy filament (low voltage) and they
are made in a variety of sizes, from 25 to 350 candle-
power with current ratings* from 3.50 to 7.5 amperes.
71. Comparison of electric lamps. — An important matter in
connection with a lamp is the distribution of light around the
lamp. Thus the candle-power distribution curves of carbon-
filament and tungsten-filament glow lamps with and without
Fig. 93.
Fig. 94 a.
shades are shown in Figs. 64, 65 and 71. Candle-power dis-
tribution curves of the more important types of arc lamps are
shown in Figs. 94 a and 94 b. The numbers of the curves corre-
spond to the serial numbers in the following tables. f Curve 4
in Figs. 94 a and 94 b refers to the same lamp, namely, the 6.6
ampere magnetite-arc lamp equipped with an enamel reflector,
* Series tungsten lamps are rated on the basis of current and candle-power
(mean horizontal candle-power).
t Candle-power distribution curves of mercury-vapor lamps are given by Sydney
W. Ashe, Transactions of the Illuminating Engineering Society, Vol. VI, pages
5I3-SI6, June, 1911.
144
ELECTRIC LIGHTING.
as furnished by General Electric and Westinghouse Companies
for street lighting.
In laying out the lighting plans of a shop or factory one needs
to consider the intensity of illumination on the working plane as
explained in Art. 81. The following table* gives the values of
Fig. 94 6.
Ih (horizontal illumination) produced by various arc lamps.
The height of the lamp above the working plane is in each case
assumed to be 50 feet, and x is the horizontal distance from the
lamp to the point on the working plane where Ih is reckoned.
By making use of the law of inverse squares (Art. 48) it is
easy to use this table to find the intensity of illumination (hori-
zontal) at a point at any given distance d horizontally from any
one of the lamps placed at any given height H above the working
plane. The rule is as follows: Find from the table the value of Ih
for the lamp 50 feet high, and for x = d X 5o/#> and multiply the
value of Ih so found by (so/ H)2.
* This table was calculated from the candle-power curves of Figs. 940 and 946,
using equation (166).
LAMPS, LAMP SHADES AND REFLECTORS.
145
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146 ELECTRIC LIGHTING.
Example. — To find the horizontal illumination at a point 80
feet from an inclined-carbon flame-arc lamp 40 feet above the
working plane. Multiply 80 by 50/40, giving x = 100 feet.
The value of IH in the table corresponding to this value of x
is 0.102, which, multiplied by (50/40)2 gives the desired result,
namely, 0.127 foot-candle.
To find the distance d from a lamp H feet above the working
plane to give a prescribed horizontal illumination, multiply the
prescribed horizontal illumination by (H/5o)2 to get IH as per
table, find the corresponding value of x from the table and multiply
this value of x by ( Hl$o) to get the desired value of d.
Example. — To find d for which a 6.6-ampere magnetite-arc
lamp hung 30 feet high will give 0.5 foot-candle horizontal
illumination; the value of (H/^o)2 X 0.5 is 0.18 foot-candle,
and the corresponding value of x is 50 feet, so that the desired
value of d is 30 feet.
Comparative costs. — The following table* shows the approxi-
mate cost of producing 100,000 downward lumens 6 hours per
day 300 days per year using different kinds gf lamps. It must
be remembered that this table refers to averagef conditions, and
to interpret the table properly the following matters must be
taken into consideration.
(a) Multiple arc lamps and series arc lamps. — When few arc
lamps are to be installed, it is always most convenient to supply
them from existing constant-voltage mains. Each lamp is pro-
vided with a ballast, as explained on page 128, and the lamps are
connected singly J across the constant voltage mains. Lamps
designed to be connected in this way are called multiple lamps.
When many arc lamps are to be installed, they may be con-
* This table has been prepared from data collected from various sources. A
discussion of costs of street lamps is given in Bulletin No. 51 of the Illinois Engineer-
ing Experiment Station by J. M. Bryant and H. G. Hake, on Street Lighting.
f See statement concerning averages on page 2.
J Sometimes two lamps are connected in series. In case of a 5oo-volt supply
six or seven lamps can be connected in series. Lamps designed to be connected in
this way are called series-multiple lamps.
LAMPS, LAMP SHADES AND REFLECTORS.
OrovONO
147
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148
ELECTRIC LIGHTING.
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LAMPS, LAMP SHADES AND REFLECTORS. 149
nected in series to a constant-current supply (see Art. 87). This
arrangement reduces the cost of wiring to a minimum and it
eliminates the wasteof energy in lamp ballasts. Lamps designed
to be connected in this way are called series lamps.
A multiple lamp is rated by specifying the voltage of supply
for which the lamp is designed and the current which the lamp
will take when it is properly adjusted. A series lamp is rated
by specifying the current for which the lamp is designed.
All of the arc lamps referred to in the table are series lamps.
Nearly every type of arc lamp, however, is offered for sale either
as a series lamp or as a multiple lamp; a multiple lamp uses
about 1.4 times as much power as a series lamp when the same
amount of power is expended at the arc.
(b) Cost of energy.* — As a rule series lamps are used under
conditions which involve low cost of energy (long hours of service
and large demand for power), whereas multiple lamps are, as a
rule, used under conditions which involve high cost of energy (short
hours of service and small demand for power) . Thus a company
might furnish power for operating the street lamps of a city
(about 4,000 hours of service per year) at 2 or 3 cents per kilowatt-
hour, and be fully justified in charging 8 or 10 cents per kilowatt-
hour for power for operating two or three arc lamps in a store
(about i ,000 hours service per year) .
(c) Deterioration factor. — The number of lamps in column 3 is
reckoned on the basis of initial candle-power, whereas a fair com-
parison of costs must be based upon average candle-power during
the life of a lamp. The ratio, average candle-power during the
life of a lamp divided by the initial candle-power of the lamp, is
called the deterioration factor of the lamp. The annual costs in
column 14 should be divided by the deterioration factors. The
values of this factor are as follows:
* See Art. 87, page 183.
150
ELECTRIC LIGHTING.
TABLE OF DETERIORATION FACTORS*
Tungsten.
Carbon-arc.
Magnetite-arc.
Enclosed Flame-
arc.
Cooper-Hewitt.
0.90 to 0.95
0.80 to 0.85
0.90
0.85
0.65 to 0.75
(d) A given number of downward lumens does not mean the
possibility of illuminating a certain floor area. — Thus the light
from a few very high candle-power lamps cannot be satisfactorily
distributed over a large floor space unless the lamps are placed
at a sufficient height overhead and unless the space is free
from obstructions such as beams and belts and shafting (see
Art. 78). It is misleading to compare the costs of small lamps and
large lamps on the basis of quantity of light.
Moderately small tungsten lamps give the cheapest satisfactory
illumination when the height of the lamps is limited to 12 or 15
feet or where there are many obstructions. On the other hand
quartz tube lamps are only suitable for illuminating large open
spaces where the lamps can be placed 40 or 50 feet high. Be-
tween these two extremes there is a wide field of usefulness for
high candle-power tungsten lamps, for Cooper-Hewitt lamps and
for magnetite-arc and flame-arc lamps.
(e) Maintenance. — The maintenance cost as given in column
10 includes in every case the cost of regular inspection, the cost
of cleaning globes and reflectors, the cost of material and labor
for renewal of parts which wear outf or are occasionally broken,
and the cost of material and labor for repairing lamp mech-
anisms.
The maintenance cost varies greatly: (a) because different
kinds of service differ greatly in the required frequency of cleaning
* These results are based upon very few observations, and they are therefore
not to be depended upon. This is especially true in view of the fact that fre-
quency of cleaning of globes and reflectors has a very great deal to do with
deterioration.
t Such as tungsten lamps, arc lamp electrodes, Cooper-Hewitt vapor tubes,
globes, etc.
LAMPS, LAMP SHADES AND REFLECTORS. 151
of globes and reflectors and in the amount of breakage, (b) because
in some cases the lamps are difficult of access and the cost of
trimming and cleaning is excessive, and (c) because the main-
tenance labor can be more efficiently organized when a great many
lamps of a kind are to be cared for than when the number of
lamps is small.
The maintenance cost in the table refers to two or three or four
thousand hours use per year. When lamps are used only a few
hundred hours per year the maintenance is more expensive per
hour.
(f) Color. — When whiteness of light is a necessity, it is of
course meaningless to compare the cost of carbon-arc lamps and
tungsten lamps with the cost of flame-arc lamps and mercury-
vapor lamps. See Art. 76.
72. Lamp globes, shades and reflectors.* — Let one consider
the lamps which one sees everywhere, on city streets, in stores
and public halls, and in residences, and one will realize that lamps
are almost universally equipped with shades and reflectors.
These shades and reflectors are used for three distinct purposes,
namely, (a) to eliminate glare, f (b) to throw the light in a desired
direction, and (c) for decoration.
The use of a shade for the elimination of glare is exemplified
by the opal and ground glass globes which enclose indoor arc
lamps and Welsbach gas lamps, and the use of a shade for
throwing the light of a lamp in a desired direction is exemplified
by the canopy reflectors commonly used on street lamps.
In most cases shades and reflectors are used for the double
purpose of eliminating glare and directing the light from a lamp.
*See Cravath and Lansingh, Practical Illumination, pages 25-135, McGraw
Publishing Company, 1907.
The results of an extensive series of experimental studies of globes and reflectors
by R. B. Williamson and J. H. Klinck are given in Journal of Franklin Institute,
Vol. CXLIX, page 66, 1900.
Also see papers by V. R. Lansingh, Transactions of Illuminating Engineering
Society, Vol. II, pages 37i~399. and Vol. V, pages 49-74.
fSee Art. 77-
152 ELECTRIC LIGHTING.
Thus the shades which are used on desk lamps eliminate glare
by hiding the lamp itself from view, and they throw the light
downwards upon the desk.
Lamp shades for indoor use should always be to some extent
decorative. Decorative effects are, indeed, the primary con-
sideration in the elaborate and deeply colored shades which are
frequently used in parlors, and these shades are highly effective
in the elimination of glare; but if a shade is to direct the light of
a lamp where it is needed, the shade must not depart very widely
in shape from a simple cone or bowl ; and if excessive loss of light
by absorption is to be avoided, the shade must not have colored
parts which are intended to transmit light.
73. Extensive, intensive and focusing shades. — Lamp shades
which are not primarily decorative may be classified according to
their directing action on the light of a lamp. Thus we have the
focusing shade which throws the light downwards in a very intense
narrow beam, the intensive shade which throws the light down-
wards in a fairly narrow beam of moderate intensity, and the
extensive shade which throws the light downwards in a wide beam.
Thus curve B of Fig. 64 shows the distribution of candle-power*
around a bare tungsten lamp, curve E shows the distribution of
candle-power when the lamp is equipped with a typicalf extensive
reflector, curve I shows the distribution of candle-power when
the lamp is equipped with a typical intensive reflector, and curve
F shows the distribution of candle-power when the lamp is
equipped with a typical focusing reflector.
Extensive shades or reflectors are the most generally used.
They are adapted to residence lighting where small rooms with
low ceilings are the rule. Intensive shades are suitable for
large rooms with high ceilings where the lamps are distributed
* The radius vector of one of the curves in Fig. 64 represents the candle-power
in that direction, and therefore it is strictly correct to speak of the curves as repre-
senting the distribution of candle-power. Indeed the expression distribution of
candle-power is better than the more general expression distribution of light.
t In fact curves E, I and F refer to standard line prismatic glass reflectors of
the Holophane Company.
LAMPS, LAMP SHADES AND REFLECTORS. 153
uniformly over the room. Focusing shades are used for rooms
with very high ceilings and for producing intense local illumina-
tion on a desk or draughting board or on a work bench.
To classify shades according to their directing action tends to
take one's attention away from an equally important matter, the
elimination of glare. This matter is best considered, however,
in the following description of particular shades.
74. Metal and milk-glass reflectors. — A familiar type of re-
flector is the sheet metal cone, which is made deep for the focusing
type, less deep for the intensive type, and nearly flat for the
extensive type. In the cheaper grades, this shade is made of
sheet tin painted white on the inside, but the better grades are
made of pressed sheet steel with white porcelain enamel on the
inside. Milk-glass is also extensively used for these cone re-
flectors.
When lamps which are used for illuminating tables and desks,
are also depended upon to illuminate the upper part of the room,
metal reflectors are not very satisfactory, especially intensive
and focusing types of metal shades are not satisfactory under the
stated conditions because metal shades allow no light to pass
from the lamp to the upper part of the room. Milk-glass cones
are, however, quite satisfactory in this respect as are also the
prismatic reflectors which are described in Art. 75.
Porcelain enamel reflectors are used very extensively in street
and mill lighting. As compared with prismatic glass, enamel
reflectors are cheaper, they do not catch and hold the dust as
badly, and when properly made they throw a greater portion
of the light of a lamp downwards. For store and residence
lighting, however, prismatic glass reflectors are more extensively
used than enamel reflectors for reasons above stated and because
prismatic glass is more decorative.
When the shades above described are not deep enough to hide
the lamp from view, the lower portion of the lamp bulb should
be frosted* to reduce the glare of the visible portion of the lamp
* Lamps so treated are said to be bowl-frosted.
154
ELECTRIC LIGHTING.
filament. This is quite necessary when brilliant tungsten lamps
are used, and it is advisable even when the lamps with their open
shades are hung near the ceiling of any ordinary room because
it is impossible in an ordinary room to place a lamp entirely
outside of the field of vision.
75. The prismatic glass reflector is a cone of clear glass with
vertical prismatic ribs on its outside surface. Its action may be
inside
outside
Fig. 95.
Fig. 96.
Fig. 97.
understood from Figs. 95, 96 and 97. Any ray like r, Fig. 95,
is turned backwards (and downwards) by total* reflection,
whereas such rays as 5 and t pass through the rounded edges of
the prisms and the rounded bottoms of the intervening grooves.
*When light in a dense medium like glass strikes the surface obliquely it is
totally reflected. This phenomenon is exemplified by the brilliant silvery appear-
ance of the surface of the water in a tumbler when the surface is viewed obliquely
from below.
LAMPS, LAMP SHADES AND REFLECTORS.
155
Fig. 96 is a top view of a prismatic reflector showing a section
of the reflector along the plane cd in Fig. 97. The small circle
at the center in Fig, 96 represents the lamp. The rays of light
from the lamp strike the faces of the prismatic ribs very obliquely
and are totally reflected downwards as shown in Fig. 97.
The open cone-shaped prismatic re-
flectors are not usually deep enough to
completely hide the lamp from view and
the lamp should therefore be bowl- ;
frosted to reduce the glare.
Another type of prismatic glass
shade has horizontal prismatic ribs
which act partly by refraction and
partly by reflection as shown in Fig.
98 in which the dotted lines represent
rays of light from the lamp. The faces
ab and cd are refracting faces and
the faces be are total reflecting faces. This type of prismatic
lamp shade was brought out in England in 1882 by Mr.
A. P. Trotter.* It is now manufactured in a variety of rather
ornamental forms by the HolopKane Company. These orna-
mental prismatic shades are usually made in the form of com-
plete spheres which enclose the lamp, and they eliminate glare
almost completely.
* A very interesting account of the development of this shade is given in Trotter's
Illumination, pages 263-274, Macmillan and Co., London, 191 1.
Fig. 98.
CHAPTER VI.
INTERIOR ILLUMINATION.
76. The illumination of a room.* — A room may be said to be
well lighted when the eye is easily able to distinguish the various
objects in the room in minute detail of perception. This com-
pleteness of visual perception depends upon three conditions:
namely, (a) a sufficient brightness of illumination, (b) a proper
location of the light sources so as to bring out that combination
of soft shadows which is so essential to the perception of form,
and (c) a proper composition! of the light so as to bring out
those physical differences in objects which the eye perceives as
variations of color.
(a) The necessity of having a sufficient intensity of illumina-
tion is, of course, known to everyone. The ability to perceive
fineness of detail (called visual acuity) depends chiefly upon
intensity of illumination.
Visual acuity is always measured in an arbitrary way, for example, one may
measure visual acuity as the distance from one's eye at which clear black print
of a chosen size may be read, and the dependence of visual acuity upon intensity
* An extremely interesting discussion of the conditions which determine visual
perception is given by Helmholtz in his popular lecture on The Relation of Optics
to Painting which is translated (by E. Atkinson) in the second series of Helmholtz's
Popular Lectures, Longmans, Green & Co., 1903. Everyone who is concerned with
the practical problems of illumination should read this lecture. Helmholtz's
Popular Lectures are published in German under the title Vortriige und Reden,
2 volumes, Braunschweig, Vieweg und Sohn, 1884.
Three lectures in Helmholtz's first series (translated by Dr. Pye-Smith; Long-
mans, Green & Co., 1873), On the Theory of Vision, also have a bearing upon the
important practical subject of illumination.
See also the lectures by Percy W. Cobb and by Robt. M. Yerkes, pages 525-604,
Vol. II, Johns Hopkins University Lectures on Illuminating Engineering, Baltimore,
1911.
t The composition of light refers to the relative intensities of the various wave-
lengths which are present in the light.
I56
. g,
2 g
INTERIOR ILLUMINATION. . 157
of illumination may be determined by finding the distance at which the given
type can be read for different intensities of illumination. In this way it is found
that visual acuity is very low when the intensity of illumination is one or two
tenths of a foot-candle. It increases rapidly up to one or two foot-candles and
then it increases slowly and reaches a maximum at about eight or ten foot-
candles.
(b) The importance of the second condition is illustrated
by Figs. 99, 100 and 101, which show a face illuminated in three
different ways. In Fig. 99 the face is illuminated by light
from a single concentrated source (an electric arc), without any
reflection from the walls of the room to soften the effect, and the
shadows are extremely harsh; in Fig. 100 the face is illuminated
by light from a broad source and largely from one side, and the
shadows are soft; in Fig. 101 the face is illuminated by light
coming equally from all directions and there are no shadows at all.
A room may be sufficiently illuminated by a single arc lamp
but such illumination is unsatisfactory, even when the eye is
shaded from the direct light of the lamp, because the excessive
harshness of the shadows renders the perception of form almost
impossible. The light from a single brilliant lamp is always
softened, however, by the reflection from the walls and ceiling
of a room.
The vsecond condition is not important where purely flat-
surface vision is required as in a draughting room, where indeed
it is important to eliminate all shadows on the sheet of drawing
paper.
(c) The importance of the third condition is evident when one
attempts to distinguish delicate colors by ordinary lamp light.
Thus the light of an ordinary kerosene lamp is very deficient
in the short wave-lengths (blue and violet), and a deep blue or
violet piece of cloth appears almost black by kerosene lamp light,
False color values are produced in a very striking way by the
light from a mercury- vapor lamp on account of the almost
complete absence of the longer wave-lengths (red) in the light
from this lamp. The most striking illustration of false color
values, however, may be obtained by illuminating a batch of
158 . ELECTRIC LIGHTING.
brilliantly colored worsteds by the light from a sodium flame in
a room from which all white light is excluded. All differences of
tint disappear under these conditions, and a given piece of
worsted merely appears to be light or dark according as it is able
or unable to reflect the yellow light of the sodium flame.
The carbon-arc lamp gives a nearer approach to daylight than
any other commercial form of lamp.* The whiteness of the light
from the carbon-arc lamp is spoiled, however, by the excess of
violet light from the arc stream and by the excess of red and
orange light from the moderately heated parts of the carbons.
These defects are corrected to some extent in the intensified
carbon-arc lamp which burns with a short arc thus reducing the
violet light, and small carbons are used thus reducing the mod-
erately heated areas near the ends of the carbons.
77. Glare. — The presence of excessively brilliant lamps or
excessively brilliant patches of light in a field of vision greatly
hinders visual perception. The eye adapts itself automatically
to the brightest lights in the field of view, and all perception of
detail in the shadows is lost. This effect is called glare, and it is
especially marked when the field of vision includes a bright
unshaded lamp.
The explanation of glare is as follows: In the first place a
beam of light entering the eye from a bright source illuminates
the whole interior of the eye just as a beam of sunlight entering
a window illuminates a room. This diffused light in the eye
illuminates and excites the entire retina, including those portions
where the images of the deeper shadows fall, and thereby tends
to obliterate all detail of perception. In the second place the
portions of the retina upon which the brilliant light falls become
greatly reduced in sensitiveness by fatigue, the continual wander-
ing of the eye brings the image of a dark region upon this fatigued
* The Moore vacuum-tube lamp (with carbon dioxide) is better than the carbon-
arc lamp. The use of bluish glass for absorbing the excess of red and yellow
light from a tungsten or carbon-arc lamp is briefly discussed in the General Electric
Review for December 1911.
INTERIOR ILLUMINATION. 159
portion of the retina, and the result is almost total blindness like
that produced when one looks out of a window and then turns
towards a dark corner of a room. In the third place the pupils
of the eyes contract greatly when there is a bright light in the field
of vision, and this contraction lessens the effective brightness
not only of the bright portions of the field, but also of the deep
shadows; but the deep shadows are already insufficiently illu-
minated and the contraction of the pupils of the eyes tends to
make them (the shadows) appear like black patches entirely
devoid of detail.
An interesting case of excessive contrast or glare is that
in which a workman at a loom, for example, has his immediate
work illuminated to a fair degree of brightness while the remainder
of the room is left in darkness. If the workman could keep his
eyes upon his work incessantly, it is conceivable that this kind
of illumination might be satisfactory; but the eye moves about
in spite of everything one can do, and, under the assumed condi-
tions, the workman would be unable to see when he glanced
about the room and he would be blinded when he glanced back
at his work. To avoid this impracticable situation a general
illumination of the room is necessary. If a brilliant light is
needed upon one's work, the whole room must be fairly well
lighted, and the necessary local illumination must be produced
in addition thereto.
It is very important, in arranging for the illumination of a
room, to place the lamps outside of the field of vision if possible,
so that no light can enter the eye directly from the lamps and render
the eye insensible to the delicate shading of surrounding objects.
The excessive discomfort that is produced by the glare of im-
properly located lamps, such, for example, as the exposed foot-
lights of a poorly arranged stage, is due not only to the physical
pain that is associated with long-continued looking at a bright
light but more especially to the incessant effort of trying to peer
into the dark region beyond.
When a lamp cannot be removed from the field of vision the
160 ELECTRIC LIGHTING.
bad effects of glare may be greatly reduced by enlarging the lumin-
ous surface of the lamp by means of a translucent globe or shade.
78. Small lamps versus large lamps. — A small lamp, as the
term is here used, is a lamp which gives a small amount of light;
and a large lamp is a lamp which gives a large amount of light.
A given amount of light can be produced more cheaply by large
lamps than by small lamps because large lamps are, as a rule,
more efficient (less watts per lumen) than small lamps and be-
cause a few large lamps are cheaper to install and cheaper to
maintain than many small lamps. The use of large brilliant
lamps is, however, limited by two conditions as follows:
(a) Satisfactory distribution of light. — Whenever it is necessary
to use a large number of lamps in order to get a satisfactory
distribution of light, small lamps are used because to use large
lamps would give an unnecessarily large quantity of light. It
is not desirable, however, to have light too uniformly distributed
(by using a great number of small lamps) because the resulting
illumination is flat, that is, devoid of satisfactory shadows.
(6) Elimination of glare. — A large lamp an one's field of vision
produces a much more unpleasant glare than a small lamp, and
therefore (even if a proper distribution could be secured) it is
not advisable to use large lamps in rooms with low ceilings be-
cause with a low ceiling a lamp cannot be placed high enough to
remove it entirely from one's field of vision. Large lamps must
be placed high overhead. This is especially true of lamps which
have a high intrinsic brilliancy; such lamps must not be placed
in the field of vision unless they are shaded.
When the indirect system of lighting is employed, however,
very large brilliant lamps can be used in small rooms.
79. The indirect system of lighting.* — A favorite, although
somewhat extravagant, system of illumination is to place the
* A good discussion of indirect lighting is given by L. B. Marks, Johns Hopkins
University Lectures on Ilhiminating Engineering, Vol. II, pages 691-702, Baltimore,
1911. See also an article by J. R. Cravath, Transactions of the Illuminating En-
gineering Society, Vol. IV, pages 290-306, 1909.
INTERIOR ILLUMINATION.
i6r
famps entirely out of sight, and so that the light from the lamps
may fall upon the ceiling of the room. Thus Fig. 102 shows the
essential features of such an arrangement. The lamps are placed
ceiling
wall
Fig. 102.
in a cove within a few feet of
the ceiling and are hidden from
view by a high moulding as in-
dicated in the figure.
The indirect system of illum-
ination gives an extremely
diffused light which is itself
beautiful and pleasing, but it
does not give the shadows
which are essential for the vis-
ual perception of form. This
system is satisfactory for auditoriums and draughting rooms,
but it is not satisfactory where the perception of form is of great
importance. It should never be used where the walls and ceiling
are liable to become even slightly discolored by dust or smoke.
A modification of the indirect system of lighting is to place
arc lamps or verv high-candle-power tungsten lamps with re-
flectors to throw the light
upwards against the ceil-
ing or against a white dif-
fusing surface. Thus Fig.
103 shows an arc lamp with
an opal reflector for throw-
ing the light upwards
against a corrugated dif-
fuser having a white enamel
surface. This type of
lamp and diffuser is now
practically obsolete; it is,
like every other device for indirect lighting, too wasteful.
80. Influence of absorption on illumination. — Everyone is
familiar with the fact that more lamps are required to illuminate
12
Fig. 103.
162 ELECTRIC LIGHTING.
a room with dark walls than are required to illuminate a similar
room with light walls. This is because the useful light in a room
comes, not only directly from the lamps, but is also reflected
from the walls and objects in the room to the object which is in
the field of vision. Indeed, if all the illuminated surfaces in a
room could be made to reflect all the light which falls upon them,
then the degree of illumination of the room would increase
steadily after the turning on of a lamp; and the ultimate degree
of illumination would be infinitely great. The walls and objects
in a room, however, always absorb light, and after a lamp is
turned on the intensity of illumination in a room increases quickly
(almost instantaneously) until the rate of absorption of light by the
illuminated surfaces is equal to the rate of emission of light by
the lamp.
A given surface absorbs a definite fractional part of the light
which falls upon it and this fraction is called the coefficient of
absorption of the surface. Thus a surface which absorbs 0.4
of the light which falls upon it has a coefficient of absorption
equal to 0.4.
Let / be the average intensity of illumination of the walls and
objects in a room in foot-candles (lumens per square foot), let
A be the area in square feet of the walls and objects in the room,
and let k be the average coefficient of absorption of the illu-
minated surfaces. Then A I is the number of lumens of light
falling upon the illuminated surfaces and kAI is the number of
lumens absorbed. That is to say, the amount of light which is
being continually absorbed is kAI lumens, and this must be
equal to the total amount of light L (in lumens) which is being
emitted by the lamps. Therefore we must have:
L = kAI (20)
Example I— Consider one room B which is twice as long,
twice as wide and twice as high as another room A, the character
of all surfaces being the same in both rooms, and the furniture
area being four times as great in the larger room. Under these
INTERIOR ILLUMINATION. 163
conditions the total absorption area is four times as great in the
larger room, and, since the coefficient of absorption is assumed to
be the same, it will take exactly four times as much light to
illuminate the larger room to the same intensity as the smaller
room. The amount of light required to illuminate a room to a
given intensity of illumination is proportional to the total area of
the illuminated surfaces, the coefficient of absorption being given.
Example 2. — According to equation (20) the amount of light
required to illuminate a room to a given intensity of illumination
is proportional to the absorption coefficient (average) of the
illuminated surfaces in the room. Thus ten lamps give a desired
intensity of illumination in a given room when the walls are dark
and have a coefficient of absorption equal to 0.80. The same
intensity of illumination (average) will be produced in the room
by one half as many lamps if the walls are given a light finish of
which the coefficient of absorption is 0.40.
Example j. — A room is 15 feet wide, 20 feet long and 12 feet
high. The floor has an area of 300 square feet and the effect of
furniture is to add, .say, 150 square feet to this amount making a
total area of 450 square feet of floor and furniture. The average
coefficient of absorption of floor and furniture is 0.88. The
coefficient of absorption of the ceiling and walls of the room is
0.40. Required, the number of lumens to give an average in-
tensity of illumination in the room of one foot-candle (one lumen
per square foot).
The average coefficient of absorption of the illuminated surfaces
in the room is found approximately as follows:
450 square feet X 0.88 = 396
1,140 square feet X 0.40 = 456
Sum total = 852
Dividing this sum total by the entire area of the exposed surfaces
in the room (1,590 square feet) we have 0.54 as the average value
of k. Therefore, substituting in equation (20) A = 1,590,
164
ELECTRIC LIGHTING.
k — 0.54 and / = i.o, we find L = 852 lumens or 67.7
spherical-candles.
The method of calculating the average coefficient of absorption
of the illuminated surfaces of a room as shown in this example is
not strictly correct,* but the result of the above calculation is
sufficiently exact for most practical purposes.
81. Calculation of light flux (lumens) required to illuminate
a room. — In planning for the illumination of a room equation
(20) might be used as in example 3 of Art. 80, but in practice the
following method is used.
INTENSITIES OF ILLUMINATION RECOMMENDED FOR VARIOUS
CLASSES OF SERVICE.
(Foot-candles.)
Auditorium or ball room 2.0
Cafe 2.5
Car, passenger 2.0
Car, mail 7.0
Church 2.0
Desk 4.0
Draughting and engraving 7.0
Factory and shop
(a) General illumination 1.5
(6) Bench and machine-tool illu-
mination, local, in addition
to a 4.0 to 5.0
(c) General illumination to take
the place of a and b 3.0 to 5.0
Garage 2.0
Library
Stack room 1.5
Reading room when local desk
illumination is not supplied in
addition 3.5
Reading room when local desk
illumination is supplied in ad-
dition 0.7
Office . . 4-0
Stores
Art 4.0
Baker 3.0
Book 3.5
Butcher 3.5
China 2.5
Cigar « 3.0
Clothing 5.0
Cloak & Suit 5.0
Confectionery 3.0
Decorator 3.0
Department (see each depart-
ment).
Drug 3.0
Dry goods 4.0
Florist 3.0
Furniture 5.0
Furrier 5.0
Grocery 3.0
Haberdasher 3.5
Hardware 4.5
Hat 4-0
Jewelry 3.5
Lace 3.0
* The correct expression for the total amount of light absorbed is S£7 -AA,
where AA is an element of surface, k is its coefficient of absorption, and / is the
intensity of illumination at AA. Therefore Z,=S£/-AA; but this formula would
lead to extremely tedious calculations even if all the necessary data were known.
INTERIOR ILLUMINATION.
165
Leather 3.5
Meat 3.5
Men's furnishings 3.5
Millinery 4.0
Music 3.0
Notions 3.0
Piano 4.0
Post cards 3.0
Show 3.5
Stationery 3.5
Tailor 4.0
Tobacco 3.0
Street
Business streets ( in addition to
light from show windows and
signs) 0.5
Residence streets o.i
Prominent streets in residence
districts 0.2
Country roads 0.05
Theater
Lobby 3.0
Auditorium . . .2.0
Reading (book print) 2.0
Reading (newspaper print) 2.5
Residence
Porch ^ 0.2
Porch (reading light) i.o
Hall (entrance) 0.7
Reception room 1.5
Parlor 1.5
Sitting room 1.5
Library 2.0
Music room 2.0
Dining room 1.5
Pantry 2.0
Kitchen 2.0
Laundry 1.5
Hall (upstairs) 0.5
Bed room 1.5
Bath room 2.0
Furnace room 0.7
Store room 0.7
School room 2.5
Shop (see factory).
Show window
Light goods 8.0
Medium goods 16.0
Dark goods 20.0
Sign 8.0
Stable i.o
(a) It is assumed that the surface to be illuminated is a plane
at a height of 30 inches above the floor. This plane is called the
working plane, and the problem is to determine the number of
lamps required to give a specified average degree of illumination
on this plane. The intensities of illumination required for various
kinds of service as found from practice are given in the accom-
panying table. Multiply the desired intensity of illumination in
foot-candles (lumens per square foot) by the area of the working
p'ane in square feet to get the required light flux in lumens.
(b) A certain fraction, only, of the light emitted by a lamp
reaches the working plane and the accompanying table gives
the values of this fraction under various conditions. Divide the
total lumens required on the working plane by this fraction to get
the lumens delivered by the lamps.
1 66
ELECTRIC LIGHTING.
(c) Glow lamps are always rated in mean horizontal candle-
power, and to find the total lumens delivered by a given lamp
one must know the factor by which mean horizontal candle-
power must be multiplied to give mean spherical candle-power.
The following table, however, gives the rating in lumens of the
present regular types of lamps. Divide the total lumens to be
delivered by the lamps by the rating of the chosen type of lamp in
lumens to get the number of lamps.
PERCENTAGE OF LIGHT DELIVERED TO THE WORKING PLANE BY
INCANDESCENT LAMPS.*
(When globes and reflectors are clean.}
Equipment of Lamp.
Ceiling.
Walls.
Percentage.
Clear holophane reflector
light
light
"?7
Clear holophane reflector
light
dark
4C
Clear holophane reflector
dark
dark
og
No shade or reflector
light
light
on
No shade or reflector
light
dark
2*1
Opal reflector
light
light
co
Opal reflector
light
dark
41
See pages 147 and 148 for data concerning arc lamps.
Example. — It is proposed to install electric lights in a men's
furnishing store 80 feet long, 25 feet wide and 12^ feet high.
The ceiling is light, but the walls are covered with shelves con-
taining dark goods, and therefore the walls cannot be counted
on to reflect much light.
Referring to the table we find that an illumination of about
3.5 foot-candles is usual in stores of this kind, but the store under
consideration is not in a metropolitan district where comparisons
would be made, and therefore 3.0 foot-candles may be taken as a
sufficient degree of illumination.
The chosen degree of illumination of 3.0 foot-candles (or
3 lumens per square foot) is to be produced over the "working
* From the publications of the Holophane Company. The percentage is less
for a tungsten lamp than for a carbon-filament lamp especially when the lamps
are bare. The table refers primarily to tungsten lamps and the values may be
used for carbon lamps without serious error.
INTERIOR ILLUMINATION.
I67
plane" which contains 2,000 square feet. Therefore 6,000
lumens of light are required on the working plane.
TOTAL LUMENS GIVEN BY REGULAR TYPE LAMPS.*
This table gives the total light emitted by regular type lamps when operated at
"top efficiency." Light is expressed in lumens. For ratings of arc lamps (in
downward lumens) see pages 147 and 148.
Rated
Watts.
Tungsten.
Tantalum.
Metallized
Carbon.
Carbon.
100-130
Volts.
200-260
Volts.
100—130
Volts.
200-260
Volts.
100-130
Volts.
100-130
Volts.
200-260
Volts.
IO
21
IS
no
2O
150
50
25
185
125
84
30
105
96
35
84
40
320
300
220
160
So
275
250
205
175
60
5OO
455
250
210
170
80
445
4OO
335
100
830
760
420
350
120
420
340
125
525
ISO
1,250
i,i37
187.5
785
250
2,I7O
i,895
1,050
40of
3,520
Soof
4,400
4,030
It is intended to use tungsten lamps with holophane reflectors,
and according to the above table such lamps so equipped deliver
45 per cent, of their light to the working plane in a room with
light ceiling and dark walls. Therefore the total amount of
light to be delivered by the lamps is 13,333 lumens.
Dividing the total lumens by the rating of the various sizes
of tungsten lamps as given in the above table, we find that the
required average degree of illumination of the working plane
would be produced by any of the following:
* This table is taken from the publications of the General Electric Company
and it is standard at this date, April i, 1912. The table is reissued by the company
whenever changes are made in the ratings of regular lamps.
t Round bulb lamps; all other lamps in the table have regular type bulbs.
1 68 ELECTRIC LIGHTING.
seventy-two 25-watt tungsten lamps,
forty-two 4O-watt tungsten lamps,
twenty-seven 6o-watt tungsten lamps,
sixteen loo-watt tungsten lamps,
eleven 150- watt tungsten lamps,
six 25O-watt tungsten lamps,
or three 5oo-watt tungsten lamps,
The choice of size of lamp is considered in the following article,
where this example is carried to a conclusion.
82. The choice of size of lamps. — Economy in first cost and
economy in operation leads one to choose the largest size lamps
that can be used in a given room, and the limit of size is deter-
mined by the necessity of producing a fairly uniform illumination
of the working plane. In general the higher the ceiling the larger
the lamps that can be used to give satisfactory illumination.
The following rules relating to spacing and heights of lamps serve
as a basis for choice of size of lamps. These rules have been
formulated by the engineers of the Holophane Company.
Rule a. — In narrow stores a single row of lamps may be used.
In this case the lamps should be equipped with extensive re-
flectors, the height H of the lamps above the working plane
should be from four tenths to five tenths of the width of the
room, and the distance apart s of the lamps should not exceed
two times their height above the working plane.
Rule b. — In large rooms with unusually high ceilings, divide
the space as nearly as possible into equal squares, place a lamp
,at the center of each square, use focusing reflectors, and make
fthei height of lamps above the working plane equal to about one
.and one. third 'times their distance apart.
Rule c. — in large rooms .with ordinary ceiling heights or in
stores in which it is intended to use two or more rows of lamps,
place lamps according to rule &, but use intensive reflectors and
make the height of lamps above the working plane equal tp
four fifths pf their distance apart.
INTERIOR ILLUMINATION.
169
Where architectural restrictions make it impossible to follow
this rule, the height of lamps above the working plane may be
varied from 0.66 to i.o times their distance apart without
seriously affecting the uniformity of illumination on the working
plane.
Rule d. — Where outlets are located too far apart for rule c,
or where it is found impracticable to supply as many outlets
as rule c requires, divide the room into approximately equal
squares, place a lamp at the center of each square, use extensive
reflectors and make the height of the lamps above the working
plane approximately one half their distance apart.
Example. — The example given in Art. 81 may now be carried
to a conclusion. The given room is I2j^ feet high, and the
working plane is 2^/2 feet above the floor. It does not look well
to place lamps close up against the ceiling; therefore let the
lamps be placed one foot below the ceiling. This gives a height
of 9 feet (= H) above the working plane. The lamps with
the chosen type of reflectors (intensive reflectors) should there-
fore be II feet apart (= s = 5/4 #). Consequently the room
should be divided into squares approximately 1 1 feet X 1 1 feet.
< 80- feet >-
4
"V
4 4
i
4
4 I -0-
i
4
f
1
i
or
4
r
4
i
4
<i> i 4.
i
1
1
1
n
Fig. 104.
Therefore the room may be divided into 16 squares as shown
Fig. 104 each square being 10 feet X I2j^ feet, and the
^desired quantity of light would be produced by placing a 100-
-watt tungsten lamp at the center of each square (see Art. 81),
or the room may be divided into 12 squares each 13.3 feet X I2j^
ieet _and the ^desired quantity of light would ,be produced by
170 ELECTRIC LIGHTING.
placing a 150- watt tungsten lamp at the center of each square.
The sixteen loo-watt lamps would give a slightly more satis-
factory illumination, but the twelve 150- watt lamps would
be slightly cheaper to install. Either arrangement would be
satisfactory.
CHAPTER VII.
•
STREET LIGHTING.
83. Detail vision and block vision. — Every one knows that
to see the fine details of an object one must look directly at
the object. Let the reader fix his eyes on this single letter A
and consider how narrow his field of acute vision really is; it
is scarcely possible to recognize any of the surrounding letters
while looking directly at A. Everyone knows also how quickly
one sees, for example, a hand which is moved up along side of
one's head from behind, although one may have to turn and
look directly at the hand before one recognizes that it is a hand.
That kind of vision where one looks directly at an object
and sees minute detail may be called detail vision, and that
kind of vision where one sees things without minute detail
may be called block vision. Detail vision requires strong illu-
mination and the field of detail vision is very narrow. Block
vision does not require strong illumination and the field of
block vision is very wide. In fact block vision is very good when
the intensity of illumination is 0.02 of a foot-candle, which is the
intensity of illumination in full moon light. An important char-
acteristic of block vision in very dim light is that the eye must
be kept in the dark; after a momentary exposure of the eye to
bright light one can scarcely see at all in very dim light, and the
blinding effect of the bright light lasts for five minutes or more.
Block vision in very dim light is sometimes called twilight vision.
Two kinds of organs are recognized in the retina of the eye, namely, the rods
which are distributed over the whole retina except a small central spot which is
called the fovea, and the cones which are crowded together in great numbers in the
fovea and which are distributed rather sparsely over the remainder of the retina.
To see the fine details of an object the image of the object must fall on the fovea,
The fovea is used for detail vision and the remainder of the retina is used for block
vision; or the cones are used for detail vision and the rods are used for block vision.*
* This statement is perhaps not strictly correct. An interesting discussion of
vision, including color vision, is given by Percy W. Cobb on pages 525-574. Vol. II,
Johns Hopkins University Lectures on Illuminating Engineering, Baltimore, 1911.
I/I
172 ELECTRIC LIGHTING.
Therefore detail vision is sometimes called cone vision, and block vision is some-
times called rod vision.
84. Intensity of illumination required for street illumination.*
— The intensity of illumination required for interior lighting
varies from one to five or six foot-candles (see table on page 164),
and this brilliant illumination is required because it is detail
vision that must be provided for; furthermore the perception of
colors requires brilliant illumination, in very dim light all color
differences disappear. It is out of the question to provide street
illumination sufficiently bright to give complete detail vision
and color vision, the cost would be prohibitive.
It is customary in the discussion of street lighting to specify
intensity of illumination normal to beam. This quantity is repre-
sented by the symbol In; see Art. 52. Furthermore, an intensity
of, say, 0.05 foot-candle of normal illumination at a point mid-
way between two street lamps is understood to mean 0.05 due
to each lamp. The intensities of illumination actually used for
street lighting range from o.oi foot-candle (average) to o.i foot-
candle (average) in well lighted cities, as follows:
(a) Streets where the night traffic is heavy require good
illumination, as do also certain streets where criminal disturbances
are likely to occur. For such streets a minimum of 0.05 foot-
candle (normal to the beam) and an average of o.i foot-candle
is quite satisfactory.
(b) Ordinary residence streets and streets where the night
traffic is light are satisfactorily lighted if an average of 0.05
foot-candle with a minimum of 0.025 foot-candle (normal to
beam) is provided. Streets so lighted are as bright as full
moonlight at the darkest places.
(c) Streets where the houses are scattering and where there
is very little night traffic are satisfactorily lighted when a mini-
mum of o.oi foot-candle (normal to beam) is provided, and the
* A very good discussion of this matter is given by Louis Bell on pages 795-837-
Vol. II, Johns Hopkins University Lectures. on. Illuminating, Engineering, Baltimore,
.1911.
STREET LIGHTING. 173
effectiveness of this dim illumination is very greatly increased
by placing the lamps (small lamps, of course) high overhead so
as to avoid local regipns of intense illumination which tend to
destroy the extreme sensitiveness of the eye in very dim light
as stated in Art. 83.
A condition which favors vision on a street at night is as
follows: When one is at a dimly lighted part of the street one
sees a dark object on the street projected against the brightly
illuminated field near a distant lamp.
85. Arc lamps for street lighting. — Everyone is familiar with
the street arc lamp. In the earlier days this was an open carbon-
arc lamp operated by direct-current from a Brush or Thomson-
Houston generator. Later the enclosed carbon-arc lamp was
extensively used for street lighting, and in some cases these
carbon-arc lamps (open and enclosed) were operated by alternat-
ing current. In new installations magnetite-arc lamps are most
extensively used, and the long-burning flame-arc lamp (the
enclosed flame-arc lamp) and the quartz tube mercury-vapor
lamp are coming into use.
Arc lamps are suitable only for streets which are to be brightly
lighted, and for ordinary first class street illumination (minimum
0.05 foot-candle, average o.i foot-candle normal to beam) the
4-ampere magnetite-arc . lamp is perhaps the most economical.
Very high candle-power lamps are wasteful for street lighting
(unless very brilliant illumination is desired) even when they are
placed very high above the street, because the diameter of the
circular field illuminated by such a lamp is usually three or four
or five times the width of the street.
A street with many trees cannot be properly lighted by arc
lamps at a reasonable cost; such streets should be lighted by
many small lamps (tungsten lamps).
A street lamp should give the greater part of its light in a
direction slightly below the horizontal. Thus the magnetite-arc
lamp (curves 3 and 4, Fig. 94 a) and the vertical-carbon long-
174
ELECTRIC LIGHTING.
burning flame-arc lamp (curve 7, Fig. 94 b) are well adapted to
street lighting.
Arc lamps are not, as a rule, hung sufficiently high on the
streets of American cities, the usual practice being to hang the
4-ampere magnetite-arc lamp 20 or 25 feet above the street and
the 6.6-ampere magnetite-arc lamp 25 or 30 feet above the street.
0.6
A — A
0-4
\
7
Fig. 105.
The ordinates of the curves 3, 4, and 7 in Fig. 105 show the
values of Jn (intensity of illumination normal to beam) at various
horizontal distances along a street from the various lamps, the
heights of the lamps above the street being 30 feet, 40 feet,
and 50 feet respectively, as represented by the small crosses in
the figure. The values of In are reckoned at the surface of
the street. The inclined-carbon flame-arc lamp is not adapted
to ordinary street lighting.
The accompanying table gives the values of In at points on a
street distant x feet horizontally from the various kinds of lamps,
the height of the lamp in each case being 50 feet.
STREET LIGHTING.
175
S
Q
£
<C
V
£ «
2 -2
a I S
o -SI
^ « b
t> 5
d :?
^
ro
3
vl
8
8
8
8
d
d
d
d
N
Tf
2i
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10
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t^-
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d
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Type of Lamp.
fl • a
60 n 00
d 9- d
•J-1
s 2 a
d *J d
;te-arc lamp .
[ined-carbon
ame-arc lamp
tical-carbon
ame-arc lamp
* *^j 1
-M O
f^« VH
^3
4 o
£
>
c^l^
19 «•.«'«.
I76
ELECTRIC LIGHTING.
By making use of the law of inverse squares (Art. 48) it Is
easy to use this table to find the intensity of illumination (normal
to beam) at a point on the street at any given distance d hori-
zontally from any one of the lamps placed at any given height H
above the street. The rule is as follows: Find from the table the
value of Jtt for the lamp 50 feet high and for x — d X 5O/ Ht and
multiply the value of /n so found by (5O/ H)z.
Fig. 106.
Also the table can be used to find the horizontal distance d
from a lamp ( H feet above the street) to the point on the street
where the normal illumination has a prescribed value. The rule
is as follows: Multiply the prescribed normal illumination by
( H/$o)2 to get In as per table, find the corresponding value of x
from the table and multiply this value of x by (H/^o) to get the
desired value of d.
86. Glow lamps for street lighting. — The great advantage of
glow lamps for street lighting is that a fairly uniform distribution
of light along a street can be produced much cheaper by small
lamps than by large lamps. Tungsten lamps, for example,
equipped with suitable reflectors (see below) and properly spaced
along a street give an illumination which is entirely satis-
STREET LIGHTING.
177
factory for residence and suburban districts, and the cost is
less perhaps than any other kind of street
lighting. ^ ^
Figure 106 shows a common form of sus-
pension fixture and reflector for a tungsten
street lamp. The reflector is made of sheet
metal with a white enamel surface, and it has
radial flutings. Figure 107 shows an ornamental
street lighting cluster of tungsten lamps mounted
on top of a post and equipped with holophane
street reflectors.
The dotted curve in Fig. 108 shows the dis-
tribution of candle-power around a 4O-candle-
power tungsten lamp without a shade, and the full-line curve
shows the distribution of candle-power of the same lamp
equipped as shown in Fig. 106.
Fig. 107.
Fig. 108.
For sidewalk lighting 32-candle-power or 4O-candle-power
tungsten lamps are usually employed and hung 10 or 12 feet
above the walk. For street lighting larger tungsten lamps are
'3
178
ELECTRIC LIGHTING.
used and they are hung over the middle of the street at heights
of from 1 8 to 24 feet above the street.
surface of street
k
Fig. 109.
NORMAL ILLUMINATION IN FOOT-CANDLES DUE TO 40-CANDLE-
POWER TUNGSTEN LAMP * WITH RADIAL REFLECTOR AS
SHOWN IN FIG. 106 OR 108.
Height of Lamp H.
10 Feet.
12 Feet.
15 Feet.
18 Feet.
0
0.260
O.lSl
O.II5
0.0803
.60 5
0.288
O.2OI
O.I27
0.0860
<u +* IO
O.222
0.174
0.123
0.0884
to 4J 15
0.146
0.125
0.0985
0.0774
^ C 20
0.098
0.0882
0.0744
O.O622
<uX 25
O.O688
0.0637
0.0565
0.0496
c o^ 35
0.0383
0.0368
0.0342
0.0316
S w 5°
0.0196
0.0193
O.OI85
0.0177
3 75
0.00856
O.OO875
O.OO872
0.00858
100
0.00466
0.00483
0.00489
O.OO492
From this table the normal illumination at any point on a
street produced by a tungsten lamp of any candle-power C
(equipped like Fig. 106) can be found by multiplying the tabu-
lated value of In by C/4O.
If it is desired to find the intensity of illumination (normal)
produced at a distance d horizontally from a lamp hung //
* This table refers specifically to the special low-voltage tungsten lamp which
is described on page 143 and shown in Fig. 93. the lamp being equipped with a
"radial wave " reflector as shown in Fig. 106.
STREET LIGHTING. 179
feet above the street, the method used in Art. 85 can be em-
ployed as shown by the following examples:
Example I . — What«is the normal illumination at a point on the
street distant 150 feet from a 2OO-candle-power lamp like Fig. 106,
the lamp being 24 feet above the street. Divide the given
distance (150 feet) and the given height (24 feet) by some factor
b to give a height, say, of 12 feet which appears in the table.
In this case b = 2. Find In from the table for this reduced
distance (75 feet) and reduced height (12 feet), and divide the
value of In so found by b2. This gives the normal illumination
which would be produced by a 4O-candle-power lamp at a
distance of 150 feet, the height of the lamp being 24 feet; and
if we multiply this by 200/40 we have the desired result, namely,
0.0109 foot-candle.
Example 2. — How far apart must 2oo-candle-power tungsten
lamps (like Fig. 1 06) hung 24 feet above the street be placed to
give a minimum of 0.025 foot-candle (normal) at a point on the
street midway between two lamps. Let 2d be the desired
spacing, then the problem is to find the distance d from a 200-
candle-power tungsten lamp for which the normal illumination
due to the lamp is 0.025 foot-candle. Divide the specified height
(24 feet) and the distance d by a factor b which will reduce the
height to say 12 feet which appears in the table. In this case
the value of b is 2. Multiply the desired illumination, 0.025, by
40/200 to get the illumination which would be given by a 40-
candle-power lamp. Multiply this result by b2 (=4) to get the
illumination (0.020) corresponding to reduced height (12 feet)
and reduced distance (dJ2\. Find the value of x from the
table corresponding to a height of 12 feet and an illumination of
0.02. This value of x (which is found to be a little less than
50 feet) is equal to d/2. Therefore the desired spacing (2d) is
a little less than 200 feet.
87. Systems of street lighting. — The kinds of lamps used for
street lighting are mentioned in Arts. 85 and 86. It remains
i8o
ELECTRIC LIGHTING.
to discuss the methods of connecting the lamps in groups and
the mode of delivery of current to the groups of lamps.
Single arc lamps are always connected across constant-voltage
supply mains. Such lamps are called multiple lamps as stated
in Art. 71. Multiple lamps are seldom used for street lighting.
suspension
A C arc lamps in series
constant current
A C supply
constant voltage
Fig. 110.
When a great number of arc lamps are used in one installation,
the lamps are always designed to be operated in series; and a
group of lamps in series must be operated by a constant current.
In the early days of electric street lighting the constant current
for operating arc lamps in series was supplied by a "constant-
current" generator of the direct-current type, but this arrange-
ment is now obsolete. New arc-lamp street lighting installations
are now series magnetite-arc lamps operated by constant direct
current derived from a constant-voltage alternating source by
means of the constant-current transformer and the mercury vapor
rectifier. Flame-arc lamps can be operated by direct current
and these lamps (if they have the proper current rating) can be
operated in series with magnetite-arc lamps. A large group of
flame-arc lamps would be most conveniently operated by a con-
stant alternating current derived from a constant- voltage supply
by means of the constant-current transformer.
Figure no shows the scheme for supplying a group of series
arc lamps with constant alternating current derived from a
constant-voltage supply. The lamps used in this case cannot be
magnetite-arc lamps because such lamps cannot be operated
by alternating current. Figure in shows the scheme for supply-
STREET LIGHTING.
181
ing a group of series arc lamps with constant direct current
derived from a constant- voltage alternator. The lamps used in
this case may be magnetite-arc lamps or flame-arc lamps or
both. A general view of a constant-current transformer is
shown in Fig. 112. This transformer has a movable secondary
coil which is delicately counterpoised. When one or more lamps
are taken out of service (by short-circuiting, or by-pass switches)
the tendency is for the current to increase but this tendency is
counteracted by the movement of the secondary coil.
constant- current transformer
D C arc lamps in series
mercury- vapor
rectifier
constant current
Fig. Ill
Glow lamps for street lighting are sometimes connected in
parallel to constant-voltage supply mains in the same way that
house lamps are usually connected. In fact this arrangement is
always used when a very few glow lamps are used at widely sepa-
rated parts of a town or city. The lamps are connected across
the low-voltage terminals of a transformer which supplies the
neighboring houses.
When many glow lamps are used on the streets of a town or
city the lamps are always connected in series, and two different
schemes are employed to supply current to such series groups of
lamps as follows:
1 82
ELECTRIC LIGHTING.
(a) The series group may be connected directly to the constant-
voltage bus bars in the station. Thus twenty no-volt lamps
may be connected in series to a 2,2OO-volt supply. In this case
provision must be made to place an auxiliary lamp in circuit when
one of the service lamps breaks, as explained in connection with
Figs. 1 8 and 19 in Chapter II.
Fig. 112.
(b) Each series group of lamps may be supplied with a constant
alternating current derived from a constant-voltage source by
means of a constant-current transformer exactly as in the case of
a series group of alternating-current arc lamps as represented in
Fig. 1 10. In this case provision must be made to close a by-pass
around a lamp which burns out or is broken. This is accom-
plished exactly as explained in connection with Figs. 18 and 19
in Chapter II, except that no auxiliary lamp is used.
Operation of lamps of different current ratings in a series circuit
using alternating current. — Given a series group of arc lamps
STREET LIGHTING. 183
operated by, say, 12 amperes alternating current. A series group
of lamps of any current rating may be operated in conjunction
with the given group by connecting as shown in Fig. 113. A
constant -current glow lamp circuit
tratt*former
-X
constant-current arc lamp circuit
transformer* connected as shown in Fig. 113 gives a secondary
current which is equal to Z'/Z" times the primary current, where
Z' and Z" are the numbers of turns of wire in primary and1
secondary coils respectively.
Increased cost of power due to the use of constant-current trans-
former and rectifier. — A slight addition to the cost of power is
involved in the use of the constant-current transformer and
rectifier on account of the interest on the cost of the transformer
and rectifier, depreciation of non-renewable parts, cost of renewals
of rectifier bulbs, and loss of energy in transformer and rectifier. f
*It is distinctly misleading to call this transformer a " series " transformer.
It is simply an ordinary transformer.
t See Bulletin No. 51 of the Illinois Engineering Experiment Station (Bryant
and Hake), pages 46-47.
CHAPTER VIII.
ELECTROLYSIS AND BATTERIES.
88. Electrolysis.* — Two sheets of copper A and C, Fig. 114,
dipping into a solution of copper sulphate are connected to direct-
current supply mains as shown and the flow of electric current is
indicated by the arrows. During the flow of current the copper
plate A is slowly dissolved and metallic copper is slowly de-
posited upon the plate C.
The slow dissolving of the plate A and the slow deposition of
metallic copper upon plate C are evidences of chemical action
at A and C. Chemical action thus produced by the electric
current is called electrolysis, the solution through which the
current flows is called an electrolyte, the arrangement VV is
* The methods of electroplating and electrotyping are described by Samuel Field
in Principles of Electrodeposition, Longmans, Green & Co., 1911. The most com-
plete discussion of this subject is Electrolytische Metallniederschldge, by W. Pfan-
hauser, Jr., Berlin, 1910. See also Handbuch der electrolytischen Metallniederschldge
by Georg Langbein, Leipzig, 1906.
The electrolytic refining of copper is a simple process of electroplating in which
pure copper is deposited out of a solution while the impurities are left in the solu-
tion. See Electrochemical and Metallurgical Industry (now Metallurgical and Chem-
ical Engineering}, Vol. I, pages 561-562, December, 1903.
The extraction of aluminum from bauxite is described by Joseph W. Richards,
Electrochemical and Metallurgical Industry (now Metallurgical and Chemical
Engineering), Vol. I, pages 158-162, Jan., 1903.
The electrolytic manufacture of alkali and chlorine is described by L. E. Baeke-
land, Metallurgical and Chemical Engineering, Vol. V, pages 209-212, June, 1907.
The manufacture of chlorates by electrolysis is described by G. Rossert.
L'Eclairage Electrique, beginning July 27, 1907.
The manufacture of metallic sodium and of sodium peroxide is described in the
Electrochemical and Metallurgical Industry (now Metallurgical and Chemical Engi-
neering), Vol. I, pages n-22, Sept., 1903.
Electrolysis is used extensively for recovering tin from tinned iron scrap, for
refining gold and silver, and for reducing lead ore. Most of these processes are
described in the Metallurgical and Chemical Engineering
184
ELECTROLYSIS AND BATTERIES.
185
D C supply
mains
rheostat
called an electrolytic cell and the copper plates A and C are
called electrodes. The electrode A at which the current enters
the solution is called £he anode, and the electrode C at which the
current leaves the solution is called the cathode.
Solutions of acids and salts generally are electrolytes, also
fused salts are electrolytes. That is to say, the flow of electric
current through such a solution or
through a fused salt produces chem-
ical action at the point where the
current enters the liquid (at the
anode) and at the point where the
current leaves the liquid (at the
cathode) .
A good example of electrolysis is
the electrolysis of a solution of hy-
drochloric acid (HC1) between elec-
trodes of carbon. In this case
hydrogen (H) is liberated at the
cathode and chlorine (Cl) is liber-
ated at the anode. In general the
molecule of any dissolved salt or
acid is separated into two parts by
electrolysis ; one part is liberated at the cathode and is called the
cathion,and the other part is liberated at the anode and is called
the anion. Thus hydrogen (H) is the cathion and chlorine (Cl)
is the anion of hydrochloric acid. In all metallic salts the metal
constitutes the cathion and the acid radical or halogen consti-
tutes the anion. In acids the hydrogen constitutes the cathion
and the acid radical or halogen constitutes the anion. Thus in
the case of copper sulphate (CuSO4) the cathion is copper (Cu),
and the anion is the acid radical (SO4) .
The dissociation theory of electrolysis.* — Many of the known facts of electrolysis
* The dissociation theory is used very extensively in advanced treatises in the
correlation of experimental results. A good discussion of this subject is given in
Chapter 7 of Nernst's Theoretical Chemistry, Macmillan and Co. See also Chapters
9-12 of Whetham's Theory of Solution, Cambridge University Press. A good dis-
cussion of electrolysis is also given in H. C. Jones' Elements of Physical Chemistry,
The Macmillan Co.
Fig. 114.
1 86 ELECTRIC LIGHTING.
may be clearly conceived in terms of the dissociation theory which is briefly as
follows: Consider a solution of common salt (NaCl) for example. Every molecule
of the salt in a dilute solution is supposed to be separated into positively-charged-
sodium-atoms ( + Na) and negatively-charged-chlorine-atoms ( — Cl) which are
called ions. The positively charged sodium atoms are called cathions, and the
negatively charged chlorine atoms are called anions. Ordinarily these ions wander
about in the solution, but the application of an electromotive force to the electrodes
produces an electric field throughout the solution, and the forces exerted on the
ions by this electric field cause the cathions to drift towards the cathode and the
anions to drift towards the anode. When the cathions reach the cathode they give
up their positive charges and enter into chemical combination or are deposited as
neutral metal or hydrogen; when the anions reach the anode they give up their
electric charges in the same way.
In the electrolysis of hydrochloric acid the cathion material
(H) is actually set free at the cathode and the anion material
(Cl) is actually set free at the anode. In most cases, however,
the cathion material is not actually set free at the cathode nor
is the anion material actually set free at the anode. Thus in
the electrolysis of a solution of sodium chloride (NaCl), the
cathion material (Na) when it is "liberated" at the cathode
immediately reacts with the water forming NaOH and free
hydrogen; in the electrolysis of a solution' of copper sulphate
(CuSOJ between copper electrodes, the anion material (864)
combines with the copper of the anode forming fresh CuSOi
which goes into solution, or it is deposited as crystals on the
anode if the solution is saturated; in the electrolysis of H2SO4
between inert electrodes, the hydrogen is set free at the cathode
as a gas and the anion material (SC^) reacts on the water ac-
cording to the formula 864 + t^O = H2SO4 + O, and the free
oxygen escapes as a gas.
89. Current density at the electrodes. — Generally the flow of
current from the anode plate into the electrolyte and from the
electrolyte into the cathode plate is not uniformly distributed over
the surfaces of the plates. There is always a tendency for the
flow of current to be concentrated at the sharp edges of the
plates and at any sharp projecting part of the plates. Thus Fig.
115 represents a top view of an electrolytic cell, A A being the
ELECTROLYSIS AND BATTERIES.
I87
anode and CC being the cathode, and the fine curved lines repre-
sent the stream lines of the electric current through the electro-
lyte. The crowding together of the stream lines at the corners
of the electrodes and at the sharp point on CC represents the con-
centration of the current-flow at these places. With electrodes
placed as shown in Fig. 115 there is extremely little flow of
current into or out of the back faces bb bb of the electrodes.
glass jar
Fig. 115.
When the electrodes are parallel flat plates at a distance apart
which is small as compared with the size of the plates, then the
flow of current is almost wholly confined to the front faces ffffot
the electrodes as shown in Fig. 116, the flow of current, further-
more, is distributed over the faces // // with approximate uni-
formity, and the total current divided by the area of one of the
front faces // is called the current density.
The current density at an electrode has a great deal to do with
the character of the chemical action at the electrode. Thus, if
the electrolyte contains zinc sulphate and copper sulphate, copper
only is deposited on the cathode if the current density is low,
but both copper and zinc (and also some hydrogen) are deposited
on the cathode if the current density is large. In the operation
of silver plating or copper plating or nickel plating the deposited
metal is soft and granular if the current density is too high.
90. Definition of electrochemical equivalent. Chemical cal-
culations in electrolysis. — The amount of silver deposited per
188
ELECTRIC LIGHTING.
second in the operation of silver plating is proportional to the
strength of the current in amperes, and the amount of silver
deposited in one second by one ampere is called the electrochemical
equivalent of silver; it is equal to 0.001118 gram per ampere-
second or 4.025 grams per ampere-hour.
In the great majority of cases no material is actually deposited
on either electrode in an electrolytic cell, but chemical action is
always produced in the immediate neighborhood of the elec-
trodes, and it is important to consider the amount of chemical action
which takes place in a given time due to the flow of a given current
through the cell. A general statement of this matter involves
the use of a number of chemical terms. These terms are ex-
hibited in the following schedules.
The valencies of various metals, acid radicals, etc., are shown
by the numbers in the following exhibit which shows the chemical
symbols of several common acids and salts.
EXHIBIT OF VALENCIES.
Name.
Hydrochloric
Acid.
Silver Nitrate.
Njtric Acid.
Sulphuric Acid.
Chemical symbol
Valency
H
i
Cl
I
Ag
i
N03
i
H
i
N03
i
Hf SO,
2 2
Name.
Cupric Sulphate.
Zinc Sulphate.
Aluminum
Sulphate.
Chemical symbol
Cu
2
SO4
2
Zn
2
SO4
2
A'.
o
(S04)3
6
Valency...
The chemical equivalents of various metals, acid radicals, etc.,
are shown in the following exhibit. One chemical equivalent of
a metal or acid radical is hereafter called a gram-val of the sub-
stance.
EXHIBIT OF CHEMICAL EQUIVALENTS IN GRAMS.
Symbol of Substance.
H
Ag
Cl
N03
S04
Cu
Zn
Al
Atomic or molecular
weight.
I OI
1 08
5e.t
62
06
63.6
6iJ.4
27.1
Valency
I
I
I
I
2
2
2
T.
Chemical equivalent in
grams. (The gram-
val)
1. 01
1 08
35-5
62
48
31-8
32.7
9-°3
ELECTROLYSIS AND BATTERIES. 189
The number of grams of a substance in one gram-val of that
stance is equal to the atomic or molecular weight of the substance
divided by the valency of the substance. Thus one gram-val of
silver is 108 grams of silver, and to deposit one gram-val of
silver on the cathode in a silver plating cell requires 96,540
ampere-seconds or 26.82 ampere-hours. In general, 96,540
ampere seconds " liberates " one gram-val of anion material at
the anode and one gram-val of cathion material at the cathode
whatever the particular electrolyte may be. It is evident there-
fore that 96,540 ampere-seconds is an important unit of current X
time; this unit is called the faraday. For example :
One faraday (96,540 ampere-seconds) "liberates"
at the anode at the cathode
62 grams of NOs from nitric acid or any 23 grams of Na from a solution oi
nitrate solution. NaOH, or from a solution of any
sodium salt.
48 grams of SO4 from sulphuric acid or 31.8 grams of Cu from a solution of any
any sulphate solution. cupric salt.
35.5 grams of Cl from hydrochloric acid 63.6 grams of Cu from a solution of any
or any chloride solution. cuprous salt.*
16.01 grams of OH from a solution of 9.03 grams of Al from a solution of any
caustic soda or potash, etc., etc. aluminum salt, etc., etc.
91. The electrochemical unit of work. — Consider an electro-
lytic cell through which a current of I amperes is flowing and
across the terminals of which the electromotive force is E volts.
Work is being delivered to the cell (done on the cell) at the rate
El watts, and in / seconds the amount of work done is Elt
joules. f
It is important to consider the amount of work done by an
electromotive force of one volt during the flow of one faraday
(96,540 ampere-seconds) through a cell. This amount of work
may be conveniently called a volt-faraday , it is evidently equal
to 96,540 joules and it is therefore equivalent to 23,000 calories.
* Cupric copper has a valency of 2, cuprous copper has a valency of i. Thus
cupric chloride is CuCh and cuprous chloride is CuCl.
f It takes 4.2 joules to raise the temperature of one gram of water i° Centi-
grade. That is, one calorie is the heat equivalent of 4.2 joules,
190 ELECTRIC LIGHTING.
The work done by E volts during the flow of one faraday is
E volt-faradays, or 96, 540 £ joules and it is equivalent to
23,oooJ3 calories.
92. Expenditure of work in electrolysis. Heat and chemical
work. — A portion of the work done in forcing a current through
an electrolytic cell is converted into heat. This is shown* by
the fact that the temperature of an electrolytic cell rises during
the flow of current. Also a portion of the work done in forcing a
current through an electrolytic cell is left tied up, as it were, in
the chemical changes which are produced by the current. This
work which becomes tied up in chemical changes is called chemical
work. Thus, when dilute sulphuric acid is electrolized between
electrodes of carbon or platinum, hydrogen and oxygen gases are
set free, and it is evident that energy is tied up in these free gases
because if the gases are re-combined by burning, energy is ob-
tained in the form of heat.
The amount of heat developed by the current in an electro-
lytic cell depends in part upon the resistancef of the electrolyte
in ohms and it depends in part upon irreversible { actions at the
electrodes; when the current is very small the energy which is lost
as heat is usually negligible in comparison with the energy which
becomes tied up in the chemical changes which are brought about
by the current.
93. Decomposition voltage. — Consider the electrolysis of dilute
sulphuric acid between inert electrodes of carbon or platinum,
the current being so small that the loss of energy in the production
of heat is negligible, and let E be the electromotive force across
* This argument is not strictly correct because the chemical work done in an
electrolytic cell may be in some cases greater than the electrical work delivered to
the cell, the cell being actually cooled in the process.
t The matter of electrolyte resistance is discussed at some length in Whetham's
Theory of Solution and in H. C. Jones' Physical Chemistry,
J This is a thermodynamic term which the beginner is not expected to under-
stand. See two papers on Reversible and Irreversible Polarization by W. S.
Franklin and L. A. Freudenberger, Transactions of the American Electrochemical
Society, Vol. VII, pages 33-49; and Vol. VIII, pages 227-237.
ELECTROLYSIS AND BATTERIES. 191
the terminals of the cell. During the flow of one fcraday through
the cell E volt-faradays of work will be done on the cell, and,
heat losses being negligible, all of this energy will be tied up in
the i .01 grams of free hydrogen and the 8 grams of free oxygen
produced.
Now the amount of energy tied up in these gases is approxi-
mately* equal to the heat of combustion of i.oi grams of hydro-
gen, and the heat of combustion of hydrogen is 34,700 calories
per gram. Therefore the setting free of i.oi grams of H and
8 grams of 0 involves the tying up of the energy equivalent of
35,000 calories, which is 147,000 joules or 1 .52 volt-faradays, and
this must be equal to the work done on the cell, namely, E
volt-faradays. Therefore we have
E volt-faradays = 1.52 volt-faradays
and consequently E, which is the voltage required to send a very
small current through the given electrolytic cell, is equal to 1.52 volts,
and it is called the decomposition voltage of sulphuric acid.
The decomposition voltages of some common acids and salts
between inert electrodes are given in the following table:
DECOMPOSITION VOLTAGES, f
(For Normal Solutions.)
Sulphuric acid 1.67 volts. Barium nitrate 2.25 volts.
Nitric acid 1.69 volts. Sodium nitrate 2.15 volts.
Hydrochloric acid .... 1.31 volts. Calcium chloride 1.89 volts.
Oxalic acid 0.75 volts. Potassium chloride. . . 1.96 volts.
Sodium hydroxide .... i .69 volts. Sodium chloride 1.98 volts.
Qualifications of Above Statements Concerning Decomposition Voltages. —
The above statements concerning decomposition voltages are not in accord with
experiment in the following particulars:
* The heat of combustion includes the heat of condensation of the water vapor
produced by the combustion, but a small amount of available energy is represented
by the placing of the condensed water back into the acid solution. This small
amount of energy is neglected.
t As determined by observation by LeBlanc, Zeitschrift filr Physikalische
Chemie, Vol. VIII, page 299, 1891. One must not be surprised at the discrepancy
between the value 1.52 volts above calculated and the value 1.67 volts as observed
by LeBlanc for dilute sulphuric acid. See page 192.
192
ELECTRIC LIGHTING.
(a) A very small current through sulphuric acid between inert electrodes does
not set free hydrogen and oxygen gases. A trace of oxygen is dissolved in the
solution and it combines with the hydrogen as it is "liberated" at the cathode,
and the supply of dissolved oxygen is replenished by diffusion from the neighbor-
hood of the anode. Also a trace of hydrogen is dissolved in the solution and it
combines with the oxygen as it is "liberated" at the anode, and the supply of dis-
solved hydrogen is replenished by diffusion from the neighborhood of the cathode.
Any voltage, however small, can maintain a very small current through sulphuric
acid between inert electrodes, and the same is true of any electrolyte whatever.
There is, however, a definite voltage below which no oxygen and hydrogen gases
are set free, and this is the decomposition voltage above referred to. Similarly,
there is a definite decomposition voltage for any electrolyte between inert electrodes.
(5) The setting free of oxygen and hydrogen gases at a rate which is actually
perceptible, by electrolizing sulphuric acid between inert electrodes, requires about
1.67 volts. Therefore 1.67 volt-faradays of work is done on the cell during the
flow of one faraday through the cell, 1.52 volt-faradays of this work is tied up in
the free oxygen and hydrogen gases, and the remainder, namely, 0.15 volt-faraday,
is converted into heat at the electrodes because of irreversible actions at the elec-
trodes. That is to say, the heat generated in an electrolytic cell does not always
become negligible as the current approaches zero. The heat generated in the body
of the electrolyte because of the resistance of the electrolyte (in ohms) does become
negligible.
(c) The application of thermodynamics to electrolysis shows that it is pos-
sible for the "chemical work" done in an electrolytic cell to exceed the electrical
work done on the cell, the deficiency being made up by the cooling of the cell. In
such a case the "decomposition voltage" would be less 'than what is calculated by
the theory above outlined.
94. Electrode polarization. — When a metal plate is allowed to stand in an acid
or salt solution a definite potential-difference or voltage comes into existence be-
tween the solution and the metal. This potential-difference or voltage measures
what is called the electrode polarization. Thus, according to Neumann* the
values of electrode polarization between ordinary metals and solutions of their
salts are as follows, the voltage being reckoned as positive -when it is from the solution to
the metal:
ELECTRODE POLARIZATION VOLTAGES.
(Equilibrium Values in Volts.)
Metal
Salt of Metal.
Sulphate.
Nitrate.
Chloride.
Zinc
— O ^24,
— O 4.77
— O ^O7
Iron
— O OO"?
— o 087
Lead
-i-O 1 1 c
-j-o 005
Copper
4-o ej t
-f~o 615
* Zeitschrift fitr physikalische Chemie, Vol. XIV, page 229, 1894.
ELECTROLYSIS AND BATTERIES.
193
The polarization voltages given in this table are equilibrium values, that is,
the values which exist when no current flows from metal to electrolyte or from
electrolyte to metal. When there is a flow of current the polarization voltage
.changes considerably. TMs change is due chiefly to the change of concentration
of the electrolyte which always takes place near an electrode as explained in con-
nection with the lead storage battery in Art. 105.*
wire
zinc plate
—ZnS04
solution
-CuSOj.
solution
copper
plate
Fig. 117.
Fig. 118.
One might think that the polarization voltage between a solution and a metal
plate P could be measured by connecting a voltmeter as shown in Fig. 117, but
there is a polarization voltage between the solution and the wire W so that the
voltmeter would measure the sum:
volts from wire W to solution + volts from solution to plate P,
or the difference
— volts from solution to wire W + volts from solution to plate P.
The measurement of the polarization voltage between the metal plate P and a
solution depends upon the use at W of an electrode -whose polarization voltage has been
determined.^ Such an electrode is called a standard electrode.
Example. — Consider the electrolytic cell which is shown in Fig. 118, in which the
zinc sulphate solution floats on the heavier copper sulphate solution. Neglecting
the voltage across the contact cc of the solutions, the voltage indicated by the
voltmeter V is the sum:
volts from zinc to solution + volts from solution to copper,
* Another cause of change of polarization voltage with current is discussed in
two papers on Reversible and Irreversible Polarization by W. S. Franklin and L. A.
Freudenberger which are referred to on page 190.
t Two methods have been employed for measuring the polarization voltage of
the standard electrode. This matter is fully discussed in Whetham's Theory of
Solution, Chapter XI, Cambridge University Press, 1902.
194 ELECTRIC LIGHTING
or the difference
— volts from solution to zinc + volts from solution to copper.
According to the above table, voltage from solution to zinc is — 0.524, and voltage
from solution to copper is + 0.515, so that the voltage indicated by the voltmeter
would be 1.039. This voltage depends upon the degree of concentration of the
solutions. With a concentrated solution of copper sulphate and a fairly dilute
solution of zinc sulphate the voltmeter would indicate about 1.08 volts.
Calculation of electrode polarization. — The total voltage (the decomposition
voltage) required to force an infinitesimal current through an electrolytic cell may
be calculated from the chemical work as explained in Art. 93; and if one could
determine the portion of the chemical work which is done at the anode and the
portion which is done at the cathode then the total decomposition voltage could be
divided into two known parts, and these parts would be the anode polarization and
the cathode polarization respectively. There is, however, no chemical data in
existence upon which such a calculation can be based, and even if such chemical
data did exist the results would be subject to the qualifications outlined in the fine
print in Art. 93.
95. The voltaic cell.* — The chemical action produced by the
flow of current through an electrolytic cell is confined wholly
to the immediate neighborhood of the electrodes, and this chem-
ical action is usually forced, that is, work has been done to bring
it about, or, in other words, an outside electromotive force is re-
quired to push the current through the cell. But in many cases
the chemical action produced by the flow of current through an
electrolytic cell is a source of energy. In such a case the electro-
lytic cell itself can maintain a current through the electrolyte
from electrode to electrode and through an outside circuit of
wire which connects the electrodes. Such an electrolytic cell is
called a voltaic cell or primary battery.
Example. — When a strip of clean zinc and a strip of copper or
carbon are dipped into dilute sulphuric acid, no chemical action
takes place. But when the plates are connected together by a
wire, a current immediately starts to flow through the circuit,
leaving the cell at the copper or carbon electrode (the cathode)
and entering the cell at the zinc electrode (the anode). This
current decomposes the sulphuric acid (H2SO4), the hydrogen is
* A number of voltaic cells connected together constitute a voltaic battery.
The word battery is, however, frequently applied to a single cell.
ELECTROLYSIS AND BATTERIES. 195
set free at the copper or carbon cathode and escapes from the cell
as a gas, and the sulphuric acid radical (SO4) which is "liberated"
at the zinc anode combines with the zinc and forms zinc sulphate
(ZnSO4) which goes into solution. The combination of Zn and
SO4 develops more energy than is required for the decomposition
of the H2SO4 so that the chemical action in this cell is a source of
energy. The cell here described is called the simple voltaic cell.
96. Electromotive force of a voltaic cell. — A clear idea of the
electromotive of a voltaic cell may be obtained by the following
argument : (a) The amount of chemical action which takes place
in a given voltaic cell is proportional to 7 X t, where / is the
current and / is the time during which the current continues
to flow, as explained in Art. 90. Furthermore the energy evolved
by the chemical action is proportional to the amount of chemical
action; therefore the energy evolved by the chemical action is
proportional to I X t and it can be expressed as elt where e is
a constant for a given type of voltaic cell.
(6) The energy delivered to an electric circuit is equal to
RPt joules, where R is the resistance of the circuit in ohms, /
is the current in amperes, and / is the elapsed time in seconds.
(c) If all of the energy of the chemical action were available for
the maintenance of the current then elt (the energy used to main-
tain the current) would be equal to RPt (the energy which ap-
pears in the electric circuit) . That is :
elt = RPt
or
Or, in words, the current produced by the given voltaic cell in a
circuit of resistance I is equal to the factor e [as denned under
(a)] divided by R. Now this relation is what is familiarly known
as Ohm's law and the factor e is the electromotive force of the
given voltaic cell.
The electromotive force of a voltaic cell is entirely independent
196 ELECTRIC LIGHTING.
of the size of the cell, it depends only on the character of the
chemical action in the cell.
The electromotive force of a voltaic cell is most easily measured
by connecting a voltmeter to the terminals of the cell.
The above argument may well be repeated as applied to a
particular case, (a) Consider the energy evolved by the dis-
solution of the zinc in the simple voltaic cell which is described
in Art. 95. The net result of the chemical action in this cell is
represented by the formula
Zn + H2SO4 = ZnSO4 + H2.
During the flow of one faraday through such a cell one gram-val
(32.7 grams) of zinc would be dissolved and a corresponding
amount of hydrogen would be set free. Now the dissolution of
one gram of zinc in dilute sulphuric acid develops 578 calories
of heat which is the equivalent of 2428 joules or 0.822 volt-
faradays of work.
(b) Let E be the electromotive force of the cell. Then during
the flow of one faraday the cell would deliver E volt-faradays
of electrical work.
(c) If all the energy evolved by the dissolution of the zinc in
the simple voltaic cell were available in the form of electrical-
energy output then, from (a) and (b) we would have
E volt-faradays = 0.822 volt-faradays
or
E = 0.822 volts.
(d) As a matter of fact the electromotive force of the simple
voltaic cell under discussion is 1.03 volts on open circuit and it
falls off very greatly when the cell delivers current.
97. Polarization of a voltaic cell. — The electromotive force
between the terminals of a voltaic cell is always less when the
cell is delivering current than it is when the cell is not delivering
current. This difference is at first due chiefly to the loss of
voltage due to the resistance of the cell. Thus a voltaic cell has
ELECTROLYSIS AND BATTERIES. 197
an "open-circuit" electromotive force of 2 volts and an internal
resistance of 0.05 ohm, and the electromotive force between the
terminals of the cell drops instantly to 1.5 volts when the cell
is called upon to deliver 10 amperes. The loss of voltage due
to internal resistance is in this case 0.5 volt and it is equal to
the current of 10 amperes multiplied by the internal resistance
of 0.05 ohm.
When a voltaic cell continues to deliver current the electro-
motive force between the terminals of the cell falls off more and
more. This falling off of the electromotive force of a voltaic
cell is called polarization.* The chief cause of the polarization
of a voltaic cell is as follows: The chemical action in the neighbor-
hood of the electrodes brings about local changes of composition
and of concentration of the electrolyte, less energy is evolved by
the chemical action at the electrodes, and consequently the
voltage of the cell decreases.
98. The bichromate cell. — The available energy of the chemical
action which takes place in the simple voltaic cell which is described
as an example in Art. p$ may be greatly increased by providing an
oxidizing agent in the neighborhood of the cathode so that the hydrogen
may be oxidized at the moment of its "liberation" by the current.
The increase of available energy because of this oxidation gives a
greatly increased voltage. An oxidizing agent used in this way
is called a depolarizer, f The bichromate cell furnishes a good
example of the use of an oxidizing agent in a voltaic cell.
The simplest form of bichromate cell, which is sometimes
called the Grenet cell from its inventor, is shown in section in
Fig. 1 19 a. The electrodes are a carbon plate C and an
amalgamated J zinc plate Z, and the electrolyte e e e is dilute
* This term must not be confused with the term electrode polarization as defined
in Art. 94.
t In the whole history of physics words without meanings have been used for
things not understood. Thus the word polarize does a great variety of questionable
duty in the subject of electrolysis in the same way that the word induce does a
great variety of questionable duty in electromagnetism ! It would be a great
help if all such words could be thrown away.
t Covered with a thin coating of mercury.
198
ELECTRIC LIGHTING.
sulphuric acid in which potassium bichromate or chromic acid
has been dissolved. Without the potassium bichromate the
hydrogen escapes as a gas and the voltage of the cell is 1.03;
with the bichromate the hydrogen is oxidized and the voltage of
the cell is 1.90. There is a very rapid waste of zinc (and acid)
in this cell and the cell is now seldom used.
wire
wire
=
c
Z
?
•*- g lass
~ - -=~ — "•
e
jar
e
c
e
Z
Fig. 119 a.
Fig. 119&.
A modified form of bichromate cell, known as the Fuller cell,
is shown in section in Fig. 1196. In this cell the electrolyte is
dilute sulphuric acid but the zinc anode is contained in a porous
earthenware cup and the potassium bichromate or chromic acid
is dissolved only in that portion of the electrolyte which surrounds
the carbon cathode. There is not a rapid waste of zinc (and
acid) in this cell and the cell is extensively used.
99. Voltaic action and local action. — Two kinds of chemical
action are to be distinguished in a voltaic cell : (a) the chemical
action which depends upon the flow of current, and does not
take place when there is no current; and (b) the chemical action
which is independent of the flow of current, and which does take
place whether the current is flowing or not.
The chemical action which depends on the current is propor-
tional to the current, it is essential to the operation of the voltaic
ELECTROLYSIS AND BATTERIES. 199
cell as a generator of current, its energy is available for the
maintenance of the current, and it is called voltaic action.
The chemical action in a voltaic cell which is independent of
the flow of current does not help in any way to maintain the
current, it represents absolute waste of materials, and it is called
local action.
Local action takes place more or less in every type of voltaic
cell and it is especially great in the Grenet cell where the oxidizing
agent comes into contact with the zinc plate. Local action is
greatly reduced by coating the zinc plate with a thin coating of
metallic mercury and by using very pure zinc.
The amount of zinc usefully consumed by voltaic action while
a voltaic cell in delivering a given current for a specified time,
is equal to the amount of zinc that would be deposited by the
given current during the specified time upon the cathode of an
auxiliary electrolytic cell containing a solution of a zinc salt.
For example five amperes flowing for one hour will deposit 6.1
grams of zinc, and therefore 6.1 grams of zinc (and a correspond-
ing amount of acid and bichromate) are usefully consumed in a
Grenet cell in the delivery of 5 amperes for one hour. In an
actual test of a Grenet cell delivering 5 amperes for one hour the
loss of zinc was 30 grams. Under the conditions of the test,
therefore, 23.9 grams of zinc (and a corresponding amount of
acid and bichromate) were wasted by local action and 6.1 grams
of zinc (and a corresponding amount of acid and bichromate)
were usefully consumed.
100. Open-circuit cells and closed-circuit cells. — A voltaic cell
which can be left standing unused but in readiness at any time
for the delivery of current when its circuit is closed is called an
open-circuit cell. An open-circuit cell must, above all things, be
nearly free from local action. The cell most extensively used
for open-circuit service is the LeClanche* cell which is described
as the manganese-dioxide cell in Art. 103.
A voltaic cell which is suitable for delivering a current steadily
is called a closed-circuit cell. A closed-circuit cell should be of a
200 ELECTRIC LIGHTING.
type of which the voltage does not fall off greatly with continued
delivery of current, and, of course, local action should be elimi-
nated if possible. The gravity Daniell cell, the Fuller cell, the
copper oxide cell, and the lead storage cell are most extensively
used for closed circuit work.
101. The gravity Daniell cell. — The essential features of the
gravity Daniell cell are shown in Fig. 118. The usual form of
the cell is shown in Fig. 120. During the
operation of the cell metallic copper is
deposited upon the copper cathode at
the bottom of the cell, and the SO± com-
bines with the zinc of the anode, form-
ing ZnSCV The electromotive force of
this cell varies from about 1 .05 volts to
i.io volts, depending upon the degree of
concentration of the zinc sulphate and
copper sulphate solutions.
This cell has a considerable amount of local action when it is
allowed to stand unused because of the upward diffusion of the
copper sulphate. It is used very extensively in telegraphy and
for operating the "track circuit" relays in automatic railway
signalling.
1 02. The copper-oxide cell. — In this type of cell the anode is
zinc, the electrolyte is a solution of caustic soda, and the cathode
is a highly compressed block of copper oxide. The flow of
current through the cell "liberates" Na at the cathode and OH
at the zinc anode and the following reactions take place :
At the cathode Na + i(CllO) + J(H2O) = JCll + NaOH
T direction of flow of current through the cell.
At the anode OH + |Zn + NaOH = |(Na2ZnO2) + H2O.
The atomic weights (or molecular weights) of the various
substances in this schedule, multiplied by the factor J or not as
the case may be, express the number of grams of the various
ELECTROLYSIS AND BATTERIES. 2OI
substances involved in the chemical action produced by the flow
of one faraday through the cell.*
The copper-oxide cell has but little local action and its electro-
motive force is about 0.6 volt. This cell is used extensively for
operating railway signals; that is for operating the small motors
which move the signal arms. The track relays are usually
operated by gravity cells.
103. The manganese-dioxide cell. — In this cell the anode is
zinc, the electrolyte is a solution of ammonium chloride (sal
ammoniac) and the cathode is a plate of carbon with bits of
coke and manganese dioxide packed closely around it. The
earliest cell of this type is called the LeClanche cell from its
inventor, and in this cell the manganese dioxide and coke are
contained in a porous earthenware cup. The ordinary dry cell\
is a manganese-dioxide cell in which the containing vessel is
made of sheet zinc and it serves as the anode, the electrolyte is
held in a porous mass of saw-dust or other absorbent material,
and several thicknesses of unglazed paper keep the manganese
dioxide and powdered coke away from the zinc.
The flow of current through the manganese-dioxide cell "liber-
ates" chlorine at the zinc anode and NH4 at the carbon cathode
and the following reactions take place :
At the cathode NH4 + i(MnO2) = NH3 + i(HiO) + |(MnO)
Direction of current through the cell.
At the anode Cl + JZn = J(ZnCl2)
There is but little local action in the manganese-dioxide cell if
the zinc and ammonium chloride are pure, J but the cell polarizes
rapidly when it delivers steady current. Reliable manufacturers
* This statement applies also to the reaction schedules given on pages 204, 205
and 206.
f The dry cell has been denned as a cell which being sealed is always wet, whereas
the wet cell being open to the air often becomes dry.
J See important papers on the dry cell, Transactions of the American Electro-
chemical Society, Vol. XVI, pages 97 and 109; Vol. XVII, page 341; and Vol. XIX,
page 31.
202 ELECTRIC LIGHTING.
always stamp the date of manufacture on their dry cells, and the
purchaser should not accept a cell which is more than two or three
months old. The best test of a dry cell is to observe the short-
circuit current by connecting the cell momentarily to an ammeter.
A fresh cell 2\ inches in diameter and 6 inches high should give
at ordinary room temperature about 20 amperes short-circuit
current. The electromotive force of the manganese-dioxide cell
is about 1 .6 volts.
104. Regeneration of a voltaic cell by a reversed current. —
An essential feature of voltaic action is that it is reversed if a
current is forced backwards through a voltaic cell by an outside agent,
provided that no material that has played a part in the previous
voltaic action has been allowed to escape from the cell. Thus,
in the operation of the simple voltaic cell consisting of a zinc
anode and carbon cathode in dilute sulphuric acid, the H2SO4
is decomposed, ZnSC>4 is formed at the anode, and hydrogen is
liberated at the cathode. If the current is reversed so that the
carbon plate becomes the anode and the zinc plate the cathode,
then the ZnSCX previously formed will be decomposed, metallic
zinc will be deposited upon the zinc cathode, and SO* will be
liberated at the carbon anode where it will combine with the
trace of hydrogen that is clinging to the carbon plate and form
H2SO4. In this cell the greater part of the liberated hydrogen
has of course escaped and the reversed chemical action, due to a
reversed current cannot long continue. Local action, on the
other hand, being independent of current, is not affected by a reversal
of the current.
The storage cell. — A voltaic cell which is free from local action
and in which all of the materials which take part in the voltaic action
are kept in the cell, may be regenerated after use by sending through
it a reversed current. This regeneration is due to the reversed
chemical action that is produced by the reversed current, as
explained above. A voltaic cell which can be thus regenerated
ELECTROLYSIS AND BATTERIES.
203
is called a storage cell. The process of regeneration is called
and the use of the cell as an electric generator is called
discharging. 4
The capacity of a storage cell is expressed in ampere-hours.
Thus a cell which can deliver 10 amperes for 8 hours is said
to have a capacity of 80 ampere-hours.
The electrode out of which current flows while a storage cell
is discharging is called the positive electrode, and the other
electrode is called the negative electrode. This matter can be
positive main
positive
grid
D C supply mains
negative main
negative
grid
rheostat
Fig. 121.
positive
grid
Fig. 122.
most easily remembered with the help of diagrams. Thus Fig.
121 shows a storage cell discharging, and Fig. 122 shows a
storage cell being charged.
Almost any kind of voltaic cell can be used to some extent
as a storage cell, that is to say, almost any kind of voltaic cell
can be regenerated to some extent by forcing a reversed current
through it, but a good storage cell must be free from local action,
and the materials which take part in the voltaic action must
be kept in the cell, as pointed out above; and the electrodes
must not crumble to pieces with frequent charging and discharg-
ing of the cell. The only voltaic cells which, up to the present
204 ELECTRIC LIGHTING.
time, have been found to meet these requirements are the
lead cell* and the nickel-iron cell.f
105. The lead storage cell. — When thelead cell is fully charged
it has a positive electrode of lead peroxide (PbO2), a negative
electrode of spongy metallic lead (Pb), and an electrolyte of
dilute sulphuric acid (H2SO4). When the cell discharges the
lead peroxide is reduced to lead oxide (PbO) which absorbs sul-
phuric acid from the solution and is converted into insoluble lead
sulphate (PbS04), and the spongy metallic lead is oxidized and
similarly converted into insoluble lead sulphate.
The lead peroxide and the spongy metallic lead (or the insoluble
lead sulphate into which these materials are converted by dis-
charge) constitute the active electrode materials of the lead cell.
These active materials are held in grooves or pockets, in plates
or grids of solid metallic lead.
The chemical actions which take place in the charging and
discharging of the lead storage cell are shown in the following
schedule :
DISCHARGING.
Positive grid H +$ (PbO2) + |(H2SO4) = H2O + £(PbSO4)
I Direction of current through the cell
Negative grid |(SO4) + ^Pb = £(PbSO4)
CHARGING.
Positive grid |(SO4) + |(PbSO4) + H2O = H2SO4 + £(PbO«)
T Direction of current through the cell.
Negative grid H + ^(PtfSOO = i(H2SO4) + |Pb
Effects of charge and discharge. — The conversion of the PbO2
and the Pb into PbSO4 on discharge causes a great decrease in
the concentration of the electrolyte, especially in the pores of
the active material, and an increase of volume of the active
* The details of construction of the lead storage cell are very fully described
on pages 147-200 of Lyndon's Storage Battery Engineering, McGraw-Hill Book Co.,
1911.
t Sometimes called the Edison cell. The earlier type off nickel-iron storage
cell is described by A. E. Kennally, Transactions of the American Institute of
Electrical Engineers, Vol. XVIII, pages 219-244, May, 1901.
ELECTROLYSIS ARD BATTERIES. 205
electrode materials. The reconversion of the PbSOi into
and Pb by charging causes a corresponding increase in the con-
centration of the electrolyte and a decrease of volume of the
active electrode materials.
The changes of concentration of the electrolyte are the chief
causes* of the decrease of voltage of the cell during discharge
and of the increase of voltage of the cell while it is being charged
(see Fig. 123).
The expansion and contraction of the active electrode materials
is the chief cause of the disintegration of the electrodes, and it
also tends to cause the plates or grids to buckle or warp, especially
if the action is not the same on both sides of a plate. A well-
designed storage battery grid allows the active electrode material
to expand and contract with a minimum of mechanical damage
to the grid.
106. The nickel-iron storage cell. — When the nickel-iron cell
is fully charged it has a positive electrode of nickel peroxide
(NiOo), a negative electrode of spongy metallic iron (Fe), and
the electrolyte is a solution of caustic potash (KOH). When
the cell discharges, the nickel peroxide is reduced to nickel oxide
and the spongy metallic iron is oxidized.
The nickel peroxide and the spongy metallic iron (or the nickel
and iron oxides into which these materials are converted by
discharge) constitute the active electrode materials of the nickel-
iron cell. These active materials are held in grooves or pockets,
in plates or grids of metallic nickel and steel.
The chemical actions which take place in the charging and
discharging of the nickel-iron storage cell are shown in the fol-
lowing schedule:
DISCHARGING.
Positive grid K + J(NiOj) + 5(H2O) = £(NiO) + KOH
L Direction of current through the cell.
Negative grid OH + £Fe = |(FeO) + l(HjO)
* The increase and decrease of voltage during charging and discharging are also
due in part to the resistance of the cell and in part to what is called irreversible
actions at the electrodes.
206 ELECTRIC LIGHTING.
CHARGING.
Positive grid OH + i(NiO) = i(NiOi) + £(H,O)
f Direction of current through the cell.
Negative grid K + |(FeO) + |(H2O) = |Fe + KOH
Effects of charge and discharge. — The NiO2 contracts and the Fe
expands during discharge, and vice versa] but there is no general
increase or decrease of concentration of the electrolyte due to
charging and discharging. During discharge, however, there
is an increase of concentration near the positive grid and a de-
crease of concentration near the negative grid and vice versa.
107. Charging and discharging curves. Comparison of the
lead storage cell and the nickel-iron storage cell. — The ordinates
of the curve in Fig. 123 show the change of voltage between the
Fig. 123.
terminals of a "3O-ampere" lead storage cell when it is charged
for 8 hours and discharged for 8 hours, the current being 30
amperes in each case. The ordinates of the curve in Fig. 124
show the change of voltage between the terminals of a "30-
ampere" nickel-iron storage cell when it is charged for 5.5 hours
and discharged for 5 hours, the current being 30 amperes in each
case.
ELECTROLYSIS AND BATTERIES.
207
From these figures it is evident that the voltage of a lead
storage cell stands at a more nearly constant value during dis-
charge than the voltage of a nickel-iron storage cell. The average
voltage of a lead cell while discharging is about 81 per cent, of
the average voltage while being discharged, whereas the average
volt
r.?o
.1.60
•1.50
140
1,20
t •
1.10
hours
discharge
•> 4 S 6
Fig. 124.
voltage of a nickel-iron cell while discharging is about 72 per cent,
of the average voltage while being charged The energy effi-
ciency of a lead storage cell when charged and discharged as
represented by the curves in Fig. 123, is about 80 per cent.; and
the energy efficiency of a nickel-iron cell when charged and dis-
charged, as represented by the curves in Fig. 124, is about 60
per cent.
The nickel-iron storage cell seems to make a better portable
cell than the lead storage cell because the nickel-iron cell is
lighter than the lead cell and because the nickel-iron cell may
be allowed to stand for a long time partially or wholly discharged.
Also the nickel-iron cell is perhaps better than the lead storage
cell for driving electric vehicles because the nickel-iron cell does
not demand careful attention. For electric vehicle driving a
constant-voltage supply of current is not necessary and therefore
the great change of voltage of the nickel-iron cell is not especially
objectionable for this kind of service.
208
ELECTRIC LIGHTING.
The lead storage battery is better than the nickel-iron storage
battery for stationary service of all kinds because of its lower
first cost, because of its more nearly constant voltage, and because
of its higher efficiency. The greater constancy of voltage is
especially important when current is to be supplied to incan-
descent lamps; the voltage even of a lead storage battery must
be regulated when it is used for this purpose.
108. Portable type and stationary type of storage cells. Costs
and weights. — There are two more or less distinct types of lead
storage cells, namely, the portable type which is made as light
as possible by using thin grids and hard-rubber containing jars,
and the stationary type which has very heavy grids and glass
jars, or, in the case of very large cells, lead-lined wooden tanks.
The portable type of lead storage cell has about 10 watt-hours
of storage capacity (a normal discharge rate of 1.25 watts) per
pound of gross weight. The stationary type of lead storage cell
has about 4 watt-hours of storage capacity (a normal discharge
rate of 0.5 watt) per pound of gross weight. The nickel-iron
storage cell has about 14 watt-hours (2.8 watts normal discharge
rate) per pound of gross weight.
Some idea of the cost of storage cells is given by the following
schedules :
LEAD STORAGE BATTERY, HEAVY STATIONARY TYPE, 50 CELLS, 400 AMPERE-
HOURS.
To deliver 5 kilowatts for 8 hours.*
Cost.
Weight.
Total.
Per
Kilowatt-hour
of capacity.
Total.
Per
Kilowatt-hour
of capacity.
In glass jars .
$1,400
1,650
$35.oo
41.25
10,300 Ibs.
14,600
258 Ibs.
365
In lead-lined wooden tanks,
Depreciation 6 or 7 per cent, per year when properly cared for.
* Or 7 kilowatts for 5 hours, or 10 kilowatts for 3 hours, or 20 kilowatts for i
hour. See page 211.
ELECTROLYSIS AND BATTERIES.
209
LEAD STORAGE BATTERY, LIGHT PORTABLE TYPE, 50 CELLS, 200 AMPERE-HOURS.
To deliver 2.5 kilowatts for 8 hours.*
*
Cost.
Weight.
Total.
Per
Kilowatt-hour
of capacity.
Total.
Per
Kilowatt-hour
of capacity.
In covered rubber jars
$800
540
2,340 Ibs.
117 Ibs.
Depreciation 15 per cent, per year or more.
NICKEL-IRON BATTERY, 60 CELLS, 225 AMPERE-HOURS.
To deliver 3.24 kilowatts for 5 hours.
Cost.
Weight.
Total.
Per
Kilowatt-hour
of Capacity.
Total.
Per
Kilowatt-hour
of Capacity.
In covered steel tanks
$960
$59-25
1,200 Ibs.
71 Ibs.
Depreciation unknown.
109. Comparative costs of electrical energy from storage
batteries and from ordinary primary batteries. — (a) A storage
battery is essentially like any ordinary battery except that a
storage battery can be regenerated by forcing a current through
it backwards. A storage battery which has delivered one kilo-
watt-hour of electrical energy can be made as good as new by
the expending of a little more than a kilowatt-hour in forcing
current backwards through the battery at a cost of say 20 cents.
Therefore, the output of a storage battery may cost as low as 20
cents per kilowatt-hour.
(b) A Grenet or Fuller cell can be regenerated after use by
replacing the zinc and the electrolyte. Therefore the cost of
the electrical energy delivered by a Grenet or Fuller cell is equal
to the cost of the materials consumed plus a few cents for the
labor of setting up the cell. The voltaic action corresponding to
100 ampere-hours represents the consumption of 0.26 pound of
zinc at 15 cents per pound, 0.40 pound of potassium bichromate
* Or 3.5 kilowatts for 5 hours, or 5 kilowatts for 3 hours, or 10 kilowatts for I
hour.
15
210 ELECTRIC LIGHTING.
at 15 cents per pound and 0.6 pound of sulphuric acid at 2 cents
per pound (the zinc is reckoned considerably higher in price
than ingot zinc for several reasons, one of which is the cost of
mercury for amalgamating the zinc). Therefore, counting five
cents for the labor cost we have a total cost of 16.1 cents for 100
ampere-hours. The electromotive force of the bichromate cell
is about 2 volts, therefore 100 ampere-hours represents 200 watt-
hours, and 200 watt-hours at 16.1 cents gives a rate of 80 .cents
per kilowatt-hour. But the total consumption of materials in
a Grenet cell is at least five times the consumption corresponding
to the voltaic action alone, and the total consumption of materials
in a Fuller cell is at least two times the consumption corresponding
to the voltaic action alone. Therefore the output of a Grenet
cell costs about $4.00 per kilowatt-hour and the output of a
Fuller cell costs about $1.60 per kilowatt-hour.
(c) When an ordinary dry cell is discharged the entire cell is
thrown away, and therefore, the first cost of the cell is the cost of
its output of electrical energy. Thus a dry cell costing 25 cents
has about 50 ampere-hours of discharge capacity at 1.6 volts*
which is equivalent to 80 watt-hours, and 25 cents for 80 watt-
hours is at the rate of $3.12 per kilowatt-hour.
Comparing (a), (b) and (c) it is evident that a storage battery
is very much cheaper than an ordinary primary battery provided
the storage battery can be charged without excessive loss of
energy in a rheostat and without carrying the battery to a
charging station. The following example shows the excessive
cost of a storage battery where these two conditions are not
realized. A three-cell storage battery having a capacity of 50
ampere-hours at 6 volts is delivered to the proper place for
charging at a cost of 50 cents counting return delivery and the
battery is charged from no- volt direct-current mains so that
5,500 watt-hours f of energy is consumed in charging the battery.
* No allowance is here made for the fact that the terminal voltage of the cell
may be considerably less than its open-circuit voltage.
t The battery would be connected to the supply mains in series with a rheostat
and about 94 per cent, of the energy taken from the mains would be lost in this
ELECTROLYSIS AND BATTERIES. 211
At 15 cents per kilowatt-hour this energy amounts to 82 cents,
and the total cost of $1.32 for charging the battery is the cost
of the 300 watt-hours* of battery output, which is at the rate of
$4.40 per kilowatt-hour.
no. The management and care of a lead storage battery.* —
The lead storage battery deteriorates rapidly in service when it is
not properly cared for, and, the first cost of the storage battery
being'high, it is important that it should have proper care. The
deterioration shows itself by a decrease of ampere-hour capacity,
by a continued disintegration of the active materials of the
electrodes, by a slow corrosion of the massive lead grids and by
warping and buckling of the grids.
Setting up a storage battery. — Detailed directions for setting up
a storage battery are always supplied by the manufacturer. A
person who has not had experience in handling acids must
exercise great care. The concentrated acid should be poured
into the water in a thin stream and the water should be stirred
with a wooden paddle, great care being taken to avoid splashing.
The acid should be mixed in an earthenware jar or in a clean
wooden tub. Metal must not be used.
The electrolyte. — The electrolyte is dilute sulphuric acid having
a density of about 1.21 at 70° F. when the battery is charged.
This acid must be quite pure (free from iron, hydrochloric acid
or nitric acid), and pure water, preferably distilled water, must
be used for mixing the electrolyte.
When the surface of the electrolyte falls because of evaporation,
pure water must be added so as to keep the tops of the grids
covered to a depth of about one-half inch.
Discharging. — The normal discharge current of a lead storage
rheostat. To avoid this loss of energy many storage cells must be connected in
series for charging from no- volt mams.
*See Chapters XXII and XXIII of Lyndon's Storage Battery Engineering,
McGraw-Hill Book Company, 1911.
Manufacturers of storage batteries publish circulars giving instructions for
setting up and operating, and the manufacturers are usually glad to send these
circulars to any one who is interested in storage battery work.
212 ELECTRIC LIGHTING.
cell (on the basis of an eight-hour discharge) is about 5 amperes
per square foot of positive grid area, both sides of each positive
grid being counted.
A current exceeding 4 or 5 times the normal discharge current
should never be taken from a storage cell; if a greater current
must be taken from a cell it should be for a few minutes only
and the battery should be at full charge.
A lead storage battery should never be discharged so* as to
cause the voltage to drop below 1.75 volts per cell, while the
normal discharge current is flowing.
A lead storage cell should never be allowed to stand discharged.
Charging. — Usually a lead storage battery is charged by a cur-
rent equal to the normal discharge current, the time required
for charging being eight or eight and one-half hours.
The charging current may be high, however, when the battery
is nearly discharged, and it should be low when the battery
approaches full charge, especially after evolution of gas begins.
A good rule for rapid charging is to deliver 35 per cent, of the
total ampere-hours during the first hour, 52 per cent, during the
next two hours, and 14 per cent, during the fourth hour. Thus a
loo-ampere-hour cell may be completely charged in four hours by
using a charging current of 35 amperes during the first hour, 26
amperes during the second and third hours, and 14 amperes
during the fourth hour.
Overcharging. — A battery should be overcharged once a week,
or once every two weeks if it is not used daily. This overcharge
is a prolongation of the regular charge (at the normal eight-hour
rate) until the voltage across each cell reaches a maximum, that
is, until five successive voltmeter readings, 15 minutes apart,
show no further increase of voltage, or until gas is developed in
all the cells freely.
Voltmeter test. — The voltage of each cell should be taken just
before the end of the weekly overcharge with current flowing at the
normal eight-hour rate. The normal voltage under these con-
ditions is about 2.56 volts per cell. The voltage normally reached
ELECTROLYSIS AND BATTERIES. 213
during the regular charging is about 2.45 volts per cell. An
abnormally low voltage shows that a cell has been discharged
by internal short circuit.
Inspection. — Just before the weekly overcharge, every cell
should be inspected carefully, especial attention being given to
those cells which have shown abnormally low voltage on previous
tests. The object of the inspection is to see that no internal
short circuits exist. Short circuits are to be removed by means of
a thin strip of hard wood pushed down between the grids. Evi-
dences of sulphatation should also be noted as explained under
the heading sulphatation.
Treatment of cells which show abnormally low voltage. — If the
voltage of a cell does not rise to the normal value during an
overcharge, it must be cut out of circuit when the battery is dis-
charged and cut in again just before beginning the next charging.
If this does not bring it up to normal voltage the process must
be repeated.
Sediment. — The accumulation of sediment in the bottom of the
jars must be watched and the sediment must be removed before
it reaches the bottom of the grids. In the case of small cells
the grids may be lifted out after the battery has been fully
charged, the electrolyte drawn off, and the sediment washed
out of the jars. It is important to get the elements back and
covered with electrolyte again as quickly as possible. Fresh
electrolyte must be added to make up for the electrolyte lost
with the sediment.
Sulphatation. — Sulphatation of the grids of a lead storage cell
consists* of the conversion of portions of the active material
wholly into lead sulphate. This pure sulphate is a very poor
conductor and, once it is formed, it is difficult to make it act as
anode or as cathode and thus reconvert it to lead peroxide or to
spongy lead respectively. A layer of pure lead sulphate some-
times forms between the active material and the metallic lead
* It is claimed by some authorities that sulphatation consists in the formation
of hydrated lead sulphate.
214 ELECTRIC LIGHTING.
of the grid, and sometimes the external surface of the active
material becomes covered with a crust of pure sulphate. Pure
lead sulphate is white and whenever white spots appear on the
grids of a lead storage cell, the cell should be subjected to a very
long-continued over-charge in the attempt to reduce the pure
lead sulphate into active material.
A very good method* for treating sulphated cells is as follows:
1. Remove the acid electrolyte and rinse with pure water.
2. Fill the cells with a solution of pure sodium sulphate using
200 grams of the crystallized salt per liter of water.
3. Charge the battery in the usual way at the 8-hour rate for
50 hours or more.
4. Remove the sodium sulphate solution and rinse with pure
water.
5. Replace the acid electrolyte, using a little fresh acid to
bring it up to correct strength.
6. Charge the battery
One change of water is sufficient for each rinsing. The cost
of the entire treatment counting labor, materials and energy is
about 21 cents per cell for cells rated at 6o-ampere-hours.
Variation of capacity with discharge rate. — When a storage cell
is discharged slowly, the discharge can be carried further than
when the cell is discharged rapidly, that is to say, the ampere-hour
capacity is greater with a small ampere discharge than with a
large ampere discharge. The relation between ampere-hours of
capacity and amperes of discharge rate for the stationary bat-
teries of the Electric Storage Battery Company is as follows:
A cell that can deliver 12.5 amperes for eight hours can deliver
17.5 amperes for five hours, 25 amperes for three hours or 50
amperes for one hour.
in. The use of storage batteries.f — Storage batteries are ex-
tensively used in the place of ordinary primary batteries in
*See a paper by C. W. Bennett and D. S. Cale; read before the Boston Gen-
eral Meeting of the American Electrochemical Society, April 18, 1912.
t Fundamentally, of course, a storage battery is used to store electrical energy
at a given time and place in order that the energy may be used when and where
it is needed.
ELECTROLYSIS AND BATTERIES.
215
telephone and telegraph work and in railway signalling.* Stor-
age batteries are also used for driving electric vehicles and for
railway car lighting, and very large storage batteries are used in
central stations for one or more of the following purposes:
(a) For supplying the station output during the hours of small
demand. In this case the battery is charged while the station
is in operation, and discharged during the remainder of the day,
thus obviating the expense of operating the station continuously.
280
240
160
6
AM
charge^
/discharge
^
10 12 2
Fig. 125.
6
PM
(b) For equalizing a fluctuating station load. In this case pro-
vision is made for the battery to charge while the station load
is below the average and to discharge while the station load
is above the average. This is an important use of large storage
battery installations, and the cost of installing and maintaining
the battery is set over against the saving in the first cost of the
station and the saving in the cost of operating the station.
* In many cases a small motor-generator is used to take current from no- volt
mains (direct-current or alternating-current) and deliver direct current at low voltage
for charging. In some cases direct current for charging is derived from alternating-
current supply mains by using the mercury-vapor rectifier.
216
ELECTRIC LIGHTING.
(c) As a reserve. — The primary object of a storage battery
may be to supply the output of a station during certain hours
of the day or to equalize a fluctuating load on a station. In both
cases the battery will be valuable also as a reserve to supply the
station load in case of a break-down.
Figure 125 illustrates the use of a storage battery for supplying
the total station output during the hours of small demand. The
10
12 3. 6 9 12 3 6 9 12
curve represents the operation of a small direct-current plant at
Milan, Michigan, in 1902. The engine and generators were
operated from 5:30 P. M. to 10:30 P. M. From 5:30 to about
6:20 P. M. the generators supply the station load (which is small)
and charge the battery. Between 6:20 P. M. and 8:40 P. M.
the generators supply the station load, only, and the battery is
disconnected. Then from 8:40 P. M. until 10:30 P. M. the
generators supply the station load (which is small) and charge
the battery. The engine is shut down at 10:30 P. M. and the
battery carries the entire station load until 5 :3O the next evening.
The use of a storage battery for equalizing the load on a
ELECTROLYSIS AND BATTERIES.
217
generator is shown in Fig. 126. This curve shows the operation
of the central station of the Hartford Electric Light Company on
December n, 1905. The battery was charged from about 10:30
P. M. to 6 A. M., and discharged from about 4 P. M. to 10:30
P. M., during the peak of the station load.
The use of a storage battery for equalizing the rapidly fluctuat-
ing load of an electric railway station is shown in Fig. 127. The
dotted curve in this figure shows the actual generator load and
CONNECTICUT Railway AND LUSHTING* Co
New Bn
I I I I I
Fig. 127.
the full-line curve shows the rapidly fluctuating station load be-
tween 12 :o6 P. M. and 12:15 P. M. Readings were taken every
five seconds.
The use of a storage battery as represented in Figs. 125, 126
and 127 depends upon the employment of controlling devices
as described in the following articles.
112. The use of a storage battery for supplying the output of
a station during the hours of small demand. — When a storage
battery is used for this purpose it is nearly always desired to
21 8 ELECTRIC LIGHTING.
deliver current at constant voltage, and some device for con-
trolling the voltage of the battery is necessary as explained below.
A sufficient number of storage cells is used to give the required
voltage when the battery is discharged and has 1.8 volts per cell,
and the controlling device is arranged to take up the excess
voltage when the battery voltage is higher than the desired value.
Control of voltage by rheostat. — The current, /, delivered by
the battery flows through a resistance, R, Fig. 128, and this
resistance is adjusted so that the excess of battery voltage may
be used up as the voltage drop RI in this resistance. When the
station output is constant this method of control is fairly satis-
factory, for, in this case, the resistance has to be adjusted only
occasionally as the battery voltage falls off. When the station
output fluctuates, however, the rheostat, R, Fig. 128, requires
constant attention because the voltage drop RI in the rheostat
changes when the station output changes.
Control of voltage by counter-electromotive-force cells. — When
current flows through a low-resistance electrolytic cell consisting
of plain lead plates in dilute sul-
phuric acid, the voltage drop
through the cell varies from about
2.3 to 2.5 volts according to the
value of the current. The excess
voltage of a discharging storage
battery may be taken up by caus-
ing the current to flow through a
number of such cells connected in
series, the number being reduced
as the battery voltage decreases.
to lamps
The advantage of this arrange-
Fig 12g ment is that the voltage which is
lost in these controlling cells does
not vary greatly with the current. This method of voltage con-
trol is seldom used in practice. It has no advantage over the
rheostat method when the load is constant, and the end-cell
method is usually preferred when the load is variable.
ELECTROLYSIS AND BATTERIES
219
Control of voltage by end-cells. — This method of control will be
explained by giving an actual example of a battery delivering
current at no volts. , The lowest permissible voltage at the end
of the discharge is usually taken to be 1.8 volts per cell. There-
fore the number of cells required to give a minimum of no volts
is no -f- 1.8, which is equal to 61. The highest voltage is about
2.15 volts per cell at the very beginning of the discharge (see
Fig. 123), and 51 cells are therefore required at the very beginning
of the discharge to give no volts. Therefore, the entire battery
being fully charged, 51 cells are used at the beginning of the dis-
charge, and as the voltage of the battery falls off the number of
cells is increased, by connecting-in additional cells at one end of
the set, until, when the battery reaches the limit of discharge,
all of the 6 1 cells are in service. Under these conditions it is
evident that the end-cells, which are in service only a portion of
the time during the delivery of current by the battery, are not
completely discharged Therefore, when the battery is re-
charged, the end-cells are placed in circuit at the start and cut
out one by one as they become
fully charged, as indicated, for
example, by the copious evolu-
tion of gas.
An important detail in the car-
rying out of the end-cell method
of voltage control is the design
of the switch for connecting and
disconnecting the end-cells with-
out interrupting the delivery of
current, and without momen-
tarily short-circuiting the indi-
vidual cells. The essential fea-
tures of this end-cell switch* are
shown in Fig. 129. The terminals of the end-cells are
brought out to a series of contact blocks, cccc, which are
* Various types of end-cell switches are described on pages 285-324 of Lyndon's
Storage Battery Engineering.
Fig. 129.
220
ELECTRIC LIGHTING.
rather widely separated from each othep. The movable con-
tact arm of the connecting and disconnecting device has two fin-
gers, a and b, which are far enough apart to bridge across be-
tween two of the blocks cc as shown in the figure. When the
contact arm is moved it stands for a moment in the position
shown in the figure and short-circuits one of the cells of the bat-
tery, but this short-circuit takes place through the resistance R
so that no damage is done. The contact arm is arranged to move
quickly past the position shown in the figure and stand with both
fingers a and b in contact with one of the blocks c.
113. The booster. — Consider, for exam pie, the use of a storage
battery for supplying the output of a station during the hours
of small demand, the voltage of the station being, say, no volts.
A battery of 61 cells would be required as explained above, and to
charge such a battery a voltage of about 150 volts would be
Main
Main
Fig. 130.
required towards the end of the charge (2.45 volts per cell).
Now the battery is usually charged from the main generator
of the station while the generator is supplying regular station out-
put at no volts, and therefore the generator voltage is not
sufficient to charge the battery. In practice a small auxiliary
generator B, Fig. 130, is connected in series with the storage
ELECTROLYSIS AND BATTERIES.
221
battery and this auxiliary generator helps to force the charging
current through the battery. The auxiliary generator B is
called a booster.
114. Automatic boosters.* — When the station load changes
slowly, as is usually the case in an electric lighting station, there
is ample time for an attendant to connect up a booster and charge
a storage battery when the station load is small, and to disconnect
the booster and make the necessary arrangements for discharging
the battery when the peak of the load comes on. When, how-
ever, the station load fluctuates rapidly and irregularly as is
usually the case in an electric railway power station, hand control
of the storage battery is impossible. In such cases an automatic
booster must be used.
The differential booster. — Fig. 131 shows an arrangement,
due to Mailloux, in which a booster, B, is actuated by variations
Fig. 131.
of line current. The booster has two opposing field windings,
5 and S'. When the demand for current is at its average value
the windings, 5 and 5', balance each other, the small generator,
B, develops no electromotive force, and the battery neither
charges nor discharges. When the line current is excessive the
* A very full discussion of boosters and booster systems is given on pages 325-470
of Lyndon's Storage Battery Engineering.
222
ELECTRIC LIGHTING.
winding, S, predominates, and the voltage of B helps the bat-
tery to discharge; when, however, the line current is small the
winding, S', predominates and the reversed voltage of B helps
the line voltage to charge the battery.
Booster with automatic carbon rheostat control. — Fig. 132
shows a carbon rheostat, RRf, connected across the terminals of
the storage battery ; and the field winding, F, of the booster, B,
is connected from the middle of the rheostat to the middle of the
battery. The solenoid S pulls on an iron plunger which is
attached to one end of the lever II and two lugs on this lever
push on two piles of carbon plates R and Rf which constitute
the rheostat. A large line current gives a strong pull of the
solenoid which compresses the pile R of carbon plates and greatly
Line
Line
Fig. 132.
reduces its resistance. A small line current reduces the pull of
the solenoid and the pull of the spring compresses the pile of Rf
of carbon plates thus greatly reducing its resistance. The current
in the field winding F of the booster is zero when the resistances
of R and R' are equal, and the current through the field winding
ELECTROLYSIS AND BATTERIES. 223
is in one direction when R is greater than Rf and in the opposite
direction when R is less than R'. In this manner the field of
the booster is so excited as to cause the booster to help the
storage battery discharge when the station output is large and
to help the station voltage to charge the battery when the
station output is small.
The ordinates of the extremely irregular curve in Fig. 127
represent the fluctuating demand for current on a railway power
station during a period of ten minutes. Without a storage
battery the generators would have to meet this extremely irregular
demand, varying from a minimum of about 180 amperes to a
maximum of about 850 amperes. The ordinates of the slightly
undulating dotted curve show the values of generator output
when an adequate storage battery is installed and controlled by
a booster as shown in Fig. 132 with the field excitation of the
booster under the control of a carbon rheostat. When the total
load curve is above the dotted curve (generator output) the
battery discharges, and when the total load curve is below the
dotted curve the battery charges.
The general average of the generator load must be slightly
greater than the general average of the station output because
some energy is lost in the battery, but the average generator
load during a short period may be greater or much less than the
average station output during that period. Thus the average
station output during the ten minute period, which is shown in
Fig. 127, was evidently greater than the average generator
load during that period so that the battery was on the whole
discharging.*
115. The floating battery. — The simplest arrangement for
causing a storage battery to operate automatically and tend to
equalize a station load, is that which is frequently employed in
connection with long feeders over which a considerable drop of
voltage takes place when a large current is delivered. This
* A good example of a large storage battery installation is described by Franklin
E. Moore in the Street Railway Journal for September 21, 1911.
224
ELECTRIC LIGHTING.
arrangement is shown in Fig. 133, in which G is the main
generator and B is the storage battery. Any great demand for
Long feeder _•_-•. ,
Long feeder
a
(°X°3tl
Fig. 133.
current causes the voltage, E, to decrease, so that the battery
can discharge, and when the demand for current is small the
voltage, .E, rises and the battery is charged. A battery con-
nected as shown in Fig. 133 is called a floating battery. Such a
floating battery cannot completely equalize the demand on the
station, inasmuch as the rise and fall of the voltage, E, depends
upon some decrease and increase of the current flowing through
the long feeders.
116. The negative booster. — An arrangement which produces
an effect which is exactly equivalent to Fig. 133 is shown in Fig.
A generator G supplies current at constant voltage and
Tramps
Fig. 134.
an elevator motor takes current from the constant voltage mains
through a series motor SM. This series motor is belted to the
ELECTROLYSIS AND BATTERIES. 225
main generator G so as to run at constant speed, and so that
the power generated by SM may be belted back to the main
generator. When the elevator motor takes large current the field
of the series motor is strongly excited and its counter electro-
motive force is large so that the voltage E2 is much less than EI.
Under these conditions the storage battery discharges. When
the elevator motor takes small current the field magnet of the
series motor is only weakly excited and its counter electromotive
force is small so that E% is nearly as large as EI and the storage
battery charges.
The series motor SM in Fig. 134 is called a negative booster,
and the loss of voltage in the series motor due to its counter
electromotive force is exactly analogous to the drop of voltage
in the long feeders in Fig. 133. That is to say the battery in
Fig. 134 acts exactly like the floating battery in Fig. 133.
16
CHAPTER IX.
MISCELLANEOUS APPLICATIONS.
117. The Morse telegraph.* — An insulated wire leads from
one station to another and back again (the earth is generally
used instead of a return wire) . An electric current from a battery
is sent intermittently through this circuit by operating at one
station a key which makes and breaks the circuit. This current
excites an electromagnet at the other station, and the armature
of this electromagnet makes a record on a moving strip of paper
or produces sound signals which are interpreted by the operator
at the other station.
Relays and sounders. — A fairly strong electric current is re-
quired to operate the instrument which produces the signals at
the receiving station, and it is not desirable to send so strong a
current over a long line because of the great number of voltaic
cells that would be required. This difficulty is obviated by the
use of a relay. A small current flows over the line and through
many turns of fine wire wound upon an electromagnet (of the
relay) at the receiving station. This magnet actuates a very
light lever, and this lever is arranged to open and close what is
called a local circuit as it moves back and forth between stops.
The local circuit which is opened and closed by the light lever of
the relay contains a battery which supplies a moderately large
current for the operation of the instrument which produces the
sound signals. This instrument is called a sounder. It consists
* A good treatise on telegraphy is American Telegraphy by William Maver, Jr.,
New York, 1892.
It is not practicable to operate a very long telegraph line as one circuit for reasons
which are explained in the article on submarine telegraphy. Long circuits are,
therefore, broken up into sections. In the early days messages were repeated
from one section to another by hand, but an automatic device called a repeater is
now used.
226
MISCELLANEOUS APPLICATIONS.
227
of an electromagnet which is wound with moderately coarse wire
and which actuates a massive lever, and the lever produces sharp
clicks as it moves back and forth between stops.
Way stations. — An ordinary telegraph may include relays
placed at points along the line, and a make and break key may be
operated at any point along the line if all the other keys are
local battery
Fig. 135.
closed. When any key is thus operated all of the instruments
on the line respond simultaneously. The simple railway tele-
graph is usually arranged in this manner. It is not unusual
to have a single circuit one hundred and fifty miles or more in
length containing fifteen or twenty way stations.
The arrangement of relay and sounder is shown in Fig. 135, aa
being the wires which connect the fine-wire winding on the relay in
home station way station distant station
key keif
INT
_J relay
ground
relay
Fig. 136.
ground
circuit with the telegraph line. Figure 136 shows a simple
telegraph circuit with two end stations and one way station.
The local circuits and sounders (one at each station) are omitted
from this diagram for the sake of clearness. Of course all of
228
ELECTRIC LIGHTING.
the keys are normally closed, and when a telegram is to be sent
from any station the key at that station is manipulated so as to
make and break the circuit of the line.
118. Duplex telegraphy. — The sending of two messages (in
opposite directions) over one line wire simultaneously is called
000000(5000
battery
home relay
d(~ artificial line)
"UTblTo o o o o!T5
Fig. 137.
duplex telegraphy. There are two systems of duplex telegraphy,
namely the bridge duplex, and the differential duplex. Way sta-
tions cannot be used in the duplex system.
Figure 137 shows the principle of the bridge duplex. The four
resistances a, b, c, and d constitute a Wheatstone bridge ar-
rangement, and no portion of the battery Current flows through
the home relay when the home key ic closed. The resistance c
represents the line and the apparatus at the distant station (which
is interpolated at p). The actual arrangement of the bridge
home station ... distant statio*
line
key
Fig. 138. Bridge duplex.
duplex is shown in Fig. 138. In Fig. 138 the distant relay re-
sponds to the home key and the home relay responds to the dis-
tant key. The local circuits and sounders are omitted for the
sake of clearness.
MISCELLANEOUS APPLICATIONS.
229
The differential duplex makes use of the differentially wound
relay or the differential relay, and the principle of the differential
duplex is shown in Fig- 139. The battery current divides equally
c(=ttne)
«!
^
c. b
=- bntteri
^
, 00000000000
home
differential
relay
d(= artificial line)
>*
1
00000000000
Fig. 139.
between the two similar branches c and J, and the two equal
parts of the battery current circulate in opposite directions in the
two windings a and b of the differential relay so that the iron
core of the differential relay is not magnetized when the key is
closed in Fig. 139. The resistance c represents the line and the
apparatus at the distant station (which is interpolated at p).
The actual arrangement of the differential duplex is shown in Fig.
140. In Fig. 140 the distant relay responds to home key and
the home relay responds to the distant key. The local circuits
and sounders are omitted for the sake of clearness.
home station
a
key
bf:
line
distant station
key
- ; differential differential ^
^ relay relay ;r;
^ d
?— **5S
* ::
ry
ound
.11—. ed
ooooootftTtitP *—" '
fc
fjrounc
S-==S=5=
Fig. 140. Differential duplex.
The bridge duplex prevails in Europe and especially in England,
and the differential duplex is almost universal in the United
States. The bridge duplex requires the use of a larger battery
than the differential duplex.
230
ELECTRIC LIGHTING.
The artificial line. — An ordinary telegraph line has not only
resistance but also a certain amount of inductance, and there is
also a certain electrostatic capacity between the line and the
ground. The artificial line d in Figs. 138
and 140 must duplicate the properties of
the real line in every respect in order to
completely eliminate the effect of the home
battery on the home relay in Figs. 138 and
140. This artificial line is arranged as
shown in Fig. 141 in which r and r' are
adjustable resistances, C is a condenser
and L is an inductance. This arrange-
ment does not enable a very long line to be exactly matched.*
119. Diplex telegraphy. — The sending of two messages (in the
same direction) over one line wire simultaneously is called
diplex telegraphy. Diplex telegraphy depends upon the use of
ground
Fig. 141.
Fig. 142. Polarized relay.
* Artificial duplicates of very long lines and submarine cables are described in
Maver's American Telegraphy, pages 276 to 280.
MISCELLANEOUS APPLICATIONS.
231
two kinds of relays, namely, (a) An ordinary relay with a fairly
stiff spring so that the lever of the relay responds to an increase
and decrease of current, the current being never reduced to zero;
and (b] The so-called polarized relay, of which the lever responds
to reversals of current. The ordinary relay is usually called
the neutral relay to distinguish it from the polarized relay.
The polarized relay. — A general view of a polarized relay is
shown in Fig. 142, and the essential features of the relay are
Fig. 143.
Fig. 144.
shown in Figs. 143 and 144. An ordinary electromagnet (with
soft iron cores) is mounted on one pole of a U-shaped permanent
magnet of steel, and a light iron lever, a pivoted at p, plays
between the two poles NI and N2 of the electromagnet.
When current flows in a certain direction through the coils
of the electromagnet one of the poles, say NI, is greatly
strengthened and attracts the lever a. When the current is
reversed the other pole N2 is strengthened and attracts the
lever a. Thus the lever a is pulled towards NI or N2 accord-
ing to the direction of the current, and therefore the lever a
may be made to open and close a local circuit in response to
reversals of the line current which flows through the windings on
N and N%.
232
ELECTRIC LIGHTING.
Diplex telegraphy. — Figure 145 shows the essential features of
the arrangements for diplex telegraphy. The action is evident;
the polarized relay responds to the reversing key R, and the
neutral relay responds to the increase-and-decrease key, J. An
home station
reversing
increase and
decrease key
resistance
line
distant station
polarized neutral
relay relay
ground
Fig. 145. Diplex telegraph.
important thing which is not shown in the figure is that the
reversing key R must be arranged so that it is impossible for
the operator to hold its lever midway between the contact points,
because the reversal of current must take place as quickly as
possible so that the lever of the neutral relay may not have time
to respond. The lever of the reversing
key is therefore usually actuated by an
electromagnet, and the electromagnet
*H" is controlled by a hand-operated key
[ m which opens and closes the local circuit
-=- of the electromagnet. Also it is an ad-
'-=- vantage to connect condensers as shown
in Fig. 146 so as to eliminate sparking,
and to ensure the quickest possible re-
versal of current.*
A neutral relay and a polarized relay
might be placed in circuit with a diplex line at a way station so
* The action of a condenser in causing a quick reversal of current is explained
in Franklin and MacNutt's Electricity and Magnetism (The Macmillan Co.); see
index.
ground
Fig. 146.
MISCELLANEOUS APPLICATIONS.
233
that the way station and the distant end station could both re-
ceive messages from the sending station. This arrangement,
however, is never used. Indeed diplex telegraphy is used only
in conjunction with duplex telegraphy to give quadruplex teleg-
raphy as explained in the next article.
120. Quadruplex telegraphy. — The sending of four messages
(two messages each way) over one line wire simultaneously is
line
"
neutral relay
polarized relay
Fig. 147. Bridge Quadruplex.
called quadruplex telegraphy. This is accomplished by combining
the arrangements for duplex (either bridge duplex or differential
duplex) and diplex telegraphy. Thus a key arrangement like
that shown in Fig. 145 may be installed at each station in Fig.
^differential polarized relay
r V- line
differential neutral relay
Fig. 148. Differential Quadruplex.
138, and the single relay at each station in Fig. 138 may be re-
placed by two relays, a neutral relay and a polarized relay, as
shown in Fig. 147. The local circuits and sounders are omitted
for the sake of clearness.
Figure 148 shows the combination of the diplex and the dif-
234 ELECTRIC LIGHTING.
ferential duplex. The differential duplex has an advantage over
the bridge duplex in that the resistances a and b in Figs. 138
and 147 are not necessary in the differential system, and therefore
it is possible to operate the differential system with less battery
power.
In Figs. 147 and 148 the neutral relay at each station responds
to the I key at the other station, and the polarized relay at each
station responds to the R key at the other station.
The quadruplex system is very extensively used where the line
wires are not used also for telephones as explained in Arts.
129-135.
Way stations cannot be served in the quadruplex system.
121. The printing telegraph* is an arrangement by means of
which a simple form of typewriter is operated at a distant station
from a key board at the sending station. The simplest form of
printing telegraph is the well known ticker which prints in one
line on a long strip of paper. The action of the ticker is as
follows: Twenty-six equidistant pins are arranged in a helical
row around a long metal cylinder. This cylinder is rotated by a
small electric motor or by clock work, and. above the cylinder is
a bank of twenty-six lettered keys so arranged that when a key
is depressed one of the pins comes against it and the cylinder
is stopped in a certain position; the next key would stop the
cylinder 1/26 of a revolution farther on, and so on. Attached to
the rotating cylinder is a device for reversing an electric current
* The ticker as now generally used in American cities is somewhat different from
the device here described. See Maver's American Telegraphy, pages 395-420.
When a person is thoroughly familiar with the elements which enter into the
construction of a machine, that is, when a person is familiar with shafts and wheels
and with simple devices like switches for opening and closing circuits and for re-
versing connections, a more easily intelligible description of a complicated machine
can be made without illustrative diagrams and drawings than can be made with
the help of diagrams and drawings. Indeed it would be confusing under the speci-
fied conditions to have recourse, even, to a working model of a complicated machine
when the object in view is to impart a clear idea of its fundamental features. The
only element of a ticker which may not be familiar to the student is the escapement
device, the oscillations of which turn a toothed wheel notch by notch.
MISCELLANEOUS APPLICATIONS. 235
fifty-two times for each revolution of the cylinder. This re-
peatedly reversed electric current passes over the telegraph line
and through two electromagnets at the receiving station. One of
these electromagnets is like a neutral relay with a heavy lever, and
the other is like a polarized relay with a light lever which oscil-
lates with the rapid reversals of current and actuates an escape-
ment which turns a type wheel with the twenty-six letters ar-
ranged around its periphery. This type wheel is thus turned
step by step, keeping pace with the rotating cylinder at the
sending station. When the cylinder at the sending station is
stopped by depressing a key, the A-key for example, the current-
reversing device stops also, a steady current flows through the
line, the lever of the polarized relay stops oscillating, the type
wheel stops, and the steady current excites the neutral relay, the
lever of which pushes a strip of paper against the type wheel and
prints the letter A. When the key at the sending station is raised
the current reversals begin again, the type wheel at the receiving
station starts, and at the same time the lever of the neutral relay
falls back and actuates a device which moves the strip of paper a
step forward for the printing of the next letter.
122. Submarine telegraphy. — Figure 149 shows a full size
sectional view of a submarine telegraph cable. The conductor
at the center consists of a number of
strands of copper wire. Surrounding
this is a layer of gutta percha, and the
whole is protected by a covering of
tarred hemp and steel wire.
The conductor and metal sheath of
the cable, together with the intervening
insulating material, constitute a con-
denser of large electrostatic capacity.
The effect* of this large electrostatic
capacity is as follows: At the instant a battery is connected to a
* The effect which is here described is exaggerated by the action of the inductance
of the cable.
236
ELECTRIC LIGHTING.
Fig. 150.
cable a very large current begins to flow into the cable. Most of
this current goes to charge the cable, and, as the cable becomes
charged, the entering current falls off in value, settling finally to
a steady value which is de-
termined by the resistance
of the copper wires of the
cable. The ordinates of
curve A, Fig. 150, show the
successive values of current
which enters a cable from
a battery, the abscissas
being time reckoned from
the instant the battery is
connected.
At the distant end of
the cable an infinitesimal
current begins to flow out
of the cable almost at the instant the battery is connected
to the cable at the sending station, and as the cable be-
comes charged this outflowing current rises in value until it
reaches a steady value very nearly equal to the steady value of
the entering current. The
curve B, Fig. 150, shows
the growth of current flow-
ing out of the distant end
of a cable after a battery
is connected to the near
end. When the battery is
disconnected, the entering
current ceases at once, but
the outflowing current at
the distant end of the ca-
ble drops slowly to zero as
the accumulated charge flows out of the cable.
Distortion of current pulses by a cable. — The curve a, Fig. 151,
shows the character of the current pulse which enters a cable
elapsed time
elapsed time
Fig. 151.
MISCELLANEOUS APPLICATIONS. 237
when a battery is momentarily connected to the cable, and the
curve, b, shows the character of the current pulse which flows
out of the distant end of the cable. The action of a cable in
thus altering the character of a current pulse is called distortion.
Land lines distort current pulses to some extent, and it is for
this reason that a very long telegraph line cannot be satisfactorily
operated as a single circuit. Distortion very seriously impairs
the distinctness of telephonic transmission in land lines four or
five hundred miles long or more.*
The distortion of electric current pulses by a submarine cable
is analogous to the distortion of water-current pulses by a long
thin-walled rubber tube. If water is forced into one end of such
a tube in sharply denned pulses, the water will flow out of the
other end of the tube in one long continued pulse, and a succession
of separate pulses of inflowing water would show themselves as
slight variations of outflowing current.
The curves aaaa, Fig. 152, represent four short current pulses
sent into a cable at one end, and the curve b represents the pulse
of current which flows out of the
cable at the other end. The four
success've pulses of inflowing
, . elapsed time
current show themselves as four
slight humps on the curve b
of outflowing current, and it is
evident that these four success-
ive pulses of inflowing current
elapsed time
could not be detected by means Fig 152
of an ordinary relay and sounder
at the distant end of the cable. The receiving instrument in sub-
marine telegraphy is a galvanometer arranged to trace the curve
of outflowing current at the receiving end of the cable, and the
separate current pulses that are sent into the cable at the sending
*Wave distortion is very fully and simply discussed on pages 29, 30, 108-115
of Franklin's Electric Waves.
238 ELECTRIC LIGHTING.
end are inferred from the slight humps in the curve which is
traced by the receiving instrument.
123. The syphon recorder.* — The receiving instrument com-
monly used in submarine telegraphy is called the syphon recorder.
The current flowing out of the distant end of a cable passes
through a D'Arsonval galvanometer, the moving coil of which
produces sidewise motion of a pen which traces an ink line on a
moving strip of paper; the pen thus traces a current curve like b,
Fig. 152.
124. The telephone. — The telephone set includes a transmitter,
a receiver, and an arrangement for calling. The transmitter is a
device for producing over the line a current which is reversed
with each to and fro movement of a diaphragm, the diaphragm
being set into vibration by a speaker's voice ; and the receiver is a
device in which a diaphragm is set into vibration by these rapidly
reversed currents (which come to it over the line from the trans-
mitter) thus reproducing the original sound.
The transmitter. — A sectional view of a telephone transmitter
is shown in Fig. 153, and the connections are shown in Fig. 155.
An electric circuit contains a battery, the primary of a small
transformer (induction coil), and a mass of granular carbon
* The syphon recorder was devised by Lord Kelvin, who contributed more,
perhaps, to the development of transatlantic telegraphy than any other man. In
an article by Professor W. E. Ayrton, which appeared in the London Times shortly
after Lord Kelvin's death (reprinted in Popular Science Monthly for March, 1908),
much interesting information is given concerning what Kelvin did for submarine
telegraphy. "When signals through the 1858 Atlantic cable became weak, and a
message from the President to our Queen took thirty hours in transmission although
containing only 150 words, and which would need only three or four minutes to
transmit through any one of our good Atlantic cables of to-day, the only remedy of
those who looked down upon the theories of the young Glasglow professor was to
use Whitehouse's "thunder pump," a magneto-electric machine which produced
a sudden large electromotive force when the armature of a permanent magnet was
jerked off the poles of the magnet. But these shocks only sent sparks through the
gutta-percha insulating coating and hurried the poor cable to its doom, so that
even the three words per minute which would have been the utmost limit of speed
possible had this cable been entirely uninjured, were replaced by absolute silence."
MISCELLANEOUS APPLICATIONS.
239
between corrugated carbon blocks, all in series. The black
patches in Fig. 153 represent the carbon blocks, one of which is
supported rigidly, a/id the other of which is attached to the
diaphragm DD. The speak-
er's voice causes the dia-
phragm to vibrate and the
resistance of the granular
carbon increases and de-
creases as the diaphragm
moves to and fro. This
variation of resistance
causes the battery current
to increase and decrease,
and this increase and de-
crease of battery current in
Fig. 153.
the primary of the small transformer produces in the second-
ary a current which flows in one direction and the other alter-
nately as the diaphragm moves to and fro.
The receiver. — The simplest type of telephone receiver is shown
in Fig. 154. A coil of very fine wire, C, is wound around one
end of a permanent steel
magnet MM, and the
reversals of current from
the distant transmitter in
flowing through this coil
strengthen and weaken
the steel magnet alter-
nately, and the thin iron
diaphragm dd is moved to and fro by the variations of strength
of the steel magnet, thus reproducing the original sound. The
most approved form of telephone receiver has a bi-polar
magnet.
Two telephone stations all connected up for talking are shown
in Fig. 155. In order to give a call at the distant station a small
Fig. 154.
240
ELECTRIC LIGHTING.
magneto generator is used to operate a bell,* and the change
from connections required to operate the bell to connections re-
quired for the operation of transmitter and receiver is made by
receiver
&~
transmittcr
-^
induction coil
or transformer
•ground
ground
Fig. 155.
the movement of the hook when the telephone is taken from the
hook. Figure 156 shows the hook down, and the connections,
as indicated by the full lines (dotted lines are dead) , are proper
receiver
transmitter
line
honk
Fig. 156. Connections for ringing.
for operating the bell at the distant station. Figure 157 snows
the hook up, and the connections are proper for operating the
transmitters and receivers.
*Let it be understood that we are not discussing central exchange telephone
systems, but simple two-station telephone lines such as are extensively used in
railway work. The student is referred to Kempster B. Miller's American Telephone
Practice for full information on telephone practice.
receiver
MISCELLANEOUS APPLICATIONS.
line
transmitter
hook
line
Fig. 157. Connections for talking.
125. The ground return versus the metallic circuit. — Many
private and railway telephone lines use a single wire with ground
return. Such lines are objectionable for two reasons, namely,
(a) The atmospheric electricity gathered by such a line flows
to ground through the telephone receivers and makes an almost
incessant crackling sound which is very annoying; and (b) It is
impossible in the case of such a line to eliminate the disturbances
due to adjacent electric light and power lines. First class tele-
phone service demands therefore a wire circuit (two wires), and
such a telephone line is called a metallic circuit. The
advantages of the metallic circuit are (a) That disturb-
ances can be more completely eliminated when two
wires are used, and (b) A two-wire line lends itself
more readily than a single-wire line to combination
uses as explained later in connection with simplex,
composite and phantom circuits.
126. The use of divided choke-coils on metallic
telephone circuits. — A divided choke-coil is a con-
tinuous winding of wire on an iron core with a lead — *
wire brought out from the middle of the winding, as
shown in Fig. 158. There is great inductive opposition to the flow
of alternating current through the entire coil, but equal alternating
currents can enter at a and c and flow out at b without induc-
242 ELECTRIC LIGHTING.
live opposition because the magnetizing action of one half of the
winding is neutralized by the opposite magnetizing action of the
other half of the winding.
Figure 159 shows a metallic telephone circuit (the telephone
sets being like those shown in Figs. 156 and 157) with a divided
telephone set line telephone set ^
m
divided choke coil divided choke
line
-=-- ground ground
Fig. 159.
choke-coil connected between the line wires at each end of the
line, the middle lead of each choke-coil being connected to earth.
The high frequency telephone currents cannot flow through the
choke-coils to any appreciable extent, but any current (alternating
or direct) which flows in the same direction in both line wires can
flow without inductive opposition through the two halves of a choke-
coil and to ground without affecting the telephones.
Thus the atmospheric electricity which gathers equally on the
two line wires has an easy path to earth without flowing through
either telephone, and any current which is induced equally and
in the same direction in the two line wires has an easy path to
ground without flowing through either telephone.
A
/"•-•
telephone
ground ground
Fig. 160.
Figure 160 shows a metallic telephone circuit in which the high
frequency telephone currents are delivered to the line (and from
the line) by two small transformers A and B; and the trans-
former coils which are connected to the line have their middle
MISCELLANEOUS APPLICATIONS.
243
points grounded. This arrangement is equivalent to the arrange-
ment shown in Fig. 159. The small transformers A and B
in Fig. 1 60 with the, lead coming out of the middle of one of their
coils are called divided repeating coils
127. The phantom telephone circuit. — Two metallic telephone
circuits like Fig. 159 (or like Fig. 160) can be used as telephone
circuits and at the same time a third telephone circuit can be
established as indicated in Fig. 161, in which A A' is one set of
telephones like Fig. 159, BBf is another set of telephones like
H
!« a' f
n r n
u.
c^=4
|c cr|
"^^ ground k ground -°4?~
>c-
H
p u
s 6 ^fc' 6' 1
— r>
Fig. 161.
159, and CCf is a third set of telephones, all of which operate
independently of each other. Telephone current (high frequency
alternating) from C cannot flow across the choke-coil c but
can enter the two wires / and /' through the two halves of choke-
coil a, flow through the telephone set Cf and return through the
two wires k and k'. This circuit is called the phantom circuit:
128. The choke-coil and the condenser. — The simultaneous use"
of wires for Morse telegraph and for telephone depends in part
upon the use of choke-coils and in part upon the use of con-
densers; and it is important to understand that high frequency
alternating current cannot flow through a choke-coil but can
flow freely through a condenser, whereas a very low frequency
alternating current or a direct current can flow freely through
a choke-coil but cannot flow through a condenser.
If the main rod in Fig. 162 oscillates back and forth at high
frequency the heavy weight does not move perceptibly, but all
244
ELECTRIC LIGHTING.
of the motion of the main rod is accommodated by motion of the
end C of the lever CL. If the main rod oscillates back and
forth at very low frequency the end C of the lever does not move
spring
Fig. 162.
perceptibly, but all of the motion of the main rod is accommo-
dated by motion of the end L of the lever. If any agent A
causes the main rod to oscillate back and forth at high frequency
and if another agent B causes the main rod to move back and
forth at low frequency the two motions are added together so far
as the main rod is concerned, that is the mam rod performs both
motions simultaneously, but the end C of the lever will move
as if agent A were acting alone and the end L of the lever will
move as if agent B were acting alone; indeed, end C of the
lever will respond to agent A and end L of the lever will
respond to agent B.
main line
C
•
capacity
i
ground return
L
or
I
ooo (ToTo 000 O'O 0
inductance
wire return j
Fig. 163.
In action the mechanical arrangement in Fig. 162 is exactly
analogous to the electrical arrangement in Fig. 163. If one agent
A produces a high frequency alternating current through the
MISCELLANEOUS APPLICATIONS.
245
circuit //// and if another agent B produces at the same time
a low frequency alternating current through the circuit, then the
high frequency current produced by A will flow through the
condenser (capacity) and the low frequency current produced by
B will flow through the inductance.
129. The railway composite. — The arrangement for using an
ordinary ground-return telegraph line for telephone service at
the same time that it is being used for telegraph service is called
the railway or one-wire composite. Such an arrangement with
a way station served both by telegraph and telephone is shown in
Fig. 164.* The high frequency telephone currents and the low
frequency telegraph currents flow together over the line and
condenser
Cation A
choke
coil
relay Q
fa*T
station B
condenser
telephone
-^ se^
ooooo _
choke relay key
coil
way station
i
ground
Fig. 164. The railway composite.
return through the ground, but the telephone currents, only,
flow through the condensers and telephones, and the telegraph
currents, only, flow through the choke-coils, relays and keys
(which are of course all closed but one).
The arrangement shown in Fig. 164 is not very satisfactory
because a number of telephone sets do not operate satisfactorily
in series. It is better to connect the telephones all from line to
* The telephone calls are usually made by means of the telegraph. See Art. 137.
1
246 ELECTRIC LIGHTING.
ground so that any transmitter supplies current to all of the
receivers in parallel. This arrangement, which is shown in Fig.
165, allows all of the telegraph relays to be operated in series and
choke ret,... , at the same time it allows any
coil r~^ key
— WffWffffinrxJ — * — ) telephone transmitter to deliver
— 1 lin-Z current at all of the telephone
receivers in parallel.
The excessively quick change
of current due to the opening
and closing of a telegraph key
telephone causes a momentary flow of cur-
rent through the condensers and
^ telephones so that the telegraph
signals are audible in the tele-
Fig. 165.
phones. This difficulty is to
a great extent obviated by "bridging" a condenser across each
key or across each key and relay taken together, as shown in
Figs. 1 68 and 169. Each relay should also be shunted by a non-
"inductive high resistance so as to eliminate high frequency oscil-
lations around the circuit which is formed at each station by the
telephone and telegraph apparatus (at the way station by the
telegraph apparatus and the condenser C in Fig. 165). Of
course the relays are themselves choke-coils and in some cases
therefore the additional choke-coils shown in Figs. 164 and 165
might be omitted.
130. The simplex circuit. — The railway composite is useful
but it has all of the disadvantages of a ground-return telephone
line (see Art. 125) and the telegraph signals cannot be entirely
eliminated from the telephones. An arrangement in which these
objectionable features are avoided is the simplex circuit which
is shown in Fig. 166. The action of this arrangement may be
understood with the help of the discussion of Arts. 126 and 127.
The two wires of the metallic telephone circuit serve as one wire
for a ground-return telegraph circuit, and, if there are no way
MISCELLANEOUS APPLICATIONS. 247
stations, this telegraph circuit can be operated duplex or quadru-
plex by installing apparatus like Figs. 147 or 148 for the simple
telegraph apparatus shown in Fig. 166.
^telephone set
n
L
r~
relay
battery
ground
Fig. 166. The simplex telegraph circuit.
Figure 167 shows a simplex circuit with a telegraph set at a
way station. The way station may also be served by a telephone,
the telephone set* being connected across ("bridged" across)
between the two wires on either side of the condensers in Fig. 167.
131. The simplex on phantom. — Telegraph apparatus can be
inserted in the two ground leads in Fig. 161, thus giving three
metallic telephone circuits and one ground-return telegraph cir-
cuit on four wires.
Duplex or quadruplex apparatus like Figs. 147 or 148 can be
inserted in the ground leads in Fig. 161, thus giving three inde-
pendent metallic telephone circuits and permitting the sending
-rc — j B t. : — TL
r*
relay
Fig. 167. Telegraph way station on simplex.
of four telegraph messages over the four wires of Fig. 161 all at
the same time. The matter of duplex and quadruplex working
on telephone lines is discussed briefly from a practical point of
view in Art. 138.
* The magneto and bell are not shown in Figs. 166 and 167. See discussion of
telephone calls in Art. 137.
h i*
L=J
r=i .
n r!
248
ELECTRIC LIGHTING.
132. Phantom on two simplex circuits. — A phantom telephone
circuit may be superposed upon two simplex circuits like Fig. 166.
This arrangement is shown in Fig. 1 68. Theoretically both of
H
1 — •
H
h'
cH "
P Ijyl
L,c'
choke
coil
relay
ke
w
•*&• ground ""f5"
Fig. 168. Telephone phantom on two simplex circuits.
the telegraph circuits in Fig. 168 can be operated duplex or
quadruplex. See Art. 138.
133. The two- wire composite circuit. — A metallic telephone
circuit making use of two ordinary ground-return telegraph lines
is called a two-wire composite circuit. Such an arrangement is
shown in Fig. 169.
134. Phantom on two two-wire composites. — A phantom tele-
phone circuit may be superposed upon two two-wire composite
circuits as shown in Fig. 170.
135. Simplex blocks worked in series for telegraph. — A num-
ber of metallic telephone circuits such as are used for communicat-
ing between signal stations on a railway can be connected for use
MISCELLANEOUS APPLICATIONS.
249
ground
I coi/
*^p" ground -^^
Fig. 169. Two-wire composite.
m-
H^
*
=nd
^o
H f=^
Fig. 170. Telephone phantom on two two-wire composites.
250
ELECTRIC LIGHTING.
as a long telegraph line as shown in Fig. 171, and the telegraph
circuit can be carried onwards as a single-wire line as shown in
Fig. 172.
block A block B
block C
H
n
s
jj
rn
s g
n P
rn
h rf
r
relayQ
key}
1 f "\ / ' /
e/a^
?!/
T
ikt
ground ground
Fig. 171. Simplex blocks in series for telegraph.
136. Way stations in general. — In the simple Morse telegraph
a number of way stations can be arranged, the relays and keys
being all in series. Five or six way stations can also be arranged
on a telephone line (metallic circuit or ground-return) ; in this
case it is best to use telephone receivers and call bells wound
with many turns of fine wire and to connect the telephone set at
block C
extension of telegraph circuit
-=•
ground
Fig. 172. Extension of telegraph circuit of Fig. 171.
each station between the two wires of the line or between the
single line wire and the ground. That is, all of the telephone
sets are in parallel.
Way stations cannot be arranged in duplex or quadruplex
systems.
MISCELLANEOUS APPLICATIONS. 251
In simplex circuits and composite circuits telegraph way sta-
tions may be arranged by breaking the telegraph circuit* with a
condenser and shunting the telegraph set and a choke-coil around
the condenser.
In simplex circuits and composite circuits telephone way sta-
tions may be arranged either by shunting the telephone appa-
ratus (with a condenser) around the telegraph apparatus (with
a choke-coil), or by connecting the telephone apparatus (with
a condenser) between the two wires or legs of the telephone
circuit.
137. Telephone calls. — The ordinary magneto generator which
is used for operating telephone call bells gives an alternating
current of which the frequency is about 16 cycles per second, and
a one or two microfarad condenser is a very great obstruction to
the flow of such low-frequency alternating current. Therefore
the ordinary magneto and bell cannot be used for making tele-
phone calls on composite circuits such as are shown in Figs. 164,
169 and 170. Telephone calls are frequently made on composite
circuits by a momentary use of the telegraph apparatus. An-
other arrangement is to use a small induction coil with a high-
frequency interrupter for producing moderately high-frequency
alternating current for calling. These high-frequency currents
can flow through the condensers and operate a bell which is
specially designed to be operated by high-frequency current,
or the telephone receiver can be left permanently in circuit in
which case the high-frequency current will produce a loud howling
sound in the telephone receiver. This latter arrangement is
called the howler call.
The divided choke-coils (or the divided repeating coils) which
are used in the simplex circuit can be made large enough to
obstruct the flow of the i6-cycle bell current without hindering
the telegraph current and therefore the ordinary magneto and
bell can be used on simplex circuits.
* If a pair of wires forms one side of the telegraph circuit both wires must be
broken as stated. See Fig. 167.
252 ELECTRIC LIGHTING.
138. Duplex and quadruplex on simplex and composite cir-
cuits.— There are two difficulties involved in the use of duplex
and quadruplex telegraph apparatus or simplex and composite
circuits, namely, (a) the complexity is such that the balanced
condition between the "line" and the "artificial line" is difficult
to maintain, even to a degree sufficient to keep the different
telegraph signals separated, and (b) large voltages (sometimes
150 volts or more) and heavy currents are required, especially
for quadruplex working, and the telegraph signals are usually
heard in the telephones. // is essential to keep the telegraph current
as low as possible in simplex and composite circuits. Therefore
the quadruplex is practically abandoned on such circuits.
139. The automatic railway block signal. — When railway
trains are run closely following each other it is quite necessary to
install a system of signals to show to the engineer that he has
a mile or two of clear track ahead, the signal system being so
designed that the presence of a train ahead or any chance derange-
ment of the apparatus will show a danger signal.
rail A
1
i
\
1
| na B bond?
% battery
HUP relaa
7
Fig. 173. Short railway block with single-arm semaphore.
The essential features of the block signal system are shown in
Fig. 173. The rails of a block are separated from the rails of the
adjoining blocks by insulating joints iiii, and the rails in the
block are connected together by wire bonds so as to make each
rail a continuous conductor. A battery with some resistance r
in series with it* is connected between the rails at one end of
the block, and the windings of a relay are connected between
* Gravity Daniell cells are generally used, and the internal resistance of such a
battery is usually sufficient without the insertion of any additional resistance r.
MISCELLANEOUS APPLICATIONS. 253
the rails at the other end of the block. The battery current thus
flows steadily through the relay, and the signal arms are held in
the position which shows that the track is clear. When a train
comes into the block the wheels and axles of the train make a
short-circuit connection from rail to rail, and the voltage between
the rails falls to zero so that no perceptible current flows through
the relay. The relay lever is therefore released and allowed to
fall back, a local circuit is opened and the signal arms move to the
"danger" position. It is of the utmost importance that the danger
signal be displayed when any derangement of the signal apparatus
occurs; therefore the arms of the semaphore are weighted so as
to fall to "danger" position when the local circuit is opened
either by the track relay or by accident.
When the train moves out of the block, current again flows
through the relay, the local circuit is closed and a small motor in
the local circuit moves the signal arms to the "safe" position.
Copper oxide cells are extensively used for the local circuits for
operating the small motors for moving the signal arms.
1
y
•-mWs
TT
Fig. 174. Arrangement for working very long section of track as a single block.
There is always considerable leakage of current across from rail
to rail in Fig. 173 through the ties and ballast, especially when the
road bed is wet, and because of this leakage of current a relay
connected as shown in Fig. 173 does not operate satisfactorily if
the block is more than 6,000 or 7,000 feet in length. When the
traffic on a railway is light it is desirable to have blocks two or
three or four miles in length, and blocks of this length can be
arranged as shown in Fig. 174. Relay A controls the motor
which moves the signal arm, and relay B makes the two sections
254
ELECTRIC LIGHTING.
operate as one block. When both sections are clear, battery b
energizes relay B and the lever of relay B connects battery a
to the rails of section A so that relay A is energized and the
signal arm is held at "safe" position. A train on either section
causes the current to cease flowing through relay A and the
signal arm falls to "danger."
140. The overlap track circuit. — A system of signals which is
extensively used is as follows: A locomotive engineer brings a
train up to the entrance to a new block, and if he sees both arms
of a double semaphore at "safe" he knows the entire block is
clear; if he sees one arm at "safe" and the other at "danger"
he knows that a train is on the distant half of the block, and if
A B
J
«*^_ .
J
relay A relaV B
Fig. 175. Arrangement for operating double-arm semaphore.
he sees both arms at "danger" he knows that a train is on the
adjacent half of the block. In the first case the engineer goes
ahead at full speed, in the second case the engineer goes ahead
cautiously at reduced speed, and in the third case the engineer
stops the train until the signals show that the first half of the
block is clear.
Figure 1 75 shows an arrangement for operating a double sema-
phore as above explained. When the train is on section B both
relays are without current and both semaphore arms (at P) are
at "danger." When the train moves into section A, relay B
is energized and one semaphore arm (at P) is moved to "safe"
position, and when the train moves out of section A both relays
are energized and both semaphore arms (at P) move to "safe"
MISCELLANEOUS APPLICATIONS. 255
position. The arrangement shown in Fig. 176 is called the
overlap track circuit.*
-
REFERENCES.
Fire alarm and police telegraphy:
Maver's American Telegraphy, J. H. Bunnell & Co., 1892
Wireless telegraphy:
Poincare-Vreeland, Maxwell's Theory and Wireless Telegraphy, McGraw-Hill
Book Co., 1904.
J. A. Fleming, The Principles of Wireless Telegraphy, Longmans, Green & Co.,
1908.
G. W. Pierce, The Principles of Wireless Telegraphy, McGraw-Hill Book Co.,
1910.
Electric furnace work:
J. B. Kershaw, The Electric Furnace in Iron and Steel Production, Van Nostrand,
1907.
Rodenhauser & Schoenawa, Electrische Of en in der Eisenindustrie, Leipzig, 1911.
J. Bronn, Electrische Ofen im Dienste der keramischen Gewerbe und der Glas und
Quarzglasererzeugung, Halle, 1910.
Borchers-Solomon, Electric Furnaces, Longmans, Green & Co., 1908.
A. Neuburger, Handbuch der praktischen Electrometallurgie, Berlin, 1907.
J. B. Kershaw, Electrometallurgy, Van Nostrand, 1908.
M. deKay Thompson, Applied Electrochemistry, The Macmillan Co., 1911.
Protection of buildings from lightning:
Oliver J. Lodge, Lightning Conductors and Lightning Guards, London, 1892.
Electric welding:
R. N. Hart, Welding, McGraw-Hill Book Co., 1910.
Ore concentration:
C. G. Gunther, Electromagnetic Ore Separation, McGraw-Hill Book Co., 1909.
Ozone:
F. M. Per kin, The Industrial Uses of Ozone, Nature, February 22, 1912.
A good discussion of the manufacture and use of ozone is given in Bulletin No. 4912
of the General Electric Company.
M. W. Franklin, Ozone ; Its Properties and Commercial Production, Proceedings
American Institute of Electrical Engineers, May. 1812, pages 597-6<>7.
* The student is referred to Maver's American Telegraphy, pages 494-508 and to
Railway Signaling published by The Electric Journal of Pittsburgh, Pa. This is a
reprint of a series of articles which appeared in The Electric Journal during 1907
and it gives a great deal of information on the subject. The Union Switch and
Signal Company of Swiss vale, Pa., and The Hall Signal Company of Elizabeth,
N. J., will send descriptive circulars to engineering students who are interested in
railway signaling.
256 ELECTRIC LIGHTING.
Electric Railroads:
W. C. Gotshall, Electric Railway Economics, McGraw-Hill Book Co., 1903.
Ashe & Keily, Electric Railways, Van Nostrand, 1905.
Wilson & Lydall, Electrical Traction, Longmans, Green & Co., 1907.
Herrick & Boynton, American Electrical Railway Practice, McGraw-Hill Book
Co., 1907.
Sheldon & Hausman, Electric Traction and Transmission Engineering, Van
Nostrand, 1911.
C. F. Harding, Electric Railway Engineering, McGraw-Hill Book Co., 1911.
Section 13 of The Standard Handbook for Electrical Engineers on Traction, by
A. H. Armstrong, McGraw-Hill Book Co.
*
APPENDIX A.
DIELECTRIC STRESSES.
The equation of the condenser is
Q = CE (I)
in which E is the electromotive force in volts applied to the
condenser plates, Q is the amount of charge in coulombs drawn
out of one plate and forced into the other plate, and C is the
capacity of the condenser in farads.*
The capacity in farads of a parallel plate condenser with air as
the dielectric is
C= 884 Xio-16^ (2)
Bv
in which a is the area of one of the plates (sectional area of the
dielectric) in square centimeters, and x is the thickness of the
dielectric in centimeters.
To substitute oil or any other dielectric for the air increases
the capacity of a condenser in a certain ratio k so that the
capacity may then be expressed by the equation
= 884 X io-16^. (3)
•v
The factor k is called the inductivity of the dielectric (also some-
times called specific capacity of the dielectric). Thus the induc-
tivity of kerosene is about 2, which means that the capacity of
an air condenser is doubled if kerosene is substituted for the
air dielectric.
In the following discussion the letter B is used to designate
the factor 884 X io~16.
* An elementary discussion of the condenser is given on pages 162-173 of Frank-
lin and MacNutt's Elements of Electricity and Magnetism, The Macmillan Co., 1908.
18 257
258 ELECTRIC LIGHTING.
Gauss's theorem. — A theorem of fundamental importance in
electrostatic theory is as follows: The total electric flux $ ema-
nating from a charged body is equal to Q -f- B, or the total charge
on a body is equal to B$, where Q is the charge in coulombs
and $ is electric flux expressed in volt-centimeters in air. (An
electric field intensity is expressed in volts per centimeter, and
the product of this field intensity by an area in square centimeters
gives electric flux in volt-centimeters, the area being perpendicular
to the field.)
When applied to a parallel-plate air condenser, Gauss's
theorem may be derived by multiplying both members of equa-
tion (2) by E (the electromotive force between the plates),
giving
T?
CE = Qcoulombt = Bd 1
but E -f- x is the electric field intensity between the plates in
volts per centimeter, so that a X E •£• x is the electric flux from
plate to plate in volt-centimeters and therefore, a X E -f- x = $
whence we have
Q = Bj. (4)
Gauss's theorem may be derived for a parallel plate condenser
with any dielectric by multiplying both members of equation
(3) by E (the electromotive force between the plates), giving
-p>
CE = Q = B .a.k-,
x
but E -f- x is, as before, the electric field intensity between the
plates and k X E -r- x may be defined as the electric flux density*
in the dielectric, so that a X kE -r- x is the total flux, and we
thus arrive again at equation (4).
* The product kf which is here called electrical flux density or electrical strain,
was called dielectric polarization by Maxwell. See Maxwell's Treatise.
DIELECTRIC STRESSES.
259
MAGNETIC AND ELECTRIC PARALLEL.
c8 = n&C, F = kf,
is intensity of magnetic where / is intensity of electric field
in volts per centimeter (E-s-x), k
is the inductivity of the medium,
and F is the electric flux density
in volt-centimeters per square cen-
timeter.
where
field in gausses, /n is the perme-
ability of the medium, and oB is the
magnetic flux density.
ELECTRICAL STRESS AND MECHANICAL STRESS.
The intensity of an electric field in
volts per centimeter (or the volts
per centimeter in a layer of dielectric
between metal plates) is frequently
called electrical stress, and the electric
flux density kf in the dielectric is
frequently called the electrical strain.
Therefore we have
The stretching force per unit of sec-
tional area of a rod is called the
stress on the rod, and the elonga-
tion of unit length of the rod is
called the strain; and the strain is
proportional to the stress. That is
( mechanical
I strain
nical) f mechanical) (
in J=WXt stress /' I
electrical ) _ , ( electrical )
strain ) \ stress f*
where n is a constant for a given
substance.
The potential energy of mechanical
strain per cubic centimeter of the
strained substance is equal to one-
half the product of stress and strain.
The elastic condition of a substance
can be specified as follows:
(a) By giving the stress in pounds per
square inch;
(&) By giving the strain, as for
example the percentage elongation of
a wire under tension; or
(c) By giving the potential energy per
unit volume of the strained substance.
where k is a constant for a given
dielectric.
The potential energy of electrical strain
per cubic centimeter of the dielectric
is equal to one-half the product of
electrical stress (/) and electrical
strain (kf).
The electric condition of a dielectric
can be specified as follows:
(a) By giving the electrical stress in
volts per centimeter;
(&) By giving the electrical strain in
volt-centimeters or in coulombs per
square centimeter*; or
(c) By giving the potential energy per
unit volume of the dielectric.
* Electric flux can be expressed in coulombs according to equations (2) and (3)
and therefore electric flux density can be expressed in coulombs per square centi-
meter. If a metal ball has Q coulombs of charge per square centimeter of its
surface, then Q/B volt-centimeters of electric flux emanate, from each square centi-
meter of the ball, according to equation (4), or, in other words, the electric flux
density in the dielectric near the surface of the ball ( = kf) is Q/B volt-centimeters
per square centimeter, and therefore the electric field intensity near the surface
of the ball is Q/B -f- k volts per centimeter.
260 ELECTRIC LIGHTING.
Electric stresses in plane layers of different dielectrics. —
Consider two metal plates with air and glass between them as
shown in Fig. I. The thing which is constant throughout the
region between the metal plates, that is, the thing which has the
same value in glass and air is the electric flux density kf, because
there are equal and opposite charges on two plates, and, therefore,
according to Gauss's theorem the total flux passing out from the
positively charged plate (+ (?) is equal to the total flux passing
in towards the negatively charged plate ( — Q) . Now since kf
is the same in the glass and in the air, and since k = I for air
and k = 6 for glass, therefore, the electric field intensity or stress
in volts per centimeter (/) is six times as great in the air as in the
glass.
Consider the special case in which the glass and air are of
equal thickness as indicated in Fig. I. Then six sevenths of the
battery voltage is impressed on the air layer and one seventh on
the glass layer. If glass and air are each I centimeter thick, and
if the total voltage is 35,000 volts, then, assuming the air not to
break down, the voltage across the air will be 30,000 volts,
and the voltage across the glass will be 5,000 volts.
If the glass plate is removed, leaving 2 centimeters of air,
then the electrical stress on the air will be 17,500 volts per centi-
meter. Therefore the electrical stress in the air between two
plates 2 centimeters apart is increased from 17,500 volts per
centimeter to 30,000 volts per centimeter by filling half of the
space between the plates with glass of inductivity 6.
This effect can be shown in a very beautiful manner by con-
necting two metal plates to a high-voltage transformer and ad-
justing the plates to a distance such that the intervening air
layer is barely sufficient to sustain the voltage. Then if a glass
plate be introduced between the metal plates, the electrical stress
in the remaining air will be increased sufficiently to break the
air down at each reversal of the alternating voltage, as shown by
the bluish luminosity of the air layer.
The above discussion of the stresses in layers of glass and
DIELECTRIC STRESSES.
261
air as based on Fig. I can be simplified as follows: Imagine a
thin sheet of metal mm to be placed between the air and glass
as shown in Fig. 2. We thus have two exactly similar conden-
sers, C' and C, of glass and air, and the capacity of the glass
— I'l'l'lil'l'l'l'l
Fig. 1.
Fig. 2.
condenser is six times as great as the capacity of the air con-
denser, according to equations (2) and (3). But the charges
on C' and C are the same because they have been charged in
series. Therefore the voltage across the glass condenser is one-
sixth of the voltage across the air condenser, according to equa-
tion (i).
The concentration of the greater part of the voltage upon
the air layer in Figs. I and 2 is exactly analogous to the con-
centration of the greater part of the magnetomotive force of a
dynamo field-winding upon the air gap in the magnetic circuit;
only a small portion of the magnetomotive force is required to
force the magnetic flux through the highly permeable iron, and
a large portion of the magnetomotive force is required to force
the magnetic flux through the less permeable air layer. A small
portion of the battery voltage is required to force the electric
flux through the highly inductive glass in Fig. I and a large
portion of the voltage is required to force the electric flux through
the less inductive air.
Mechanical analog of Fig. 1. — A difficulty in obtaining a simple
mechanical idea of the concentration of the greater part of the
262
ELECTRIC LIGHTING.
battery voltage on the air layer in Fig. I arises from the following
fact : the glass and the air are in series in Fig. I (and the electric
flux density or electric strain or yield, in the two is the same),
whereas two mechanical elements have the same stress when they
are in series; to have the same strain or yield, two mechanical
elements must be in parallel. Thus Fig. 3 shows a column of
steel and a column of rubber equally compressed between two
bars A and B (the steel and rubber columns are in parallel
Fig. 3.
Fig. 4.
and they are equally shortened) ; but the easily yielding rubber
(high inductivity) supports a small part of the compressing
force, and the stiff steel (low inductivity) supports a large part of
the compressing force.
Distribution of electrical stress in the region between core
and sheath of an insulated cable, core and sheath being cylin-
drical and coaxial. — Consider unit length of the wire core of a
cable and let Q be the amount of electric charge thereon. Let /
be the electric field intensity in volts per centimeter at the point
p in the insulation distant r from the axis of the cable and let k
be the inductivity of the insulating material at p. Then kf
(see Fig. 4) is the electric flux density at p, and 2wr X kf is the
flux across the cylindrical surface cc (of unit length), that is
2wrkf is the flux emanating from Q, and, therefore, according
to equation (4), we have
DIELECTRIC STRESSES. 263
Q = B X 2irrkf
or
In interpreting this equation we will consider two cases,
namely, (a) The case in which the cable insulation is all of one
kind of material, and (b) The case in which the cable insulation is
built around the core in layers of decreasing inductivity.
In the first case r is the only variable in equation (5) and the
electrical stress at any point in the cable insulation is inversely
proportional to the distance r from the axis of the cable. The
electrical stress is greatest near the wire core and least near the
sheath. This concentration of the stress near the wire core of a
cable makes it impossible to utilize the full electrical strength of
a cable insulation in case (a). In a somewhat similar manner the
mechanical stress in the steel of a gun barrel is concentrated near
the bore and consequently it is impossible to utilize the full
mechanical strength of a solid forged gun barrel. The concentra-
tion of stress near the bore will start cracks in the walls while
the outer portions of the gun barrel are very far indeed from
being severely strained.
In the second case if we could select the materials for the suc-
cessive layers of cable insulation so as to decrease k as r increases
it would be possible to keep the product kr constant and then the
electrical stress / in volts per centimeter would be the same in
value throughout the insulating material. It is impracticable
to accomplish this result completely, but high-voltage cable
insulation is usually put on in two or three layers decreasing in
inductivity outwards. Such a cable is said to have a graded
insulation.
There is an interesting mechanical analogy to the graded cable
insulation. If a thick-walled steel tube is subjected to internal
pressure as in a cannon, the material next the bore is stretched
to its stress-limit before the outer portions of the steel are brought
into full action. If easily yielding (highly elastic like rubber) steel
264
ELECTRIC LIGHTING.
could be used for the inner portions of the gun tube, then the
greater yield of the inner material would tend to bring all of
the material of the tube up to the limiting stress simultaneously.*
There is in fact but little variation in the elastic coefficient of
various kinds of steel, and this method of gun construction is
therefore impracticable. There are, however, great differences
in the inductivities of different insulating materials, and therefore
the grading of cable insulation is to some extent practicable.
Observable effects dependent upon variations of dielectric
inductivity. — The greatest obstacle to a clear understanding of
the theory of dielectric stress is that students and engineers are
not familiar with the simple observable effects which involve
inductivity. Indeed some of these effects are so simple that it-
is sufficient merely to describe them as follows:
Fig. 5.
Fig. 6.
The lines of force in an electric field converge upon and pass
through a glass rod (high inductivity), and the lines of force
in a magnetic field converge upon and pass through an iron rod
(high permeability). A glass rod suspended in an electric field
oscillates to and fro through an equilibrium position parallel
to the field in the same way that a suspended iron rod oscillates
in a magnetic field. (Figs. 5 and 6.)
A glass plate is drawn into the intense electric field between
positively charged metal plates in the same way that a piece of
iron is drawn into the intense magnetic field between two opposite
magnet poles as shown in Figs. 7 and 8. In the same way oil
* The steel tube of a cannon is strengthened in practice by shrinking a series of
jackets over the tube.
DIELECTRIC STRESSES.
265
and especially water is drawn into the most intense part of an
electric field.
A thin glass cell partly filled with oil and provided with
metal terminals A and B is placed in a lantern and the terminals
A and B are connected to a Toepler-Holtz machine, as indicated
glass plate
iron plate
j
^
H^
x^
I "/
N
4—
4-
s z
) /
\
/
=±=
\
,,,,,..,,~,-\
~___ _,
f/t Tt, ,,,,, ,,,,\
Fig. 7.
Fig. 8.
in Fig. 9. The oil (high inductivity) is drawn up as shown, and
eventually a column of oil is formed reaching up to terminal A.
In the same way a magnetic liquid (permeability greater than
unity) would be drawn up to a
magnet pole. Bubbles of air ris- _j
ing in oil in front of a pointed
metal terminal (charged) are re-
pelled.
A charged gold-leaf electro-
scope is placed in a lantern with
the plate of the electroscope con-
nected by a fine wire to an in-
sulated plate PP on the lec-
ture table, as shown in Fig. 10. When a slab of paraffin
W is placed in the region CC, the electroscope leaves fall
slightly. The capacity of the condenser CC has been in-
creased by the paraffin slab and a greater portion of the charge
on the insulated system flows into PP thus decreasing the
Fig. 9.
266 ELECTRIC LIGHTING.
charge on the electroscope leaves. If one had two inflated
rubber bags connected by a tube, and if one were to make the
walls of one bag more yielding by dissolving off a portion of
the rubber (if that were possible) , then the weakened bag would
swell and the other bag would shrink. The plate of paraffin
makes the dielectric around PP more yielding and some
charge flows from EE into PP.
Dielectric hysteresis. — The most prominent kind of dielectric
hysteresis is a kind which is closely analogous to what is tech-
nically called elastic lag in mechanics. Glass, for example, when
subjected to a mechanical stress takes on a certain amount of
strain (deformation) quickly, after which the strain slowly in-
creases for a time; and when the stress is removed, a remnant of
the strain persists for a time. This kind of hysteresis is some-
times called viscous hysteresis, and it is very different from the
magnetic hysteresis in iron or steel, although a slight amount of
viscous hysteresis does exist in very soft iron.
Dielectric hysteresis of the viscous type has long been known
to exist, and it is the cause of the so-called "residual charge"
which accumulates in a Leyden jar when the jar is highly charged
and then completely discharged and allowed to stand.
A Leyden jar is charged. The coat- A rubber tube is stretched. This
ings of the jar are then momen- stretch corresponds to the elec-
tarily connected by wire, and then trical strain of the glass walls of the
the jar is left standing on open Leyden jar. The end of the tube
circuit. After a time the coatings is momentarily released, and the
are again connected and a second end is then clamped fast in what
slight discharge is obtained. seems to be its equilibrium posi-
tion. After a time the end is again
released and a second slight "dis-
charge" or movement takes place.
DIELECTRIC STRESSES.
267
Dielectric strength. — The voltage required to puncture a layer
of dielectric between flat metal plates is approximately propor-
tional to the thickness of the dielectric layer. That is to say, a
definite electrical stress in volts per centimeter is required to
break down a dielectric, and this limiting electrical stress meas-
ures what is called the dielectric strength.
TABLE OF DIELECTRIC STRENGTHS.*
Substance.
Strength in
Volts per Inch.
Substance.
Strength in
Volts per Inch.
Oil of turpentine
235,000
Beeswaxed paper
1,350,000
217 ^OO
Air (thickness 5 cm )
CQ CQO
Olive oil
2O5,OOO
CO2 (thickness 5 cm.) ....
56,750
Paraffine (melted)
I4O,OOO
O (thickness 5 cm.)
55,500
Kerosene oil
I25,OOO
H (thickness 5 cm.)
37,750
Paraffine (solid)
•*2c,,ooo
Coal gas (thickness 5 cm.)
55,750
Paraffined paper
900,000
Concentration of electrical stresses by points. — The ease with
which a bar of hard tool-steel can be broken when a sharp-bot-
tomed nick is made in one side of the bar is well known. Fig. 1 1
shows the lines of stress pass-
ing around the bottom of a
sharp groove in a bent bar.
The stress is very greatly con-
centrated near the bottom of
the groove, and the groove
deepens by the formation of a
crack. The stress is then con-
centrated at the edge of the crack, and the crack is extended
farther and farther until the bar is broken in two.
It is perhaps not generally known that the glass-cutting
diamond does not make a scratch. Such a scratch would be a
shallow flat-bottomed groove, and no very great concentra-
tion of stress would occur at the bottom of such a groove when
the pane of glass is slightly bent. The end of a cutting diamond
*From the measurements of Macfarlane and Pierce, Physical Review, Vol. I,
page 165, 1894.
Fig. 11.
268
ELECTRIC LIGHTING.
is a perfectly rounded "corner" of a natural diamond crystal
(the diamond is a crystal with curved faces) , and when a cutting
diamond is drawn properly across a pane of glass a minute crack
is formed under the diamond on account of the excessive local
compression. This crack causes a very great concentration of
stress when the pane of glass is subjected to a very slight bending
action, and the result is that the crack runs through the pane.
Fig. 12.
When a diamond is drawn heavily across a pane of glass a very
considerable exertion is required to break the glass and the crack
does not always follow the groove. When a diamond is drawn
properly across a pane of glass a very slight bending effort is
sufficient to break the glass, and the break nearly always follows
the minute crack produced by the diamond.
A very interesting accident occurred at the Bethlehem Steel
Works a number of years ago when an attempt was made to
strengthen a crank-disk by shrinking a collar upon it. The disk
had a crank-pin on one side, and the disk sheared off along the
dotted line ap in Fig. 12 on account of the excessive concentra-
tion of stress at the reentrant angle a. The fine curved lines
show the approximate trend of the stress lines in the disk due
to the collar CC.
DIELECTRIC STRESSES.
269
W
p
p
Fig. 13.
An interesting experiment is to place a small piece of window
glass on a flat plate of steel (or plate glass) and press a sharp-
pointed file against it as shown in Fig. 13.
The stresses in the window glass are very
greatly concentrated at the sharp point of the
file, and it takes but little force on the file
to break the glass to pieces. If, however, a
bit of soft copper is placed under the point
of the file, one cannot push hard enough to
break the glass; the copper yields (breaks down mechanically)
and distributes the stress.
When a voltage is applied to the metal terminals MM in
Fig. 14, the electric lines of force (the electrical stress lines)
converge upon the sharp metal point, and the electrical stress
is very greatly concentrated near the point. Indeed a compara-
tively low voltage will rupture the glass plate in Fig. 14 because
of the starting of an electric rupture by the excessive concentra-
tion of the stress near the metal point. To produce this result,
however, the region rr must be filled with a substance of great
electric
lines of force
Fig. 14.
Fig. 15.
dielectric strength like turpentine or wax. If the region rr
is filled with a substance of low dielectric strength like air, the
portion in the immediate neighborhood of the metal point breaks
down electrically and becomes a conductor, and the resultant
distribution of electrical stress in the glass plate (which is shown
270
ELECTRIC LIGHTING.
in Fig. 15) is the same as if the glass plate were between two
flat metal plates as shown in Fig. 16. Under these conditions
the electrical stress in the glass is nearly uniform, and a very
high voltage is required to puncture
the glass plate, because there is no re-
gion of concentrated stress to start
the electrical break- down.
Having air around the metal point
in Fig. 14 is like having a bed of soft
copper around the point of the file in
Fig. 13. The copper breaks down
mechanically and distributes the
stress, thus preventing excessive con-
centration of stress near the point of
the file and the starting of a crack thereby. The air breaks
down electrically and distribute! the stress, thus preventing ex-
cessive concentration of stress near the metal point and the
starting of an electric puncture thereby.
An electrical breakdown in a solid dielectric (and usually in
liquid and gaseous dielectrics also) is always in the form of a
puncture, that is the breakdown occurs along a line; and this
line of breakdown is an electrical conductor. Therefore the elec-
trical stresses in the dielectric are concentrated at the end of an
incipient puncture, as at a metal point, and the puncture is thus
Fig. 16.
Fig. 17.
carried through the dielectric or into regions where the electrical
stresses were far below the breakdown value before the puncture
started. Thus Fig. 17 shows the electric lines of force between
DIELECTRIC STRESSES.
271
two metal balls, and Fig. 18 shows how the electric lines of force
rearrange themselves when an electric puncture starts.
Fig. 18.
Maximum stress in homogeneous cable insulation for given
voltage between core and sheath. — Equation (5) cannot be used
to calculate the actual value of the electrical stress / at a given
distance r from the axis of the cable because the value of Q is
not known. The quantity which is always specified or which
can be most easily observed is the voltage E between the core
and the sheath, and, therefore, it is desirable to derive an equation
which gives / in terms of E as follows: — Let RI be the radius
of the wire core and let Rz be the inside radius of the sheath,
both expressed in centimeters. It is required to find the total
voltage along the line ab, Fig. 19. Consider the element Ar of the
wire
Fig. 19.
line ab. The voltage along this element is /-Ar because/ is the
volts per centimeter at Ar (compare Fig. 4). Therefore we have
AE = /-Ar, or using the value of / from equation (5) we have
272 ELECTRIC LIGHTING.
Q Ar
whence by integrating* between the limits r = R\ to r = Rz we
have
Therefore the entire factor Q/27rBk inequation (5) is equal to
E/[\oge(Rz!Ri)], and equation (5) may be written:
(7)
1 Kz\ r
loge I «• I
\.Ki/
or, reducing to common logarithms, we have
0435 -E i
log
(t) '
The greatest value of / occurs at the surface of the wire core
where r = R\ and therefore from equation (8) we have
0.435 E X v
/max ~~
in which /max is expressed in volts per centimeter if E is ex-
pressed in volts and RI and RZ in centimeters, or in volts per
inch if E is expressed in volts and RI and RZ in inches. For
example consider a cable having a quarter-inch wire core (Ri =
0.125 inch) and one half-inch of insulation (R% = 0.625 inch) with
10,000 volts between wire and sheath. Then the maximum
electrical stress is 49,700 volts per inch and the electrical stress
near the sheath is 9,940 volts per inch. On the other hand,
half an inch of insulation between flat metal plates would be under
a uniform stress of 20,000 volts per inch with 10,000 volts be-
tween the plates.
* Of course k is assumed to be constant; that is the cable insulation is all one
kind of material.
DIELECTRIC STRESSES. 273
Maximum electrical stress between parallel wires. — Figure 20
is a sectional view of the two wires W and W" and it is desired
to find the expression for the electrical stress / at any point p
distant x centimeters from the axis of W when there is + Q
coulombs of electric charge on each centimeter of W and — Q
coulombs on each centimeter of W". The wires are small in
diameter as compared with their distance apart D, and therefore
A-^7^^
Fig. 20.
the charge may be assumed to be uniformly distributed around
each wire, and the electric field due to either wire alone may therefore
be assumed to radiate symmetrically around the wire exactly as
if the wire were surrounded by a co-axial sheath.
Let /' be the electrical stress at p due to W and let /"
be the electrical stress at p due to W". Then according tc
equation (5) we have:
f = Q • L G)
2irBk x
and
1" = 2wBk ' (D - xY ,
But the total electrical stress at p is /' + /" and therefore we
have
and the voltage AE along the element A* is equal to /-A*
so that
_ \x, (iii)
19
274 ELECTRIC LIGHTING.
whence, by integrating* between the limits x = R and x =
D — R (from surface to surface of the wires in Fig. 20) we have:
E = — — • loe
where R is the radius of each wire and D ' is the distance between
centers of wires.
From equation (iv) we find the value of the factor Q/(2wBk)
to be E/{2 loge [(D — R)!R]} so that equation (10) becomes
(V)
The maximum value of / occurs at the surface of either wire
where x = R (or where x = D — R). Furthermore i/R is
quite large as compared with i/(D — R). Therefore substitut-
ing R for x in equation (v) and discarding i/(D — R) as
negligible in comparison with i/R, we have
R
whence, using ordinary logarithms we have
0435 E
/m»* - / r> 7P\ ' (jj)
For most practical purposes D — R is sensibly equal to D
and therefore equation (n) may be written:
- 0-435 £
/max -
2 R log i R
in which /max is expressed in volts per centimeter if E is ex-
pressed in volts and D and R in centimeters, or in volts per
* Of course k is assumed to be constant; that is the wires are surrounded by
insulating material all of one kind.
DIELECTRIC STRESSES.
275
inch if E is expressed in volts and D and R in inches. For
example consider a transmission line consisting of two quarter-
inch wires (R = 0.125 inch) 24 inches apart center to center
(D = 24 inches) with 50,000 volts between the wires. Then
the maximum electrical stress is 38,100 volts per inch.
The equalization of the electrical stresses in the insulation of
transformer terminals. — A certain amount of electric flux starts
out from the wire core of a cable, and this same amount of flux
continues outwards unchanged in value, and therefore the flux
density decreases at increasing distances from the core. In the
case of a long cable, the electrical stress in the insulation can be
end view
side view
Fig. 21.
made uniform by the grading of the inductivity of the insulation
as above explained. In the case of a short rod, the electric flux
which emanates from the rod can be more and more crowded
together endwise at increasing distances from the rod so as to
compensate for the circumferential spreading and thereby give the
same electric flux density and the same electrical stress throughout
the insulation. This crowding together endwise of the electric
flux is accomplished by dividing the insulation into layers of equal
thickness which are separated by sheets of tin-foil as shown in
276
ELECTRIC LIGHTING.
Fig 21. This arrangement of the insulation of a rod is called
the condenser type of insulation.
The principle of the condenser type of insulation may be
understood with the help of Fig. 22, which shows two condensers
c and C connected in series to a
battery. The two condensers receive
the same amount of charge Q when
arranged in this way, the voltage
across c is Q/c and the voltage across
C is QIC, or, in other words, the
voltages across the respective con-
densers are inversely as their capac-
ities. Any layer of insulation together
with the adjacent sheets of tin-foil in Fig. 21 constitutes a
condenser, and the condensers formed by all the layers of insula-
tion and sheets of tin-foil are in series. Therefore the voltage
is the same across every layer if the various capacities are equal.
To make the various capacities equal (with same thickness of
dielectric in each case) the sectional areas* of the various layers
of dielectric must be the same, that is to say, the length parallel
to the rod of each successive layer must be reduced in proportion
to the increasing circumference around the rod.
Fg. 22.
APPENDIX B. PROBLEMS.
CHAPTER I.
COSTS.
1. Calculate the values of station load factor corresponding
to each of the curves in Fig. 5, to the curve in Fig. 6, and to
each of the curves in Fig. 7.
2. From the data given in the table on page 12 calculate each
item of cost of operating the i5O-kilowatt plant at 0.2 load factor
and at 0.8 load factor.
3. From the data given in Fig. 8 calculate the following items
of cost of operating a io,ooo-kilowatt steam turbine plant at
full load and at 30 per cent, load: (a) Coal and water [see page 12
for statement as to quality of coal and cost of coal per ton];
(b) boiler room and engine room labor, coal and ash handling,
oil and engine room supplies ; and (c) fixed charge.
4. A i5O-kilowatt lighting plant operates night and day at 0.2
load factor and the schedule of operation costs are shown in the
table on page 12. It is impossible to increase the lighting load
because the peak of the load already reaches the limit of overload
capacity of the plant. It is possible, however, to increase the
output of the plant by supplying current for motors off the peak
if the motor rate is made very low so as to attract customers.
What would be the cost to the station per kilowatt-hour of addi-
tional output if the load factor of the station were raised to 0.4
by supplying motors off the peak?
5. Find from the curve A of Fig. 9 the probable peak load
of a station supplying 20 residences in each of which 60 lamps
are installed, 50 residences in each of which 40 lamps are installed,
100 residences in each of which 20 lamps are installed, and 200
residences in each of which 10 lamps are installed.
6. A certain customer might be asked to pay $2.00 per month
277
278 ELECTRIC LIGHTING.
"connection" charge, his maximum demand is 5 kilowatts on
the peak for which he might be asked to pay at the rate of $60
per kilowatt per year, and his yearly consumption is 5,000 kilo-
watt-hours for which he might be charged at the rate of 3 cents
per kilowatt-hour. What would be the cost of electrical energy
to this customer per kilowatt-hour?
Note. — Compare table on page 19.
7. A small customer has ten 2O-watt lamps. Asssuming 10 cents
per month as a reasonable connection charge (without a meter),
$60 per year per kilowatt of maximum demand, and 3 cents per
kilowatt-hour of consumption what would be the equivalent flat
rate for the 10 lamps, an excess indicator being installed to limit
the maximum demand to 160 watts, the yearly consumption being
43 kilowatt-hours?
8. A Thomson watt-hour meter without a starting coil starts on a 75-watt
load. The meter is adjusted to give a true watt-hour record when run on a 500-
watt load. What will the instrument indicate after running for 4 hours on a con-
stant load of 200 watts, running friction being assumed to be equal to half of start-
ing friction. See note to problem 10. Ans. 702.8 watt-hours.
9. The watt-hour meter specified in problem 8 is provided with a starting coil
so as to start, on no- volt mains, when the power delivered to the receiving circuit
is 40 watts. At what load will the meter start on 55-volt mains? See note to
problem 10. Ans. 66.25 watts.
10. The watt-hour meter of problem 9 is adjusted to record a 500- watt load
correctly on no-volt mains. At what load will it record correctly on 55-volt main?
Ans. 5,750 watts.
Note. — The driving torque, not counting that due to the starting coil, is propor-
tional to the watts delivered to the receiving circuit, and it may be conveniently
expressed in "watts." The driving torque due to the starting coil (with given
voltage between the supply mains) may be expressed as the difference between the
starting watts with and without the starting coil. The running friction (a torque)
may be expressed as one half the starting load in watts without the starting coil.
The speed of the meter may be conveniently expressed in "watt-hours recorded
per hour."
Subtracting from the total driving torque (including the torque due to the starting
coil) the running friction, gives the net torque used to overcome the retarding action
of the damping magnets, and the speed of the meter is proportional to this net torque.
The torque produced by the starting coil is proportional to the square of the voltage
between the mains.
11. The net assets of the Wallingford plant year after year
are represented by the differences between the ordinates of the
PROBLEMS. 279
curves A and B in Fig. 13, and the capitalization at the begin-
ning was $55,000. Find the rate at compound interest which is
represented by the growth of the net assets to $96,881 on July 31,
1910 (lof years from the beginning). Ans. 5.53 per cent.
Note. — This rate of interest does not represent the real profits of the plant;
to find the real profits one must take into consideration the annual payment of
bond interest as explained in problem 12. If the Wallingford plant continues in the
future to make the same profits it has made in the past then in 1920 the net assets
will be $161,700 and there will remain $106,700 of net assets after the bonds are
paid. Furthermore, the accumulated depreciation charge will in 1920 probably
amount to more than the actual depreciation so that the $106,700 will be real
tangible assets.
12. The Wallingford plant has been paying $1,925 annually as
interest on its bonds, beginning on August I, 1900, so that on
August i, 1910, eleven payments had been made. Find the
accumulated cash value on August I, 1910, of all these payments
(the accumulation being reckoned at 3^ per cent, compound
interest), add this to the net assets on August I, 1910, and find
the rate at compound interest which is represented by the growth
from $55,000 in io| years. Ans. 7.9 per cent.
CHAPTER II.
ELECTRIC DISTRIBUTION AND WIRING.
13. A span, 150 feet long, of hard-drawn copper wire, No. 8 Brown and Sharpe
gauge, is to be strung at a temperature of 75° F. at a place where the winter tem-
perature sinks to — 20° F. The maximum tension of the wire is to be 164 pounds.
Find: (a) The sag at —20° F.; (6) the sag at 75° F., and (c) the tension at 75° F.
Ans. (a) 0.86 foot; (b) 2.86 feet; (c) 49 pounds.
14. Five hundred glow lamps each taking one-half an ampere
at 1 10 volts are supplied with current from a 1 15.5-volt generator
at a distance of 1,000 feet from the lamps. Find: (a) The size
of copper wire required, (b) the total weight of the wire, and (c)
the total cost of the wire at 16 cents per pound. Ans. (a)
982,000 circular mils; (b) 5,950 pounds; (c) 953 dollars.
15. Five hundred glow lamps each taking one-half an ampere
at no volts are supplied with current from a 231 -volt generator
280 ELECTRIC LIGHTING.
at a distance of 1,000 feet from the lamps. The Edison three-
wire system is used and the system is balanced. Find: (a) The
size of copper wire required for the outside mains; (b) the total
weight of all three mains, the middle main having one-half the
sectional area of either outside main; and (c) the total cost of
the three mains at 16 cents per pound. Ans. (a) 245,500 circular
mils; (b) 1,860 pounds; (c) 298 dollars.
16. The three-wire system of problem 15 supplies 300 lamps
(150 amperes) on one side and 200 lamps (100 amperes) on the
other side, all at a distance of 1,000 feet from a 231 -volt gen-
erator. A balancer is used in the station to take care of the
current in the middle main and to keep the voltage between the
middle main and each outside main equal to 115.5 volts. Find:
(a) The voltage across the set of 300 lamps; and (b) the voltage
across the set of 200 lamps. Ans. (a) 104.5 volts; (b) 1 15.5 volts.
Note. — If the lamps above specified are all exactly alike it is evident that the
current in each lamp of the 300 set cannot be the same as the current in each lamp
of the 200 set. It is usual, however, in wiring calculations to consider that lamps
of a given size and type take a definite amount of current irrespective of the slight
variations of voltage.
17. The three-wire system of problem 15 supplies 300 lamps
(150 amperes) on one side and 100 lamps (50 amperes) on the
other side, and the total voltage of 231 volts at the generator is
equally divided by the balancer as explained in problem 16.
Find: (a) The voltage across the set of 300 lamps; and (b) the
voltage across the set of loo lamps. Ans. (a) 100.1 volts; (b)
122. 1 volts.
18. A group of ten lamps, each taking one-half an ampere, is
ten feet distant from ii5-volt mains, (a) Find the size of wire
required in order to give a drop of 5 volts, (b) What size of
wire (rubber insulation) would be required according to the table
of safe carrying capacity given on page 55? Ans. (a) 14.7 mils
diameter; (b) No. 16 Brown and Sharpe gauge (51 mils diameter).
Note. — It is evident that a wire 14.7 mils in diameter would be excessively heated
by a current of 5 amperes. Usually the size of wire for supplying lamps near to the
generator or center of distribution is determined by the table of safe carrying ca-
pacity.
PROBLEMS. 28l
The insurance rules forbid the use of wire smaller than No. 14 Brown and Sharpe
gauge for house wiring.
19. A pair of street mains leading out from a central station
delivers 50 amperes of current to a consumer at a distance of 200
feet from the station, 75 amperes to a second consumer at a
distance of 350 feet from the station, and 40 amperes to a third
consumer at a distance of 600 feet from the station. The station
voltage is 115 volts and the voltage at the distant end of mains
is no volts. Find: (a) The size, weight, and cost of mains of
uniform size; and (b) the size of each section of the mains, and
their total weight and cost, when the size is reduced in steps so
as to give the specified voltage-drop with a minimum amount of
copper. The cost of copper is to be taken at 16 cents per pound.
Ans. (a) 260,300 circular mils, 946.5 pounds, 151.2 dollars, (b)
first section 319,700 circular mils, second section 267,000 circular
mils, third section 157,400 circular mils, 868 pounds, 139 dollars.
Note. — In estimating the distance, L, of the "center of gravity" of the con-
sumers in the above problem, one may use one ampere as the unit instead of one
lamp.
20. An electric railway 33,300 feet in length is divided into
three sections of which the lengths, 9,000 feet, 10,800 feet and
13,500 feet, are proportional to the schedule speeds of cars on
the respective sections so that a car running from end to end of
the line traverses each section in 10 minutes. Four cars are
always on the first section five minutes apart going each way, two
cars are always on the second section ten minutes apart going
each way, and a single car is always on the third section making
the round trip in 20 minutes. Owing to frequent stops on the
first section the cars taken an average current of 125 amperes each,
on the second section the stops are less frequent and each car
takes an average of 105 amperes, and on the third section the
stops are least frequent and the car that is always on this section
takes an average of 95 amperes.
The "center of gravity" of the four cars that are always on
the first section is at the middle of the section, the "center of
282 ELECTRIC LIGHTING.
gravity" of the two cars that are always on the second section is
at the middle of that section, and the most unfavorable position
of the single car that is always on the third section is when it is
at the extreme end of the line. Assume, therefore, that 500
amperes are delivered continuously at the middle of the first
section (4,500 feet from the city end), that 210 amperes are de-
livered continuously at the middle of the second section (14,400
feet from the city end), and that 95 amperes are delivered con-
tinuously at the extreme end of the line. If the power house is
located at the city end of the line, find: (a) The size of each
section of the feeder to give a total drop of 75 volts at the ex-
treme end of the line with a minimum amount of copper; and
(b) the total cost of feeder copper at 16 cents per pound. Ans.
(a) First 4,500 feet of feeder 1,980,000 circular mils, next
9,900 feet of feeder 1,219,000 circular mils, and remaining 18,900
feet of feeder 680,000 circular mils; (b) 16,400 dollars.
Note. — The resistance of the bonded track, which is used as a return feeder, is
very uncertain and it is here to be assumed equal to zero for the sake of simplicity.
21. (a) Find the position in which the power house should be
placed on the railway specified in problem 20 in order that the
feeder copper may be reduced to a minimum ; (b) find the size of
each section of the feeder on the assumption that the two cars on
the middle section are in the most unfavorable positions, namely,
at the two ends of the section, and on the assumption that the car
on the third section is at the extreme end of the section ; and (c)
find the total cost of the feeder copper at 16 cents per pound.
Total drop to each end of the line to be 75 volts. Ans. (a)
10,480 feet from the city end of the railway; (b) first section
441,000 circular mils, city end of second section (1,480 feet)
485,200 circular mils, suburban end of second section (9,320
feet) 536,700 circular mils, and third section 369,900 circular
mils; (c) 7,119 dollars.
Note. — The power house should be placed at the center of "gravity "of a system
in the sense in which this term is defined on page 62 in order that the amount of
feeder copper may be a minimum. Similarly, a center of distribution, from which
PROBLEMS. 283
electric lamps are to be supplied by street mains, should be located at the "center
of gravity" of the consumers, each consumer being "weighted" in proportion to the
current delivered to him.
The feeder on city section of 9,000 feet is assumed to be of uniform section of
441,000 circular mils throughout, but it would be advisable in fact to make the
extreme city end of this section of the feeder much smaller than 441,000 circular mils.
22. A nearly reentrant row of 100 lamps, each taking one-
half an ampere, is to be wired in accordance with the return loop
scheme, using wire of uniform size. The row is 200 feet long,
one end of the row is 50 feet from the service point, and the
other end of the row is 60 feet from the service point. The vol-
tage at the service point is 115 volts. Find the size of wire to
give 105 volts at the middle lamp of the row. Ans. 14,040
circular mils sectional area.
Note. — Such problems as this and problem 23 are most easily solved on the
assumption that the given group of lamps is equivalent to a so-ampere load dis-
tributed with ideal uniformity over the whole length of 200 feet.
23. Find the voltage at each end lamp in the row specified in
problem 22. Ans. 106.93 volts.
Note. — The drop all the way along ab (or cd) of Fig. 35 is equal to
ol (&=x
P— \ (X - x)dx
X Jx=o
(as may be understood from the discussion on page 65) and this is equal to %pXI.
The voltage across lamp at either end of row is the service voltage minus %pXI,
minus the drop in efa, and minus the drop in ge.
24. All the lamps except the middle lamp in the row speci-
fied in problem 22 are turned off. Find the rise of voltage at
the middle lamp. Ans. From 105 volts to 114.88 volts.
25. Find the size of wire required to supply the row of 100
lamps specified in problem 22 by the simple parallel scheme,
both service wires being led from the service point to the nearer
end of the row: (a) when the drop between the service point
and the most remote .lamp is 10 volts; (b) when the drop to the
most remote lamp exceeds the drop to the nearest lamp by the
amount (106.93 ~~ IO5) volts; and (c) when the drop to the most
remote lamp is 5 volts. Ans. (a) 16,200 circular mils sectional
area; (b) 56,000 circular mils; (c) 32,400 circular mils.
284 ELECTRIC LIGHTING.
Note. — In case (a) we have the same total drop as in problem 22, but the voltage
at the lamps ranges from 105 volts at the remote end to 111.67 volts at the near
end of the row, that is, a range of 6.67 volts; whereas with the return loop scheme as
specified in problem 22 the voltage at the lamps ranges from 105 at the middle lamp
to a maximum of 106.93 volts, that is, a range of only 1.93 volts, and the wire
in the return loop scheme is the smaller.
In case (b) the voltage at the lamps has the same range as in problem 22 and the
lamps therefore would operate equally well as in the return loop scheme as specified
in problem 22, provided the lamps are all in use or all out of use, but the wire in
case (6) is nearly four times as heavy as in problem 22. This shows in a striking way
the saving of copper by the return loop scheme, for the same range of voltage among
the lamps, when the group of lamps forms a nearly reentrant row and when the
lamps are always either all on or all off.
On the other hand, the result of problem 24 shows that the return loop as speci-
fied in problem 22 is not at all suited to the case in which part of the lamps in the
group are turned off, the effect being to cause a very considerable rise of voltage at
the remaining lamp (or lamps).
26. A group of 50 lamps each taking i.o ampere is to be
installed at a distance of one mile from a lighting station. It is
understood that whenever any of the lamps are in use all are
in use, so that the drop in the feeders which supply the lamps
may have any value that economy demands. The lamps are
to be operated for 300 hours each year.* The cost of power
at the station is 3.5 cents per kilowatt-hour, the cost of copper
is 1 6 per cents per pound, the annual charge on the cost of the
wire is 10 per cent, (interest 6 per cent., depreciation 3 per cent.,
and taxes I per cent.), and the station voltage is 125 volts.
Find: (a) The size of the feeders to give a balance between loss
of power and cost of copper, and (b) the voltage at the lamps.
Ans. (a) 76,370 circular mils; (b) 50.45 volts.
Note i. — The only objection to the application of the economic principle of the
balance between loss of power and cost of copper to a case like the one here con-
sidered is that the voltage at the lamps may be very different from the voltage which
prevails in the other parts of the lighting system, so that the station management
would have to be careful to supply special lamps suited to the special voltage. It is
evident that it is expensive at best to supply the fifty lamps at a distance of a mile,
for, under the conditions of problem 26, it requires $391.40 worth of copper with a
loss of $39.14 worth of power each year, and to transmit the required power (2.522
kilowatts, or 22.93 amperes with no volts at the lamps) with 15 volts drop would
take $892 worth of copper with a loss of $3.61 worth of power each year.
Note 2. — It is instructive to solve problem 26 graphically as follows: Assume,
PROBLEMS. 285
say, 50,000, 60,000, 70,000, 80,000, 90,000, and 100,000 circular mils. Use these
sectional areas as abscissas of two curves, A and B; the ordinates of curve A
representing the values in dollars of the power lost each year, and the ordinates
of curve B, representing the annual charge in dollars on the total cost of the copper.
Then plot a third curve, C, of which each ordinate is the sum of the corresponding
ordinates of curves A and B, and the abscissa corresponding to the minimum ordi-
nate of this curve, C, is the required sectional area.
27. The customer mentioned in problem 26 is to pay at the
rate of n cents per kilowatt-hour for all energy delivered to
his special line in excess of the usual 5 per cent, line loss. At
what rate per kilowatt-hour must this customer pay on the basis
of his watt-hour meter?
28. A consumer pays 10 cents per kilowatt-hour not only for
the energy he uses in his lamps but also for the energy that is
lost in the wires that lead from the watt-hour meter to his lamps.
If the customer uses his lamps 2 hours per day the year round,
find the size of wires he should use in his house, in circular mils
per ampere, for greatest economy, the cost of copper being 16
cents per pound, and the interest and depreciation being 8 per
cent. Ans. 4,507 circular mils per ampere.
29. The cost of power at the switch-board in an arc-lighting
station is 2 cents per kilowatt-hour. The plant supplies a current
of 6.6 amperes to a circuit of 50 arc lamps which are operated
on a moonlight schedule for 2,160 hours each year. The cost
of copper is 21 cents per pound, and the annual charge on the
cost of the wire is n per cent, (interest 6 per cent., depreciation
3.5 per cent., and taxes 1.5 per cent.). The cost of the wire is
high and its depreciation is large because the wire is insulated.
The price of 2L cents per pound is on the net weight of copper
in the wire and this price is intended to cover the cost of the
insulation. Find the size of wire to give a balance between loss
of power and cost of copper. Ans. 17,040 circular mils.
Note. — The falling of an arc light wire into the street would be very dangerous on
account of the high voltage. Therefore, it is important that an arc-lamp circuit be
very substantial. It is usually not considered allowable for this reason, to use
wire smaller than No. 6 Brown and Sharpe gauge (26,000 circular mils) for an arc-
lamp circuit.
286 ELECTRIC LIGHTING.
30. Find the cost to the station owners of 16.5 kilowatts of
power delivered for 1,200 hours each year at 220 volts over a
special line to a single customer at a distance of one mile from the
station, the wire being of such size as to give a balance between
loss of power and cost of copper. Determine the size of wire on
the basis of a 6 per cent, annual charge on the cost of the copper at
1 6 cents per pound, the cost of power at the switch-board being
2.5 cents per kilowatt-hour. Reckon the total cost of the line
at 2.25 times the cost of the copper, and reckon the total annual
cost of interest, depreciation, taxes, and maintenance of line at
15 per cent, of the total cost of the line. Ans. $1,176.80 per
year, or about 6 cents per kilowatt-hour delivered.
31. Given ten groups of lamps, each group taking 10 amperes,
the groups being 10 feet apart. The lamps are supplied with
current from U5-volt mains according to the wiring scheme
shown in Fig. 37. The end group, bb (see figure), is 10 feet
from the mains, the point, pp, is 70 feet from the mains, and
No. 2 Brown and Sharpe gauge copper wire is used throughout.
Make a drawing like Fig. 22&, showing vthe voltage at every
group of lamps. Sample answer: 1.964 volts drop to the group
of lamps which is 50 feet from the service point.
Note. — It would be permissible for practical purposes to calculate drops to the
various lamps in this problem on the assumption that the lamps constitute a load
which is distributed with ideal uniformity. It is here intended, however, that the
drops be calculated as they actually are and so represented in the drawing.
32. The accompanying figure, Fig. $2p, shows two motors,
M and Mr, two groups of glow lamps, L and Lf, and a group
of arc lamps, A, all supplied from the H5-volt service point, P.
The distances are all so small that the sizes of all wires are to be
determined from the table of safe carrying capacities. The
motor, M, takes 35 amperes, the motor, Mr , takes 18 amperes,
the group, L, contains 7 half-ampere lamps, the group, Lr,
contains 3 half-ampere lamps, and each arc lamp takes 5 amperes.
(a) Make a sketch of Fig. $2p and indicate the values of the
current at the points a, b, c, d, e and /; (b) indicate the size of
PROBLEMS.
287
WW
r
Fig. 32£.
each wire assuming rubber insulated wire to be used; (c) show
the location and mark the current rating of every fusible cut-out
and branch block required by the National Electrical Code.
CHAPTER IV.
PHOTOMETRY AND ILLUMINATION.
33. The conical intensity of a beam of light from a lamp is 50
candle-power. The lamp is 5 feet from the center of a hole in a
wall, and the diameter of the hole is 3 feet. Find the amount of
light passing through the hole in lumens.
Note. — The area of a spherical zone is equal to the area of the sphere multiplied
by the altitude of the zone and divided by the diameter of the sphere.
34. A 5o-candle-power lamp is at the center of a circular band
which is 6 feet in diameter and one foot wide. Find the amount
of light which falls on the band in lumens.
35. As seen from a given direction, the luminous area of a lamp
(projected on a plane at right angles to the line of sight) is 0.75
square inch and the conical intensity of the light in the given
direction is 150 candle-power. What is the intrinsic brightness
of the lamp?
288 ELECTRIC LIGHTING.
36. Find the sectional intensity of the light from a 5O-candle-
power lamp at a distance of 5 feet from the lamp, expressing the
result in lumens per square foot and in spherical-candles per
square foot.
37. The intensity of illumination at a distance of four feet
from a i6-candle lamp is sufficient for easy reading of ordinary
book type, (a) Find the distance from a 2O-candle lamp at
which the lamp gives the same intensity of illumination; (b) ex-
press this intensity of illumination in spherical-candles of light
per square foot of illuminated surface; and (c) express this in-
tensity of illumination in luxes. Ans. (a) 4.47 feet; (b) 0.0796
spherical-candle per square foot; (c) 12.21 luxes.
38. The glow lamp which is used as a standard in a Bunsen
photometer has a candle-power of 16.8 candles in the direction
towards the photometer screen. Another lamp B is placed
at the other end of the photometer bar and when the screen is
adjusted to equality of illumination on both sides, it is 2.61 meters
from the lamp B, and 1.80 meters from the standard lamp.
What is the candle-power of B in the* direction towards the
screen? Ans. 35.3 candle-power.
Note. — This problem is to be solved with the help of the law of inverse squares.
Equality of illumination on the two sides of the screen means that the beams from
the two lamps have the same sectional intensity at the screen.
39. Find the intensity of illumination in foot-candles at a point
on a floor distant 6 feet horizontally from a lamp which is 8 feet
above the floor, the candle-power of the lamp in the direction
towards the specified spot being 65.
40. Let the brightness of daylight with the sun in the zenith
be taken as unity. What is the brightness of daylight when the
altitude of the sun is 75°, 60°, 45°, 30° and 15°, above the horizon
respectively, ignoring increase of atmospheric absorption with
increase of zenith distance of the sun?
Note. — The relative brightness of daylight is inversely proportional to the area
of country covered by a beam of sunlight of, say, one square mile in sectional area,
and this is inversely proportional to the sine of the sun's altitude above the horizon.
41. A certain photographic lens gives a good photograph with
PROBLEMS. 289
an exposure of 1/50 second when the sun is 75° above the horizon.
What exposure would be required with the same lens when the
sun is 5° above the hprizon, ignoring increase of atmospheric
absorption with increase of zenith distance of sun?
42. A direct-current arc lamp gives the following distribution
of candle-power:
Angle from vertical.
10°
20°
30°
40°
SQ°
60°
TOO
80°
Candle-power
290
440
670
i, 080
1,220
i, 080
795
580
Calculate the intensities of illumination at points along a level
open street distant h tan 10°, h tan 20°, h tan 30°, etc., hori-
zontally from the lamp: (a) When the height h of the lamp
above the street is 15 feet, and (b) when the height h of the
lamp above the street is 50 feet. Express the intensities of
illumination in foot-candles.
Plot two curves showing horizontal distances from the lamp
as abscissas and intensities of illumination as ordinates.
43. A beam of light consisting of parallel rays has a sectional
intensity of 100 foot-candles. Find the conical intensity of the
beam after it passes through a lens of which the focal length is
1 8 inches.
44. An open-arc lamp is placed at a distance of five feet from a
converging lens, and an image of the arc is formed at a distance
of one foot beyond the lens. The light from the lamp has a
conical intensity of 2,500 candles. Assuming that the luminous
surface of the lamp is negligibly small, and ignoring loss of light
at the lens by reflection and absorption, find the conical intensity
of the beam beyond the image. Ans. 100 candles.
45. Two lamps A and B are placed at the ends of a Bunsen
photometer bar, and the photometer screen is adjusted to give
equality of illumination on its two sides. The screen is then
one meter from lamp A and 3 meters from lamp B. A lens of
which the focal length is 25 centimeters is placed 50 centimeters
Jrom lamp B, and the screen is left in its original position. Find
290 ELECTRIC LIGHTING.
how far lamp A must be placed from the screen to give equal
illumination on the two sides of the screen, neglecting losses of
light in the lens. Ans. 0.67 meter.
46. An acetylene flame is placed at the focal point of a lens
which is 8 inches in diameter and the focal length of the lens is
25 inches. The luminous area of the flame is 0.7 square inch.
Find the approximate candle-power of the light beyond the lens.
47. The powerful arc lamp of a searchlight emits a beam of
which the conical intensity is 10,000 candle-power. The lumi-
nous area of the arc is o.i square inch, the diameter of the search-
light lens is 12 inches and the focal length of the searchlight lens
is 25 inches. What is the approximate conical intensity of the
searchlight beam?
48. A 35.3-candle-power lamp is placed at a distance of 35 inches
from the center of a large mirror which reflects the light from the
lamp along a photometer bar towards the photometer screen,
and when the screen is adjusted to give equal illumination on its
two sides it is 92.5 inches from the standard lamp and 91 inches
from the center of the mirror. The candle-power of the standard
lamp is 1 6. 8 in the direction towards the photometer screen.
Find the factor by which the apparent candle-power of any lamp,
when measured by the light reflected from the above mirror must
be multiplied in order to correct for the loss of light at the mirror.
Ans. 1.13.
49. Calculate the mean spherical candle-power of the bare
glow-lamp from data given in Fig. 65. Ans. 13.33 candle-power.
Note. — Solve this problem by the method explained at the top of page 114.
50. Construct a Rousseau diagram for the candle-power curve
shown in Fig. 65, and, if a planimeter is available, measure the
area of curve c'c'c' (see Fig. 72) and calculate the mean spherical
candle-power of the lamp.
PROBLEMS. 291
CHAPTER V.
ELECTRIC LAMPS. LAMP SHADES AND REFLECTORS.
51. A closet or cellar lamp is used on the average one minute
per day and energy costs 10 cents per kilowatt-hour. Compare
the yearly cost (including interest on cost of lamp) of using a
2O-candle-power (5O-watt) carbon-filament lamp and a 6o-watt
tungsten-filament lamp. Assume that the tungsten lamp is
broken once every two years by rough handling.
Note. — The table on page 135 gives all the data required for the solution of this
problem.
52. From the tables on pages 135 and 167 find the annual
cost of producing 13,333 lumens 6 hours per day for 300 days
per year (see example on page 166) by 6o-watt tungsten lamps
and by 5O-watt metalized carbon lamps, the cost of energy being
8 cents per kilowatt-hour. Include interest at 6 per cent, per
year on cost of lamps and assume no breakage due to rough
handling.
53. Find the annual cost 13,333 lumens produced by 6o-watt
tungsten lamps for 1,800 hours per year when energy costs 2
cents per kilowatt-hour and when 8 Cents per kilowatt-hour —
lamps to be burned at top-efficiency and at bottom-efficiency in
each case. Include interest on first cost of lamps at 6 per cent,
and neglect breakage.
Note. — See tables on pages 167, 139 and 135.
CHAPTER VI.
INTERIOR ILLUMINATION.
54. Half the light from a lamp is reflected from the walls of a
room. When this reflected light again strikes the walls half of it
is reflected and so on. How much light is there crossing and
re-crossing the room expressed in terms of the amount of light
coming directly from the lamp?
55. The mean distance across the room in problem 54 is 20 feet. What fraction
of a second elapses after turning on the lamps until the light in the room has
cached 1023/1024 of its final steady value?
ELECTRIC LIGHTING.
CHAPTER VII.
STREET ILLUMINATION.
55. Using the table on page 175 find the distance apart of
lamps No. 3, No. 4 and No. 7 to give 0.05 foot-candle normal to
beam (due to each lamp) at a point midway between the lamps
when the lamps are hung 24 feet above the street.
56. Using the table on page 178 find distance apart of 350-
candle-power tungsten lamps (equipped like Fig. 106) to give
0.05 foot-candle normal to beam (due to each lamp) at a point
midway between lamps when the lamps are hung 24 feet above
the street.
57. The dimensions of a certain city block are shown in Fig.
Find the minimum mean value of normal illumination
1
L
X OO°
X
XT
he-*
{
a
1
1
|
J375 feet
i
x a o Q
X
jr.
!
600 feet
Fig. 57 p.
(/„) and find annual cost per mile of street with 4,000 hours of
service per year and energy at 3 cents per kilowatt-hour :
(a) With 6.6 magnetite-arc lamps at crosses and 35o-candle-
power tungsten lamps at circles.
(b) With 4-ampere magnetite-arc lamps at crosses and 200-
candle-power tungsten lamps at circles.
(c) With 2OO-candle-power tungsten lamps at crosses and 50-
candle-power tungsten lamps at squares.
Note. — By mean value of In at a given point on the street it is here intended
to refer to half the sum // + /„", where /»' and In" refer to the two lamps
between which the given point lies.
PROBLEMS. 293
Assume all lamps to be 24 feet high and plot curve for /,/ and Jn" with the
help of the tables on pages 1 75 and 1 78. Then plot the curve of which the ordinates
represent \(In' + In")- Assume, in the absence of more exact data, that mainte-
nance, first cost, interest and depreciation are the same for a zoo-candle-power
tungsten lamp as for a 35o-candle-power lamp.
In reckoning the cost per mile of street note that four crosses and four circles
(or four crosses and ten squares) represent 3,900 feet of street in Fig. STP-
A serious objection to the use of many small lamps along a street is the cost of
the lamp-supporting structure. The cost of this structure is not to be considered
in this problem.
CHAPTER VIII.
ELECTROLYSIS AND BATTERIES.
58. The anode of an electrolytic cell is a copper rod I inch
in diameter and the cathode is a hollow copper cylinder 6 inches
inside diameter; the two electrodes are co-axial and they stand
vertically in an electrolyte 8 inches deep. A current of 5 amperes
flows through the cell. Find the current density at the cathode
and the current density at the anode.
59. Calculate the number of cubic centimeters of oxygen and
the number of cubic centimeters of hydrogen liberated in one
hour by a current of one ampere; inert electrodes being used in
dilute sulphuric acid or in a solution of potassium or sodium
hydrate. The gases being reckoned dry at o° C. and 760 milli-
meters pressure. Ans. 209 cubic centimeters of oxygen and 418
cubic centimeters of hydrogen.
Note. — The density of dry oxygen at o° C. and 760 millimeters pressure is 0.00143
grams per cubic centimeter and the density of dry hydrogen at o° C. and 760
millimeters prssure is 0.0000902 grams per cubic centimeter. The atomic weight
of silver is 107.93 and the atomic weight of hydrogen is i.oi (o = 16).
59. An electrolytic generator* for oxygen and hydrogen re-
quires 3 volts per cell. Find the cost of one cubic foot of oxygen
* A good form of electrolytic generator for hydrogen and oxygen is described by
W. S. Franklin, Physical Review, Vol. IV, pages 61-64, July, 1896. A large gener-
ator of this type using cast iron frames and sodium hydrate solution has been in use
for about 13 years by the Nernst Lamp Company; and the depreciation and repairs
have been negligibly small. The generator consists of 35 cells in series supplied
with current from no-volt mains. See American Electrician, Vol. XI, pages 526-
527, November, 1899.
294 ELECTRIC LIGHTING.
and two cubic feet of hydrogen when energy costs 2 cents per
kilowatt-hour making no allowance for interest on cost of gen-
erators and no allowance for depreciation and repairs of generator.
60. The heat of combustion of one gram of hydrogen is 34,700
calories. What fraction of the energy delivered to the generator
of problem 59 is represented by or tied up in the oxygen and
hydrogen produced? Ans. 50.7 per cent.
61. The cost of gravity-cell zinc is, say, 6 cents per pound, and
the cost of copper sulphate crystals (CuSO4 + 5^0) is, say,
6.5 cents per pound. Half of the materials consumed in a gravity
cell is wasted by local action and about one third of the zinc is
left as scrap and is worth about 2 cents per pound. Furthermore
the copper which is deposited on the cathode is worth, as scrap,
about 10 cents per pound. The terminal electromotive force of
the cell while it is delivering 0.16 ampere is about 0.72 volt.
What is the cost per kilowatt-hour of the output of the cell making
no allowance for cost of labor? Ans. $1.64.
62. The electromotive force of a gravity cell is 1. 08 volts.
Find the rise of temperature when 10 grams of finely divided zinc
are stirred into 2,000 cubic centimeters (approximately 2,000
grams) of dilute copper sulphate solution.
Note. — The specific heat of dilute copper sulphate solution is sensibly the same
as the specific heat of water. In a Daniell cell (gravity cell) arranged to have no
local action the whole of the chemical energy is converted into electrical energy.
62. A lead storage cell delivers 10 amperes for 8 hours. Find
the increase of weight of each electrode. Ans. The positive
electrode gains 0.2105 pound and the negative electrode gains
0.3232 pound.
63. The storage cell specified in problem 62 contains 4,000
cubic centimeters of dilute sulphuric acid of which the density at
1 8° C. is 1.700 grams per cubic centimeter when the cell is fully
charged. Find the density of the electrolyte (at 18° C.) after
the cell has delivered 10 amperes for 8 hours. Ans. 1.1286 grams
per cubic centimeter.
Note. — For the solution of this problem the following table is needed.
PROBLEMS. 295
DENSITY OF DILUTE SULPHURIC ACID IN GRAMS PER CUBIC CENTI-
METER AT 1 8° C.
Percentage Strength. Density.
o 0.9986
10 1.0673
2O I.I4I4
30 1. 221
Percentage strength in this table means the number of grams of H2SCU in 100
grams of the solution.
To solve the problem find grams of H2SO4 and grams of H2O in the solution at
the beginning.
Then find grams H2SO4 taken from the solution and grams of I^O given to the
solution by the discharge.
Then find percentage strength of solution after discharge and find density from
table.
INDEX.
Absorption coefficient, definition of, 162
coefficients, table of, 100
of light, 99
Acuity, visual, 156
Alternating current lines, 77
Anion, definition of, 185
Anode, definition of, 185
Arc lamp, the, 126
mechanism, 128
lamps, 129
and glow lamps compared, 143
cost of lighting by, 147
luminous, 130
magnetite, 130
the flame, 130
for street lighting, 173
the electric, 126
the luminous, 126
Balancers for three-wire systems, 42
Batteries, 184
Battery, storage. See storage battery.
the primary. See voltaic cell.
Bichromate cell, the, 197
Block signalling for railways, 252
vision and detail vision, 171
Booster, the, 220
the negative, 224
Boosters, automatic, 220
Brilliancy of a lamp, intrinsic, 90
Bunsen photometer, the, 105
Cable insulation, graded, 263
Candle power curves, 109
unit, definition of, 89
Carbon arc lamp, intensified, 158
filament lamp, the, 134
Carcel lamp, the, 89
Carrying capacity, safe, of wires, 54
Cathion, definition of, 185
Cathode, definition of, 185
Chemical calculations in electrolysis,
187
work and heat, 190
Closed circuit cells, 199
Composite, the railway, 245
2-wire, the, 248
Condenser type of insulator, 275
Conical intensity, change of, by lenses,
99
of light beam, 89
Connection cost of electric service, 16
Constant current transformer, the, 182
Consumption cost of electrical service,
17
Cooper-Hewitt lamp, the, 131
Copper oxide cell, the, 200
Corona formation as a factor deter-
mining the size of wires, 70
Cosine law, Lambert's, 97
Cost, comparative, of electric lamps, 146
of electric service, 16
of electrical power, 5
of power, influence of load factor
on, 7
of steam power, 2
Daniell cell, the, 200
Decomposition voltage, 190
voltages, table of, 191
Demand cost of electric service, 17
Density of current in electrolysis, 186
Deterioration factors of lamps, 149
Detail vision and block vision, 171
Dielectric stresses, 257
Diplex telegraph, 230
Dissociation theory of electrolysis, 185
Distribution of light around a lamp, 108
series and parallel systems of, 36
Diversity factor, the, 14
Double current generator, the, 42
Dry cell, the, 201
Duplex and quadruplex on simplex and
composite circuits, 252
telegraph, 228
Edison Lalande cell. See copper oxide
cell,
storage cell. See storage cell, the
nickel-iron.
three-wire generators and bal-
ancers, 42
3-wire system, the, 39
Electrical power, cost of, 5
Electric arc, the, 126
code, the national, 74
296
INDEX.
297
Electric furnace, 255
plant of Wallingford, Conn., 27
railroads, 255
service, cost of, 16
rates for, 18
welding, 255
Electrochemical equivalent, definition
of, 187
unit of work, 189
Electrode, definition of, 184
polarization, 192
Electrolysis, 184
chemical calculations in, 187
dissociation theory of, 185
Electrolyte, definition of, 184
Electrolytic cell, definition of, 184
Electromagnetic ore concentration, 255
Extensive shades, 152
Faraday, definition of the, 189
Fechner's ratio, 107
Fire alarm and police telegraph, 255
Flame arc lamps, 130
Flat rate system, the, 20
Flicker photometer, the, 116
Floating battery, the, 223
Flux, of light, measurement of, 112
Focussing shades, 152
Foot-candle, definition of, 91
Fuller cell, the, 198
Furnace, electric, 255
Gauss' theorem, 258
Glare, discussion of, 158
Globe photometer, the, 123
Globes and shades for lamps, 151
Glow lamp ratings, 138-143
the, 133
lamps and arc lamps compared, 143
cost of lighting by, 135
for street lighting, 176
Graded cable insulation, 263
Gram-val, definition of the, 189
Gravity cell, the, 200
Grenet cell, the, 197
Heat and chemical work, 190
Hefner lamp, the, 88
unit, definition of, 89
Holophane reflector, the, 154
Illumination and photometry, 86
calculation of, 168
intensities of, for various kinds of
service, 164
intensity of, 95
oblique, 95
of a room, 156
Illuminometer, the, 119
Incandescent lamp. See glow lamp.
Indirect system of lighting, the, 160
Induction watt-hour-meter, the, 23
Insulation of pole line, 72
Insulator, condenser type, 275
Intensified arc lamp, 158
Intensities of illumination required for
street lighting, 172
Intensity of illumination, definition of,
95
Intensive shades, 152
Interference of lines, 83
Intrinsic brilliancy of a lamp, 90
Ions, definition of, 186
Kelvin's law, 66-70
Lambert's cosine law, 97
Lamp globes, shades and reflectors, 151
intrinsic brilliancy of a, 90
Lamps, choice of size of, 168
comparative cost of electric, 146
standard, 88
Law, Lambert's cosine, 97
of inverse squares, the, 92
LeClanche cell, the, 201
Lenses, change of conical intensity by,
99
Light, absorption of, 99
and radiant heat, 86
conical intensity of, 89
distribution of, around a lamp, 108
flux, measurement of, 112
luminous intensity of, 87
physical intensity of, 86
sectional intensity of, 89
units, 88, 89
Lighting by the indirect system, 160
cost of, by arc lamps, 147
by glow lamps, 135
Lightning protection, 255
rods, 255
Line interference, 83
Load factor, influence on cost of
power, 7
of customers, 14
Local action and voltaic action, 198
circuit, the, 226
Lumen, definition of, 90
Luminous arc lamps, 130
lamp, the, 127
intensity of light, 87
Lux, definition of, 91
Magnetite arc lamps, 130
Manganese dioxide cell, 201
Maximum demand meter, the, 26
Mercury vapor lamp, 131
rectifier, the, 181
298
INDEX.
Meter for maximum demand, 26
the watt-hour, 21
Meter-rate system, the, 20
Motor-generator balancer, 42
National electric code, the, 74
Negative booster, the, 224
Nernst lamp, the, 134
.Neutral relay, 231
Oblique illumination, 95
Open circuit cells, 199
Ore concentration, 255
Ozone, 255
Parallel and series systems of distri-
bution, 36
Pentane lamp, the, 88
Phantom circuit, the, 243
on two 2-wire composites, 248
Photometer, the, 87, 105
the Bunsen, 105
the flicker, 116
the globe, 123
laboratory type, 117
portable type, 119
Photometry, and illumination, 36
Polarization of electrode, 192
of voltaic cell, 196
Polarized relay, the, 231
Pole line insulation, 72
Power, cost of, 2
cost of, influence of load factor on, 7
Primary battery, the, 194
Printing telegraph, 234
Prismatic glass reflector, the, 154
Quadruplex telegraph, 233
and duplex on simplex and com-
posite circuits, 252
Quartz lamp, mercury vapor, 133
Radiant heat and light, 87
Railroads, electric, 255
Railway block signalling, 252
composite, the, 245
Rates for electric service, 18
Rating tungsten lamps, three-efficiency
scheme of, 139
Reactance drop and resistance drop, 78
Reactances of line, table of, 79
Rectifier, the mercury vapor, 181 •
Reflection coefficients, table of, 100
Reflectors and shades for lamps, 151
Relay, neutral, 231
polarized-, 231
Relays, telegraph, 226
Resistance drop and reactance drop, 78
Return loop scheme, 64
Rousseau's diagram, 114
Safe carrying capacity of wires, 54
Search light, the, 102
Sectional intensity of light beam, 89
Series and parallel systems of distri-
bution, 36
Service, electric, rates for, 18
Shades and reflectors for lamps, 151
Sharp-Millar photometer, the, 119
Simplex blocks in series, 248
circuit, the, 246
on phantom, 247
Size of lamps, choice of, 168
Solid angle, unit of, 90
Sounders, telegraph, 226
Spectrophotometer, the, 125
Spherical angle, definition of, 89
candle, unit of, 90
Standard lamps, 88
Steam power, cost of, 2
Storage batteries, control of, 217
use of, 214
battery, 202
the floating, 223
the lead, management and
care of, 211
cell, the, 202
the lead, 204
the nickel-iron, 205
cells, costs and weights of, 208
Strain insulator, the, 73
Street lighting, 171
by arc lamps, 173
by glow lamps, 176
intensities of illumination for,
172
systems of, 179
Stresses, mechanical, in aerial wires, 46
Submarine telegraph, 235
Suspension insulator, the, 73
Syphon recorder, 238
Systems of street lighting, 179
Table of absorption coefficients, 100
of carrying capacities of wires, 55
of coefficients of reflection, 100
of decomposition voltages, 191
of line reactances, 79
resistances of wires, 75
Tantalum lamp, the, 134
Telegraph, diplex, 230
duplex, 228
fire alarm and police, 255
Morse, the, 226
printing, the, 234
quadruplex, 233
recorder, the syphon, 238
relays and sounders, 226
INDEX.
299
Telegraph, submarine, 235
way stations, 227
wireless, 255
Telephone, the, 238
calls, 251
receiver, 239
transmitter, 238
Thomson watt-hour-meter, the, 22
Three-efficiency scheme of rating tung-
sten lamps, 139
Three- wire generators and balancers,
42
system, Edison, the, 39
Transformer, constant current, the, 182
Tungsten lamp, the, 134
lamps, three-efficiency scheme of
rating, 139
Twilight vision, 171
Two-rate meter, the, 26
Ulbricht's globe photometer, 123
Vernon-Harcourt lamp, the, 88
Visual acuity, 156
Voltage drop as a factor in determining
size of wires, 54
of decomposition, 190
Voltaic action and local action, 198
cell, the, 194
the bichromate, 197
the copper oxide, 200
the dry, 201
the Fuller, 198
the Grenet, 197
the LeClanche, 201
the manganese dioxide, 201
polarization of, 196
regeneration of, 202
cells, open circuit and closed circuit,
199
Wallingford electric plant, the, 27
Watt-hour-meter, the, 21
the induction, 23
the Thomson, 22
the two-rate, 26
Way stations, 227
in general, 250
Welding, electric, 255
Wire calculations, 58-70
for alternating current, 77-84
Wireless telegraph, 255
Wire table, 75
Wires, aerial, mechanical stresses in, 46
Working plane, definition of, 165
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