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THE BELL SYSTEM

TECHNICAL JOURNAL

A JOURNAL DEVOTED TO THE

SCIENTIFIC AND ENGINEERING

ASPECTS OF ELECTRICAL

COMMUNICATION

EDITORIAL BOARD

]. ]. Carty Bancroft Giikrardi F. B. Jew in t

E. B. Craft L. F. Morehousi: O. B. Blackuell

H. P. CHARLESWORTH IC. H. COLPITTS H. D. ARNOLD

R. W. Kin.,— ErfiVor T. O. Pi;rrine~.;.w/. Editor

VOLUME IV
1925

AMERICAN TELEPHONE AND TELEGRAPH COMPANY
NEW YORK

Bound
Periodical

^ 25 '26

5(>|(I4;{

The Bell Systeiri Technical Journal

January. 1925

Engineering Cost Studies'

By F. L. RHODES

In rK()i)i( TKiN

Tm-I ^ulijcct assigiicnl to me in the ".Notes Rc'Kardinj; the Pro-
i;r.im of the Conference" is "The Theoretical Principles of
Kcononiic Studies and Tlieir Possible Application in I'ndergraduate
Courses." With your permission, I shall digress somewhat from a
literal consideration of this title. I shall not undertake to deri%e
formulae, to set up efjuations and to obtain maxima and minima
from them. The mathematics can readily be obtained from available
sources. On the other hand, I shall attenipt to outline the field for
economic studies in engineerini; work, usini; iilusi rations drawn from
telephone engineering practice.

What is an engineering cost study? When you or I reiich a de-
cision to purchase a certain pair of shoes, making a selection from
an assortment ranging in price from (say) So to S15, we have per-
formed, consciously or unconsciously, some of the reasoning of an
engineering cost study. Among the factors influencing our decision
will be the probable length of ser\-ice life of different pairs, as well
as the ability to extend this by an expenditure, to be made at some
future time, for maintenance as represented by new soles and heels,
which, perhaps, can be applied economicalK' to a moderately costly
pair but not so to the cheapest.

These two elements, depreciation and current maintenance, are
factors entering into engineering cost studies but they are not all
of the factors. Whether we have the necessary capital in hand, or
are obliged to hire or otherwise raise it, the annual cost of the capital
must be taken into consideration, and treatment of the matter of
flepreciation is incomplete without consideration of sal\"age value
and cost of removal.

Thus, unless we pursue our inve.stigalion into tletails that arc not
ordinarily considered when buying shoes, it is evident that our

' .Votes of a Talk given at the Bell S\stem Educational Conference, -August, 1924.

1

2 Hiii.i.' !:)'<i'T'iiir-^ TEt}ix'iC;^nJioT.Ry.AL

homely illustration, while ser\ing'"hC'.c«nter our attention on certain
important subjects to he taken uiJ-rfi- Vliis paper, falls short in resjiect
of others that can not be neglected in engineering cost studies.
Broadly speaking, engineering cost studies deal with the comparati\e
annual costs of alternative projects. Frequently they also invo!\e
comparisons of expenditures to be made at different times in the
future. They are of value to industrial executives in assisting ihcin
to arrive at decisions where several courses of action are open. Imi
they are nut ilie sole guides in arriving at decisions. No hard and
fast formulae can l.ike liu- place of judgment based on experience.
I'nrnuilae of this naturt- are |)n)periy used as guides to assist jud.unu'nl .

The necessit\- for guidance from studies of this kind arises most
frequently in a growing i)lant. The telephone plant always has
been, and .so far as we can anticipate, will continue to be a rapidK'
growing thing.

This means that whenexer an addition is to be maile, the cjuestion
arises, how much cai)acity for growth is it most economical to pro\ide
for? As an illustration of this, consider with me the proljlem that
arises when it becomes necessary to place somewhere an undergroimd
cable. Obviously it would be imeconomical to construct an under-
groimd conduit of one duct for this cable and next year or the >ear
atler to dig uji the street and lay another ditct for a second cable
and sii on in i>iecemcal, hand-tn-iiioiitii fashinn.

< 111 the iitiier liaiKJ. it would not lie ecunomira! In oliinate the
iuhiiIkt ot cai)les that \\(juld be recjuired in a hundred years, e\en if
we could foresee the needs so far ahead with any degree of certainty,
and to place at the outset sufficient ducts to care for all the cables
re(|uired along that route in the next century, for in that event, the
carr>ing charges on the idle ducts would prove much more expensi\e,
in the long run, than woidd additions made at infrec|uent intermediate
limes. Somewhere between one \ear and one hundred years is the
most economical period for which to pro\idc duct capacity in ad-
vance. The determination of this period, based on suitable con-
struction costs, the expected rate of growth in r,ii>le leciiiifemenls,
and other factors is one of the useful results obtained from an engi-
neering cost sliid\-.

I'lider our organizalion, practicalh' all t\pes of plant and e(|iii|)-
nieiit are <le\eloped by the Central Staff. These are slan(lai<lize(l
in a range of sizes sufficient to meet all the needs of the business.

The choice of standards and sizes to meet specific situations arising

nXGlXF.F.Rl.W; COST swniF.s 3

in the ticld is ih.kU- !>>• the proptT niVici.ils of tlu- asxxi.itcd opcr.itiii^;
i-onipanics.

If a pitve of apparatus or o(|uipnient, correctly clesiRtitxl within
itself, is installinl in tlu- wrong place, or if a wrong size is selcclcil,
loss will result.

Questions of where to place plant and what size to employ, ;i4k1
when to replace existing plant constantly confront the ofK'rating
engineers in the field. In the telephone business ever%- major con-
struction project is described in what we term an "estimate" which
is nothing more or less than a detailed design for the project, cm-
luxlied in drawings and specifications, accompanied by a carefully
preparetl estimate of its cost. These estimates originate in the Plant
Departments of the Associated Companies and are really the bids
of the construction forces for performing the work. These estimates
pass through the hands of the Chief Engineer of the Associatcxl
Company for his scrutiny and approval before they proceed to the
higher officials of that company for final authorization. The Chief
Engineer considers these estimates in their relation to the general
plans of the Company with reference to the growth of the business
and the plant. F"or many years the chief of the Department of which
I am a member, \'ice President General John J. Carty, occupied the
post of Chief Engineer of the New York Telephone Company, the
largest associated company of the Bell System. I have heard him
say that when, while occupying that position, an estimate for some
six-cific piece of work came before him for re%'iew, he asked himself
three questions regarding it:

1. Why do it at all?

2. Why do it now?

3. Why do it this way?

Rigorous proof sufficient to answer these three questions will
justify the endorsement of any engineering project, and, furthermore,
each question generally involves an engineering cost study.

Fl.ND.\.MKNT.\L Pl.WS

Of all the engineering cost studies that are made in connection
with the telephone industry, none is more far-reaching in its effect
than those involvetl in what we term our "fundamental plans." In
firder to give a fair idea of the importance of the work done under
our fundamental plans, it will be necessary to describe briefh- what
a fundamental plan is.

4 BELL SYSTEM TECHNICAL JOURNAL

In coiiipletetl form a fundamental plan shows what the general
lay-out of the telephone plant in a city is expected to be at some
definite time, usually from 15 to 20 years in the future. It shows:

(a) The number of central office districts that will be recjuircd to
provide the telephone service most economically, and the
boundaries of these central office districts.

(b) The number of subscribers' lines to be ser\'ed b\- each central
office.

(c) The ()ro|KT liKution for ihe ceiilral offKe in i:acli district to
enable the service to be gi\en most economically with regard
to costs of cable plant, land, buildings and other factors.

(d) The proper streets and alleys in which to build underground
conduits in order to result in a comprehensi\e, consistent and
economical distributing system reaching ever\- cit\ bloik lo
be ser\-ed by underground cable.

(e) The most economical niunber of tlucls lo ])ro\ ide in each con-
duit run as il is buili.

These arc all \vr\ detiniU' iirohlenis tliat confront the execuli\es of
our Associated Companies when plant extensions are required. Our
experience has shown that our fundamental plans reduce guessing
to a minimum b\' utilizing the experience of years in studying
questions of telephone growth in order to make careful forecasts
on the best possible engineering basis. A few words as to liow funda-
mental plans are matie may not be out of place.

The basis of the fundamental plan is what we term a commercial
survey, which is a f(jrecast of the future community showing the
probable amount, distribution and character of the population and
the probable market for various classes of telephone ser\ice.

Before making this forecast, it is important to know what are the
present conditions as to population ami use of the telephone ser\icc.
To ascertain the.se facts a census of the community from a telephone
point of \iew is made. Present telephone users are classified into:

Residence TcK^phones.

Business Teleiihones in Rcsitlcnce Areas.

Telephones in Business Section.

In analyzing Roidence telephimcs all f.imiiies are di\i(k'd among
those occupying:

(a) Private Residences.

(b) Two-famil\' Houses.

F.\ci.\'F.r.Rixc. COST srmir.s =,

(f) ApartnuMits.
(i\) l.<Hli;iii,k; lloiisis.

Ill f.uli tl.i-is, Mil>»li\ i>ioiis .no lu.uli- .urnriliiij; lo llic i»-iil p.iid
as it has bivn foiiiul thai a ilosi- rrlation exists hoiwi-cn ront and (hi-
class of ti'li'plioiio sor\icc iisi-d. Husincss ti-lcphoiu's an- dividi'd
iiiti) 21) or M) dirtVrt'nt dasst-s. An important factor in the forecast Ls
the future population of the city, both as a whole and l)\- sections!

This involves, in each particular problem, not only study of the
past growth of the city in <iuestion, but also careful and detailed
comparis<ins with the growth history of other cities where condi-
tions have been such that the experience in those places is usefid
in making the pretliction for the city being studied.

Having arrived at forecasts, for certain future dates, as to the
number of telephone users to be providc<l for, where they will be
locatetl. what character of service they will recpiire, what time of
day they will call, and how freiiuently, and where they will call, it
lHHX)mes a definite, although intricate engineering problem to de-
termine the most economical number, size and location of buildings
and switchboards and the location and size of conduit runs. All of
the promising combinations of future offices and districts as indi-
cateil by experience anil the geographical characteristics of the city,
are laid out on working maps and the annual costs are figured. The
arrangement which gives the lowest equated annual costs o\er tiie
pericxi of time for which the stutly is made is, in general, the one
which is adopted. Fundamental plans are reviewed every few years,
particularly when some major plant addition, for example, the open-
ing of a new central otlice, comes up for consideration. In this way
we are constantly looking ahead and following a coordinated plan;
but this plan is not a rigid, fi.xed thing. It is modified as frequenth'
as may be necessary to meet the constantly changing requirements.
In work of this kind, future expenditures must be given greater or
less weight accordingly as they are required to be made in the near
future or at some more distant time. This is taken into account b\-
equating future expenditures in terms of their present worth; that
is, the sum in hand, at the present time, which, at compound interest,
will be just sufficient to proxide for the future expenditures when
they are required.

Transmission St.vnd.vrds .and Stiuies

-An interesting and typical annual cost problem which arises in
connection with fundamental plans is that of obtaining a proper cost

6 BF.LL SYSTEM TECHNICAL JOURNAL

balance between the circuits eniplo\ed for subscribers' loops and
those employed in intenjftice trunk lines. The larger the wire, the
belter will be the talk. But it will also be more expensi\c. The
first step in solving this i^roblem is to decide how good the trans-
mission must be to afford satisfactory service to the telephone using
public. Our present standartls are a matter of growth; the accumu-
lated results of long and extensive experience. They are live, working
standards constantly being intelligently scrutinized and, when neces-
sary, modified. A discussion of the values of the standards employed
would uiuluK' prolong this |)aper. Therefore, let it suffice, at this
time, to slate that the telephone offices in a large city, including its
einirons, ma>' be divided into metropolitan offices and suburban
offices; that is, the central business offices separated from the subur-
ban residential offices. Between subscribers in difTen-nt districts
suitable standards of transmission are decided iipdii.

Before descril)ing this stud\' further, reference must be made to the
practical necessity for the standardization of construction materials.
Subscribers' loops run in length from a few hundred feet to 3, 4 or r>
miles. If we tried theoretically to make all talks exactly equal in
loudness, we should have as many different sizes of wire in our cables
as there are different lengths of loop. To reduce the complexit>, our
cable conductors are of certain standard sizes, which experience has
shown are sufficiently close together to meet the needs of the busi-
ness. These standard sizes, in American Wire Gauge, are Nos. '24,
22, 19, 16, 13 and 10; the three latter not being used in subscribers'

lonps.

Having adopted st.mdards of transmission and standards of cabU'
conductor sizes, our problem is to obtain the standards of transmis-
sion with the standards of cable contluctors in the most economical
nianiuT.

The nn'ihdd of doing this, in brief, is to tigiiie out the annual costs
\\lii( h would lie iiu lured in doing it a number of different ways and
to select the wa\ that gi\es the lowest annual cost. In this kind of
a stud\', which we call a "loop anil trunk" study, it has been con-
venient to designate the subscribers' loops b\- their maximum circuit
resisUuice. .Adojiting this form of designation, it may be assunuil.
first, ih.it all of the subscribers' loops will ha\e an average transmit -
tini; ami receiving efficiency as good or better than a 350-ohm looj);
as a second assumption, that they will be as good or better than a
H)()-ohm loop; and, as third and fourth assumptions, 450 and oOO-olim
loo[)s, respecti\eK-. In assuming, for example, a 3.50-ohm loo[) in

F.XaiXF.l-.RIXC COST SIC PI IS 7

\i). ■Jl-^aiim" i'.il)li-, it is, of course, iiri-i'ss.ir\- tli.il .ill silliscriinTs
lia\'ii)^ loops lon^rr th.in tho aiuount of No. 2I-Kaiij;c cable rcpri'scnti-d
!)>• this resistance sh.ill hv put in No. 22-^augc or No. 19-Raune calile
as ni.iy he recpiireil.

Tlie transmission losses, iuitli ir.uisinit ling an<l receiving, ari-
then coinputeil for the assunieil loops. The transmission losses in
central otVue apparatus are constant and known. Subtracting ifie
losses in the otVices and in the substation loops for each assumed
grade of loop from the transmission standards, leaves the amount
()f transmission loss which can he allowed in the interoffice trunks
correspomling to each limiting grade of suhscril)cr's loop. On the
h.isis of this allowable transmission loss in the trunks and knowing
the distances between central offices, we are enabled to fix the size
of conductor reijuired in the trunks.

Knowing the grade of loops and trunks reciuired for each of the
above assumptions, we can then compute the total annual charge
of giving .service according to that assuminion. If the assumptions
h.ive lieen wisely chosen it will usually work out that the first
assumption, that is, a very high grade of subscriber's loop, will not
be as economical as some others, due to the relatixcly high cost of the
subscribers' loops taken as a whole. Neither will the last assumption,
that is, a very low grade of subscriber's loop, be the most economical,
on account of the relatively high cost of the triniks. Somewhere
between, however, there will be sf)me assumption wiiicli will show
the smallest total annual charge.

To find more precisely the most economical arrangement, the vari-
ous values are plotted with the assumptions as to subscribers' loops
forming one set of ordinates and the total annual cost forming the
other. The point on the curve representing the lowest annual cost
then indicates the proper grade of subscribers' loops to employ. In
the case of the longer interoffice triniks, loading is, of course, em-
ployed. In the design of toll lines antl toll switching trunks generally
similar cost balancing methods are employed.

In many cases, the problem can be solved b\- the determination
of what we term "the warranted annual charge" of transmission
which may be defined as the annual cost of improving the talking
efficiency of the circuit in the cheapest way by a definite small amount.
By means of studies of this kind, we obtain a plant closely approxi-
mating a balanced cost condition. That is, in such a plant, a dollar
can be spent in improving transmission efficiency, ncj more effectivelv
in one part than in another.

8 BEJ.L SYSTEM TECfl.XICAL JOrRXAL

Oniiik Aim i.u ATioNs of 1-;m.im;i:rin(. Cost Snniics

l'"rom wlial has uIr'.kK liccii said, it should ikiL lie ink'ncd lh.it
the sole application ol eii.uiiieerin.n cost studios is in connection with
the problems arising in the operating field. The question whether
or not a more efficient piece of apparatus at a higher cost is war-
ranted enters into most of our develcjpment problems. The econ-
omies of the case lie at the root of our development work in all (ion ions
of the plant.

At this point I should like to call attention lo the fact that our
development work covers not only what are termed "transmission"
matters, but also very important problems in switchboards, outside
plant and other phases of the business.

The service which we provide is a communicatioji service, which
involves important problems affecting the means for connecting
and disconnecting the parties as well as those other important prob-
lems, to which your attention has been particularly directed, relating
to the loudness and quality of the transmitted speech.

In cable design, particularly in the case of intercity cables and
interoffice trunk cables, the average separation between wires in
the cable affects the electrostiitic capacity of the circuits and there
is a definite capacity which represents the most economical degree
of concentration of the w'ires in the cross-section of the cable. The
spacing and inductance of loading coils presents another problem
in balanced costs. K\-en in the case of wooden poles we make use of
economic cost studies.

The length of life of a jjole depends upon a \'ariet>- of factors, the
most important of which are the character of the timber; whether
or not a preservati\e treatment is employed and, if so, the nature
of the treatment; the local climatic and soil conditions and the
original size of the pole.

The strength of a pole varies with the cube of the diameter of the
sound wood at the weakest section. If the original size of the pole
is onh- slightly more than the critical size at which replacement
should be made, the life of the pole will be \cry short, as dcca\ will
reduce the size at the ground line to the critical size within .1 lew
years. On the other hand, a pole of huge size at the ground line
would have a very long life before rotting sufficiently to require
replacement, but the first cost of so stout a pole might readily be
so great that its annual cost would exceed that of a smaller and
cheaper pule. In f)ur specifications for poles we have constantly

F.s'Gixr.r.RixG COST sri'nirs 9

Id hear in niiiid that tlu> fliniiiiatioii of poles rontaiiiiii^; (inilitT
(lolVrts 4>f Olio kiiiil or anoihcr iiUMiis that wi- arc adding soniclhiii);
to the llrst cost of our poles and the criterion must always he whether
or not liic ciiniinalion of tlies*.- defects will snllicicnlly proioiij; the
life of the poles to w.irranl the incre.isi-d first cost.

I'here ha\e now heen |)laci-d hefore yon several exaniples of proh-
lenis occurring in the telephone industry in the solution of wlmh
enj;inivring cost studies may he advantageously em[)l()yed, and,
prohahly, enough has heen said to make clear the importance of
this form of economic anaKsis.

Factors Hnti:rin(. into Axmal Costs and Tiii:ir
evaliation

Let us now consitler together the principal factors entering into
aiuuial cost, and how, in the course nf our work, wc ov.iluate them.

The several factors are these:

1. Cost of money.

2. Ta.ves.

'.i. Insurance.

4. Depreciation.

5. Current Maintenance.
<). Administration.

7. Operating Costs.

Cost of Money. The operating companies of the Bell System
ohtain the new money that they use in e.xtensions to their plants
from the sale of their capital stock and securities — bonds and notes.
Such a return must be paid the investor, by the Company, as will
induce a constant flow of new capital into the business. This steady
influx of new capital is required because the System can not decline
to expand. It is obligated to meet the increasing needs of the public
it serves. Its need for new capital is a direct result of public demand
for the service it renders. The rates for service which public utilities
may charge are regulated by the commissions, l)ut neither the com-
missions nor the utilities can fix the worth of money. Public utilities
must pay the cost of money just as they must pay the cost of labor,
poles and other material. No investor can be forccfl to invest. If
the rate is below what money is worth in the general money market,
he will keep out. Utility companies must bring their offerings to
a general money market anfl submit them, in open competition, with

10 BELL SySTEM TECHXIC.IL JOIRX.IL

the offerings of iinik-riakiiigs of f\iT\- kind n-(|iiiriiig rapii.il. Tlu're
arc two \va\s of ueiiint; now nioiu'\-:

1. IVom iiut-siors williiiii to li-nd. Tliese are tlie l)oiul and note

hokiers.

2. 1-Voni imestors \\illiii.u to lun-omc i)artners in ow iicr>lii|). Thesi-

are the stockholders.

\c)t oni\- do stockholders expect a higher return than bond and
nnic- holders, hut if the stockholders' earnings are insufficient, the
bond in\esior will take his money to some safer market. Taking
into account the ratio which must be prudently maintained between
funded debt and stock, a proper figure should be obtained as re[)re-
scnting the average annual cost of money. This figure shoidd not be
confused with the figure that represents a fair rate of retin'n includ-
ing a margin for surplus and contingencies.

Taxes. Taxes are levied by various governmental botiies, munici-
pal, county, state and federal, on many different bases. In some
specific plant problems, taxes ha\e to be computed to meet the con-
ditions of the case at hand but, in general, it is sufficient to employ
a percentage charge for taxes based upon the average experience.

Insurance. In the case of buildings, and equii)ment contained in
buildings, an annual cost item to cf)ver insurance should be included.

Depreciation. Depreciation ma\' be defined as the usini; u|) of
property in service from all causes. These causes include:

(a) Wear and tear, not co\cred by current repairs.

(b) Obsolescence.

(c) InadefiuacN'.

(d) Public Requirements.

(e) Extraordinary Casualties.

.All Iflcphoni' propertx', e\rr])l Kind, is sulijert to deterioration,
and the continued consnnijjtion ol the inxesinH'nl is a part ot the
cost of the service which must Ik- pro\ ided for !)>• charges against
earnings. Only a small portion of the i)lant actually wears out in
service. Instances of this are llu- rotting of poles and the rusting of
iron wire, a relati\ely small amount of which is used in the plant.

( )n the oilirr hand, it h.is licc-n I he liisiorx' of the telephone business
that enormous amounts of |)lant ha\e been taken out of str\-icc
through no defect in their plnsical comlition but lither because
they had become obsolete through the <le\elo[)menl of some itiore
economical or efficient type of c(iiii|innnt, or because they had
become inadequate to serve the growing needs of the business.

F.NCINHF.RfXC COST SIIDIFS II

An fx.implc ol ol)si)lcs(vnci' is ilu- rcpl.K'ciiu-nl of .iiiii(|ii.ilcil
nu'tliiHls (it (lisirilmtion l)\ inon- iiiimUtii tyiu-s. ICx.mipU ;> of in.ul-
i'(|Ii;h\- art" tin- n-plari'iiioiit of oih-ii wiri-s hy cilili-, and llu> rt-placf-
nu-nt of sni.ill caMi's by l.irijiT ones. I'.x.implfs of public ri-(|iiiri'nK'nt
are the .ibandonnu-iit of polo linrs and tlii-ir ri-plaivini-iit li\- undi-r-
^round i-otistnu'tion dm- to road iinjirovfiniMUs, and tlu- rdinildinK
of si'ctions of undi;r>jrounil conduit dui; to chanijcs in the ^;radc of
strt'i-ts or to the construction of transit subways. Kxampiis of
extraordinary casualties are fires, sleet storms and tornadoes.

The annual charge for depreciation is an amount which, if entered
in operating expenses each year during; the ser\ ice life of a unit of
plant, vvoyld, at the end of that service life, yield a sum ecjual to
the total depreciation of that unit; th;it is, its first cost in place less
the net siilvagc obtained at its remo\-aI. The consumjition of capital
is a necessjiry part of the cost of furnishing stTvice and must be pro-
videtl for by charges against earnings during the life of the [)roperty.
In arriving at this depreciation charge the best thing we can do is
to take our experience of years and look o\cr the vvliole situation
and apply our judgment to it. The A'aliie of this judgment depends
on the exi^rience. knowledge, abilit\- and iiitegritx fif the (n'ople
who exercise it.

The amoimt of this charge should be determineil for each broad
class of plant and it depends upon the a\erage service life and the
net salvage value. Net sal\"age value is gross salvage \'aluc minus
cost of removal, and takes into consideration both value for reuse
and junk value. For instance, the net salvage value of station
apparatus is relatively high because a large part of the equipment
can be reused in another location. In other cases, such as iron wire,
the net salvage value may be a minus quantity, as there is little or
nothing to offset the cost of remo\al.

Current Maintenance. (."urrenl maintenance charges comprise
the cost of repairs, rearrangements and changes necessary to keep
the plant in an efficient operating condition during its service life.
In cost studies, current maintenance charges should be derived from
exf)erience and expressed, generalK", on a unit of plant basis, as.
for example, per pole, per mile of wire, per foot of cable, or per sta-
tion, according to the kind of plant being considered. Cienerally
speaking, they bear no direct relation to first cost of plant as other
annual charges do.

I-"or this reason, when comparing the .inruial co>l> ot two or more
plant units of different sizes or types, an incorrect result would be

12 nr.LL SYSTEM TECHNICAL JOURNAL

obtained if ni.iiiUcnanco charges wore oxpiessod as a ptMcciilage of
the first Ci»i.

However, for coinparalixe cost studies of a\erai;e plant, main-
tained under average conditions, it is sonieiinies within ll)e i)recision
of the study to employ figures expressed as a percentage of the first
cost, provided the figures were derived from the cost of maintaining
average plant where axeragc conditions were know n to obtain.

Adminislralion. In certain cost studies, a small allowance is
usually made to cover that portion of the salaries and expenses of
the general ofiicials of the C"ompan>- which is fairly chargeable to
the administration ol the |)lant.

Operating Costs. In certain classes of engineering cost studies,
comparisons may involve the situation where one type of plant
costs initially more than an alternative type, but permits sa\ings
to be made in the daily operating labor which may or may not offset
the additional first cost. In such cases, to obtain a true comparison,
the operating labor costs under each plan must be combined with
the total annual charges which are applied to the first costs of the
respective plant quantities.

Prksknt Worths

luigineering cost studies fre(iueiill\' in\(]l\e a lialaiur between
|)lant installed at the present time and plant installed at some future
liini'. An example of this would be the comparison of a pole whose
life was to be extended by attaching it to a stub after (say) 15 years,
with a stouter and more expensive pole installed at present or with a
pole to which preser\-ative treatment was applied prior to its installa-
tif)n.

In such cases it is not sufficient to compare annual costs which
arc to be incurred at different times w'ithout reducing them to a
basis upon which the\' can properly be compared. If a gi\x>n amount
is required to be expended at some future time, it obviously recjuires
a smaller stun at jiresent in iiand to meet tliis obligation if the fixed
time is far disl.uit than il il is in the ininiediale future.

Let us picture oursehes at the vml of the \X'ar l!t2l. 1 1 an annual
charge of §1,000 is to be paid each \e,u' for the 5 years beniiuiing J.m-
uar\- 1, 1925 and ending Deceniix-r '.i\. 1920, tluTc will be required,
to ])ro\ide for these five SI, 000 pa>'menls, the sum of SI, 100, in hand,
assuming that interest is comiiounded annually at 7 ])cr cent. On
the other hand, if these five annual payments of SI, 000 each instead

F.NGI\F.F.RINC COST STUDIES

of iH'Kinnint; in 192o wore ti> Ijogin ten years later, thai i>. if ihev
were Id run from Jainiar>- 1, l'.>;i.'i to the end of ID.'Jf), we should re-
<|uire, in hand, S2,()84, that is, oidy about half as much.

To compare, upon a fair basis, expentiitiires that have to be made
at dirterent times, it is customary, as has Ikiii done in the prere<ling
example, to rwhice these different expenditures tf> their "I'resejit
Worths," or the equivalent in eipiated or accumulated annua!

charges

SlMMAKV

From all that has lieen siiiil, it becomes e%ident that, whenever a
specific addition is made to a growing plant, we are, to a greater or
less extent, committing ourselves to a definite programme for reliev-
ing, reinforcing or replacing it at some future time in order most
economically to provide for the requirements of growth.

The underlying thought, which can not be overemphasized, is so
to plan the plant that, as far as practicaiilc, it will serve for its full
life, and require no wholesale changes invoking the abandonment
of substantial portions of the installation. While the design should
be base<l up<in the best estimates of future growth that are obtain-
able, it must be recognized that the most carefully designed plant
layouts employing the Ix-st possible estimates of growth, may not
always meet the ultimate requirements of flexibility. The chances
of a comprehensi\e plan not fitting in with future de\elopnient
can, howe\er, l)c reduced to a minimum 1)\- tiiouijlitful initial
planning.

Generally speaking, our distributing plant layout, once it is estab-
lished, can not readily nor economically be materially changed.
Consequently, if it is not sutftciently flexible in the fundamentals of
its design to meet reasonable future possibilities, it ma>- affect ad-
versely the carrying out of proper and economical relief measures,
or may require abnormally early reconstruction or replacement. It
is vcr>- desirable, therefore, alwa\s to keep in mind, in any plant
layout work, the progressi\e relief steps which are likely to be re-
quired to meet the changing conditions affecting the service require-
ments. Whenever plant is moved, or taken out of ser\ice, property
loss is realized. Certain expenditures for these pur|)oses represent
the most economical way of conducting the business. But it is of
the utmost importance that they should always be incurred along
the line of maximum economy, which means that behind every plant

14 BELL SYSTEM TECIIXIC.IL JOVRS'AL

additiuii must be engineering cost studies to assist in luinisliing
the answers to the three questions:

Why do it at all?
Why do it now?
\\'h\- do it this way?

But it must always be borne in mind that these studies do not and
can not, in themselves, constitute the sole criterion for determining
what should be done. They are, at the best, only an aid, guide and
check to be utilized, within their limitations, in arri\-ing at conclu-
sions that must, in the last analysis, rest upon seasoned judgment
and experience.

Nevertheless, so great do we find the importance of these engineer-
ing cost studies in our work, and so great must be their importance in
the engineering of any other kind of growing plant, tiiat the question
might be raised whether, in courses of engineering instruction, a few
hours at least could not advantageously be devoted to acquainting
the student with the nature and importance of these economic
problems.

The Limitation of the Gain of Two- Way Telephone
Repeaters by Impedance Irregularities

By GEORGE CRISSON
InTRODU TION

BHCAl SI-', of the fact that it is a (liftiriill anil exfK-nsive matti-r
to l)iiil(l and maintain tin- lii^li K^aili' circiiils that are ro(|uiri-cl
for motlcrn lonn distanre li-lophonc transmission with repeaters,
nKin\- workers in this held ha\e attempted to devise some form of
two-way repe.iter which would he ahle to ii'ivv as large a gain as
desiretl without singing or poor <iiiality due to irregidaritics existing
in the lines. The>' have thought that if such a rei>eater could he
constructed it would permit the use of lines less carefully built and.
therefore, cheaper than are at present retjuired, and that fewer
repeaters would he re(|uired ln-caiisi' larger gains could be obtained
at each repc-ater.

As a matter of fact the irregularities in ihe lines have a very im-
portant effect and control, to a great extent, the repeater gains which
can lie used whene\er a telephone circuit is arranged so as to be
capable of transmitting in both directions over a single pair of wires
with constant efficiency.

It is the object of this paper to explain, in a \er>- simjile wa\',
why this is true. To do this the phenomenon of electrical reflection
is first made clear. Then a two-way repeater system is introduced
and the effects of reflection upon this system are explained. After
mentioning several of the types of repeaters which have been used
successfully, the paper concludes with an explanation of the fallacies
underlying a numlx-r of schctiies which ha\e been jiroposed from time
to time by various in\entors.

Ri:i-I.IiCTI().N IN TllIKlMloM-: i.I.NKS

Whenever discontinuities or irregularities exist in telephone cir-
cuits, reflection of a certain part of the speech wave takes place
at each irregularity. In order to appreciate why it is that irregularities
in two-wire telephone circuits affect ver>' greatly the amount of
repeater gain which can be secured whenc\-er two-way operation is
desired, it is first necessary- to obtain a clear picture of why it is that
reflections take place at irregularities.

Fig. 1 represents an infinite ideal telephone line without repealers.
If such a line is non-loaded or continuously loaded each part of it

15

16 BELL SYSTEM TECLINICAL JOURNAL

is exactly like every other part lia\ing the same length. If the line
is loaded with coils then each luaiiing section is exactly like e\cr\-
other loading section.

When a telephone transmitter or other signaling device A acts
upon such a line it causes a wave to travel over the line away from

1-ig. 1

the source. If the line includes resistance or other losses liiis wave
gradually becomes smaller until it is too weak to be detected but no
portion of the wave returns to the source after once leaving it.

If some portion of the line difTers in its electrical makeup from
other portions of the line it constitutes an irrcgularit\- and interferes
with the passage of the wa\e.

Fig. 2 shows a line exactly like that of Fig. 1 except that an irreg-
ularity B has been introduced. This irregularity has been shown

I-ig. 2

as a series resistance though any other departure from the regular
electrical structure of the line would produce similar efTects.

When a wa\e encounters such an irregularity, it splits into two
parts one of which continues in the original direction of propaga-
tion along the line while the other is propagated in the opposite
direction toward the source.

In order to understand this phenomenon, which is called reflection,
imagine that a wave is traversing the line from left to right. As it
passes the point B a current flows through the series impedance
which constitutes the irregularil\- and this causes a drop of potential
through the imjicdance. ()b\ i((Usl\-, this changes the state of alifairs
as there is now a sudilen alleralion in the \-oltage across the line as
the wa\e ])asscs llie irregularity wlurias there is no such alteration
without the irregularity.

Suppose that for the impedance element we substitute the output
terminals of a generator which has a negligible impedance and arrange
the generator so that it is excited i)y the wave tra\cling over the line
but that the excitation is not afTected by the voltage set up by the
generator itself. Such an arrangement is shown in Mg. 3. The

i,,//.v ()/ /ii(Mi./i iiiii'iinxi: la.ri.ii IKS 17

.irraiigi'im-iU for i'\iiiiii_i; tin- j-cm-rator is siipposi-d iidI to rc<|uiri'
an api»ri'ciabli' ainouiii of power or to conslitulc an irri'nularity.
This gfiR-ralor tlu'H rcscinhk's tlio si-rii's iiiipr<latu°c of l'"itj. - in lli.it it
procliici's no ilisturbance in the line when no wa%es arc passing hut as
s<H>n as a wa\f arri\es the generator becomes active and produces a

Fig. 3

\i)ltage in series with llie line. By proper adjustment of the exciting
mechanism of the generator the voltage across its output terminals
can he made just equal to the disturbance produced by the impedance
element at B in Fig. 2 and so exactly reproduce the effects of the
irregularity. In order to do this the generator might have to absorb
energy from the wave passing over the line instead of giving it out,
but it would establish the desired \()ltage relations.

Now as the generator has no appreciable impedance the wave passes
through it without interference but the e.ni.f. which it sets up ob-
viously sends out waves in each direction from the generator.

On the right of the irregularity will be found one wave made up
of the original undisturi)ed wa\'e combined with that from the gene-
rator and traveling onward in the original direction. The combined
wave will usually be smaller than the original wave though it
might under some circumstances be larger and its shape might or
might not be altered depending upon the nature of the irregularity
and the character of the line.

On the left of the irregularit\' will be found the original wa\e
traveling from left to right and the retk-cted w.ise tra\fling from
right to left.

By a similar process of reasoning the reflection caused by bridging an
impedance across the line at the point B can be illustrated. In this
case the output terminals of the generator should be bridgetl across
the line and made of very high impedance.

Any departure from the regular structure of the line such as occurs
at the junction of two lines of different types or where loading coils

18 liEU. SVSTliAf TECIIMC.tL Jdl'KX.II.

lia\c the wrong inductance or are wroiij^K' sixiccd causes reflections
in the manner ciescriherl ai)o\c.

Ii)i;ai. RkpkativR on an Ii)i;ai. I.ini-;

Fij;. 4 shows an ideal telephone circuit consisting of two sections
of line L\ and L-^ which are free from irregularities and are joined
by a repeater R. The remote ends of the line sections are connected

to terminal apjiaratus A] and .1^ which ha\e impedances which

B

Q

Fig. 4

s-mc(,thl\' terminate the lines, that is, if either line had originally
extended to an infinite distance from (he repeater and had liecn cut
to connect it to the terminal apparatus, this apparatus would ha\'e
the same impedance as the part of the infinite line which was cut off.
The construction of the repeater R is limited onh- by the recjuire-
n.ent that if an electric wave arri\cs at the repeater terminals T\
or 7'; o\er either line a similar but larger wa\-e is transmitted from
the repeater (i\ er ihi- other line. The gain of the repeater deter-
mines the relati\e si/es of the waxes arrixing at and departing from
the repeater.

If now a wave is started at one end of the circuit, for exam[)le -li,
it traverses the line Li and is absorbed or dissipated in the portion of
the repeater connected to the terminal 'J\. This wave acts upon
the internal mechanism of the repeater in such a way as to send out
a larger wave which tra\erses the line L^ and i> completeK' dissi-
pated in the terminal apparatus A->.

Ii)i;ai. Kki'KATIck on a Linic C"()NTaimn(. Irrkci i.AKiniis

Fig. 5 illustrates a line exactly like that of F^ig. 4, except that an
irregularit\- Bi (or J5») has been introduced into each section. If a

B

Q

Fik'. .'^

wa\e leaves one terminal such as A i, it traverses the line Ai e\entuall\-
arriving at the terminal T\ of the repeater R with a ceri.iin striiigih.
This wa\e is ; niplificd and traiiMnitted into ihe line /,■_• which it

(;.//.v or /ico-ic.;)' iiu.i-.riio\r. nui'i-.-hhns i'»

follows until it t-ncountiTs the irri'(j;iilarity H-. At Bi it is pari i. illy
re tinted, one |X)rti»n returning to the repeater anil the other travel-
ing to the terniinal -Ij where it is ahsorlad. The reflected wave
passes ihrouuli the refx-ater, is ani[)litux! and iraiisversi-s the line
L\ until it encounters the irregularity B\ where it is again reilecied,
one iKirt Uing propagated to the terminal At where it is dissipated,
while the other part returns to the repeater and repeats the cycU
of anipliliration and reflection. This action continues indefinitely
the wave being reflected alternately from the irregularities B, and 5|,

If the total gain in the round trip path is greater than the tcjtal
loss the wave will Ix; stronger on each arrival at any point in the
circuit than on the preceding trip and will continually increase in
power until the power limits of the repeater or some other cause
prevents a further increase and a steady sing is established. If the
gain is less than the loss, the wave will become weaker with each
trip from Bi and B^ and back until it falls below the strength which
can be detected.

KvidentK-. if the repeater gain is made so great that a steady sing
is established, satisfactory- telephoning o\cr the circuit will be im-
possible. Serious quality impairment ma\- occur, however, when
the gain is not so great as this. Consequently, when irregularities
are present in a line containing repeaters, the repeater gains are
necessarily limited.

In the above illustration, it was assumed that two irregularities
were present. Serious effects, however, due to the production of
echo effects which may Ik? heard by the talker, may be produced !)>'
reflection from a single irregularity. Consequently, a single irreg-
ularity in the circuit will set a limitation on the repeater gain even
though it could not cause singing if a 22-type repeater were used.

Frf)m the foregoing explanation, it is evident that the effect of the
reflections at the irregularities, which limits the repeater gains, is
not dependent upon any special prof)erties of the telephone repeaters.
These limitations will necessarily exist with any types of repeater
whatsoever which have the property of producing amplification
in lM)th directions at the same time.

Ki'iKcT oi" IsiNi, Tin: Wkonc; Link Fmpkd.vm r;

The discussion will now i)e extended to show tiiat not rinly must the
lines with which a repeater is to work be smooth, if limitation of the
gains is to be avoided, but also the repeaters must be designed to fit

20 BELL SYSTEM TECHNICAL JOURSAL

lines of out- n-iriinilar \\\k-. Ii li.is just Uvn shown that rcllection
takt-s pla(X' if a st-rit-s or a i)riilv;i-ti inipetlamo is inserted in a line.
This rolkttion will take place whether the impedance is inserted
al some interme«liaie |)«>int in a line or atljacent to a repeater. In-
serting such an im|K-<lance adjacent to a re|)eatcr would, on account
of this reflection, sc-riousK limit the gain which could be produced
by the repeater. Now insiTling an irregularity adjacent to a repeater
amounts to the s;»me thing as substituting a line having a different
im|Miiance for the line with which Uie repeater is designed to function.
Since any change in the impe<iance of a line connected to a repeater
away from the imix-dance with which the repeater is designed to
work is equivalent to inserting an irregularity adjacent to the repeater,
it is evident that it is impossible to construct a repeater system whose
amplification u-ill be constant in both directions and whose ^ain will
not be limited by irrev,ularities in the lines and by any departure of the
line impedance from that for which the repeater is designed.

SiccKssi-ti. Tvi'i;s OF Ri:pi:.\ti;rs

Two forms of rejx'ater circuit, the well known 21 and 22 t\'pc
circuits, have In-en develoix-d to the |M)int where they have become
highly important and successful parts of the telephone plant. These
have lieen m) completeK" descrilK-d in a pafier entitled, "Telephone
Refx-aters" by Messrs. Ciherardi and Jewett,' that no further de-
Mription will be attempti-d here. It is suflicient to point out that
in the case of the 22 ty|X' re|X'ater the necessiiry impedance require-
ments arc met b\' providing netwurks which imitate closely the
characteristic im|x-<lances of the two associated lines. Any de-
parture of the line imjKxIance from the \'aluc for which the network
was designi-*! or any irregularities in the line or terminal equip-
ment im|)ose limits on the obtainable gain in the manner described
alwtve. In the case of the 21 type circuit the impedance require-
ments are met by putting the repeater between two similar lines
whose im|K-dances i>.dance each other.

.\nother ty|x- of re|Kater circuit, called the booster circuit, was
mi'niione<l in the pa|X'r just referretl to. This circuit does not de-
ixnd ufxin im|H-<lance b.ilance in the simc way as the 21 and 22
tyjx- < ircuits and it is capable of giving two-way amplification but
its iN-rformaiUT is even nmre seriously affected by impedance devia-
tions in the lines than the latter circuits. The booster form of re-
|xMtor <irriiit has niit yet pro\e<l useful in a commercial way.

' rtoccttlinic* o( the .Vnicricin Inslitiiti: of ticclrical linKiiiccrs, 1919, page 1255.

(7.//.V or rii(^ n\iy rni.r.nioxr. Rr.i'r.irrRs 2\

I>i:viii;s K.MrioMM. \ou !■: (omkoi.i.i d Ki i.\\-^

Maiu' (iilTercnt ticvirvs .liiuinii to sriiin- llu- pr.ii-tiral (.•(|iii\.iU-iU of
t\vi)-way rcfKMter operation by moans of rulaxs (inri-li.inical or
ihcrinionic) rontrollcti by the voice currents tluMUselvcs have Inrn
suggestetl. In these devices the action of the rela\s is such that
when transmission is passing in one direction throiij;ii a reix-ater,
the transmission in the opposite direction is either wholly or par-
tially blocked. K\i(lently the gain of such a repeater as this is not
limited by impedance irregularities in the lines, since it is really a
one-way device during the passiige of speech currents.

Repeaters controlled by voice operated devices will not be dis-
cussed here further in view of the fact that the principal object of
this paper is to treat repwater systems which are truly two-way in
their operation.

Other Types of Repe.\tf.r That H.we Been Proposed

Several of the arrangements that have been proposed by inventors
who sought unsuccessfully to produce two-way repeaters not subject
to limitation by line irregularities will now be described.

1. Repeaters Involving Balance. A great many circuits ha\e been
devised which involve the principle of balance. These always in-
volve the same fundamental principle as the h\brid coil used in the
repeaters now in commercial service though often the arrangement
appears quite different. This principle is that the output energy
of the amplifier working in one direction, for example, the east bound
amplifier, is divided into two parts, one of which is sent into the line
east and the other into the corresponding network. The input
terminals of the west bound amplifier are so connected that the effect
on them of the current entering the line east is opposed by the effect
of the current entering the network and consequently the impedances
of the line and network must accurately balance each other to keep
the output energy of one amplifier out of the input circuit of the
other. Sometimes the balance is effected by connecting the line
and network into a common electrical circuit and connecting the
input terminals of the amplifier to two points of equal potential
in this circuit. In other arrangements two fluxes which depend
upon the currents entering the line and network are balanced against
each other in the core of a special transformer so that a winding
connected to the input of the amplifier is not affected.

Usually the impedance of the network equals that of the line, but
arrangements are possible and even have certain advantages in

22

BF.U. SYSTEM TllCIISlCAL JOIRSAL

which ihc iiierKV is not wiu.illy dividi-tl l»tl\veen the line ant! net-
work ami the im|x-<lanre of the network is either greater thim or
less than that of the line in a ixrtain ratio.

Throunh unfaniiliarity with the principles involvid the iiiveiUors
sometimes assume that an approximate halance such as might be
obtained by using a simple resistancx- is sulTieient lo meet all re-
quirements. .\onc of these- arrangements, however, can avoid the
effects <»f departures of the line impedane-c from the values for which
the networks are designetl nor cun they in-tter the performance of
the present refx-aters in respect lo the effects of impedance lieparturcs.
Usually such circuits are inferior in .some imix>rtanl respect to the
arrangements now in us*.-.

2. Circuits usiii^ Rectifitrs. In one t\pe of circuit the inventors
propose to use rectifiers to prevent the output energy of one amplifier

Fig. 6

.iiiiiiK ii|«>n the input circuit of liie oilitr. .\ simple diagram illus-
trating the ojKration of this scheme is given in Fig. 0. Rectifiers are
placetl in series with the input and output circuits of both amplifiers
and [xjled in the directions indicated by the arrow heads which point
in the direction the rectifier is supposed to permit current to pass.
It is argued that the rectifier in the output circuit of each amplifier
permits only currents of one |X)larity to enter the line and that the
rectifier in the input circuit of the opposite amplifier is so poled that
these cnitput currents cannot [wss it into the input circuit and, there-
fore, singing cannot iKcur.

If a wave arrives, for example over the line west, the p.jsiiive half
waves |xiss through the rectifiers 1 and 2 into the input of the e.ist
Uiund and the output of the west bound amplifier respectively.
The negative half wavc-s are suppressed by the rectifiers. This is
illustr.ited by I-"ig. 7 which shows the wave arri\ing over the line and
Fig. S which shows the part of the wave which enters the amplifiers.

That jxirtion which reaches the output of the west bound amjili-
fier IH hist while the [xirtion which reaches the input of the east bound

c.iix or iiioif.iy ii-.i.i.riiosi'. kiweatf.ks

2.\

amplitiiT, is amplituHl, and passt-d on llirmiuli llif ri-clifiiT :{ to tlir line
I'.ist. If llu' .implituT wtTi- loinpli-ti-ly distort ioiiU-ss and, tluTi-fort-,
rapabli- of antplifs inn direct riirri-nts .iiid tlu- ri-rtilii-rs ptrfi'it, that is,
olTcrinn zero resistance to currents in one direction and inl'inile resist-

Fig. 7

Fig 8

ance to currents in the opposite direction, the currents transmitted
to the line east would have the \va\e shapes shown in Fig. S.

As it would be impracticable to make llii' amplifier amplif\- the
direct-current component of the wave shown in I-"ig. 8 the amplifier
would tend to send out a wave somewhat like that shown in Fig. !»,

which is the wave of F'ig. 8 with the direct component removed.
The rectifier 3 then suppresses the negative half waves, finally per-
mitting the wave shown in Fig. 10 to pass to the line east. On account

Fig. 10

of the great distortion involved the c|uality of speech would be greatly
impaired if, indeed, the speech would not be rendered unintelligible.

Assuming, however, that intelligible speech is possible in spite of
this distortion, the rectifiers would not prevent singing. Suppose the
repeater shown in Fig. 6 to be cut into the line shown in F"ig. 5 at R
and that waves are arriving from the line west. There are certain

-M HULL SYSTEM TECIISIC.M. JOIRSAL

line niiKlitions wliirh ari' praciiiMlly irrtaiii to exist and which wouUl
sond back ri-tk-* iwl waves that would reversi- the [xUcntial across
the line east at the terminals of the reiK-ater, causing ini[nilscs to
reach the input of the west hound amplilier. These im|)ulses will be
amplitieil and returne<l to the line west where, if similar tondilions
exist, they will oncx- more enter the east bound amplifier. If the
gains are great enough to offset the losses caUM-d by the rectifiers,
the system will sing.

It is, thereffjre, e\ ideiil that rectifiers offer no chance for improving
on the aciinn ..f ilu pri-ciii typc-s of repeaters because they cause

Fig. 11

serious distortion and do not pre\eiil singing exce|)i under certain
six'cial conditions not likely to l>e found under practical conditions.

3. Circiiils usinn ] I ii^h- Frequency Sxcilfhint:,. Another device which
is fre<|uentl\ prr>iH>si'd in one form or another is illustrated in Fig. 11.
In this case an amplifier is pro\ided for each direction of transmission.
These amplifiers are so designed that their amplifying power can he
destro\ed and rest(»red |X'ri(Klically at high fre(|uency by currents
frtmi a suitable source, the amplifier in one direction being active
when the other is inactive. The frecpiency of the controlling cur-
rents is aUive the audible range. In a \arialion of this scheme a
single amplifier is use<l which is |xiinted first in one direction and
then in the other at a fre(|Uency alK)ve the au<lible range, it i^
argued that since there is amplification in onl\- one direction al .ui\
given instant the s>stem <-annot sing.

Imagine such a rejiealer to Ik- inserted in the line .it R in Fig. 5,
.ind that voitx- waves are arriving over the line from /I i. Owing to
the nature of the re|iealer these waves will be cut up into a series

(/.(/.V OF IliOir.iy TEI.EI'IIOM- KIU'F.AIERS 25

(if piilMS li.i\ini; .1 fr»«nuiuy im|ii.i1 Id tli.il nf tlu- lonlrollinj; currrnl
and \.ir\iiii; in in.i^nitiKli- .urordinj; to llic shii|H- of tin- voicr w.ixi-
litinj; iransmiltid. riii-sc piilsi-s will W pailialK rrtlrctiil at tin-
irrt-nularity B^ and pari of •heir t>nerg\- will ritiirn to tlu- rt(KMtiT.
Dur to ihc fad that a tinilt' time is ritiuirud for ihu pulses to pass
from R to Bi and bark, tlun' an- likily to arri\i' at tliu riKlU in<jmi'nt
to fnul the anipliliLT set for ainplit'iration in the opposite dirertiort,
in which case they will pass through towards .-1. l"or a single irrcg-
ularit>-, it wonkl !«? possible to select a freciuency such that the pulse
would return when the repeater is set against it, but this would re-
quire a dilTcrent fre(iuency for each irri'i;ul,iril\ which is obviously
impossible.

In case the line cannot transmit the high fretiuency pulses, their
energy would be stored in the inductance or capacit>- of the first ele-
ments of the line L^ and returned to the amplifier when it is in condi-
tion to transmit from Li to L\. To a\oid the latter objection it has
lx!en proposed to employ low pass filters on the output side of each
one-way amplifier to convert the high frecjuency pulses back into
ordinary voice waves before passing thcni into the line, but this
obviously defeats the object sought in using the high frequency
control of the amplification because each amplifier now receives
ordinary voice waves and gives out enlarged copies of them which
are subject to the same reflections as if plain one-way amplifiers
without the high frequency control had been used.

From these considerations it will readily be seen that repeater
systems depending upon high frequency variation of the gain to
avoid singing and the necessitN- for impedance balances are inherently
unworkable.

Practises in Telephone Transmission
Maintenance Work

Bv W. H HARDEN

W

Synopsis: This imikt (IfstriUi. the prailk-al appliralions of transmission
nuiinlrnanrc nu-thmls in a lelcphone system. Tho nu-thmls applirable to
toll cinuils of vaiious ty|K-s an- first <li«uss<.-<l, information JK-ing included
in tfiif conniition on ihr niainti-nanif of the amplifier circuits involved in
telephone rejieaters and carrier. Testing methods applicable to the local
or exchange area (ilant arc next desirilietl. the destription including both
manual and machine switching systems. 'I"he results accom|)lished in
toll anil local transmission maintenance work arc considered from the
standixiint of the kinils of trouble which can be clin)inatc<l and the effect
which thi-se troubles have on service.

The metho<is descrilietl in the main Inxly of the pa|)or relate particularly
to tests of volume efhciency. Certain other transmission maintenance
testing methotls dirivtly as.s<iciate<l with volume efliciency tests are briefly
descril>etl in .\p|>endi\ \ of the pa|K-r.

IT is the purixise df litis paper to present a neiieral |)iilure i>t the
practical applications of inelhrKls of nieasurinj; transmission
efticiency in the Bell S\stein which have iteen developed by study
and exfK-rience under plant o|K'ratinn conditions. The rapid growth
of the telephone industry has made it necessary that these niethtKls
be such as to allow them to be applied on a large scale in a sys-
tematic and economical manner tliereb\- [iroNiding for a tpiick
(x-ritKlic check of the el1icienc\- of the variotis t\|)es of circuits as
ihcy are usc-<l in se.rvice.

Transmission maintenance can l>e broadK' detinetl as that mainten-
ance work which isdirectetl primarily towartis instiring that the talking
elViciencies of the telephone circuits are those for which the circuits are
designitl. There are, of coursi>, many elements which afTect the talking
efticiency and various d-c. and a-c. tests are available for checking the
electrical characteristics of circuits ami equipment to insure that these
characteristics are ln-ing maintained in accordance with the proper
standards. In the final analysis, however, an overall test of the trans-
mission et>icienc\ of the circuit in the condition it is used in service
will show at once whether it is giving the loss, or in the case of ampli-
fier circuits, the gain which it should give. Transmission tests,
theref(»re, offer .i means whereby main- of the electrical characteristics
of circuits can lie tjuickly .ind accurateh checked.

In referring to transmission testing apparattis in this paper, four

si.indard l> jks deMriU-d in pre\ious pajnTs are involved. The first

ihri-e iy|R-s listed lielow were descrilx-d by Best and the fourth by

'V.i]trT i>rc»?nlc«l at the P.uilir Cojst Convention, .1. T. E. E., October l')24-
aUltiictcd in tfir Journal, .1. /. E. E., Vol. 43, p. 1124, 1924.

26

TF.l.F.rilOSE IR.IXS.MISSI(K\' M.IIM l-X.IXCE 27

Clark.' RrftTiiur in ilii-sf pajH-rs w.is also luaiic In tin- ^latulartl
OM-illators UM'<I ii) suppKiiij; llu- inrasuriiin riirn-nts for the suls.

I- .-1 'I'ransniission .\/c«.v«r/Hi; Set. This is an "car h.ilanci'"
jHirtablo set siiitaMi' for loop traDsinissioii li-s(iiin only and (li'si^;iu-(l
primarily for ifstiiii; i-tiiiipincnl .iiul ciicnits in the •^in.illiT irntr.il
ofTices.

3 — A Transmission .\ffasiirinii Set. This i> a "nu-irr halanci- '
portable set suit.ibk' for both loop and strainlu.i\va\ I raiisniis^ion
testing and designed priniariK' for letting circuils and e(|uipnient
in the larger eenirat otViees.

4 — .-1 'I'ranstnission Maisurinti Scl. This is a "niL-ler balance" set
suitable for both loop and straightaway' transmission testing and
designed for (H'rmanent installation al the larger toll otfu'es i)rini,iriK
for testing toll eireiiits.

2 — .1 Citin del. This is a "meter balanre" set designed lor miMsiir-
ing amplifier gains.

Certain other testing methods in addition to Noliime cfficiencN'
tests are also extensiveh' used in transmission maintenance work
and some of the more import. int of these are lirietK' discussed in
.Ap|H;iuli.\ .A of this paper.

Since the routine procedures in testing toll circuits using the above
apparatus ditTer considerably from those followed in the local or
exchange area plant, the toll and local practices have been considered
separately in the following discussions:

Transmission Tests on Toll Cik( ins

The importance of having available means for ([uickK checking
the transmission efificiency of toll circuits and of economicalK' main-
taining the proper standard of transmission is evident when it is
considered that in a plant such as that operated by the Bell System
there are at the present time more than 20,000 toll circuits in service.
The circuits making up this system are of various types and con-
struction, depending on the service requirements and length, and
also upon certain other factors determined In- engineering and
economical design considerations.

From the standpoint of maintaining transmission etticiency between

toll offices, the various types of toll circuits can be di\ ided into three

general classes: one, non-rcpeatered circuits, two, circuits equipped

' F. H. Best, "Measuring Methods for Maintainini; the Transmission EtTiciency
of Telephone Circuits," Journal of the A. I. E. £., February, 1924. .\. B. Clark,
"Telephone Transmission over Long Cable Circuits," Journal of the A. I. E. E.,
January-, 1923.

2S HELL SySTF.M TECIISICAL JOIRX.IL

with lelcpljonc repeaters and three, circuits equipped for carrier
operation. The latter two classes are alike in many respects as far as
the maintenance nietluHls are coiicerne<l and both require somewhat
more attention than the circuits not equipixxi with amplifying
apparatus. The length and numlx^'r of repeaters involved are also
imixirtani factors which must he taken account of in tandem repeater
and carrier circuit maintenance. Wry long tandem repeater circuits

Fig. 1 — Illustrjtiun of 4-.\ Transmission .Measuring Set and 4-B Oscillator Installed
in a Toll Test Room

such, fur ex.imple, as the long toll cable circuits described by Clark-
ref|uire s[H'cial maintenance procetlurcs similar in many respects to
those re<iuire<l in carrier maintenance.

The l-.\ t\|H- of transmission measuring set generally used for
testing toll circuits may be considered as a toll transmission test
desk. Fig. 1 shows a |)icture of one of the latest models together
with an oscillator for supplying the measuring current, installed at
a toll ortice for use in routine testing. The set is provided witli
trunks to both the toll testboard and toll switchboard, and also
with call circuits to toll o|K?rators' positions for use in ordering up
circuits for test. The electrical measuring circuit is designed so that
tests may l)e made on two toll circuits loopetl at the distant end, or
str.ii;;hi.iw.i\ on one loll circuit the distant terminal of which termi-

TELlil'llOM: IN.IXSMISSIOX M.IIXIF..\.l\Cn 29

nates in an dIVicc also (iiiiipin-d wiih ,i ii.insnii><'<iiiii inctMiriiig set
of the s.inK' t\ |H'.

To illustrate tho application of this toll transmission test desk,
Fig. 2 shows seheinatieally an arrangement of four toll olVires having
circuits hetween them of the three general classes non-re|K\itere(l,
refK'atcritl aiul carrier. OlVices A anil 1) are e(|iiippe(l with trans-
mission measiirim; sets of the t\pe shown in I'ii;. 1. .\ l(>j;ical testing

te*' r«o<«lTi^ Crcmf

I* = 3

S

=D=

H

=|3

o

Fig. 2 — Schematic Diagram of Typical Tull Cin iiit Layout to Illustrate (ieneral
.Methotl of Testing Non-Rcpeatered, Rcpeatcrcd and Carrier Circuits

proccthirc for the arrangement in Fig. 2 is for offices A and D to test the
non-repcatered circuits 1 to 4 and 10 to Vi by ha\ing thejn looped
two at a time at the distant terminal offices B and (". \W "iriangti-
lation measurements" on an%- three circuits in each group, the equi\-
alent of each indi\-idual circuit can be readily computed.

For the circuits o to 9 extending between offices A and D equii)ped
with telephone repeaters or carrier, straightaway measurements
can be made in each direction with the two transmission measuring
sets pro%-idetl. Loop tests could, of course, also be made on the
circuits from either office A or U, but this would require cutting

ni.i.i. srsTi-.M inciiMc.iL jovrnal

the telephone repeaters out of one circuit or having available a non-
repoatcre<i or non-carrier circuit, since the gains of the repeaters in
the two directions intrtxiuce variable factors in the overall equivalents
which do not permit triangulation computations to be made. The
overall tests on the carrier circuits do not differ in any way from
the tests on repcateretl or non-rei)eatereti circuits, each carrier channel
iK'inn testeil as a separate circuit through the switchboards. The

.e

Vi

l-.K. .i .\l..pMn

HIS In Hull .Sysuri
Measuring .Sets

>l I'riiiMiient Transmission

me;isuring current is modulad-d and demodulated in the s;ime manner
as voice currents under regular operating conditions and the measured
if|uivalent, therefore, indicates the overall transmission efficiency.

The map of I-'ig. 3 shows the locations in the Bell System of trans-
mission measuring sets of the general type described above. At a
number of the larger toll centers, such as New York and Chicago,
where the number of toll circuits to be tested require it, several trans-
mission measuring sets are installed. There arc now in operation
ln'twii-n -10 anfl .">() of these sets, making it possible to test all of the
longer and more important toll routes in the system. The shorter
toll circuits radiating out from the large toll centers are also tested
with tlies<' s;mie sets. At the smaller clTiccs where fixed transmission
measuring sets are not warranted, the toll circuits which cannot be
I)icke<i up liy the larger oftices arc tested by portable transmission

Ilil.lil'IIOM: IK.IXSMISSIOX M.IIXriiW'IMIi .11

iHcasurinn sirts of tin- I-A or '.\-.\ typrs in ((iiiiu-clion willi uiIut m.iiii-
tenaiuv work.

Diu- \cry essi-ntial ri'<iiiiriMm-iit in carr\iiin on a sN>.tiMnatic trstinn
(>ro^;rani is to have rt-cords of tlu- di-taili-d inaktup of llu- toll cirriiits
which give both the circuit layouts and the (.•(iiiiptncnl associated with
the circuits. Such a record is valuaMe. not only in giving the main-
tenance forces a i)icture of the circuits and e(|iiipmeiil which they ace

r^_, ^ "'

■■-

.z:

TOLL CIRCUIT LAYOUT RECOR

1 .^ l«wn.ll

D

J"

■■

■

■:....-.==z--„;:z:;:: fc::

—

TC

— — •

JS.

E

—

e.-™

^

^

-=■

-

—

—

(r?l:i

—

* mm.

TOT*i

TiLimo

■I niP^AV

* WVa

M

(MTailuTKM

•nrm

^

^,^ p«*

^ ,I_^

rm^an

••wu ••

-,n

1* «

n

.,

J,

-tT

^-^

7?

"w-

■'

■^

IT

Fig. 4 — Sample of a Toll Circuit Layout Record Card

testing, but it also furnishes a means for establishing the transmission
standards to which they should work. When transmission tests indi-
cate trouble, this record becomes of particidar ser\ice in locating and
clearing the cause.

Fig. 4 shows a sample of the t\pe of toll circuit Uuout record card
which has proven very satisfactory and is now generally used in the Bell
System.

Telephone Repeater and Carrier Maintenance. \'oice fre(|ueiu\-
telephone rei^eaters were discussed in a paper b\- Messrs. (".herardi
and Jewetf^ and carrier systems in a paper by Messrs. ("olpitts and
Blackwell.* The various arrangements of amplifiers to provide for
telephone repeater and for carrier operation as described in these
papers tnake up integral parts of toll circuits and introduce elements

'Gherardl and Jpwett, "Telephone Kei)eaters," Transactions of A. I. !•'.. E.,
IQ19, Vol. X.W III, l>art 2, pps. 1287 to U45.

'Colpitts and Blackwell, "Carrier Current Telephony and Telegraphy," Tnins-
actions oj A. I. E. £.. 1921, Vol. XL, pps. 205 to 300.

32 HF.u. sysrr.M jhcusical jovrsal

ill the circuits wliicli h.ixc to be given particular local attention in
maintaining the overall transmission efficiency. Since both tele-
phone repeaters and carrier employ the s;ime tyjies of vacuum tubes
with very similar arrangements for power supply, the maintenance
requirements for the two are nnich the s;ime. The chief items to
be observed in both carrier and reiK-atcr maintenance are that the
gains specified to give a desired oxerall transmission equivalent be

I rlHi^i—^ ^ ' * — '

Pot.enlt»i"«t«r

n«i« Cwrfwtt and Ml«f« S31Cir^««l B«1ar«« Tnt*

hij;. 5 — Sihmiatic Diugram of a 22-Typc Telephone Re|)eatcr Showing Important
Local Transmission Maintenance Tests

kept as constant as possible, that these gains remain fairly uniform
within the range t>f frecjuencies invoh'ed, and that conditions do not
exist which will ilisiurb the overall balance between the circuits
and networks sufficiently to cause i)o<)r quality of transmission.

Consi<iering telephone repeater maintenance, Fig. 5 shows a sche-
matic diagram of a 22 type repeater antl indicates the important
tests which are made locally to insure that the apparatus is function-
ing in a s;itisfactor\ manner as a part of a toll circuit. The numbers
applied to the dilTerent tests listed in the figure show approximateh
the |)oints in the rejH'ater circuit at which the tests arc made, the
piir(>oses of the tests being evident from their names.

When carrier opi-ration is applied to toll circuits, an additional
tr.insmission system is introduced involving the use of currents of
higher freriuencies than those in the voice range. From a main-

bo c

fi

o £

@ e

34 HliU. SYSTEM TF.CHSICAL JOVRSAL

lenancc stan(l|xiint this means that certain additional testing methods
must Ik- emplo\e<l whicli will insure the proper generation and trans-
mission of the carrier currents and that the nuxiulation and de-
mmlulation of the voice fre(|uency currents is accomplished without
distortion or excess loss in overall transmission.

To give a general picture of the more important features in\olved
in the transmission maintenance of carrier systems, Fig. G shows a
schematic diagram of a carrier layout ha\ing one carrier repeater.
The particular arrangement shown is for the l>pe B system described
by Messrs. Colpitis and Blackwell.* although the same general main-
tenance considerations ai)ply to any of the present systems. It will
be noted that three si-ries of tests are rec|uired, one for the carrier
repeaters, one for the carrier terminals and one for the system as a
whole. The nature of these \arious tests and the approximate points
in the carrier ssstem where the\- are ajiplied will be e\ iilent from the
names and numln-rs used in the figure.

For both telephone repeaters and carrier systems, provision is
matie in the regular testing e(|uipment so that the tests can be ver\-
quickly ajiplied lM>th as a routine proposition and also when rec|uired
for trouiili- ioc.itiiii).

I k \N^Mi>si<>\ li.Ms ON lv\( n.\N(;ic Ari;.\ C'ikclits

The transmission conditions in the exchange area plant are im-
portant not only from the standpoint of insuring good local .service
but also to insure gcMid tcdl service, since the local plant forms the
terminals of toll connections. The exchange or local plant offers a
somewhat different transmission maintenance problem than the toll
plant, particularly with res|H-ct to the routine testing procedures
whiih must be followed to insure s^itisfactory transmission. This
will Ik- evident when it is considered that in each city and town a
com[)lete telephone system is in oper.ttion which involves the use of
a large numl)er of circuits of various types. There are also in use
three general types of iele|)hone switching efjuipmcnts; manual,
panel machine switching, and step-by-step machine switching, and
in cert.iin cities cimbinations of these eiiuipments. It is estimated
that at the present time in the Mell System there are in the neighbor-
hood of two and one-half million exchange area circuits, exclusive of
subM-riU-rs' lines, in\ol\ing eiiuipmenl other than contacts and
wiring which ma\ directly affect the transmission of speech.

The general clas.ses nf exchange area circuits in both manual and
ni.ii liiMi xuit, liiiu. .,Mi,.-s. important from ;i tr.msmission maintenance

TELEl'HOSE TKASSMISSIOX M.MSIF.XASCr. 35

standpHnt, are listed in Talili- I. Tlir oprralinj; features of inatniai
tt'lcphoiif systems are j;eiierall\' well known as are also the features
of step-l)>-stcp niarhine switehinn s\ stems, lioth ha\inn l)een in use
for man\- years. The panel machine swilchini; s\slem which is a
relatively recent <le\elopment was described in a pajier \^\ Messrs.
Craft, Morehouse and C'harlesworth.''

lAMIi: I

Clitssifitalion of Cirmits in tin' EMhnnf^e .Area Plant ImporUtnl from u Transmission
Ma inlena n ce Sta nd point

Masc.vl Officks

I..H-..1

I". H, X.

Toll

Toll

.Switiliboiirils

Switilil«xircls

Switchboaids

Test boards

Cord circuits

Cord circuits

Cord circuits

Composite set
circuits

Operators'

Operators'

Operators'

Composite ringer

circuits

circuits

circuits

circuits

Trunk circuits

Trunk circuits

Trunk circuits

Phantom & sim-
plex circuits

Miscl. circuits

Misil. circuits

Miscl. circuits

Miscl. circuits

Subscriliers' loops and sets
Operators' telephone sets

M.vcHiNE Switching Offices

Panel

District selectors
Incoming selectors
Trunk circuits
Misil. circuits

Step by Step

Connectors
Toll selectors
Trunk circuits
Miscl. circuits

Subscribers' loops and sets
Operators' telephone sets for
Special service positions

General classes of exchange area circuits involving equi|)ment
other than contacts and wiring which affect telephone trans-
mission.

While it may appear at first hand from the above discussion that
transmission testing in the exchange plant is a complicated and
expensive matter, this has not proven to be the case. It has been
found by experience that the systematic use of transmission measur-
ing sets, following the testing methods which have been developed
provides a means for peri(xlically checking transmission conditions
with a relatively small amount of testing apparatus and with a small
maintenance force. .\\\ of the transmission circuits exclusive of sub-
scriliers' lines in a 10,000-line central ofihce, either manual or machine
switching, can, for example, be completely tested by two men in a

'Craft, .Morehouse and Charlesworth, "Machine Switching Telephone System
for Large Metropolitan .Areas," Journal of the A. I. E. £., .April, 1923.

36

Hr.l.L SYSTEM TECHMC.IL JOiliX.-tL

period of Inmi iwn li. four woi-ks. thvu ami (uic-half 8-liour days per
week assumed; any trouble fouiui being cleared as the testing work
is done. The niainteiiaiue of the subscribers' lines is not included
in this work since it is taken care of by other methods as outlined
later.

In oriler to gi\e a general picture <jf the application of transmission
testing in the exchange telephone plant, a brief discussion of ttu
methcxls enii)lo\ed in both manual anil machine switching systems
is gi\en IkIow . In either system the loop method of testing proves

I

I'K-

-lllustratiun uf

.^.\ Transmission Measuring Set Iking Operated in a
Manual Office

most satisfactory, that is, one measuring set is used and where both
terminids of a circuit are available as in cord circuits, a loop test
through the circuit is made. In testing trunk circuits two trunks
are l<Ki[x?d together at their distant terminals and a measurement
maile on the two combined.

Transmission I'csis on .\finiii<il Kxcluiitt^f Area Circuits. In central
office, F'. H. X. and toll switchbo,irds, the cord circuits and associated
o(K'rators' circuits are tested by u.sing a portable transmission measur-
ing set. moving this along thelioards as required to jiick up the cords.
Kig. 7 sliiiux .1 :{. \ transmission measuring set being operated at an

lELF.rilOML TK.I\SMISSI(}.\ M.IIMF.X.INCIL .17

.1 >\vitrhl)t>.ir(l |i<>sitiiiii. Thr ntnis .iff piiki'd up .mil plii^j^cd dirrcllN-
into tlu' sfi as shown .mil mi-asinviiu'iits ni.uli' of ilu- lo>s of lioili the
i-onl .mil opir.itoi's liniiits. Trunk liniiit tisis arr ni.iilc .it ilic
switchl>oanls in llif s.inu- nianni-r as prr\ ioiisls- (k-sciilu'd foe loop
transmission li'sts on toll riri'iiits, portahU- inr.isurinj; siMs such as
shown in Kip. 7 jjcnorally hfinj; I'liiiilini-d for this work. Operators'
sets arc ins(HHti'd i)erio<licall\' and transmit Irr and riTi'i\tT crticienci^''
tcstinv; im-thods are imder field trial wliieh pro\ ide a means for test-
ing these instruments in central otThces. The miscellaneous trans-
mission circuits in an office are testetl at the points where lhe\' can
Ik; most conveniently picked up. Tlie tests on toll test hoard circuits
are made at this board and in\-olve chiefly loop tests on the equip-
ment associated with the toll circuits in the office and tests on the toll
line circuits InHween the toll testboaril and toll switchboard.

Transmission Tests on Machine Si.itchint; Circuits. The transmis-
sion circuits in panel machine switching systems are identical to those
in manual systems, while these circuits in stcp-by-step systems are
of a different design but essentially the same as far as transmission
losses are concerned. Transmission tests on machine switching cir-
cuits are similar to those on manual circuits but involve special methods
for picking up the circuits and holding them while the measurements
are made. The standard types of transmission measuring sets are
used in this work in conjunction with the regular testing equip-
ment provided in the machine switching offices and the methods
which have been developed offer a quick and con\enient means for
making the tests. In manual offices the circuits terminate in jacks
or plugs at switchboards where they are readily accessil)le. In ma-
chine switching s>stems, pro\ision is made for terminating the circuits
in jacks at test desks or frames where they can be picked iii) b\-
patching cords and tested as conveniently as the corresponding ty[)es
of circuits in manual offices. Machine switching systems otTer an
important advantage in transmission testing work, particularly in
trunk testing, in that the circuits to be tested can be looped auto-
matically b\' the use of dials or selector test sets, thereby doing away
with the necessity for ha\ing someone at the distant otfue i-nmplete
the loops manually.

In panel machine switching offices the circuits involving trans-
mission equipment corresponding to cord circuits arc the "district"
and "incoming" selectors. These are tested by setting up the trans-
mission measuring set at the district or incoming frames and connect-
ing the set to the test jacks ass<jciated with the circuits. Tests on
trunks between manual and panel machine switching offices where

.«x /</•/./. sysriiM inciiMc.ii. joikx.ii.

both sNsU-ins an- in iipi-raliiiii in ilu- s;inic- i-xchan^i.' area are generally
ma<le from the manual otVue, liie loops being dialed from the A
switchboani, while trunks l)et\veen two machine switching offices
are tested from the outgoing end of the trunks.

Fig. 8 shows a 3-A transmission measuring set as used in a machine
switching office ready for making tests on district selectors. To

'•""K- 8— lllu-tr.iliiin nf a .V.\ rr.iiisinissiuii .MtasiiriiiK Sit. Sil up in a I'aiul Macliinc
SwilihiiiK Dfl'ut for Testing District Selectors

illustrate the general methrwl of testing panel niacliine switching
circuits, the u|)iK-r diagram of l"ig. !» shows the schematic arrange-
ment for measuring trunks between two panel machine switching
offices. The transmission measuring set is located at office A, and
( rinnection made to the outgoing end of the trunks to office B through
the test jacks .it the trouble desk. A standard selector test set used

Tlil.l-.riKKM: //v-./.V,V.\//\S7().V M.IIM I.X.I.W i: .t')

ill local iiuiiiKriiaiicf work and a liiv;li iiii|H-(laii( r lioldiiiK coil art-
also roiiiU'cliMl lo till- trunks tliroii);li tin- iiHMsitriii)^ set, iIk-m- U-inn
iist'd to i-stal)iis!i till- loop and hold this loop while ihi' tests ari' ni.idr.
At otlice B two spare multiple cimiits are iro>s-(oniiefted at the main
distrilmtini; frame. An\ two trunks in ilie ^rouj) can then lie aiiio-

Trunks Incoming To Office 8

lnc«n>iM

f*<»i

1

r^i^

1

i

1 1

1

1 1

(

1 1

(i ■

rn

1 ..„

i

1

h

J

,1

F

w

b

if

J

0 1

1

r""*-H

....

__

1

0 Apparatus

(l ) Arr'w>gcment t>iowina method of making overall Trans miss ton Taste
on Trunk* between Two Panel Machine "Switching Offices

1 TrantmiMion Circu't

St

a

E

J:®

Trunks Incoming To Office B

Stfeetor Selector Connecter

s3"

ig-

:7

0 Apparatus in TraoimiMion Circuit @ Apparatus in Tran^r-ititon Circuit

(2) Arrangement showing method ofmaldrg overall Transmission Tests
cnTrunVs betwern Two Step by Step Machine Switching Offices

Kig. 9 — Schematic Diagrams Showing Metho<ls of Making Transmission Tests on

(Ai Trunks Between Panel Machine Switching Ofiices and (Bl Between Step by

Step Machine Switching Offices

matically looped together at office B by the use of the selector test
set which functions to connect the trunks to the two sjiare miihiple
circuits previously cross-connected at office B.

In step-by-step machine switching offices the circuits involving
transmission equipment corresponding lo cord circuits are the con-
nectors. Kach connector is provided with a test jack through which
connection can be made to a transmission measuring set and the

40 BELL SYSTEM TECHNICAL JOVRSAL

liHij) amiplciitl <i\cr a lest inink li\ ili.ilin^;. Lof.il si'lcclors do not
contain an>' c(|iii|>inont otluT tli.ui rontails aiul wiring in the trans-
mission circuits l)iit thc'Sf »an l»c tested in tlie same manner as con-
nectors if it is ilesired to ciieck the wiping contacts and wiring. Toll
selectors which invoUe e<|uipnient in the transmission circuit can
also 1)C teste<l in the s;ime manner as connectors. Trunks between
manual and machine switching offices can be most conveniently
tested from the manual office, the trunk loops being established
directly by dialing.

To illustrate the general method of testing step-by-step machine
switching circuits, the lower diagram of Fig. 9 shows the schematic
circuit arrangement for testing trunks Iwtween two machine switching
offices. The transmission measuring set is located at office A in a
position so that it can be patched to the outgoing trunk repeater test
jacks and an arrangement for dialing and holding is connected to the
trunks through the measuring set. At office B the apparatus in one
trunk is disconnected and this trunk used as a test trunk by cross-
connecting it at the main distributing frame to a spare subscriber's
multiple terminal. All trunks in the group can then be tested by
dialing f)\er them, from office A, the numl)er of this spare terminal
at office B which automatically loops them back over the test trunk.

Maintenance of Subscribers' Lines and Stations. The circuits
making up subscrilnrs" lines from switchboard to instruments con-
sist simply of pairs of conductors, almost always in cable, with the
necessary protective devices. These can be checked by certain
d-c. tests described in a recent |)aper." I-lquipment is also provided
in local test Ixiards for use in making talking transmission tests be-
tween the station and the test boards. Accurate machine methods
for determining the elficiency of transmitters and receivers have
been developed for testing new instruments and instruments returned
from service.

General Scheme of Testing Exchange Area Circuits. The plan
being followed in the Bell System for systematically checking the
transmission conditions of exchange area circuits is to have all offices
tested periodically by men equipped with portable transmission
measuring sets who traxel from office to office. It has been found
by experience that after an office has once been tested and any trans-
mission troubles eliminated, it is only necessary thereafter to make
transmission tests at infre(|uent intervals, these subsequent tests
serving primarily as a check on .the local maintenance conditions.

•W. II. Il.irilen, "Klitlric-.il 'IVsIs ,incl Tlu-ir Anplicalioiis in ihc Maintenance
III T< Irplione Transniivsirin," Hrll System Teclinical Journal, July, \9i4.

I

I ni.ni'llOXE TR.-l.\SMISSIO\- M.IIMI-.X.IXCr. II

Willi .1 li'sling pi. Ill of lliis kind l.irijr ,iiims ciii In.' ciiM-ri-d li\ .1 >m.ill
ir.ufliii^ font' willi .1 small anuuiiil of Uslin^; c(|uipimiii. Iliis
ii'siills ill .1 wry rcoiioniical Ir.insiiiission Icstiii^ program wliili- al
ilie saim- limo insuring; lliat Iraiismissioii coiulilioiis ar»> maintaiiu-d
-.ilisif.ictoriK .

I-ig. 10 shows a tjpicai Iraiismissioii icsliiig team layout. The
It-am is C(]uippod with an automobile which proves an economica>
means ol ir.insportation between offices and exchange areas and

fTTEk

Fig. 10 — Illustration cf a T\p

Testing Team Layout

pro\ides a con\enicnt meth(jd for carrying the testing equipment.
During transportation this equipment is packed in padded trunks
which insures against injun,-. In this particular case the equipment
includes, in addition to transmission testing sets and oscillators, other
apparatus such as a wheatstone bridge, crosstalk set and noise measur-
ing set so that other maintenance work may be done in connection
with tran^mi^ision testing whenever this is desired.

Results Accomplished

The results accomplished in transmission maintenance work can
best be appreciated by considering the kinds of troubles which ad-
versely affect transmission and which can be detected and eliminatetl
by routine testing methods. Consideration is first given to the general
causes of troubles which are detrimental to both toll nnrl jural trans-

42 /'/:/./. .V)\/7;A/ IICIIXIC.II. JiH KS.II.

niissidii, aixl l.itiT llio fe.iturcs iit this coniurlioii iudr- parliciilailv
UkMitiru"*! with tflfphoiic ri'iH-Miors and i-arrier s\slems arc discussed.
The difTereiU elassi's i)f i-ircuits i^ixcn in Tahle I arc made up of
various comliinalions of tlic following indiviihial parts:

Rc|>eating Coils
Kelurilatiun Coils
RiUiys
Coiuli-nscrs

riiiKS
Jacks
Ki\s
Ik-al Coils

Kcsislances
AuiD-Transfrirniors

l"arlKins
WiriiiK

SwiltliJMjard to M.

1). 1".

liiiliirtion Coils
l.o;i<lin)( Coils
Conis

\ C ross-ionni-ction
\ Outside
Transmitters

I<ec"ei\'ers

The above parts are coinl)ined in various ways to make up the com-
plete (i|)erating circuits such as cord circuits, operators' circuits,
trunk circuits, etc. Kach complete circuit causes a definite normal
loss to telephone transmission which must he taken accoinit of in
designing the plant to meet the \'arious service requirement^. If,
howe\er, any of the parts used are defective, if the wrong combina-
tions of parts are nsetl, or if the installation work is not correciK-
done, excess transmission losses will result which may very seriousK-
affect the transmission when the particular circuits inxotved arc
employed in an overall connection.

Classification of Common Types of Troubles. An anahsis of a
large amount of transmis.sion testing data has made it possible to
develop a definite trouble classification which is particularly helpful
in transmission maintenance work and which permits the most
efficient use of the results in eliminating transmission troubles, llx-
jHTience has shown that the troubles found can be divided into two
general classes. A— troubles which can be detected either by .siiiiplt>
d-c. or a-c. tests in connection with the regular day-by-day main-
tenance work or by transmission measuring sets, and B — troubles
which can be detected most readily by transmission measuring sets.
The most important troubles in the abo\e classes are as follows:

Claw A Class B

( l|H-|IS

I'.lctrie.il Defects

( iroiinils

Iiuiirreil Wiring

CrosMs

WroiiK lyiH' <)f i;(|iii|iiii

eiu

Ciitoiils

MissinK K<|ui|>inem
lli>;li Kesistance
Low Insiil.iiidn

If, in m.iking ir.insnii^ion tests in a cent ml office, a liigii pcr-
cent.igeof ("l,iss A troubles is found the remedy isgener.illy to instigate

lEU-.rnosi-. ih!.i\sMissi(>\ m.iim i.x.im i. a.\

mon- rii;i(l Incal m.iiiiti-ii.mcf r<iiiliiio> |),i\ini; |).irlinil.ir .iiiciilinii to
thf ly(H' of ririuits in wliirli llic iroulik-s .irt- Inc.iii'd. I'lu- |)<-i-
ifiitano of Class B troiil)U's is not as a ruU- as liinh as tlu- ("lass A
troul)lt's aiul I'xixTiencf lias shown lliat wlu-n ("lass H trouMis an-
oiH'v clinun.ttt.'(l by transmission tcslinn ini'iluxls only itifrr(|iu'nt
siibsi'cim-nt tvsts are rr(|uirf(l to take care of an\- additional troubles
of this class which may get into the plant.

In determining what constitutes an excess loss, the value of tiie
transmission as well as the practical design and manufacturing con-
sitierations to meet o|x'rating limits are taken account of. An excess
gain is also considered as a trouble on circuits etjuippeil with ampli-
fiers, since this may produce poor (juality of transmission which is
likely to be more detrimental to service than an excess loss. The
value of transmission based on economical design considerations
varies, depending on the first cost and annual charge of the particular
types of circuits involved. A gain of one TU in the toll plant is
generally worth more, for example, than one in the local plant, since
it ccsts more to provide. In transmission maintenance work the
cost of making transmission tests and clearing trouble is i)alanced
against the \alue of the transmission gained for the [>urposc of est.ib-
lishing economical transmission limits to work to.

Speiijic Examples of Common Troubles Found and Their Effect on
Transmission. Certain kinds of troubles which are detected by
transmission measuring sets do not cause excess losses which can be
quantitatively measured. Such troubles are, however, readily de-
tected by "ear balance" transmission measuring sets in that the\'
cause noise or scratches and by the "meter balance" sets from fluctu-
ations cf the needle of the indicating meter. The most common
trouble of this kind is due to cutouts or opens which may be caused
by dirty connections, loose connections, improper key and relay
adjustments, etc. While not causing a quantitative value of excess
loss, this class of trouble is very detrimental to transmission and
more serious in many instances than fixed excess losses. Indeter-
minate troubles of this nature are gi\en an arbitrary excess loss \aluc
based on experience.

Considering troubles which gi\e definite losses, the most common
kinds are caused by electrical defects in equipment, incorrect wiring
of equipment in circuits and wrong types of equipment. The other
classes of troubles, such as crosses, high resistances, and low insula-
tion, also generally give measurable excess losses but these are not
as common in the plant, since troubles of this nature are more likely
to affect the signaling and operation of the cirrin'ts and are, therefore.

BEI.I. SYSTEM Tl-CIIMC.-IL JOLR.X.-iL

fliniin.iud l>\- tlio ri-niil.ir m.iiiiUiiaruc work. Missini; iqiiipniciU
will in (-iTt.iiii rases causi' a yaiii in transmission Imi aftccls (Ik- circuits
advcrst'U- in other wa\s.

Typical examples of connnon irouliles. willi the excess losses wiiicli
they cause, are given in the following table:

Type of Circuit
and Equipment

Repeating coils in
cords, incoming
trunk circuits, select-
ors, toll connectors

Su|>ervi>>or>' relays in
"A" corii circuits

Bridged retardation
coils or relays in toll
cord circuits, coni-
(losite sets, connect-
ors ami slep-by-stcp
repeaters

l< e () e a t i n g coils on
loatknl toll switching
trunks

Iniluction coils in op-
erators' telephone sets

Cause of
Trouble

KIc-clrical defects

(dcnerally short cir-
cuited turns)

Incorrect wiring (Gen-
erally reversed wiml-
ings)

KIcctrical defects

(f) p c n non-inductive
winding)

Klc-ctrical clefc-cts (Gen-
i-rally short circuited
turns)

Wrong ty|)C of cfjuip-
ni cut, incorrect wir-
ing

Klectrical defects. In-
corri-ct wiring

Approximate Excess
Transmission Loss'

1.5 to 5.0 TU

2.0 to l.S.O TU
.\l)out 2.5 TU
1.0 to 5.0 TU

1.(1 to 4.0 TU
1.0 to 1,?,0TU

There are, of course, many other specific types of troubles delected
by transmission tests which give definite quantitative losses but the
al)ove will serve to illustrate the value of this testing work in eliminat-
ing excess losses in a telephone plant.

Muintename Features Peculiar to Telephone Repeaters and Carrier
Systems. The siime classification of troubles discussed above applies
to repeaters and carrier systems. Amplifier equipment, however,
employs certain feattires which are not common to the more simple
telephone circuits and stjme of the troubles which may occur if the
pro[KT maintenance procedures are not followed will seriously affect
servite. It is for this reason that repeater and carrier installations are
pr<j\i<led with s|K'cial testing e(|uipment which is always available
for use either in routine maintenance or in locating and clearing
any trtmbles which may occur in service. Automatic regulating
devices arc also provided where\er this is practicable in order to
reduce to a minimum the amoimt of manual rcgulailDii and
maintenance.

' \V. M. Martin, " I'lu- TransniiMion Unit," Jnunml oj the A. I. E. E., June 1924-
H. S. r. J., \\,\. 111. p. 400. 1924; C. \V. Smith, "Practical Application of Trans-
niimion Unii, ' W. .V. /. J.. Vol. Ill, ji, 4<W, l')24.

TEU-rnoM-: m.txsMissiox m.umf.n.-ixce 45

Thf imjK)rtant elemcnls in both repeaters and carriers wliieli may

directly affect tr.in>.ml^si(>n or iMiisf service troubles in olhcr ways

are as follows :

Filamiin H.iiuru^ I'litcntiomctiTs

Plate Rattcriis l"iltirs

("■rid Batteries Transmission Kqualizers

\'acuuni Tubes Signaling Kquipnient

Balancing K(|ui|>nu'iil Tatching Arrangements

The tests oiillineil in the nuiin body of tiie paper aim lo insure
that tile above essential |)arts of repeater and carrier circuits are
functioning properly and that the equipment as a whole is giving
the desired results in overall transmission efJiciency.

CoNCLfSION

The aluive discussion of testing methods and tlio results ticcom-
plishcd indicate how a comprehensive and economical transmission
maintenance program can be applied to a telephone plant to check
the volume efficiency of the circuits against the established standards.
Consideration is continually being given to new testing methods and
their applications in order that further improvements in service ma>-
be effected and increased economies in testing taken ad\'antage of.

AI'I'KXDIX A

f*KiN(iPi,i:s OF Testing Methods Closely Associ.\ri;i) uiiii
Tr.wsmissiox Efficiency Tests

Tests of \olume efficiency often need to be supplemented by other
methods of testing in transmission maintenance work. Transmission
efficiency both as regards volume and quality may be seriously affected
by noise or crosstalk, and tests for an\' conditions of this kind are
therefore important in maintenance work. Furthermore when
efficiency tests show excess losses or unsatisfactory circuit conditions
other testing methods prove very valuable in locating the cause.

To illustrate this phase of transmission maintenance the principles
of some of the more important testing methods are briefly described
below. Two of the tests employ a method very similar to loop trans-
mission testing while others employ the well known "null" method.
A special method employing three winding transformers and ampli-
fiers widely used to determine impedance balance conditions between
lines and networks is also described. Several methods which involve
simply current and voltage measurements have lieen mentioned in

46 BF.l.l. SYSTEM ir.CIIXIC.II. JOIKXAL

this paper l>iil tlu-st- art- Kt^nirally will known am! tlicrefore require
no tietaiied description.

1. Measirkmknts of Crosstalk

In the circuit shown in Kig. 1 1. if a-c. power is supplied to a circuit
known as the "disturhinn" circuit and unlialances exist between this
circuit and a second known as the "disturbed" circuit, power will be
transferred from one circuit to the other causing crosstalk in the
second. A dehnite jwiwer transmission loss therefore takes place
between the two circuits which can be measured by a loop trans-
mission test similar to the elTicicncy tests described in the main body
of the pajK'r. An adjustable shunt called a "crosstalk meter" cali-

C'oit Talk Uuijtr

MeMv-em«flU of C/ots Talk
Fig. 11 — DiaKraiii SliowiiiK I'rincipK's of ("riisstalk Measurements

lirated in either 77' or in irossialk units is subs(iluu<l tdr llie two
circuits. With the .same power supplied alternateK' to l)()lh the
"disturl)in(j" circuit and the meter and with the sending and recei\ing
end imiK-dance conditions as shown, the meter shunt is adjusted
until, in the o[>inion of the obser\er, the annoyance produced li\' the
tone in the recei\er is judged to be equal for the two conditions.
The reading of the shimt if there was no dist<jrtion of the line cross-
talk currents Wduld then give the \-olume of crosstalk which could
be e\|)ressed in Tl^ as 10 login Pr P, similar to loop transmission
testing. However, this relation only holds approximateK' in practise
since the line cro.ssialk measured is produced by various currents
having different phase relations and a certain amoimt of distortion
therefore occurs. The commercial form of crosstalk set now used is
equipiKil lo gi\e the approximate imiK-jiance relations rei|uired and
also pro\ides a feature for eliminating the effect of line noise except
in the case of one lyiK' of measurement which is made on long cable
circuits. lM»r practical reawins the results are generally expressed in

.r..--i,.ll.: iii.ii- riiluT ih.UI 77'.

Tl-.LF.I'UOSl- IR.IXSMISSIDX M.ll \ I i;\'ANCr. 47

•J. MlCASlRKMKNTS ()!• NolM:

Tin.- rninmon iiuiIuhI of mi-asurinn noisi- in ;i Iflrplioiu- ciniiil \4
^liown ill tlu- diagram of l-'in- 12. In tliis test an arliluial noisi-
curront prodiu'cd by a jifnt-rator of constant povvrr /', c.illrd a "noist-
standard" is substituted for the line noise iiirrenl. It ilic two noise
currents were exactly alike as regards wave shaiie and tlic relative
magnitude of the frequencies involved they would ])roduce the saint-
tone in the receiver and their Nolumes could be made e(iual by afl-
justnunt of the noise shunt. The power ratio, Pr/Ps, as indicated

■a ^'— i^X

Ctrcuit uoder Test

Me3«urscT)ent.s of Noise
Fig. 12 — Diagram Showing Principles of Noise Measurements

by the shunt, would then give a measure of the line noise in terms
of the noise standard. This condition, liowexer. is not met wiili in
practise due to differences in wa\e shape of the two noise currents.
For this reason noise measurements are made by adjusting the noise
shunt until the interfering eflfects of the noise on the line and from
the shunt are judged to be the same for which condition the jiower
-upplied to the receiving network by the noise standard is not neces-
sarily the same as that supplied by the line. The receiving end
im[)edances however, arc kept as nearly alike as practicable to pre-
vent reflection losses.

3. Mr.vsirkmf.nts of Lini;-Xi:tw()RK B.\!..\n< ic (21-(iR(iir
B.\i,.\N( !•: Ticsr)

The testing arrangement of Fig. 13 shows the princijile of the 21-
circuit balance test referred to in the main body of the paper in
connection with telephone repealer and carrier maintenance. In
this test the gain of an amplifier calibrated in 'I'U is used to com-
pen,s.-ue for the loss through a three winding transformer or output
coil of a telephone repeater. If the impedances of the balancing
network and line were exactly alike at all frec|uencies, i.e., Z„=Z[..
.ind no other unbalances existed in the circuit none of the power
supplied by the amplifier to the input of the three-winding trans-

48 Hl.l.l. SYSTEM TECIIMCAl. JOLRNAL

funiur would be transferred to the output, i.e., the power ratio Ps/Pr
would be infinity. However, this ideal condition cannot be produced
in practise so that there is always a finite power loss between the
input and (iut|)ut of the transformer which can be measured approxi-
mately by the yain of an amplifier calibrated in TU. An internal

BtUnung

curt, under Tect

M«»«ur«rn«ni» of lmpedinc« Balance Between Ltnet and Networks
(?ICircu't Teett on Teleptnne Bopeeiert and Carrier)

rig. I.I^Diagram Showing Principles of 21 Circuit Balance Tests

path for currents which may produce "singing" or a sustained tone is
established if the gain of the amplifier Pr'P,. is greater than the loss
P, Pt through the three-winding transformer. As unbalances between
network and line become greater the loss through the three-winding
transformer becomes less thereby ief|uiring less gain in the amplifier
to prcxluce a "singing" coiuliiion. It should be noted in this con-
nection that to produce the condition described above exactly, the
current received around the "singing" path must be in phase with
the starting current. In practise this condition obtains sufficienth
accurately so that the gain of the amplifier required to produce
"singing" gives an approximate measure of the ini|ie(larue balance
lietweeii line ami network.

1. .Mi-AsiKiiMKNrs ()!• Kksistasci:, R i:.ur.\N( k and Imim-dancf.

Diagram (a) of Fig. 14 shows the wheatstone bridge circuit for d-c.
resistance measurements. It is unnecessary to describe the well
known principles of this bridge but mention is made of it here in view
of its im|K>rtance and use in telephone maintenance work. It supplies
an indis|X'nsiible nuthnd of measurement for certain trouble locations,
such as crosses and grounds anfl emlxxlies the fundamental principles
uf all null tests.

Diagram (b) of l-'ig. II gives a bridge circuit for measuring imped-
ance, the particul.ir .irrangement shown being for measurements of
inip.il-iii. .•>. h.iving inductive reactance. The bridge measurements

TEl.EPllOXr. rR.lXSMISSlOX M.IIM r.X.IXCIi 49

express impedance in terms of its resistance component and ecjuivalent
inductance or capacit>'. In ineasurini; an im|)edance li.i\inj{ inductive
reactance at any fre(iuenc\ , /, for example, a l)alance ni\es R = Rx
and L=Lx. At tlie fre(iueni-\- /, the etTecti\e resistance is given
direcll\- 1)V tlie \alue of R and the re. ut, nice li\- the rilalinn, 1 ir f L_

(a) Otreci Current Peftr«tar>ce

Null M«ih«d of Meac<

(b) Impedance having rnducCive Pedctence
-ing Peftisiance.Peactance and Impedance

Fig. 14 — Diagrams Showing Principles of N'uU Metliotis for Measuring Resistance,
Reactance and Inipcilance

Tlie impedance is tiic \ectorial sliih of these two or v i?- + (2 ir/L)-.
In maintenance work invoi\ing; impedance measurements as will be
noted in the next testing method descrilied, the effective resistance
component and the eqiii\aleiU indtictaiue are generally used directly
without combining.

5. M E.XSCREMENTS OF LiNE IMPEDANCE AND LOCATION OI- Im PEDANCE

Irregularities

Fig. 1.5 shows a telephone circuit connected to a bridge and termi-
nated at its distant end in characteristic impedance. If the circuit
has approximately uniform impedance throughout its length the
resistance and equivalent inductance curves of this impedance within
a range of frequencies will be fairly smooth as indicated by .4 and C
of the figure. The curves are not perfectly smooth since it is not
practicable to construct the line for perfect impedance uniformity.
If at some point in the circuit an irregularity is [jresent such as an
omitted loading coil, an inserted length of line of different construc-
tion, etc., which changes the impedance, this will produce a periodic
change in the resistance and inductance cur\'es A and C such as
shown by Curve B. Curve C will be changed in the same way as
Curve -4 but for simplification this is not shown on the diagram.

The change in impedance in the circuit reflects some of the current
sent out back to the sending end where it adds to or subtracts from

50

/?/■/-/. SrSTHM ll-CHXIC.IL JOlKX.iL

the st'iulinv; lurrfiit cit'iK-iulinn on llu- phase relations of ilie iwn cur-
rents at any particular fre(|iiency. Since imix-dance equals E I its
value changes as the \alue of / changes. This is made use of in line
impedance measuring work to gi\e a location of inipedaiue irregu-
larities which mav exist somewhere in the line.

C*co»l under Tert

3

Null >MU<ed or Uwurinf I

•-^cy of MvMufMf C*rf«nl

B lmp«d»nc« md LOCM.04 l«wp«d»f>e« trrequlai

l-'ig. IS — Diagram and Imix^danrc Curves Showing Principles of Line Impedance
.Measurements by Null Method and Location of Impedance Irregularities

Referring to Fig. 1'), let d cqua\ the distance in miles to an im-
IH'dance irregularity and /, one frequency at which the resistance
comiMinent of the impedance is a maximum. The next maximum
|)oint will occur at a frequency /: such that as the frequency has
been increased, one complete wa\e length is added in the distance
lra\eletl by the reflectetl current. Maximum points at /.i, A, etc.,
occur in the s;ime way as the frequency is increased. Considering
the two values /i and /j let

r =vel<K'it\- of ciurcnl in miles per second
11*1= wave length at fre(|ucncy/i
M'; = wave length at frequency /j
.V = number of \va\i- lengths in distance Iraxeied
li\ icllti i( d I urrcni or 2 d.

TEU-rHOSI: IK.IXSMISSK >.\ M. Il.\ I i.x.iscr.
\l fir<|ui'iii\ fi tlu'ii.

V- 2'^

.in.l ,,t '... .V+l= ?y

.ilsd at 1 1. Wi= V/fx

..iulat/2. W:.= V'fi
Substituting alxixr

>ul>tracliug,

A' =

2rf/,

" V

and

.Y+l =

_2df,
V

1 =

2dh
V

2rf/,
V

J -

V

2(h-h)

which is the distance in miles froni the sending end of the circuit to
the (X)int of impedance irregularity. The velocity of propogation
V is not exactly constant within the entire frequency range but does
not vary sufficiently to materially effect the accuracy of impedance
trouble locations bv this method.

Mutual Inductance in Wave Filters with
an Introduction on Filter Design

By K. S. JOHNSON and T. E. SHEA

I'Akr I

General I'him iii.is ui W.wi-: Fii.riiR Dksign

Principles of Generalized Dissynitiielrical Xehcorks. W'c shall con-
sider first llu- inipcdanco ami propajjation cliaractcrisiics of certain gen-
eralized networks. It can be slunvn that any passive network haviir^
one pair of input and one pair of output terminals may, at any frequency,
he completely and adequately represented by an equivalent T or v net-

-? — WWV 1 WWV 9-

I.- J I,'

Z.,| V. Z.. |Zc Z..V,

Fitc. 1 — C.cntTaliztil Dishyiiiinelriral T Network Connectc<l to Itiipfdanccs Kqu.il
to Its Image Im|K^anccs

work} The impedance and propagation ciiaracteristios of an\- such
network may lie exjiressed in terms of its e(|ui\alent 7' or w network.
These characteristics are defined by (I) the image impedances, and
(2) the transfer constant, the latier including the attenuation constant"
and the phase constant.- In the case of a symmetrical network,
the image im|)e<lances and the transfer constant are, respecti\el\-,
the iterative impedances («)r characteristic impedances) and the propaga-
tion constant employi-<l by Campbell. Zobel, and iithers. The terms
inxolviHJ will be siibse»|iiently defined.

Consider the dissymmetrical T network of Fig. 1. If the 3 — 4
terminals of the T network are connected to an impedance Z/„ the

' Camplicll. G. .\., 'Tisoiclal Osiillalions," Traiisarlions A. I. E E (191 1)
Vol. XXX. Part II. pp. 873-909. ' ^ '

The 7" and » networks referred to aliovc are sometimes called star ( 1') and delta (A)
networks, rr»|:e< lively.

> The real and iniat[inary |i,irt!. o( the transfer constant have U-en called by Zobel
the dimiHUlioH ,,mil<int ,ind the ijiie»/iir (omlunl, res|:e<tivel\ . (See Hililict;ra|ihy 13.1

52

MIIV.II. IMHCT.IXCr. I\ ll-.lir. III.II.RS 5.1

imiMMl.iluc Iiinkiiii; into ilic T network at the 1 — 2 lermiii.ils will be

Siinil.irly, if the 1 — 2 termiii.ils of tiie T network arc oonnerled to an
inipeilaniv Z/,, the intpeiLince lookini; into the 3 — 4 terniinais of the

7' net work will lie , '

U Zi i is equal to the terminal impedance Z/,, and if, similarly,
Zj-i is et]iial to the terminal impedance Zj.^, the network will then be
terminated in such a way that, at either junction (1 — 2 or 3 — 4), the
impedance in the two directions is the same. In other words, at each
junction point, the impedance looking in one direction is the image
n| the impwiance looking in the opposite direction. I'nder these
conditions Z/, and Z/, are called the /wage impedances of the 7' not-
work. If equations (1) and (2) are solved explicitly for Z/, and Z/^,
the following expressions are obtained :

7 I (Z.4 +Zc){ZaZb+ZaZc+ZbZc) ,,.

^'• = \ ^^+Zc) • ^^^

_ I (Zb+Zc) (ZaZb+ZaZc+ZbZc) ...

^'^ = \ iZ^+Zc) • ^^^

If Zoc is the impedance looking into one end of the network with
the distant end open-circuited, and if Z^, is the corresponding imped-
ance with the distant end short-circuited, it may be shown that the
image impedance at either end of the network is the geometric mean
of Zee and Zsc- What is here termed the image impedance is, there-
fore, equivalent to what Kennelly has called the surge impedance.'

The propagation characteristics of a dissymmetrical network m.iy
be completely expressed in terms of the transfer constant. The
transfer constant of any structure may be defined as one-half the
natural logarithm of the vector ratio of the steady-state vector volt-
amperes entering and leaving the network when the latter is termi-
nated in its image impedances. The ratio is determined by dividing
the value of the vector volt-amperes at the transmitting end of the
network by the value of the vector volt-amperes at the receiving end.

• There is at present lack of common agreement as to the liasis of definition of
this term, and it is often defined upon the basis, not of open and short-circuit im-
pedances, but of a uniform recurrent line (See A. I. E. E. Standardization Rule
12054. edition of 1922). The formulae derived by the two methods are not equiva-
ment in the case of dissymmetrical networks.

54 PEI.l. SYSTr.M TllCIISIC.tl. JOIKX.IL

The real part of the transfer constant, that is, tlie attenuation con-
stant, is expressed by the above ilefmition in napiers or hyperbolic-
radians and the imaginary part, tliat is, the phase constant, is ex-
presse<I in circular radians. The practical luiit of attenuation here

^^ — vww — r — \w\/v — ^-

Z.^ 2. ^Zj Zi 5Z,

Z 4

Fig. 2 — Generalized Syimnetrical T Network Connected to Impedances Equal to

Its Image Impedances

used is the transmission unit* (1 y'(' = .ll")13 napicr). It can be
demonstratwl that the transfer constant, (), of the T network shown
in Fig. 1 is

e = tanh '*/^- = lanh '^

= cosh"'

{Za+ZcKZb+Zc)
1{Za+ZcKZb+Zc)

(5)

Zc'

in which Z„, and Zu are, as previously defined, the open and short-
circuit impedances of the network. The ratio Zsc/Zoc is the same at
Ixjth ends of any pa.ssive network.

Principles of Generalized Symmetrical Netuvrks. (^insider now the
impedance and propagation characteristics of the generalized sym-
metrical structure shown in Fig. 2. On account of the s>nimetry of
the structure, the image impedances at both ends are identical, and
from e{|uation ('.i) or (4) their value may be shown' to be

Z, = ^Z.Z,(l-H^). (6)

In the case of a s\inmelrical 7' structure, such as is shown in Fig. 2,
the impe<lance Z/ is called the mid-series image impedance. The
significance of this term will be evident, if the series-shunt type of

* \V. H. Martin, "The Transmissum l"nit and Telephone Transmission Reference
.System," Bfll .Sys. Teth. Jour., July, 1924; Jour. .4. /. E. E., Vol. 4.?, p. 504, 1924.

» Zobcl, O. J., "Theory and Design of Uniform and Composite Electric Wave-
Kilters." Bell Syit. Tech. Jour., Jan., 1923.

ML'll.ll. IMHCr.t.W li l\ ll\iri. lll.ll.Ks

>trinlurc shown in I'iv;. H is ri'K.irdcd .is m.idr up of >.\ iiimiMrical 7'
lU'tworks or sfclioiis, tlu- jmirliniis of which occur .il ihc luiil-poiiils
of thi' si-rii's anus.

Sup|X)so now tlial tlu- ^truclun' of Kij;- •{ is itmsidcrfd lo Ik- m.idf
up of syinnu-trical s- lu-tworks, or si-ctions, each of which is ri'|)ri'stMitcd

VvVW

AWW-

-A/VWV-

-j\tUh

Kig. J — CifiUT.ilizi'il^Kii uritiit SiTics-Sluiiit Network

3

H,

Hi'lZj. f 2Z,

Z2,% Z,.^Z:.

Fig. 4 — Generalized Syninietrical t Network Connected to Impedances Equal to
Its Image Impedances

as in Fig. 4. By nu-thods similar to those empIo\etl for tiie T network
of Fig. 2 it can be siiown'' that the iniage impwhmce of the general-
ized JT network of Fig. 4 is gi\en by

Z,=

^

z,z.

1+

(7)

In this symmetrical structure the image impedance is called the mid-
shunt imave impedance.

The image transfer constant of either a T or a tt symmetrical struc-
ture is^

e = ^l+jB = 2 sinh-"-y|^ = cosh-'(l+;^).

(8)

In discussing the generalized networks of Figs. 1, 2 and 4, it has been
assumed that the networks were terminated in their respective image
imfH-dances. In practical cases, filters must be designed to work
between inifK-dances which are, in general, not exactly efjual to their

56 PEI.L SYSTHM TECHNICAL JOIRXAL

image ini|Kxl.mits al more tliaii one or a few frcc|iieiuiej. I- or a
gi-neralizcMl strucliirf, sutli as that of Fig. 1, operating between a
sctiditiii-ciid impedance Zs and a receirin'^-ciid impedance Zr, the
current in Zr, for an electromotive force acting in Zs, is

h = ^HV X '^r . X xjif^-^^ X

^s+Zr x^AZJZr Z,,+Zs Zi,+Zr

Xt-oX y y—\ y • (9)

Zj^ — Zr AU—/.S v^-2»

Ninee A [Z^-Y'Zr] is the currenl (/«■) which would flow if the gcner-
alizetl T network were not inherled in the circuit, the ratio of the re-
ceived current, wiih and 'wilhoiil the network in the circuit, may l)c
exprcssi'd l)y the relation

Ir ^ ( Zs+Zr \ (VJZ,^) (ViZjTR)
Ik- \^AZ^r) V Z,,+Zs ' ^ Zu+Zr '

Xt-OX -y y-^ jr\ • (10)

fZi,-ZR\/Zj,-Zs\ 2»
\Zi,+Zr)\Z,,+Zs)

In general, the electromotive force does not act through a simple
sending-cnd im|)edance Z.s l)ut through some complex circuit. The
current ratio (Ir Ir) will, howe\er, he the same in either case. The
|)rinciple imderlying this fact is known ;is Thei'cniii's Theorem.''

The absolute magnitude of the current ratio, \ Ir Ir |, is a measure
of the transmission loss caused by the introtluction of the network.
The transmission loss ma\" be expressed in terms a( transmission imits
(7"t') l)y aid of the following relation

rt/ = 201og,o|(^i. (11)

Reference to e(|uatiiin (10) shows tli.il the transmission loss caused
by the iniriKluction of any network is composed of five factors. The
first three f.utors of this e(|uation ;ire all of the Siinie general type
with the exci'plion that the first of the three is reciprocal in nature
t<i the other two. These two latter factors have been called reflection
factors and determine the reflection losses which exist between the im-
[K-dances involvi^l. The fourth factor is the transfer factor and
expresses the current ratio which corresponds to the transfer con-

•("a»|)er, \V. 1.., " IVIc'|ihniic rmnsfciriucrs," Transactions A. I, E. £., March,
1924, p. 4. Thf-vi'iiin, M. L., ".Sur un .Noiivc.iii Tlieor^nicd'Klcctrkitf Ox n.imiqiie,"
Comptrs Rendus, vol. 97, p. 159. 1883.

Mlll-.ll. IMHCT.IXCr. I\ ll.irii IILTERS 57

slant. riif I.i>l f.n tor li,i> l«t«ii i .illcd ilu' inlenution factor. The
\aluf of till" ri'dfiiiKii I.U lor i> t\ idtiilK .» fimrtion sim()l\- of the ratio
of the iiniHil.mres iiuoKed, while the ahsoliile \aliie of tlie transfer
factor is t ' wliere .1 is the re.il |M>rtion of the transfer constant and
hence is the attenuation constant. 'Pile \alue of the interaction
factor is seen to i)e unity eitlier when Z i^ = Zr or whvn Zt^=Zs. It
also approaches unity if the vahie of O is sufficiently large.

In the case of a symmetrical structure, such as is shown in I'ip;. 2,
or Fii;. 4, Zi,=Zi.=Zi and e(iuation (10) reduces to

h ^ ( Zs+Zr \ (VTzJZs) (V-IZiZr)
U- V y/AZsZR' \ Z/+Z5 / ^ Z,+Zr I

Xt-ex ,y y \y 7 , • (12)

1 _ (Zi-Zr\ /Zi-Zs\ ^^,

\Z, + Zr)\Z,+Zs)

If the structure is symmetrical, and if, furthermore, the sending-end
impedance Zs is equal to the rccciving-cnd impedance Zr. equation
(12) becomes

7^.-* ^{z,+ZRr-^. (Z,-zr\^ _^; ^'^>

\Z,+Zr) '

The preceding formulae make it possible to calculate rigorously
the transmission loss caused by any network whose image impedances
and transfer constant are both known. In the symmetrical case, if
Zi=Zs = Zr, the transmission loss is determined simply by the \alue
of the attenuation constant. In general, in the attenuation range
of freciuencies, the value of 6 of a wave filter is relatively large and
the interaction factor is substantially unity. Consequently, the
transmission loss caused by any filler in its attenuation range is de-
pendent practically only upon the value of the attenuation constant
and the reflection losses between Zs and Z/,, Zr and Z/,, and Zs
and Zr, respectively. Throughout most of the transmission range
of a filter, its image impedances may be nuide very closely equal to the
terminating impedances so that the transmission loss caused by the
filter in this range is dependent simply upon its attenuation constant.
In the intervening range, between the attenuated and the non-at-
tenuated bands, the transfer factor, the reflection factors and the
interaction factor must all be taken into account.^

' Zobel, O. J., "Transmission Characteristics of Electric Wave-Filters," Bell Sys.
Tech. Jour., Oct., 1924.

58 PELL SYSTEM TECHNICAL JOURNAL

Impedatice and Profxttialion Charaiteristics of Non-Dissipative
Fillers. If thi; scries and shunt inipotlanccs of the structures shown in
Figs. 2 and 4 are pure reartances. as they would l)e in the case of a
non-dissi|)ative filter, the ratio of the quaiuit\- Z) AZ^ must be eitlier
a i)ositive or nejjative numeric. It has been shown b>' ('ampbell' and
«)thers thai the attenuation constant is zero, and that the structure
freely transmits at all frwiuencies at which the ratio Zi/4Zi lies
between 0 and — 1. Therefore, In ploitinj; values of the ratio Zi/AZi
il is [xjssible to determine the attenuation characteristic of any sym-
metrical structure as a function of fretjuency.

Iti the transmission ranne, the phase constant of the s\niiiutric.il
structure shown in Fig. 2 or Fig. 4, is

^ = 2 ^'" \l^- (14)

Hence, the expression for the image transfer constant of either of the
symmetrical structures shown in Fig. 2 or Fig. 4 is

9 = 0+7 2 sin- J Z^. (15)

In the attenuation region, Z.\ \Z.i may be cither negative or pnsiti\e.
If Zy AZt is negative anti is greater in absolute magnitude than iinii\ ,
the attenuation constant is

.■l=2cosh-'^Z^> (16)

.111(1 'he phase constant, or the imaginary' component of the image
transfer constant, is

B = (2K-\)ir (17)

when- A' is an\- integer. Ili^ncc,

e = 2cosh-' lz:|i+7(2A'-l);r. (18)

\ AZt

From e<|uation (S), when Zi/4Zj is positive, the altciiuatinn idii'-tam is
/I=2sinh-'^|_i|^ (19)

and the ph.ise c<instant B is zero. Hence,

" = -'-"'•' 'yJ^^-+JO- (20)

•( .impUII, C. .\ , "l'hv>i..tl Tliciry of ihr Klnlrir \V;i\o-Kill(r," Hrll Svs Tech
Jour., Nov., I<J22.

.uiic.ii. /.v/TC/v/At /• IX ir.ni- iii.ii.ks so

As ii result of t-<|ii,iti()iis (IS) ami (2(0, in ilic .il Icniiatinn r.mm',
the phase constant of a noii-dissipatixc s\niini-lriral lillcr section is
always zero or an (hUI multiple of ± ir.

The I iit-o[f frequencies, hy which are meant the divisional fretpiencies
whidi si-parate the transmission hands from the attenuation hands,
must always occur when i^i 4/^2 = 0 or when Zi/4Zi= — \, sin'<',
for the transmission bands, Zi -iZi must lie between 0 and —1.

The ijeneral fornudae for the image impedances of the symmetrical
networks shown in Figs. 2 and I are e(|uations (ti) and (7), respectively.
I'rom these equations, the imaRe impedances are pure resistances in
the transmission range of a non-dissipative structure. In the at-
tenuation range, howe\er, the image im])edances are pure reactances;
the mid-series image impedance is a reactance having the same sign
as Zi, while the mid-shunt image impedance is a reactance having the
siime sign as Zj. In these attenuation hands, the image impedances
(pure reactances) have positive or negative signs depending upon
whether they are increasing or decreasing with frequency. The order
of magnitude of the image impedances may he found from T.ihle I.

TABLE I

If the
Value of 1 2i 1 is

And if the
Value of |4Z, lis

Then the

Mid-Series

Image Impedance is

And the

Mid-Shunt
Image Impedance is

Zero

Zero

Zero

Finite

Finite

Finite

Infinite

Infinite

Infinite

Zero

Finite

Infinite

Zero

Finite

Infinite

Zero

Finite

Infinite

Zero
Zero t
Finite t
Finite *'
Zero* or Finite
Infinite t
Infinite**
Infinite**
Infinite

Zero

Zero t

Finite t

Zero "

Infinite * or Finite

Infinite f

Zero **

Finite **

Infinite

• When both Z, and Zj are finite and Z, = — 4Z;, the mid-series image impedance
is zero and the mid-shunt image impedance is infinite,
t This condition gives a cut-off frequency.
•* This condition results in infinite attenuation.

Types of Xon-Dissipative Series-Sliiint Sections Having Not More
Than One Transmission Band or More Than One A lien nation Band.
Since the series and shunt arms of a non-dissipative filter section may
each he composed of any combination of pure reactances, it is possible
to have an infinite number of types of filter sections. However, it
is seldom desirable to employ filters having more than one transmission
band or more than one attenuation band. Under these conditions,

60 liEl.L SYSTHM TECIIMCAL .lOlKX.IL

it is generally impractiralile t(i employ moic than four reactance ele-
ments in either of the arms of a section. Likewise, a total of six
reactance elements in liolli the series anil slnnit arms is the maximum
that can he economically employed.

T\|ies of two-terminal reactance meshes having not more than four
elements, are listed in Kii;. ."). In Fig. 6, the corresponding frequency-

rrowri nrein

— vistt/ — • It— ^ — >jifia/Hi — ■ — II — • o^ifli/-^ 1-^

12 3 i ^1

-c>- -<i- -n^ -^^--o- -"O

3b 6o 6b 7a 7b

-C^ -^ -CS-

-00-

&d
I-ig. 5 — Two-Teriniii.il KiMclaiice .Meshes Containing .\ot .More Than Four Klements

-CD

A

f/ <»

IT

1/ 1

r

5 6 7 6

Fig. 6— Rc.ictancc-Frcqucncy Characteristics, of the Meshes of Fig. 5, Shown in
Symljolic F"orni

reactance characteristics are represented. Reactance characteristics
N<)s. 1 and 2 of 1-ig. (> are reciprocal in nature, that is, their product
is a constant, independent of freciucncy. Reactance characteristics
Nos. 3 and 4 are similarK- relatetl if the frequencies of resonance and
anti-resonance coincide. Similar relations e.xist between character-
istics Nos. 5 and (», and between characteristics Nos. 7 and 8. Two
forms of reacl.incr mesh in Fig. ."> (Nos. .")a and .'jb) give the same

Mcrc.u. iXDt'CT.ixcii IX u:iri. iu.u.ks

reactaiuv i-liar.utt'iistii- (No. .") of Fijj. 11) and arc, tluTrforf, l)y projMT
design, oltrtriially o(iiiivaliMU. Cliararteristic No. <j of Fi^. (i also
corres[x>iuls to two roactaiuv inoshos of Fig. 5 (N'os. fia antl (il)) and
the latter may, therefore, be eonsidered e<iiii\alent. Likewise, re-
actance meshes 7a, 7b, 7c and 7d of Fig. 5 give characteristic No. 7
of Fig. f) and are therefore pi>tentially C(|ni\alenl; also reactance

00

/I

n

/— 1

CD

A" J

rr

n

JU

^.

n

\

A

/

V

/

y

\

V

n

—i

0

/

0

1

0

\iLJ

^ 0

\

0

\

0 f 00 0

00 0

z

CD 0

3

01 1—1 o'-^

0 f CD 0

5

00 0

7

(D 0
A

O-fCDO ODO 000 OOO OOO OOO OOO OO

' A '^ m * /uk ^ nn

mm nm

OfCDOCD 0 030 CO

OfCDO OOO COO 000 ODO COO 333

9 10 II 12

13 14

Fig. 7 — Propagation Constant (.Attenuation Constant and Phase Constant)
Characteristics, Shown in Symbolic Form

meshes .Nos. 8a, 8b, 8c and 8d of Fig. 5 are represented by reactance
characteristic No. 8 of Fig. G and, consequently, may also be designed
to be equivalent. The equivalence of the above reactance meshes
has been discussed by Zobel ' and will be subsequently treated at
length. It is to be understood that, for the sake of brevity, in what
follows, meshes Nos. 5, 6, 7 and 8 cover, respect i\'eK-, all forms of
the e(iui\alent meshes: .5a and .5b; Ga and Gb; 7a, 7b, 7c and 7d ; anrl

62

lU.LI. SYSILSt II.UIMC.IL JULKS.U.

8a, 8b, 8c and 8(1. L'sing these reactance comliinalions ' for the
series and shunt arms, there are only a relati\x'ly small number of
types of filter struct iirc-^. All of these types of filter structures arc

',-

nd^A.Ji±^^iNi

0 f 03 0 QO

1 2

0 OD

3

0 CO

0 CD 0
5

CD 0

0 00

6

'*^

0 f CD

9

10

iiJ ly/tj h:^

OD 0

0 00 0

12

I ^y

0 CD

C (E

15

+y\+/

0 CD

16

\A/ A^-K- 4.U-i \[\/ V+A A-v A""''

OfOOO mo QDO CDO 030 CDC CD

17 18 19 20 21 22 23

.M^i

-V /

_slJ

CD

2,,/ >

0 f CD
25

2G

0 00

27

-1^

26

II

ZtL

0 CD
29

+(\n-

cm

0 CD

30

31

0 CD-

32

0 f

33

CD

34

/' /* '1

'+V-»'
t^ V t I

0 CD

35

3G

V'

0 (D

37

r A"

00 0

36

h'+\'-*

CO

3^

i S

0 m
40

RESISTANCE

REACTANCE (POSITIVE (+) OR NEGATlVEH)

I-"iK. S -MulScrics and Micl-Sluint Imapc Impedance Characteristics, Shown in
Symliolic Form

li>ti'<l in Talili- II. .iiid .ire called low />(j,s.v, /n'lj/; fxiss, and hiiiid pass
filters (having only one transmission band) and baud elimination

' The grniral nuthcirl of ileriving the nttcniialion and phase characteristics of a
Mt'liiin from the rearlance-frr«|iienry characteristics of its scries ami shunt arms
in diM'Uuol by /olicl in Bililiography 13.

00

■hi J, 1

CDS —a
1

00

00

More Than

Six

Elements

c
H X ii

1 3

More Than ' More Than

Six Six

Elements Elements

1 s

r- X «)

B 2

H x«^

1 =

1^

^1

BQ

« 2

H X 1

1 S

1 =

H X u
1 "

■3 «

Si.

§:«

23 =

T

O

o

7
■»»■

1

Hi

9-21-39
9-38-25
10-21-40
10-39-25

a 2

fl 2

;= C

H X ji
1 ^

1

5

1

-!ca

t
7

-t

9-22-36
9-35-24
10-22-35
10-37-24

c „

H X u

0-7; c

1 S

i 2

H..x|

1 S

■*

3v

4-

1

7

00

1

4

1

00

4

1

1 1

00 :>

"5

■a

5

1

1

77

11

2
1

1

r5

1

1

1

1
>»>

00

3i

r-l

S

7

o^

■2 i

c ^
ME

— r3

11

"

7

1

T

J

1

il

il
Jl

il

-

(N

fO

■*

lO

>o

-

00

IV Hv .i.vnus

(A liF.I.I. SYSTEM 7 ECIIXIC.il. .lOCR.WIL

filters (having; l\v(» pass liaiuls ami onK' out' attenuation band). Their
attenuation constant and phase constant characteristics, with respect
to freqiiencN-, arc shown s\ niholically in Fig. 7. The mid-series and
mid-shiMit iniajje iniiK-Klance characteristics with respect to frequency
are shown in Ki>j. 8. In Table II, the figure at the head of each
column indicates the reactance mesh in Fig. 5 which is used for Zi
(scries impe<iance) and the figure at the left of each row indicates
the mesh in Fig. 5 which is used for Zj (shunt impedance). The
figures in the squares of the table denote, reading from left to right,
the propagation characteristics (attenuation and phase), the mid-
series image impcilance, and the mid-shinit image impedance, re-
spectively, as shown in Figs. 7 and S.

For example, the filter corresponfiing to the third column and to
the fourth row (3 — 4) has a series arm composed of an inductance
in series with a capacity as indicated by mesh 3 of Fig. 5, and has a
shunt arm compo.si'd of an inductance in parallel with a capacity,
as designated b>' mesh 4 of Fig. 5. The attenuation constant and
phase constant characteristics of this filter are shown symbolically
by diagram ."> f)f l-ig. 7, while the mid-series and mid-shunt image
impetlances are indicated, respecti\ely, by diagrams 13 and 14 of
Fig. 8. The s>nil)olic nature of the diagrams lies in the fact that
the abscissae of each diagram co\er the frequency range from zero
to infinit\-, and the ordinates of Figs. 7 and 8 cover the attenuation
constant and the impedances from zeio to infinity. For example,
the structure lited has an attenuation cijnstant characteristic (diagram
o of Fig. 7) com|K>sed of a transmission band lying between two at-
tenuation bands, the attenuation constant being infinite in one of
them at zero frequency, and in the other, at infinite frequency. The
phase constant of this structure is — »• radians in the lower of the two
attenuation bands, increases from —ir to +7r riulians in the trans-
mission band (passing through zero), and is -f ?r radians throughout
the up|)cr of the two attenu.ition bands. The mid-series image
imiKxIance (diagram 13 of Fig. 8) is a negative reactance in the lower
of the two transmission bands, decreasing from infinity, at zero fre-
(|uency, to zero at the lower cul-ofT frecjuencN-, is a imre resistance
throughout the transmission band, ami is a positi\e reactance, increas-
ing from zero to infinity, in the upper of the two attenuation bands.
The mid-shunt image imindance characteristic (diagram 14 of Fig. 8)
is reciprocal in nature, for this structure, to the mid-series image
impc<Iance characteristic. This ty|)c of filter also possesses, in the
general case, ;i double banti pass attenuation characteristic and cor-
res|X)nding phase and im|K-<lancc characteristics. A discussion of such

MViv.M. ixiHCT.ixcn ix ir.iir. rii.iiRs 65

chanirtiTistics is <>ut>i(lo tin- so>|h- of this |).i|)(t r\rn lltoiiuli rn.iiiy
i)f till" structuros listi-<l in Tahlc II will show, il c-oinpii-toiy aiuily/cd,
nnilti-l)aiul charaiterislirs. Where no specific charadorishcs are
listed in TaMe II, no low pass, hijjh pass, single i)an(l pass, or single
band elimination characteristics are ohtainaWe with a filter section
limited to six different reactance elements.

In Table II, a larjje number of the structures ha\e identically the
same types of attenuation constant and phase constant characteris-
tics. For example, six of the seven low pass filter sections have at-
tenuation constant and phase constant characteristic No. 2 of Fig. 7.
Likewise, six of the high pass structures have attenuation constant and
phase constant characteristic No. 4. Also, in Table 11, band pass
groups are to be found having respectively, the following propagation
characteristics common to each group: G, 7, 8, 9, 10, II and 12. Finally,
ten of the eleven band elimination structures listed ha\e propagation
constant characteristic No. 14.

Although six of the se\en low pass wa\e fillers ha\e ihc same at-
tenuation constant and phase constant characteristics, the various
image impetlancc characteristics differentiate the structures among
themselves. Similar differentiations exist in the high pass, band pass,
and band elimination groups of structures. In each of the four tyfjes
of filter sections however, all of those structures having the same series
reactance meshes (that is, having the same series configuration of
reactance elements) may be designed to have the same mid-series
image impedance characteristic and, similarly, all of those structures
within each type having the same shunt reactance meshes, or con-
figuration of elements, may be designed to have the same mid-shunt
image impedance characteristic.

In view of the fact that some of the structures listed in Table II
have the same attenuation and phase constants but have different
impedance characteristics, the question arises as to the relative virtues
of the latter. F'urthermore, since certain of the structures have
the same mifl-series or mid-shunt image impedances but have different
propagation characteristics, it is possible to join together such struc-
tures and obtain a composite structure which has no internal reflection
losses, that is, one whose total transfer constant is the siuii of the
various transfer c()nstants of the indi\'idual sections. In order to
minimize reflection and interaction losses in the transmission range,
it is generally desirable to use, at the terminals of the filler, sections
whose image impedances closely simulate those of the terminal im-
pedances to which the filter is connected. The choice presented by

66 Kl.l.l. Sysn:.\l II.CIIMC.II. JOi KX.iL

filter stniituns havinn ilifTeri-nt iinpitlance characteristics hut the
same propagation characteristic is, therefore, of aci\'antagc. In the
attenuation range this is als<j true wiure inipctlance conditions are
imposed at the terminals of the filter.

One class of structures which possess desirable image impedances
and whose characteristics are readily determined from simiilcr struc-
tures is the so-called derixed »;-t\pe.' The simplest forms of derived

2
-JWWV-

z,

mZ,

2

KiK. *) - Miil-Scrifs Kqiiiv.ilent w-Ty|M; i)f Section

Structures are shown in Kigs. '.t and 10. The structure of Fig. 9
has the same mid-series image impeti.ince as that shown in Fig. 2
and the value of this impedance is given b\- equation (6). The
structure of Fig. 10 has the siime mid-shunt image impedance as the ir
structure shown in I'ig. 4 and (he \alue of this impi-dance is gi\en by

111

TnZ,

l-m'

Hi

I-'in. m MldSluiiit K(|iiiv,ilt'nt m- Tyiic of Section

e<|u.iiion (7). On account (»f this identity of the respective mid-scrics
and the mid-slumt im.ige imintlances in the two cases, the structures
shown in Figs. 9 and 10 are calliil, respectively, the mid-series eqtiiva-
Init (Irrivnl »/-type and the mid-sliiinl equivalent derived 7H-type. The
7' and r structures «)f Figs. 2 ami 4 are called, respectively, the prolo-
lyprs n( the (leri\f<l wi-slructures of Figs. 9 an<l 10. In a series-
shunt filter com|)ose<i of sections of I he w-lype of l"ig. 9 or I'ig. 10,

Ml n.ll. IMHCI.IM I. I\ II. Ill I II. I IKS (.7

tlu- r.itio (Zi 'IZ-I., of the serii-s impcil.iiu r to four times llie shunt
itn|H-ti.iiirc is

(a).

"iw.)

I +(.-».')( J- )

(21)

From this expression, when Zi IZo of the prototype is 0 or —1, the
corres(>on(liiii; vahie of {Z\'AZ-i)„ for the derived w(-typc is also 0 or
— 1. lienee, the derixed l\pe has tlie same cut-olT fre(|ucn(ics and

24

o

u

CL 16

12

g 8

Z
u 4

♦=±0°-^

g

^

■;<^^

'^

//

x®'!^^

^'^y^ ^

r

4

/

-*=±I80°

W^^ — -"^=±165°

7

0.4

0.8

K =

1.2

_| Z,

1.6

2.0

4Z,

Fig. 11 — .\ttcnuation Constant (in Tf) of a Filter Sfction Kxprcssed in Ternisof the
Ratio of ItsSeries Impe<lance to Four Times Its Shunt Impetiancc (i.e., Z\l\Zi = Kj^

therefore the same transmission and attenuation regions as its proto-
type.

Impedance and Propa^al'wn Characlerislics of Dissipalivc Fillers.
It has lieen pointed out, in the rase of non-dissipative structures, that
the ratio Zi \7.-< is either a positive or a negative numeric. If there
is dissipation in the filter structure, that is, if the resistance associ-
ated witli tlie reactance elements cannot be neglected, then tiic ratio

68

BEI.L SYSTEM TECHNICAL JOURNAL

Zi/AZn will not, in general, be a numeric but a vector. However, the
general formula (8), still holds true with dissipation. For determining
the attenuation constant and phase constant of a dissipativc structure
it is convenient to use two formulae which may be derived from (8).
These formulae are

where

A =cosh ■(a- + .J(jj;_i).+4k;cos»|).
S = c(.s '( - A' + \/A'= + 2A: cos «+ 1),

(22)
(23)

'8- •-— j^asc Conmant of ,i Kilter S« lion lixiirisscd in Terms of the f<atio of Its
Scrio Impedance to Four Times Its Shunt Ini|)eiiance (i.e., 2,/4Z, S A'j z*.

MUTUAL IKinCTAXCIi IX llAfi: Ill.TI-.RS W

I'liiinnl.u- i'2'2) ,iiul ['2'.i) .in- t-xprf^cd in M,i|>ici> .iikI ciniil.ir r.iili.iiis,
ri's|Hrli\i'ly. They art- ri'|>ivsi-iit«.'<l in I'U niu\ in nuii.ins \>y f.iniilics
<»f fiirvTS siirli as art- shown in l-i^s. 1 1 and 12.

A i-omi-nii'Mt ratio wliich i-xpresst-s tlie dissipation in any rrartance
lUiinnl is the al)solutc r.itio, d, of its effective resistance to its re-
actance. Ill the case of a coil, d = R/Lw while in the case of a con-

di-nser d = RCui. The reciprocal ratio Q= y = -jr =-57^- has al.so l)een

widely used as a nieasure of dissipation in reactance elements. The
ratio (/ or Q will not, in general, Ix- constant over a wide fre(|iiency

z,

2

2

L,

2

0 '7T7TTP

2C,

2C,

L,
2

}'

—^ 0 jO 0

2

Fig. li — Typical Band Pass W'.ivc Kilter .Section (.Mid-Series Termination)

range. If the value is known at an iniixirtant frequency in the trans-
mission range, it may ordinarily be regarded to hold for the rest of
the transmission range. The effect of dissipation on the attenuation
constant is most important in the transmission band, where the at-
tenuation constant would Ix; zero if there were no dissipation. Its
effect is most pronounced in the neighborhood of the cut-off fre-
quencies where the transmission bands merge into attenuation bands.

In the attenuation bands, the general effect of dissipation is negli-
gible. It largely controls, however, the value of the attenuation
constant at those frequencies at which infinite attenuation would
occur if there were no dissipation. The effect of dissipation upon
the phase constant is most pronounced in the neighborhood of the
cut-off frequencies where resistance rounds off the atjriipt changes in
phase which would otherwise occur (see Fig. 12).

Characteristics of a Typical Filter. In order to illustrate specifically
the principles employed in filter design, consider as an example the
band pass structure 3 — 3 of Table II. This structure is illustrated
in Fig. 13. It will be assumed that the dissipation in the coils cannot
be neglected, but that the dissipation in the condensers is of negligible

70 Hr.l.l. SYSTEM TllCIISICAL JOL'RSAL

Ill.l^;nitlulc. If Ri and R- are the olTcclive rosislanri-s of tin- iiuiiictancc
iliiiunis Li aiul L-,, rcsiK-ctively, the series imix-ilance, Zi, of a series-
shunt recurrent structure CDniposed of sections of the type shown
in Fig. 13 is

Z, = /.,+,(./,.-^;.). (24)

The impedance of the siiunt arm is

Z, = R,+jLl,— \]. (25)

In substituting for /?i its vahie l.\wd and for R: its vahie L-mI, the
ratio Zi '4Zi becomes

1 -J'l - 7^r-r^

Assuming d to be zero, the ratio Z\ 4Zj is

Zi ^ L\{^LxCi-\)
AZt 4C,(u.'LjC,-l)'

(27)

Referring to Tal)le 11, the structure shown in Fig. 13 has two dis-
tinct attenuation and phase characteristics. These are, respectively,
characteristics Nos. 9 and 10 of I'ig. 7. These two sets of cliaracter-
istics arise from the fact that liie shunt arm may be resonant at a
frequency less than, or greater than, the resonant frequency of the
series arm. The two attenuation characteristics are inverse with
resf)ect to fret|uency. We shall, therefore, discuss only one of the two
cases, namely, that in which the shunt arm resonates at a frequency
greater than the resonant fre(|uency of the series arm (that is, LiC\
is greater than L^C;)- The fre<iuency at which the shunt arm is
resonant will be <lesignated as f,, due tf) the fact that in a non-dis-
sipative filter the attenuation constant is infinite at this point. In
other words,

(28)

It is evident that the fre<|iiency at which Z, is resonant is a cut-ofT
fre(|uency since Zi, and therefore Z| IZn, is zero at this point. An
insjx'ction of graphical curves '"drawn for Zi and 4Z2, under the above

'• For an illuMr.ition i)f llie conslriulion of siuli ciirvi-s sec Uibliography 12, Fig. 7,
also UililioKrapliy 13. Fik. i-

Miic.ii. /.v/Tc/'.f.vc/. i\ ir.iri iii iiks 71

(-(in< lit ions, will slmw ih.il llii> is ilit- \n\wr nl ilic Iwd ciil-olT lri'i|iii-iii-ii's
(fx). lli.U is

r,= ' . (29)

2jrv /.iC
Hs o<iiiatinn Zi AZ- In —I in t.-(|uali(>ii (27) thr iippiT (iil-nrf frc-
(liii'iu-y (/•) is found lt> lu'

■'' 27r\ C,t'2(L,+4Lj)"

(30)

For these exjilicit relations for /i. /■.. an(i/„, cfiuation (2(1) may be
rewritten

When d is zero this eciuatioii heeonies, for the iion-(lissipati\e case

4Z

From the precediii;j; formul.n' .uul trom tlu- lurxes shown in I'igs.
11 and 12, it is possible to read directly the attenuation constant and
the phase constant for the structure shown in Fig. 13, at any fre-
quency, provided the values of /i,/: and /x are known. The formulae
for the dissipative case are of use mainly throughout the transmission
bands and near the frequency /». Elsewhere, the formulae for
Zi'4Z-> for the non-dissipative structure may be employed without
undue error. The preceding formulae have been derived in a direct
manner, but may be obtained more simply by considering the structure
of Fig. 13 to be a derived form of the structure 3 — 2 in Table II.

In order to minimize reflection loss effects, it is, as a rule, desirable
to terminate a filter in an impedance ccjual to the image impedance
of the filter at the mid-frequency," (Jm) or at some other important
frequency. From equation (6) and the values of Zi and Zj, the mid-
series image impedance (Zu), at the mid-frequency in the non-dissipa-
tive case is

" Dcfine<i as the geometric mean of the two cut-ofT frequencies /i and ft; or /,

72 HIJ.L SiSriiM TECIIXIC.IL JOL KX.II.

Krimi lormulae ((5), (29), (30), and (33) the niiil-st-ries imago impedance
at aiiN' frc-<|iK'nc\' is

^ V/„ J J

An inspiTtion of fonnul.i {'A4) indicates that the mid-series image
impedance is symmetrical with respect to the niid-freciuency, /«.

In a similar way, the mid-shunt image impedance (Zo') at the mid-
fretjuency is

z'= iZjnn- ! ^' - (35)

" Vc,(g+4) Vr,(^+4)

and the mitl-shunt impedance, (Zi'), at any fre(|uency is

^,..z.._kl UlAiI^ (36)

-m'^HB'

It will lie noli'd, ihat if llif values of I he iiiiliukiiucs and resistances of
a filler are multiplied by any factor and if all the values of the capacities
are divided by the same factor, the transmission loss-frequency character-
istic is not changed'- (neither are the cut-off frequencies, nor the frequencies
of infinite attenuation) but the intake impedances are multiplied by this
factor.

From the preceding; formulae, exjilicit e.\|)ressi()ns may he derived
for the values of Li, i'l, Lj, and t\.. These expressions, which are
given by Zolx?!,' in a slightly diflferent form, are as follows:

"SiiKi- the y.iliic iif ihi- tr.insrer factor, «-«, is dependent simply u(K)n the ratio
X,/iX,, it is I'videni from ctiualiiin (111,) ihiit lite Iransmissum toss caused bv the inser-
tion of any nrtuork in a dnuit is drprndenl simt>ly upon impedance ratios. Con-
iH-<|iicntly, the alxjve thcori-ni is unite Kener.il and applies not only to filters hut to
any pauivr network.

Miu.it. /.v/'fcr./.vc /i i.\ win: viinns

As a numerical example of the determiiiatiou of the constants of a
filter section of the type uiuier consideration, assume that the lower
cut-ofT frequency, /i, is 20,000 cycles, and that the upper cut-off fre-
(luency,/3, is 2.5,000 cycles and that the fre(iuenc\' of infinite atlenu-
.ition,/», is 30,000 c>clcs. Assume, furthermore, that the value of
the mid-series image impedance, Z,,, at the mid-frec|ucncy is (500 ohms.
Then from formula (41), w = .742; hence from (37), Li = .0284 henrN-;
from (38), C, =.00224 X 10' farad; from (39) Lo = . 00.577 henry and
from (40) 6'; = .0048GX lO'* farad. Assuming d = .Ol, the value of
Zi AZ-i as given by formula (31) at/m (22,300 cycles) is found to he
.30.5 17(i°.4. Referring to formula (22), in which /v=.30.5 and <> =
170°. 4, or to the curves of Fig. 11, this value of Zi/AZ^ corresponds
approximately to .041 napiers or .30 TU. Similarly, from equation
(23), or from the curves of Fig. 12, this value of Zi 4Zo gives l.lo
radians, or 07°, for the phase constant. At zero frequency, the value
of Z\ AZz is, from equation (31), .542/0°, which corresponds to 1.3G
napiers or to 11.8 TU. Likewise, at infinite frequency, the value of
Zi 4Z2 is 1.23y'0°, which corresponds to an attenuation loss of 1.97
napiers or to 10.0 TU. From the curves of F"ig. 12, the phase constant
is zero both at zero and at infinite frequency.

Composite Wave Filters. It has previously been pointed out that
certain groups of the structures listed in Table II have the same mid-
series or mid-shunt image impedance characteristics but that the
various structures in such a group may have different attenuation
and phase constant characteristics.

If a filter is composed of any number of symmetrical or dissym-
metrical sections, so joined together that the image impedances at
the junction pwints of the sections are identical, the attenuation and
phase constant characteristics of the compxasite structure so formed,
are equal to the sum of the respective characteristics of the individual
sections. Furthermore, the image impedances of the composite filter
w ill be determined by the image imjjedances of the accessible ends of
the terminating sections. The desirability of forming such composite
filters arises from the fact that a better disposition of attenuation
and phase can be obtained by employing, in one composite structure,
a number of different types of the characteristics shown in Pig. 7.

74

/</■;/./. srsriLM ir.ciix ic.il joikxal

The dissNinmctriial networks oidinariK I'lniiloNt'd in coni]>()site
structures art- usually L t\ i>c networks each of which may be regarded
as one-half the corresponding symmetrical 7" or tt network. General-
ized forms of such networks are shown in Figs. 14A, B, and C. By
joining two of these half-sections, such as are shown in Figs. 14B

Kig. 14 — (JcniTalizcd Series-Shunt Structure Dividtvl Into Siiiccssive Half-Sections
(i,-TyiK-)

and C, we may form the full T section shown in Fig. 2. Similarly,
by joining the two half-sections illiistrateil in Figs. 14A and B, the
full w section of l-"ig. 4 results. The transfer constant, 0i,, of a half-
section, such as is shown in I'igs. 14A, B, or C, is one-half the transfer
constant of the corresponding full section, that is.

o 6 • u. K'

(42)

Hence, the attenuation constant and phase constant of a half-section
are, respectively, one-half the attenuation constant and phase constant
of a full section. An important relationshi|i between the half-section
and the full section, which makes it conxenient to use half-sections
in composite wave filter structures, is that the image impedances,
Z/, and Z;,, of any half-section are equal respectively to the mid-
series and the mid-shunt image impedances of the corresponding
full sections.

A typical example of the method of forming a comjiosite low pass
wave filter is gi\en in Fig. 1'), where three half-sections of different
types and one full section are combined into a composite lilter. The
designations Ih-Iow the diagrams in Fig. 15A refer to the number of
full sections and to the ratio/, /(. In a practical filter, the various
shunt coiulensersand series coils are combined as illustrated in Fig. l.")B.

The com|Hisite nature of the attenuation characteristic of the lilter
of l"ig. 15B is illustrated in I'ig. Ill, on a non-dissijiatixe basis. In

Mvrv.-ii. iMHCTAXcn i\ ii.iii: iii.iik^

^hIV

nIV

L,

2.. C,=pZ,, Zxp^C^CppZ,, ?,3=pC, Z,, Z,. j^Z.,

X

y(llO) 1(1.50) ^(00) 1(110)

liK. I.S A

L. + L, 3

— nrp r o

42-rO

XT

Fig. 15 B

Typical (Non-Dissipative) Composite Low Pass Wave Kilter and Its
Component Sections and Half-Sections

Fig. 16 — Attenuation Characteristic of the Composite Low Pass Wave Filter of
Fig. 15

76 nr.i.i. SrSTLM it.ciisical jolrxal

Fig. 1.')1H, tlir imagi- imi)r<laiui-, Z/,. at tlif 1 — 2 terminals has rliar-
acterisiic No. 2 of V\^. X, wiiilo llie image imix^dancc, Z/,, at the
3 — 4 terminals lias characlerisiie No. 4 of Fig. 8.

Electrically luiiiivalenl Xelworks. Reference lias been made to
the fact that any passive tiehcork having one pair of input terminals
and one pair of output terminals may be adequately represented, at any
frequency, by an equivalent T or ir network. In general, this represen-
tation is a mathematical one antl the arms of the T or ;r network
cannot be represented, at all fre(|uencies, by physically realizable
impedances.

Furthermore, any concealed network, containing no impressed electro-
motive forces, and having N accessible terminals is always capable of
mathematical representation, at a single frequency, by a network having
not more than N (A'— l)/2 impedances, which impedances are determin-
able from the voltage and current conditions at the accessible terminals.
For networks having three or more terminals, this arbitrary mesh of
impedances may possess a number of variant configurations. It is
also true that the equivalence of the arbitrary mesh to the concealed
network holds, at any single frequency, for any and all sets of e.\-
ternal or terminal conditions, and that the magnitudes of the imped-
ances of the arbitrary mesh are determinable, at will, on the assump-
tion of the most convenient set of terminal conditions for each in-
dividual case. Familiar instances are the impedance equations
derivable under various short-circuit and open-circuit conditions.

In specific cases, which arc of particular interest, one network may
be shown to be capable of representation, as far as external circuit con-
ditions are concerned, by another network which is physically realizable,
and the latter may be substituted for the former, indiscriminately, in any
circuit without consequent alteration, at any frequency, in the circuit
conditions external to the interchanged networks.

F«iuivalent meshes having two accessible terminals and employ-
ing respectively, three or four impedances in each mesh have been
discussed by O. ]. Zobel." In filter design, two-terminal meshes are
of importance only in those cases where the iinjHxlances arc essentialK'
reactances. Figs. 17A, B, C and I) illustrate the physical configura-
tions which reactance meshes emplojing not more than four elements
may t.ike. We are not generalK- interested in meshes ha\ ing more
than four olenu-nts for practical reasons which have previously been
discussed. Wheneicr any of the reactance meshes shown in Fig. 17
occur, we may, with proper design, substitute for it an equivalent mesh
"Sec .'\|>|M-nilix III <>( Hil>liu)(ru|>liy U.

Mcrc.ii. i.\i>(\ i.i.\U: i.\ if.tn: iiiiiks

77

of the associated type or types. RigDrmis oiiuivali'iu-i' exists, ei<en with
dissipation, wlii-n the ratio »)f resistance to reactance, (</), is the
s;inie for all coils and the ratio of resistance to reactance id') is the
siime for all condensers.

L, L. C

c, c

L, C,

B)o-J KW^ o-\ — o

(c)

(o).,^'iQ, -^3 hk3° ^SJ^

Kig. t" — Groups of Eciuivalcnt Two-Terminal Reactance Meshes

The relations wiiich the e(|ui\alent meshes of Fig. 17 must observe
are as follows :

17A

17B

L.=

La+Lb

La+Lb

17C

La = ^{Li+L,), Ci =--%—,. Lb = L, + L,.
L . = ^(L.i + Lb) = /.„ ( 1 + -Jt" ) '

. Lt = LA+LB = Ly = LR + Ls,

(43)
(44)
(45)
(46)

(47)
(48)

Ci =

BELL SYSTESt TECtlMC.IL JOf R.X.I L
Ca CI- (LkCr-LsCsY-

(l+^y Cr+C„- (Lr+LsV- (Cr + CsY

(49)

17C

L,=Z,:, Cr = C, + C-., C,r= ^'(C + G). (53)

170

_a:+\/jc«-4L|c.ga-

■* 2L\L\

where A' = (L,C', + /.sC', + L2("o)=-4L,f,/,..ro. (54)

^ CsCi . LxC,+L,C^+LtCi-L.CR . , .

^''^clirc,'^'-- cl^:rc-R ,Lr=u-Ls, (55)

C. =-^(C-.. + 0,) = f.. ( 1 + ;"')■■■ = ^^^^^y/^+C.)(L;.+L5)' (5g^

L\ = c;, + (■„ = C'l = C'« + t's, (57)

, ^ ^t ^ Af (LkCr-LsCsY .

^' fl + ^' ■''•• + Air {CR + CsYiLR+LsY ^ '

T -I _ LyJ^v _ LrLs ,

--.(-^^)^.-=^%.

(61)

r,=C=. Ly = L, + L:. L„=^p{L, + L,). (62)

, ^ a: + \/A= — J^iT-jCVA

2/„(V
wlurc A' = (/.,r, + A,f, + A5C2)=-4/.,C,L2C,, (63)

'■" ~ L, -L^ ' lTTX:, ,(.R = C.-Cs. (64)

Mrrc.ii. ixnii. r.iw I: i\ ir.iii iii iih\ 7<>

For t'xampli', tin.- two iiu-slirs in I'Il;. 17. \ will l)c i-cjiiiv .liciil if
Cx =.Ot)'.t inf. C's =.001 ml. /., =.001 li.

(•„ = .0(MK) mf. (■.i=.00()l mf. A, =.10()li.

.111(1 iIk- two iiu-shrs ill l-'ii;. I7M will lii' r(|iii\aU'iit if

/,, = .()()•_' h. r, = .02.') mf. /,,. = .OOS h.

/-.i = .01()li. C'.,=.001mf. /wi = .01()ii.

.\ls(). the ft)ur nu'shes of Fig. 17C will he e(|iii\alciU if

Lk = 001 h. Z..S = .002 h. Ck = .001 mf. C.s = .0(12 „if.

/,, = .0(H) h. /... = .003 h. Ci = .000:«3 mf. C',. = .001)tiC.7 mf.

/,, = .0011i. /./i=.002 1i. Ci = .003 inf. CB=.l)()()(i(i7 mf.

Lv = .003 h. Lii = .000LU)7 h. Cy = .001 mf. rii= .002 mf.

anil thf fmir meshes i)f Fig. 171) will he eciiiixaieiu if
Lr = .001 h. Ls = .001 h. Ck = .001 mf. t'.s = .002 mf .

L, = .0000555 h. U = .0005 h. Ci = .024 mf. G = 003 mf.

La = .0045 h. Lb = .0005 h. Ci = .000333 mf . Cb = .0()2f)7 mf .

Ai=.000555h. Lir=005h. C"i=.n03mf. 0= .00024 mf.

It is then evident that the following reactance meshes of Fig. 5
may he designed to he equivalent: 5a and oh; (ja and (ih; 7a, 7b, 7c,
and 7d; and 8a, Sh. 8c, and 8d. Hence, the following tiller sections

o VWW-

-AW^ o

-JWWV

Zc

Fig. 18 — Equivalent T and ir r,tncrallzffl Networks

referred to in Table II have, for the same impedance and propagation
characteristics, a number of variant forms of ph\-sical configuration.
4-6. 6-2, 3-.'), 6-4, 2-6, 5-3, 4-5, 1-5, 3-6, 5-4, 5- 1,4-8,
5-5, 6-6, 7-3, 6-3, 3-7, 4-7, 8-4 and 8-3.

Of the equivalent me.shes having three accessible terminals the
most common are the familiar T and tt networks. The general rela-
tionships which must be obser\-ed for the equiwilence of 7" or jr net-

80

BELL SYSTEM TECIIMC.IL JOURNAL

works are due to Kennelly " and fur their generalized form, as illus-
trated in Fig. 18, arc as follows:

Za = ^^

Za'Zb

Za'+Zb' + Zc"
ZaZc

ZB = yr-,

Zb'Zc

Za'+Zb'+Zc

y Zc=.

Za 'Zc

-n (65)

/:^'=Z,+Zc+^,ZB'=Z.i+ZB+'?^,Z'c = ZB+Zc+^^f^. (66)

ZA'^-Z^^Zd
ZbZc
Za

We shall discuss here only two of the principal reactance meshes of
the T and ir form, namch', those employing solely inductances and

La Le Lb'

-o o

-o o

Fij;. !*> — Ktiuivalent rand t Inductance Networks and Equivalent Tand ir Capacity
Networks

solely capacities. It is to he understood that where\er an intluctance
or a capacity mesh of an\- of the following types occurs, its variant
network may be subslitutwl for it without change in the electrical
characteristics of the circuit excluding those conditions within the
mesh or its variant. Fig. 19 illustrates equivalent T and it networks
of inductance and capacity." The formulae relaling ihc iiidiictance
and capacity meshes of Fig. 19 are as follows:

La'Lb' t Lb'Lc r _ La'Lc

La =

La'+Lb'+U"

Lb =

La' + Lh' + U"

Lc =

La'+Lb'+Lc

-,- (67)

" Kennelly, A. K., "The lu|iiivalence of TrianRJes and Tliree-I'oinlc<l Stars in
(cindiictinK .Networks," ElfftrUal World mid Engineer, New York, Vol. XXXIV,
No. \1, |>|i. 41.i 41-J, S-|>t. 1(1, IX'W. Also, ".Xpiilication of Hyperbolic Functions to
Elitlrical KngineeriiiK" (I'M 1 1 (.\p|>endix K).

" These meshes arc rJKorously couivalent, even when resistance is present if the
ratio d i» the same for all of the inductances and if the ratio d' is the same for all of
the ca|>acitiea.

MCir.ll. IXDlCT.IXi. !■: IX If.ll I: III. II. H^

C,iCc ,. , C\Cr /. » C'flCc

C.t =7T

nnr>— »-^Tr>

X

AND

Cn' •

---^r

()<)}

Cc = C.i +6c +-,-,. (70)

:.i::

-^T^^^^^di^^-"^- -H

AND

AND

h--

Fig. 20 — Typical Examples of Equivalent Filters Involving the Interchange of
Three- Terminal Networks of Inductances or of Capacities

A few examples of the variant filter strurturcs which may arise,
flue to the existence of equivalent three terminal meshes f)f capacity

82

liLl.L SYSTEM lECllSlCAL JOURNAL

and inductanci', are illustrated in Fig. 20, in which F"igs. 20A, B, and
C represent either individual sections or portions of composite filters
and Fig. 2()D represents a coini)osito filter. When equivalent re-
actance meshes occur entirely within a filter or within a section of a
filter, the filter or the section will have the same cut-off frequencies
and frequencies of infinite attenuation and the same attenuation,
phase, and image impedance characteristics, whiclu'\er cqui\alent

Fig. 21 — Generalized Forms of Kquiwili-iU .Sorics-Sliunt, HridKcd-r, and'Lattice
Type Filter Structures

form of mesh is substituted for an existing mesh. When cqtilvalent
meshes are interchange<l in either recurrent or composite filters the
substitution is generally made after the scrics-shunt structure is
designed an<l after it has been found that the substitution will effect
economies. The three terminal meshes referred to occur, in general,
in imbalanced filler structures. F'or balanced filter circuits, corre-
s|Min(ling meshes will be found for each t)f the efiuivalent networks by
the process of di\iiling e(|ually the series imi>edance between the two
series lines of the filter.

While the discussion in tlii> jj.iper is based prin(ii).ill\- on the series-
shunt structure there are two other imjjortant t\pcs of structures
which will be mentionitl. These are the so-called lattice'' type strut-

Mvnwi. i.\i>( i i.i.w I i.\ ii.nT. vii.rr.Rs w

tiiic. 111(1 thcftri</i;«/-7" t>pcstrui-ture. Typiciil series-shunt, liridned-?",
and lattice type structures are illustrated in I'Ir. '21A, B and C",
res(H>ctively. Tiie three circuits shown are electrically eciuivalent,
except for balance helwei-n the series arms, if the following relations
hold:

Z..i = (l+/^.)/.. /.H = {l + -2K)Z,, Zc=Z,, (71)

Z.' = Z,. Z,' = (i+A-)Z, + Z:. (72)

In the previous discussion of ecjuivaleiit networks no reference has
been made to networks containing mutual inductance, many of w'hich
are of particular interest and importance. These will lie now discussed
in detail.

I'.XKr II

W.WE Filters Using Mutual Inductanxe

Before considering the cc|uivalent meshes which may be formed by
the use of mutual inductance between pairs of coils, and the types of
wave filters which may be obtained by the use of these equi\alent
meshes, it will be necessary to define certain general terms.

The self impedance between any two terminals of an electrical net-
work is the vector ratio of an applied e.m.f. to the resultant current
entering the network when all other accessible terminals arc free from
external connections.

The mutual impedance of any network, having one pair of input
terminals and one pair of output terminals, is the vector ratio of the
e.m.f. produced at the output terminals of the network, on open cir-
cuit, to the current flowing into the network at the input terminals.
Since mutual impedance is a vector ratio, it may have either of two
signs, depending on the assumed directions of the input current and
the output voltage. The sign of the mutual impedance is, in general,
identified by its effect in increasing or decreasing the vector impedance
of the meshes in which it exists. It is usually convenient, in this
case, to consider either a simple series or a simple parallel mesh of
two self impedances between which the mutual impedance acts. For
the purpose of determining the sign of the mutual impedance, we shall
confine our discussion to a sinifile series combination. Consequently,
the mutual impedance will be calletl either series aiding or series
opposing.

When a mutual impedance, Z,\t, acts between two self impedances
Zi and Z2, (Fig. 22) connected in scries in such a way as to increase
veclorially the impedance of the combination, it is called a series aiding

84

BEl.I. SYSTFM Tf.CHKlCAL JOCKX.IL

niiiliial impedance. Similari\-, wlit-n a mutual impedance acts in such
a way as to decrease vcctorially the impedance of such a combination,

Fig. 22 — Miitii.il linpidaiue Acting Between Two Si'lf Impedances Connectei
in Scries

it is lallcd a series opf>osiii'^ iiiiiliiul iniprilniue. For i-xampk-, if the
total impedance. Z, of the combination shown in Fij;. 22 is

y y {IZi + IZm) + (IZ, + IZ.X,) y ,y ,.^y „„.

/C — J = J =Zi+z-..+.^z.\/ (,/■■»)

the mutual impedance is scries aiding. On (he oilur hand, if the total
inipedaiicc. /. nl the combination is

7_l' (IZ,+IZm)+(IZ,+ IZm) y ,y _ ,_,,

the mutual impedance is series opposing.

'J'ransfonner Represenlation. If, in Fig. 22. Zi represents the self
impedance of one winding of a transformer and Z- tiie self iin|)edaiice

I o nmr^

-hfTin-

-o 3

l-'ig. 2.?— 7' .Network Coiilaining Two Self Inipediinces.'H.iviiiK Miilu.il Inip.d.mr
Hel ween Tliein

of its other winding, the series impedance of the two windings (between
terminals 1 and W in Fig. 23), as given i)y equations {l'.^) and (74), will
rletermine whether the mtilual imped, nice, Z.i/, is series .lidiiig or
M-ries opposing.

The mutual impedaiKe between the two windings ma\ be repre-
sented by an equivalent network of self imjiedances connected

Mr 1 1. II. iMHi i.i.w i: i.\ n.iri. iii.ii.ks m

.i> shown ill I'i.n. -M. llu- loiirtci iiiiii.il mlwnik illii^tr.ilril In
Kin- "-J may lia\r various conli^iirations. I'lu' r(|iii\ alcnl /' lorni is
slutwii in Fii;. "J"). In \ irw of thi- i><iui\al(niv illnslraicil in I'in. 12'),

EQUIVALENT
NETWORK

Kijj. 24 — K<)iiiv.ilcin Ni-twork Ki-prt'Sfiitation of the Striuturc Shown In KIg. 23

the two-winding transformer of Fii^. 2;j may itself l)e completely repre-
sented by a sinijle 7' network as inilieated in Fig. 2(). The theory of
the e(iui\aleiu T network representation of a transformer has been

Fig. 25 —T N'ftwork Representation of the Slriictiire of Fiy. 24

discussed l)y G. A. Campbell,' W. L. Casper "^ and others. In general,
the self and mutual impedances of a transformer will be complex
(luaiitities. The arms of its equivalent 7" network will contain resist-

-npm-

;±Zm

2 o

Fig. 2b -T Network of Self Impel

ICiiuivalent to the Si nut lire of Fig. 2.?

ance and inductance components which may be either positive or
negative. However, in the case of a transformer having no dissipa-
tion, (i.e., no (l-c. resistance, no v(\<\y current and no hysteresis

86 BELL SYSTEM JECUSICAL JOURNAL

losses) the arms of its equivalent T network arc composed simply
of positi\'e or negative inductances. Of the three inductances in-
volved, at least two of them must he positive while the third may be
either positive or negative.

From Fig. 25, it is evident thai two windings or coils, together
with their mutual impedance, may be represented by an ecjuivalent
network which aftords a transfer of energy from one winding to the
other. This ecjuivalent network may, with limitations, contain
positive or negative inductances.

While the two-winding transformer of Fig. 23 has been represented
by an equivalent 7" network in Fig. 2ti, the e(|uivalent network may
alternatively be (jf v form (Fig. 27) instead of T form, thnuigli the

Z Z -Z '

2^2,-Zj^ <JZ.Z,-Z.

Zz+Zm i i 2,+Z,

2 O-

Fig. 27 — It Network of Stlf Impedances Equivalent to the Structure of Kig. 23

general relationships for T' or ir networks previously stated. When
no dissipation exists in the transformer, either eciuivalent network
will have at least two positive inductances while the third inductance
may be either positive or negative.

From the principles previously outlined in Part I, for the ec[uivalence
of certain electrical meshes and for their substitution for one another
in any circuit, it is ol)vious that when two coils, with mutual im-
pcfiance between them, exist in a circuit, in the manner shown in
Fig. 23, either of the meshes shown in Fig. 20 or 27 may be substituted
for them or vice versa. The representation of the mutual impedance,
Zii, i)y an e(iuivalent network (l"ig. 25) makes it possible to represent
the transformer of I'ig. 23 by a T or jt network containing only self
impitlances. This afTords a great simplification in the analysis of
filter circuits containing pairs of coils having mutual impedance
between them in that it permits such circuits to be reduced to an
equivalent series-shunt (or lattice or bridged-?') type structure.
Consequently, the methods of design which have been built up for
the series-shunt and kindred tyi)e structures may be directly applied
to the solution of circuits com. lining such p.tirs of coils.

MUTUAL INlKCr.lSCI-. IX ir./l/; lll.n.RS

K7

I'uv-'I'frmiual Equivalent Meilies. A list of r(nii\.ilfni two icrmiii.il
riMitance im-shrs, tliic lo Zolu-I, has hvvn n'wvn in l"\n. 17. All of tlic
tiuslics in I-i^s- l~ii, C ami H CDiitain two indurtaiicc elements.
Mutual imiurtance may exist between any two inductive elements
without chanvjini; fundamentally the nature of the reactance meshes.
This means that when mutual inductance exists hetween two coils in

(B)

L, C,

(c) (D)

Fig. 28— Equivalent Two-Terminal Reactance Networks, Only One of Which
Contains Mutual Inductance

any of these meshes, the mesh may he designed to be electrically
equivalent to, and consequently can be substituted for, a correspond-
ing mesh of the same type having no mutual inductance.

For example, consider the mesh shown in Fig. 28A which is poten-
tially equivalent to the first reactance mesh of Fig. 17C and, conse-
quently, to the other three reactance meshes of the same figure.
The inductance elements L/ and Lj', together with the mutual in-
ductance M acting between them, may be represented by an equiva-
lent T network, as previously stated. The reactance mesh formed
by Li', Li, and M, together with its equivalent T and r forms, is
shown in Fig. 29. By means of the relations given in Figs. 29A and
B, it is possible to derive, from the structure of Fig. 28A, the equiva-
lent structure shown in Fig. 2SB. Likewise, from formulae (4.')) and
(46) for the equivalence of the two structures of Fig. 17B, the mesh of
Fig. 28C can be obtained from that of Fig. 28B. Furthermore, if the
two inductances shown in series in Fig. 28C are merged, it is again
possible, by means of the conversion formulae for the two meshes of

88 BF.LL SiSTEM TECIIMC.IL JOlKX.iL

l"ig. 17H, u> (letiTiniiR- ilif fonsi.mis of ilic iiii'sh sliowii in Fig. 28D
fruiii the known \alufs of the constants of the structure of Fig. 28C.
The relations which must exist if the structure of Fig. 28D is to be
equivalent to the structure shown in Fig. 28A, or vice versa, are given
by the following relations

Li'iLi'Li'-M-)

t\ = C,',Lt

(L2'±M)-
U±M\-

.=z./. c-,=cv(^=;;^^)

(75)
(76)

rile upper and lower of the altiTnati\e signs, in the preceding equa-
tions, correspond respecti\ely to series aiding and opposing connec-
tions. The e(|ui\ alence of these four-elenieni meshes makes it possible

L",L',-M'

(A) (B) (C)

Fig. 29 — E(|uivalfnt Thrcc-TtTiiiiTi.il Iinlint.iiKL- Networks

L,

L'.

" C.

LrrHH

Kig. 30— Kqiiiv.ili-nt Two- Terminal Reactance Networks
(onlains Mutual Inductance

Onh' One of Which

to derive at once, the relalion> which must exist between certain
(f|uivalent three-element meshes involving mutual inductance. For
e.x.imple, if the capacity Cj' of Fig. 28A is zero, tiu- nush reduces to
the three-element nush of Fig. liOA and the fornnilae given above
are then ap|)lical)Ie for the e(|uivalence of the structures of Figs.
30A and B.

In the s;imc way that the me&hes illustrated in Fig. 28 were shown
to Ik; iMJtentially e<|uivalent to each other, it is |)ossible to i)rove that

Min.n. i.\i>(CT.i\\ii i.\ ic./i / 1 1 1. 1 IKS y)

tlu' mi'shfs ol \-"\^. 'A\ .in- puiciiii.ilK ('(iiiiv .ilciii . Tin- tMiuisalciict'
(if thi- nH'sh slmwn in l-i^. MH in thai «>! lij; 'M\ is salistii-d l)y llie
relations j;i\iMi in l-i^s. 21tA and B. Tlu" u(|ui\ali-ncf i>f llie nicsh
of Fi^. Hie lo thai of I'i^. ;{1H is noNi-rm-il hy tho i'(iiialions (.")() tn (il)
for thi- i-<|iii\aU-nic i>f tlio first and last structiiros of l-'i^. 171). liii-

C,

^L. C.

{^)

ronrrs

c^^nmn-jmn-IU

HH

L,

r^'^h

Unrrwj|J

IF

(D)

Fig. 31 — Equivalent Two-Terminal Reactance Networks, Only One of Which
Contains Mutual Inductance

ally, the cciuixalence of the mesh of Fit;. 311) to that of Fig. 3IC is
controlled li\' the relations for the e(iiii\alenre of the first two struetiires
of Fig. 17D.

The formulae relating the constants of the structure shown in Fig.
31 D to the corresponding constants of the structure shown in F"ig.
31 A are as follows:

in which —

i + CV

('7)

md

L,=

ICa{La±M)±MCbY

ICa(La±M)±MCbV

(Ca + Cb)'La

u=

LaLb-M^

La •

(78)

(79)

The upper and lower of the alternative signs, in the preceding
equations correspond, respectively, to series aiding and opposing
cf)nnections.

90

BELL SYSTEM lECIIMC.lL JOiRXAL

The c(|uivalciKe of these foiir-lerminal meshes makes it possible
to derive the relations which must exist for corresponding ecjuivalent
three-element mesiies, with and without mutual inductance. For
example, if in I'ig. 31A, the capacity Ci is of infinite value, the mesh
reduces to that shown in Kig. 32A and the formulae given above are
applicable for the e(iui\alence of the meshes of Figs. 32A and B.

The remaining meshes of Figs. 17C and U have similar potential
equivalence to meshes of the same fundamental type but ha\ing mutual
inductance between the respective pairs of coils.

Three-Terminal Equivalent Meshes. Three terminal meshes con-
taining mutual inductance will now be discussed. It has been shown

l'.

(B)

Kig. 32 — Kquivaleiit Two-Terminal Reactance Networks, Only One of Which
Contains Mutual Inductance

that two coils, with nintii.ii inductance between them (I'ig. 2nA), are
ecjuivalent to certain 7' and tt structures containing only tangible
inductances (Figs. 2'.(B and C). Referring to Fig. 2'.)B, it is seen that
two coils, with series opposing mutual inductance between them
(corresponding to the upper alternative signs in Fig. 29B), are etjuiva-
lent to a 7" network ha\ing three positive inductance arms, provided
the mutual inductance .1/ is less than Li' and L;'. The values of
these arms are respecti\ely, Li' — M, Lt' — M, and M. If .1/ is larger
than Li', one arm of the ec|ui\alent T network is a negative inductance
while the other two arms are positive inductances. Similarly, if M
is larger than L/, a different arm of the T network will be a negative
inductance while the two remaining arms will be positive inductances.
It is [)hysically impossible for the \alue of ^1/ to be greater than both
Li' and Li'. Hence, it is impossible for more than one arm of the 7"
network, shown in Fig. 2*>tB, to be a negati\e inductance.

When two coils ha\e series aiding mutual inductance between them
(the lower of the alternative signs in Fig. 2'.tB) they are equivalent
to a 7" network in which two of the arms consist of positi\e inductances
viz., Li'+M and 1.2+ M, while the third arm consists of a negative
inductance of the value — Af.

MUTUAL INDfCT.IXCr. IX ll.lll- FILTERS <J1

\\'lii-iu-\i'r, ill ail f(iiii\.ili'iit /' iirlwork, our of llic .inns is a |)ositivc
(t>r lU'jjativc) ituliutami.'. a lorrospoiulinn arm of the tt network will
also In- a positi%r (or lu-iiativi') iiidurlatuo. C'onsi-ciuently, as in the
rase of the e(iiii\alent 7" network, the eciiiivalent ir network shown
in Fii;. 21K' nuu- consist of three positive inductances or two posi-
tive iiuluctances anil one iiei;ati\e iiKliictaiice, (Ii'peiuliiig upon tlie
si^n anil inagniluile of M.

It is interesting to note that, in I'ig. 2913, point 1) is in reality a con-
cealed terminal, i.e., it cannot be regarded as physically accessible.
There are, therefore, oiil\- three accessible terniiiials to the e(|iii\a!ent

(A) (B)

Fig. ii — Equivalent 7" Networks of Inductance

7' network. In the w network shown in Fig. 29C there is no such
concealed point. There are, however, as in the preceding case, three
accessible terminals A, B and C.

When the mutual inductance, M, is equal to either one of the self
iniluctanccs, Li' (or L;')i and the windings are connected in series
opposing, the equivalent Tand ir networks of the transformer coalesce
to the same L type network. For example, if Li' = M in Fig. 29A
both the T and the ir networks of Figs. 29B and C resolve into an L
network whose vertical arm has the value M and whose horizontal
arm is Lz' — M.

A problem of practical importance is the ec|uivalence of T and tt
meshes, containing three coils with mutual inductance betw'een all
of the elements, to similar 7" and jt meshes containing no mutual
inductance. The T networks of Fig. 33 are potentially eciuivalent.
The formulae governing their equivalence are

L4=L, + il/,2-|-.U,3-.l/=3, (80)

LB=L2+il/.s-.V,3 + il/23. (81)

Z,C=Z.3-M,2-|-3/.3 + ^l/23. (82)

In the above formulae, the signs correspond to the case of a series
aiding mutual inductance between all the pairs of coils. When the

92

BILI.L SYSTliM TI.CIISICAL JOLRX.IL

mutual inductaiu-f la-lwccii .iin two coils changes sign, the signs ae-
comjianying that mutual inductance in the ahoxe formulae are
reverse! 1.

M'„ m'„

(A) (B)

Fig. 34 — Kciulvalent t Networks of Inductance

Similarly, the ir networks of Fig. 34 are also poteniialK ci|ui\.iUni
The formulae governing their equivalence are

A = f .

^"= z; •

I^C = —

in w liich —

i.
La" Lb"

La" + Lb"+Lc

Lb"Lc"
La" + Lb"+Lc

La"Lc"

r,=FA/(2.

r,=F-U23,

La" + Lb" + Lc

r,^M[s,

\vh

La" = Li'±M{2±M\3,

Lb" = Li ± M12 ± M23,
Lc"=L,'±M'y.,±M:,,.

(83)
(84)
(85)

(86)
(87)
(88)

(89)
(90)
(91)

As in the preceding case, the upper of the two signs occurs with the
series aiding mutual inductance between all the pairs of coils. \\ hen
the mutual inductance between any two coils changes sign, the signs
acct)mpan\ing thai nnitual inductance in the above formulae are
re verse* I.

At least two of the three inductances (in Fig. 33M or in I'ig. 34B)
will alw.iNs be positive in sign while the third inductance may be

MriC.U. IXlHCT.IXCIi IX if.iir. III.II.RS o.t

riilier (H>siti\o or lu-^ative. ('()iisi'(|iu'n(l\', llirro coils haviiij; nuitiial
iruluctanci' iHMwt't'ii i-acli of tlu-m and ha\'inK only three arcessihie
terminals offer no ^'■•■'•i'*''' l)<)ssil)ililies than rio two coils lia\in>j nnitiial
itidiictance Iwlvveen them and havinjj three terminals. In liolh
cases the structure is etiiiivalent to a 7'or w mesh composed of three self

Fig. 35 — Equivalent Filter Sections, With .mil Without Mutual Iiulurtanrc

inductances, at least two of which must be positive. With specific
relations between the various self anfl mutual inductances, it is possi-
ble for the three coils with mutual inductance between each of them
to be equivalent (as in the case of two coils with mutual inductance)
simply to an L network composed of two positive self inductances.
Since either two or three coils with mutual inductance between
them are, in general, equivalent, at all frequencies, to a T or v net-

94

BELL SYSTEM TECIIXtCAL JOURNAL

work composeti of three s(.-lf incluctances, it is possible to substitute
the one t>[K' of mesh for tlie other in any kind of a circuit williout
affecting the currents or voltages external to tlie meshes involved.
This substitution is always physically possible provided none of the
arms of the equivalent 7" or tt networks is a negative inductance.

The structures shown in Fig. 35 are illustrative of the power of
equivalent networks as tools for the s<jlution of filter structures con-
taining mutual inductance. The equivalence of the structure shown
in Fig. 3.5B to that of Fig. \l'i.\ is evident from the equivalence of two
coils (Fig. 29) with mutual inductance (.l/ij) between them to three
inductances, L,\. Lit and Lc without iiiuttial inductance. Likewise,

r-AAAAArn

(b)

Fig. 36— RalaiHfil aii<l I'libalanccd Forms of a Filter Section, ContaininK Mutual
Inductance

the eciuivalencc of the structure shown in F'ig. 35C to that of Fig. 35B
is obtainable by successive mesh substitutions. The equivalence of
the structures shown in Fig. 3')I) and E to that of Fig. 35C arc also
obtainable from eciuivalences previously referred to. If the propaga-
tion and impctlance characteristics of either of the structures of
F"ig. 35C' or D are known, then the other structures shown in Fig. 35
will have the same characteristics. Furthermore, if the values of
the constants of any one of these structures arc known, the constants
of any of the other structures are readilv obiain.ililc 1)\- means of
transformation fornuilae.

In a large number of wave fdlers, the structures are unbalanced;
that is, all of the series imiH-flances are placed in one of the two line
wires while the remaining wire is a short circuit. ()rdinaril>-, the
object in using such an unbalanced structure is to minimize the num-
IxT of elements re(|iiiri'd in the series arms. It should be noted,
however, (Fig. 30) that in case an inductance element enters into

Ml If. II. I\ni\ T.IXi. I l.\ ll'.M / lU.IIHS 'J?

l)otl) M-rirs arms, it c.ui Ik- n-platvd, in symnu-lrical siructuri's, hy
two i'<|ual wiiulings of a sin^;Ii' coil ha\'inK iiuitual iiKliictaiiCf lH-tvvri;n
ttu-m ami of siuh \aliio that tlio si-rii-s aiding inductance of tiiese two
coils is c<iiiai to the total inductance rccjuircd in the correspond in^;
unhal.mccd structure. I'or example, the structures shown in Fins.
:?f>.\ .111(1 M are electrically e(|uivalent to each other, that is, tlu-y
have the same imaj;e impedance and transfer constant.

Types of Sections Obtainable Whose Equivalent Series-Shunt Sections
Contain \o Xe^ative Inductances. It has previously been stated that
an intinite mmiber of t>pes of series-shunt filter sections may be had,
if no limitations arc placed on the comjilexity of their reactance arms.
It has also been stated, however, that for filters employing only one
transmission or one attenuation band, the maximum number of ele-
ments which can ordinarily be used economically per section is six.
A similar limitation exists when mutual inductance is emploNcd, in
that sections can seldom be economically used whose prototype
structures contain more than six reactance elements.

Inasmuch as by the equi\a!ences which ha\e been discussed, many
varient forms of a section may exist, which forms are reducible to the
same series-shunt prototype, an effort only to list and discuss the
p:o"otype sections will be made. The prototype to which an\' given
section then reduces will readily be found by the application of the
foregoing principles. A few examples will later serve to make this clear.

In ccmsidering the prototype sections which exist when mutual
inductance is present in a filter section, we shall first list the reactance
meshes of which mutual inductance may^ form a part. Referring to
Fig. o, an inspection of the equivalences so far discussed will show-
that the following meshes may be parth- or wholly composed of mutual
inductance:

1, 3, 4, .5 (a and b),7 (a and b), and 8 (a and b).

Consequently, a large number of the sections listed in Table II and
formetl from the reactance meshes of Fig. 5 may represent not only
actual sections containing no mutual inductance, but also equivalent
prototypes of sections containing mutual inductance. Sections con-
taining mutual inductance within only the series arm or the shunt
arm, respectively, are not included in this discussion since such arms
may lie readily reduced to e(|uivalent arms, without mutual induct-
ances, by the substitution of equivalent two-terminal meshes. The
prototypes which are under discussion are listed below:

Ltw pass High pass

1-3,5-3 4-1,4-5

96 /*/:/./. Sy.STILM TFA'HMCAI. JOIRXAL

Band pass
3-1, 1-1. ■^-^^. \-\. 1-5, .'.-I, 3-7. 3-."), S-4. 4-S, .")-4,
5 — 5, and 7 — 3.

Sections rorrcsponclint; lo llie eciuhalent series-sluint prototypes
listed will lia\e the same impedance and propagation characteristics
as the protoi\pe, and ma\' be used indiscriminately in place of the
prototype, ("onseciuently, when a section has been reduced to any
of the above protot\pes, its various characteristics may be fouiui
from Table li and Figs. 7 and 8.

As an example of structures which ha\e mutual inductance and
which arc equi\alent to structures listed above, consider the section

I ^'^^ 2
0-' 0000 ^— Og-^UOT^^

. * T *

o 1 o

3 4

I- in. M —Low r.iss lilicr .V-i lion t omainiiiK I'wo Coils, Having Mutii.il Iniluctcini-c
.Acting Between 'I'hem, and a Condenser Shunted Kroni Their Junction Point

shown in Fig. 37. This section contains two coils ha\'ing mutual
inductance, and a condenser shunted from their junction point. The
three-terminal mesh forme<l b\' the two coils Z, 2 and L/2, together
with their series opposing mutual inductance ..1/, may be represented,
as in F'ig. 29B, by its e(iui\alent T mesh. The resulting equivalent
section is that shown in Fig. 38. The structure (jf Fig. 38, ha\Mng a
series reactance mesh corresi)onding to No. 1 of Fig. 5. and a shunt

% -M ^ -t--M

l-ig. .W— Killer Sci'tion (Dnt.iiniiin .No .Mulual iinlin i.inct-, iMiuiv.ilcnt lo tlic
Section of Kig. .57

reactance mesh corresponding lo No. 3 of Fig. 5 is thai listed as
I —3 in Table II and in the above list. Consequently, it has propaga-
tif)n characteristic No. 2 of Fig. 7, and mid-series image impedance
characteristic No. 1 of Fig. 8. The section of I*"ig. 37 may, conse-
(|uently, Ik- joine<l at either end to any structure ha\-ing a mid-series
image im[)e<lancc characteristic such as that designated as character-

Ml II .11. I.XIHil.l.Ml l.\ ((•/// III IIKs

07

isiic No. 1 i>f I'ig. S. The srction of I'ig. M is imt capable of niifl-
shunt termination since point (J of I'ly^. 38 is not pin sically accessible.
Similarly, the section shown in l-ij;. 39 is e<iuivalent to the series-
shunt structure of I-'iR. -JO. If the transformer mesh in Fig. 39,
formed by 2Ln, M and "iZ-s Ik- replaced by its e<iui\alent t mesh, —
assuming series opposing windings the structure of Fig. 40 results.

-M-

J_2L, 2L^J_

X

I

Fig. it — Band Pass Kilter Swlion
Containing Muliial Indiictancx-

Fig. 4() — Filter Section, Containing No

Mutual Inductance, Kquivalcnt to the

Section of Fig. 39

This structure is listed as band pass section 1-4 in Table II and has
propagation characteristic No. 7 of Fig. 7, and mid-shunt image im-
IK'dance characteristic No. 14 of Fig. 8. Consequently, the section
of F'ig. 39 may be joined efficiently to any fdter section of Table II
having the mid-shunt image impedance characteristic No. 14 of
Fig. 8 or to any section containing mutual inductance and having
the same mid-shunt image impedance characteristic. The section
of Fig. 39 is not capable of mid-series termination, since point 5 of
inductive element 1—3 of Fig. 40 is not physically accessible.

3 I A^'^"^ 3

^ <WggNI-HKggW

4 2

l-ii;. 41 -K.\.iiTii)lfs ol lilur .ScrlioTis ( oiit.iiiiliiK .Miitu.il liiclurt.iiic

Three further e.xamples of the substitutions which have been dis-
cussed are represented in Figs. 41 A, B, and C. By means of sub-
stitutions these structures are evidently equivalent to series-shunt
sections 4—1 (mid-shunt terminated), 4 — 4, (mid-shunt terminated),
and 3 — 7 (nud-series terminated), rcsjwctivcly, and they have the
characteristics detailed in Table II. The above examples represent
only a few of the many variant forms of structures which may be con-
structed by means of the various equivalences heretofore discussed.

98

FELL SYSTHM TliCllXICAL JOURNAL

Types of Sections Obtainable Whose Series-Shunt Equivalent Sections
Contain Xegative Inductances. It lias already been pointed out that
the following meshes of Fig. 5 may be at least partly composed of
mutual inductances: — Nos. 1, 3, 4, 5a, iib, la, lb, 8a and 8fc. When

^^j,,,^ ^^sm^^ ^^ '^iHH^> <ifl>

>xftfllbHl-Lj- ->Jiaay|,^ — KMiJyjH-^ tZ||_[^^]J~

Kig. 42 — Two-Terminal Reactance Meshes of Four or Less Elements, Containing
Negative Inductance and Effectively Realizable Within Filter Sections .

the connection of the coils is such that the mutual inductance effectively
results in |)roducing a negative arm in the mesh in which the mutual
inductance exists, the meshes may be shown as illustrated in Kig. 42.
The reactance-frequency characteristics of these arms arc given in Fig.
43. It is to be noted that two general forms of reactance characteristics
exist for arms oa' and o6' and that one form of reactance characteristic

5'b

FiK- -43 — Reactance-Frequency Characteristics of the Meshes of Fig. 42 Shown in
Symbolic Form

is common to the two reactance arms. This dualit\- of characteristic
arises from the fact that the arms each contain two inductances, one
positive and one negative, and that the general shape of the reactance
characteristic is determined b\' the predominance of either the posi-
tive or the negative inductance. The characteristic which is peculiar
to arm ha' occurs when the negative inductance of this arm is smaller
than the positive inductance. Likewise, the characteristic peculiar
to arm 56' occurs when the negative inductance of this arm is larger

Mcrc.n. ixixcT.iXi r. ix ii:iri: iii.iiRs <«

than till- i)<>siti\e iinluil.mri-. The cliariUU'risiic wliicli is romnioii to
Inith arms 'vt' and ">/»' c-orrt'sjiomls to tlu- altiTii.il i\o coiiditioiis rcRard-
ing the relative magnitudes of the negative and positive inductances
and the two arms .">«' and ")/>' are polentialK' etiuivalenl under these con-
ditions. M\- means of feasible combinations of the reactance arms of
Figs. ') and 42, there can he (fhysiially constructed a limited number of
prototype wave filter sections ha\ing no more than one transmission
or one attenuation band. Such sections — involving not more than a
total of six reactance elements in the scries and shunt arms — are
listed in Table III.

T.\BI.E III

TabuUition of the Propagation and Impedance Characteristics of Series-Shunt Wave

Filter Sections which can be Formed from the Reactance Meshes of Figs. 5 and 42

SERIES ARM

1

3

5a

7a or 7b

1'

No Pass
Band

17-13-*

21-22-*

Double
Band Pass

y

1S-I-*

16-13-*

Low-and-
Band Pass

Double
Band Pass

S'a

I6-16-*

17-17-*
18-13-*
19-13-*

16-22-*
20-22-*
21-22-*
22-22-*
32-22-*

More Than
Six Elements

7'a or 7'b

Low-and-
Band Pass

16-17-*
20-13-*

More Than
Six Elements

More Than
Six Elements

SERIES ARM

1'

4'

5'b

S'a or 8'b

1

No Pass
Band

25-*-9

24-*-16
26-*-16r

High-and-
Band Pass

4

23-*-14

26-*-14

23-*-19
27-*-14
28-*-14

26-*-19
31-*-14

5b

24-*-24

High-and-
Band Pass

24-*-37
26-*-24
29-*-24
30- '-24
31-*-24

More Than
Six Elements

8a or 8b

Double
Band Pass

Double
Band Pass

More Than
Six Elements

More Than
Six Elements

100

PELL SYSTEM I ECU SIC AL JOIRSAI.

The representation of the characteristits of the structures of Table
III is similar to the scheme of Table II. The figures at the top and
side (for example 1-3') indicate res|x>ctively, the series and shunt
reactance meshes of Figs. 5 and 42 which form the prototype sections.

OfCDO/OO OftDOfOD OfOOOfOO OfODOfCO

15 IG 17 IQ

OfmOfOO OfmOfCD OfOOOfOD OfOOOfCD

13 ZO 21 Zl

ofooofo) ofaoofoo ofcoofm ofooofco

23 24 Z5 26

ofroofoD ofcoofm ofooofoo oofoaofoa

27 28 23 30

OfOOfOD OfWOfOD'

31 32

Fig. 4-1 — Pro|Ktgatioii Constant (.-Xttcnualion and Phase Constant) Characteristics
of Kilter Sections Containing .Negative Inductances, Shown in Symbolic Fonii

The figures in the corres[M>iKling box (for example, 15— 1 — *) indicate
that the structure has propagation characteristic No. 15 of Fig. 44,
and mid-series image impedance No. 1 of Fig. 8. The symbol *
indicates, when inserted in the sec-ond or third position, that the
structure is not plnsicalK- capable of mid-series or mid-shunt termina-
tion, res|)ecti\el\'.

It will lje noted that only one low pass prototype section (1—3')
is given in the table, exclusive of special cases of band filter structures.

Miic.u. ixni-CT.ixtii i.\ ii-.iri iiliiks km

Its .itu-nii.ilioii cli.ir.u-liTistir (Nd. I") ul I'ij^. J I) j?, imiqin- as .1 low-
pass ihariuloristir in iliat the iittetinatioti cotislaiit is finite at all fre-
quencies. Till' phasf rharartrrislir siinul.iti-s, in a gcnoral wa>', that
of till" two I'IciiK'nt low pass tiitor (si-v propagation cliararlrristif
No. 1 of l-'ig. 7) l>iit llu> phase shift in the transmission Ihind is, in
geni-ral, dilTi-ri'iit. Sinro thi- structure has niid-scrii-s iinaRi- ini-
(K'danco rharactoristir .No. 1 it may l)e joinwl ollficiently (i.i-., without
ri'lK'ction It)sses) to sections of the 1 — 2 and I —15 i\ pes.

Similarly, high pass protot>pe section 4'— 1 has a uni(|Ue hijj;h pass
attenuation characteristic in that the attenuation constant is finite
at all fretiueiicies. The phase characteristic is, in general, similar
to that of the two element hit;h pass filter 2— 1 except for the \alues
of the phase constant in the transmission hand. The section may lie
joineil etViciently at mid-shunt to sections of the 2—1 and 4—1 tyjies —
since it has the same mid-shunt image characteristic (No. 9).

The attenuation characteristics of the band pass prototypes listed
in Table III will, in general, differ from the attenuation character-
istics of structure listetl in Table II. However, many of them differ
only in minor res[x?cts and could ha\-e been represented identically
in the sNiiibolic fashion of Fig. 7. Inasmuch as such structures will
not, howe\er, have exactly the same attenuation characteristics for
given cut-ofT frequencies and frequencies of infinite attenuation,
difTerent symbols or diagrams have been em()Ioyed to represent them.

Certain characteristics are worthy of comment because they are
not obtainable, even approximately, in structures not having negative
inductance. For example, propagation characteristics Nos. 1(5 and 26
(Fig. 44) arc band pass filter characteristics having finite attenuation
at all frequencies. Characteristics No. 22 and No. 2i) are unique in
that there exist two frequencies of infinite attenuation, located on
one side of the pass band. The attenuation constant is, in general,
finite at zero and at infinite fretiucncies. Charat'tcristics 19 and 28
are special cases of Nos. 22 and 29, respectively, and have two fre-
quencies of infinite attenuatif>n on one side of the pass band. In
the case of 19, the attenuation is infinite at zero frequency and at a
frequency between zero and the lower cut-otT freciuency. Charac-
teristic 28 has infinite attenuation at infinite frequency and also at a
fretjuency between the upper cut-ofT frequency and infinite frequency.
Characteristics Nos. 18 and 27 have confluent band characteristics
and have onl\- one frequency of infinite attenuation, located either
at zero frequency or at infinite frequency. Finally, characteristics
Nos. 20 and 31 are confluent characteristics in each of which one fre-

102 BELL SYSTEM TECUMCAL JOVKSAI.

quency of infinite attenuation occurs and the atleniialion is finite
at zero frcfiuency and infinite frec|ucncy.

As a general rule the phase shift characteristics shown in Fig. 44
are similar lo the corresponding characteristics shown in Fig. 7. The
phase characteristics of the former, within the pass bands are, in
general, however, of a distinctly different character than those of the
latter even though the phase constant at the cut-off frequency and the
mid-frefjuencN- ma\- he the sjime. Phase characteristics 21 and 24
(Fig. 44) are of special interest, however, in that while thc\- Ijelong
to the peak type sections, the phase is of the same sign throughout
the entire frcciuency range. .Also phase characteristics 22, 29, 30 and
32 have a unic|ue property, for band pass structures, in that the phase
undergoes a change in sign within one attenuation band.

In regard to the impedance characteristics, it is noted from Table III
that no novel impedance characteristics are obtained in structures
having negative inductances as compared to the structures not having
negative inductances. This is a \aluable property of the prototype
structures listed in Tai)le III as it permits composite filters to be
readily formed utilizing both the sections of Tables II and III.'*

Characteristics of a Typical Filter. In order to illustrate the deriva-
tion of design formulae for a specific prolot>'pe having negative
inductances, consider as an example the band pass structure 3 — 3' of
Table III. W'e shall neglect the effect of dissipation on the character-
istics of the structure, as the treatment of dissipation has been pre\i-
ously outlined. The proiotyi)e cited is illustrated in I-"ig. 4oA. Two

~|k5W^-j-^wjr^[-= ' — II

ABC

Fig. 45— I'roloiyiK.- Siliiin (.'ont.ilning Negative Inductance, an<l Two uf Its

I'hysically Realiz^ible Forms

meth(Kls of physically obtaining >uili a priii(ii\pi' .ire illusiraied in
Figs. I.")n and C. In this structure ilie series im|R(lance Zi is

'"=K-'''-Jc)-

(92)

" For a Kfiicral method of provinR the equality of tlio image impedances of sections
containing negative inductance and of appropriate sections cont.iining no negative
inductance, refer to the Apfx-ndix.

Mi'ir.ti. iMHcr.ixcii i.\ ii.iri-: iii.ii.ks ku

Thf imptil.iiui' (if till- ^lHlllt .irm is

Z.= -j{-L,+-[^

(93)

The ratio, Zi-lZi, which controls ihi- .uicmi.itinn and i>li,isc con-
stants, per section, of tlie structure is

Zi

Cj 1 — L\C\oi' '

(94)

I'rom the impedance characteristics of reactance meshes 3 and 3', as
illustrated in I'igs. 0 and 43, and the coml)inetI reactance character-

fjX

Fig. 46 — Reactance-Frequency Characteristics of the Series and Shunt Arms of
the Prototype Section of Fig. 45-A

istics of Fig. 46 for Zi, 4Z2 and — 4Z2, it will be noted thai the lower
cut-ofT frequency,/], is that at which Zi=0. Hence,
1

/i =

2tV'L,C,"

(95)

Similarly, the upper cut-ofT frequency is that at which Zi = — 4Z2 or
JLoLi—j,'wCi=j4wL2+j4'wC2. From this relationshi|), the upper cut-
otT frequency is

'' 2t\c,C2(L,-4Lj)'

(96)

Let /r be assumed as the frequency where Z2 is a miiiitmini, that is,
where u-LiCt=l. We may then write

104 PIU.L SYSTEM TllCHSlCAL JOURXAI.

Substituting tin- al«>\e xalut's of /"i./o and/, in formula (94) we olnain
forZ, 4Z»

_'LV (hV

2, \f

ar &

+1

From lliis last expression the attenuation and phase characteristics
may be plotted from formulae (22) and (23) or from Figs. 11 and 12.
The attenuation and phase constant ch.iracteristics are shown sym-
bolically as characteristic 10 of Fig. 44. This structure has unusual
attenuation properties which h.i\'e already been discussed.

I'Vom e(|uali(»n ((i) and the \alues of Z\ and Z2, in (92) and (91}),
the mid-series image impedance (Zo), at the niid-freijuencN', is

Since the mid-suries image imjjeilance, at an\- frequency, is the
same as that of filter section 3 — 3, we ha\e:

where /m is the miil-lre(|uency (/m = \//iA>'. ^'^ i)efore.

The prototyjK- is not capable of mid-shunt termination, hence, its
hypothetical mid-shunt impedance characteristic will not be derived.

From the preceding formulae, explicit expressions m\v be derixed
for the values of A,, C'l, Lq and ( •..

, Zotn'

T -Zo l-m'»

< if) +1

Miir.ii. iMwcr.-wcE i\ ir.iri: iii.rr.Rs

105

As .1 tuiiiu-rii-.il fx.iiiipic I'l' ilu- solution of ilu- |>|-otoi\|H- disrusM-d
.issiinif, .IS ill ilu- i-x.implr following ('(|it.iti<)n (.H ), ili.it ilu- lowiT cut-ofT
lrt<|iu'iu y /i is 2(),(HM) cNik's .iml tli.it tlu- upper lUl-otT frf(iiii-iu y /j
is J.'j.tMHt r\rlis. Assume/,, a convenient par.iineter for the families
of .ittenu.ition .iiul phase constant curves which this sectioti may
h.i\e, for .iiu- j;i\en cut-otT fretiiiency, to Ix' UO.OOO cycles. Assume
lh.it the \aiiie of the mici-series image impedance Z.. at the niid-fre-
(|iuncy isliOOtihms; then from formula (!>!•) m' = l.OS.l: hence /., =.(1412
henries. T, =.00153 X lO"' farads, L; = .00152 henries and C",; = .01SlX
10 * farads. The structure with the numerical \alues of induclance
.iiid capiirity for this specific example is shown in I'ijj. 47. \.

2C =
.00306 mf

2C =
.00306Tnf

^Cr.L!03O6w-.
L,=.C0l52h.

L=.0336h.i°g*|fl L=.0336h

: C,=.OI64nif

(!C,=.00306:nf.,, L.=.0412k ,, 2Cr.00306n,f
U=.0i3lh.|g ;M=T=.0206h.

Fig. 47 — N'umeric.il Example of Equivalent Filter Sections Containing Negative
Inductance

If, for the y mesh inductances in Fig. 47.A, we subslilute a trans-
former mesh having the \alucs shown in P"ig. 47 B, the mesh of the latter
figure is electrically equi\alent to the prototype structure and is an
example of the method of employing the structure. Similarly, F"ig. 47C
illustrates the substitution of another type of three element mesh
for the coil mesh of the prototype structure of Fig. 47A and is another
example of the inanner in which the prototype may be physically
expressed.

The structure of Fig. 47B represents a similar case to that of 48A.
However, as the mutual inductance is here series opposing, the proto-

106

Hr.l.L SrSTHM lECIISlCAL JOrRNAI.

type scries-sluiiit equivalent siruclurc is shown in Fig. 4SB ami con-
tains no negative inductances. It will be found that the values
chosen correspond to the numerical example of the structure 3 — 3
following equation 41.

2L,=
.00448 TT)/"

L=0ZO0h.

zc -
.0044a mf

.00577 h,
1 (5.0.) (

L=.0200h.

Cs = 00486 mf

e^y=.OI42hp

2C -
.00446 mf

2C,=.O0448rT
Lj= +.00577 h.
C,=.00486 mf

A B

Fig. 48— Numerical K.xamplc of a Kilter Section Containing No Negative Inductance

.\i'im:.\1)1x

Conditions kor thk Eqiai.ity of the Im.\oe Impkd.xxces of
Typu.m. Filter Structures

It has been stated that the formation of recurrent and composite
wave filters is dependent u|M)n the maintenance of equal image im-
pedance characteristics (of the sections or half-sections joined) at
each junction point throughout the filler.

.•\ general method of ascertaining the conditions for the equality-
of image impedance characteristics will lie demonstrated !)>■ illus-
trations from typical pairs of sections.

Illuslralioii \o. I — Xegalive Inductance in Shunt Arm of One Struc-
ture. Consider the filter sections listed as 3-4 (confluent structure)
in Table II, and 3-1' in Table III. It will be shown that, under
proper conditions, their mid-series image impedance characteristics
may be made equal at all fretiuencies. (By reference to the abo\e
tables, both sections have mid-.series impedance characteristic No. 13
of Fig. 8).

From equation (6)
In l"ig. »".», let

^1 -/Ji/i+^i/i=jW-i +

jiaCi

(100)

(107)

Mun:u. ixiHcr.txci: i\ ifirr. iii.ir.Rs

107

Zi' K.iZ\,\-\-K B Ziii,
ami Z:' — KiZ\\,

wluTc A.',i L\',L\,Kit (.'i t'l' .iiul A', I.i' L\.
Vnm\ (lOG)

in wliiih

/?-

Lt_ iLx

(lOH)
(109)
(110)

(ilU
(112)

¥

T ^c, -^ 2C, ?c,
'000000^ — II — o- 0 — '"O'OOOW^ — II 1 — 1|-

Fig. 49 — Two Structures Having Equal Mid-Series Image Impedances, One of
Which Contains a Negative Inductance in Its Shunt Arm

From (107) and (111)

Z,^ = R'+i{Z^A+Z,Br = l/iZ',^ + {l+K/2)R- + l/-lZ-s (113)
where K = ZiAZiB/R' = Li/Li = Ci/Ci. ^ (114)

Now from (106) and (108)

(z\r- /Ka-"

(Z;')= = Z,'Z.' + ^'" = (^"-A-.,AV)ZL.+

(^-a-«av)a-/?--+Y>

(115)

Since, by postuiation, in I'ig. lU, Z\=Zi'. we ina\- eciiiate tliecoet'ti-
cients of (113) and (llo). This gives

1 _Ka' j. j.

K (KaK

1+|=(^_^„^,)^.

and

1 _K^
4 4 ■

(116)
(117)
(118)

108 PEI.I. SYSTl.M JI.CH.XU.II. Jul KX.IL

Whence Kb ;.-, = !, (119)

and A'.,, fi = ^=-^'={=. (120)

where /i and /» are llie lower .iiid u|)|)i-r i-ul-ulT freciuencies, respec-
tively, and /.I/ V/,/.j of the structures of 1-ij;. 4(1.

From (IK)) and (120)

/c^^-±=-^.(a:^-_)= ^(.^---y.

(121)

Therefore, wiieii the relationships between the constants of the two
structures of Fij;. 4!t satisfy equations (,119), (120) and (121), the
structures will have the same mid-series image impedance character-
istics. Explicit relations for the values of Ci', Li and L/ nray be
obtained from equations (119), (120) and (121) as follows:

C/ = Cu (122)

Ai' = /-.4 (123)

'•'■=t(7:-/;)- 02*'

("on.sc(|ueniK , if the lonslants and cut-off frequencies of a conHuenl
structure are known, the constants of a structure of the .3-1' form
having an identical mid-series image imix-dance characteristic can be
derived from equations (122). (123) and (124).

llliistralion No. 2 -Negative hiditctance in Series Arm of One
Structure. Consider next the filter sections listed as 3 4 (confluent
structure) in Table II and 1' 4 in Table III. It will be shown that,
under proper conditions, their mid-shunt image impedance charac-
teristics may be made ecpial at all fretjuencies. (By reference to the
above tables, both sections ha\i' mid-slumt im()edaiice characteristic
No. 14 of Fig. 8).

I'rom e(|ualion (7)

lV=l-,r... + l",. (12.5)

where K, = l/;^,, 1^=1, ,^5 and y, = \,Zi.

\n K.ii. ixnrcT.is'cr. ix ii:irr. iii.iiks loo

III V\K .Ml. K-t

111(1

(126)

(127)
(128)

X'

21 2

L, C,

-^ ^^r ^^— L_^

Fig. 50 — Two Structures Having Equal Mid-Shunt ImaRc Impedances, One of
Which Contains a Negative Inductance in Its Scries Arm

where Ka L- L:\ K b ^ C2' , C> i\nd Kc ^ L^ L\'

From ( 12."))

in wiiirli

'^^trr.

(12<t)

(130)
(131)

From (I2()) aiul (I30i

lr=G--+l ;4(r,.,+ r:8)- = l 4n., + (l+A: 2)G= + 1 4F^b (132)
where A' s IV, Fob 'G= = Li 'L2 = G C (133)

Now from (12o) and (127)

( Y,r- = r,' ¥,' + ^' = ( 4^ - f^-^^c) Vlx +

Kb' I-.,

{'^-KBKc)K(?+^y],

(134)

Since, by postulation, in Fig. .iO, F/= F/'. we ma\- ecjiLite the roetfi-
rients of (132) and (134). This gives

T- 4 -^'^^

1 +

K /KaKb

(-^"-A'bA-c)

(135)
(136)

no BELL SVSTRM ILCHXIC.IL JOURNAL

and i=?'- (^3")

4 4

Whence Kb^% = \. (138)

J, _ij _ Lid j^ _/l /,Qg^

and K.,^j^-jj^,- ^^,-j^ KMi)

where /i and j-i are the lower and upper cul-ofT frequencies, respec-
tively, and /.\/ is the mean frequency {'^fi ft) of the structures of
Fig. 50.

From (135) and (139)

Therefore, when the relationships between the constants of the two
structures of Fig. 50 satisfy equations (138), (139) and (140), the
structures will have the same mid-shunt image impedance character-
istics. Explicit relations for the values of d', Li and Li may be
obtained from equations (138), (139) and (140) as follows:

G' = G, (141)

U = L.j\ (142)

U = ^j^I^. (143)

V/. fJ

<f

Therefore, if the constants and cut-off frccjucncies of a continent
structure are known, the constants of a structure of the 1' — 4 form
having an identical mid-shunt image impedance characteristic can be
deri\ed from equations (141), (142) and (143).

BIHLlOGkAl'IIY

1. Thrvi-nin, M. L., "Sur un .N'huvimu Thi-oremed'ElectricitO Dynamlquc," Cotnptes
Rrndus, Vol. 97, pp. I5<>-161 (188.1l.

2. KtnnfUy, \. K., "The Kqiiivalunce of Triangles and Three-Pointed Stars in
Coiiducting Networks," lUectricai World and Engineer , New York, Vol. XXXIV,
pp. 4I.J-JI4, Sept. U>, 1899.

i. CamplK-ll, (;. A., "Cisoidal Oscillations," Trans. A. L li. E., Vol. X.\.\,
I'arl II. p[). ,S73 <XW (1911).

4. CamplH.ll, C. A.. U. S. Patents Nos/ 1,227,113 and 1,227,114 (1917).

5. Gherarili, U. and Jewett, V . B., "Telephone Rerwaters, ' Trans. A.L E. E., 1919.
0. Wagner, K. W., Ardi. fur Eleklrolechnik, \o\. 8, p. 61 (1919); E. T. Z., Aug. 7,

1919.

MUTUAL t.\IU\ r.lSili IX ir.llF. ril.TF.KS 111

7. \'.in ilcr BijI, H. T., "Tlicrmioiiic \'.u iiuiii I'ulics," Piil>lishc<l 1020.
M. I'icrce. O. \V., "KIcctrir (IstiJI.itioMs .iiul Klectric Waves," I'liblislicd, 1920.
•». Colpitts, K. H. and Ul.ickwcll. (). B.. "Carrior Current Telephony and TcIcr-
rapfiy." 7><i»ij. .1. /. li. E.. l"el>.. l'>21.

10. Clement, I.. M., Rvan, V. M., and Martin, I). K., "The .Xvaion-I.o.s .AnRcles
Radio Toll Circuit/' Prot. I. K. E.. May, l'J21.

11. Kletrher, H., "The Nature of Speech and Its Interpretation," Jour. Franklin
Inst.. June, 1922.

12. Canipbell, C.. .\., "Physical Theory of the Electric Wave-Filter," Bell Sys. Tech.

Jour.. Nov., \<iU.

1.1. Zol>el, O. J., "Theory and Design of Uniform and Composite Electric Wave-
Filters," Bell Sys. Tech. Jour.. Jan., 1923.

14 Rose, .-X. F., "Practical Application of Carrier Telephone and Telegraph in the
Bell System," Bell Sys. Tech. Jour.. April, 1923.

15. Hartley, R. V. L., "Relation of Carrier and Side-Bands in Radio Transmission,"
Bell Sys. Tech. Jour., April, 1923.

It). Bown, C. D., Englund, C. R., and Friis, H. T., "Radio Transmission Measure-
ments," Proc. I. R. E.. April, 1923.

17. Peters. L. J., "Theory of Electric Wave Filters Built up of Coupled Circuit
Elements," Jour. A. I. E. £., May, 1923.

18. Demarest, C. S., "Telephone Equipment for Long Cable Circuits," Bell Sys.
Tech. Jour.. July, 1923.

19. Nichols, H. W. and Espcnschied, L., " Radio E.\tension of the Telephone
System to Ships at Sea," Bell Sys. Tech. Jour., July, 1923.

2(1. Carson, J. R. and Zobel, O. J., "Transient Oscillations in Electric Wave-
Filters," BeU Sys. Tech. Jour.. July, 1923.

21. Arnold, H. D. and Espenschied, L., "Transatlantic Radio Telephonv," Belt
Sys. Tech. Jour., Oct., 1923.

12. Best, F. II., "Measuring Methods for Maintaining the Transmission Efficiency
of Telephone Circuits," Jour. A. I. E. £., Feb., 1924.

2i. Casjicr, W. L., "Telephone Transformers," Jour. A. I. Er-E.. March, 1924.

24. Slaughter, N. H. and Wolfe, W. V., "Carrier Telephony on Power Lines,"
Jour. A. I. E .£., April, 1924.

25. Foster, R. M., "A Reactance Theorem," Bell Sys. Tech. Jour., .\pril, 1924.

26. .Martin, W. H., "The Transmission Unit and Telephone Transmission Refer-
ence System," Bell Sys. Tech. Jour.. July, 1924.

27. Zobel, O. J., "Transmission Characteristics of Electric Wave-Filters," Bell
Sys. Tech. Jour., Oct., 1924.

Some Contemporary Advances in Physics VI
Electricity in Gases

By KARL K. DARROW

1. Introduction

Till-; i)li\>iii>ts of a (jiiarttT of a century ago, who dcvoti-d iIh-iii-
selves to the study of electricity in gases, were liappiK' inspireti;
for among the myriad of intricate and obscure phenomena which
the\- observed there are some few of an extreme sinijjlicity, in which
the qualities of the individual atoms of matter and electricity are
manifest; in analyzing these they entered upon the path that led most
directly to the dee[)er understanding of nature which is superseding
the physics of the nineteenth century, and the physics of today is
founded upon their efTorts. The electron was perceived for the first
time in the course of ol)ser\ations on the electric discharge in rarefied
gases, and other experiments in the same field established the atom
in science as a real and definite object. The disco\'ery of the atom
is commonly credited to the chemists; yet fifteen years have not passed
since students of cluinistr>- were being warned by a famous teacher
that "atom" and "molecule" are figurative words, not on any account
to be taken literally! The laws of chemical combination were held
insufficient to pro\-e that atoms ha\'e any real existence; though
elements nia\' always combine with one another in imclianging propor-
tions, this does not pro\e anytiiing about the weights of the atoms, or
their sizes, or their (|ualities, or even that all the atoms of an element
have the same weight, or even that there are any atoms at all. Now
that we are past the necessity for this caution, and can count atoms,
and measure their masses, and infer something about their structure,
and estimate how close together they can a|)proach, and know wliai
happens to them when they strike one another or are struck 1)\-
electrons; now that we can fill in the jiicture of the atom with so many
and so diverse details, we are indebted for this progress chiefly to the
men who gathered the daUi and made the theories concernini; the
conduction of electricity in gases. Many will remember how in ihc
years before the great war this field of research seemed the most vital
part of physics, the most inspired with a sense of new life and swift
advance; now others share with it the centre of the stage, but they
won tiieir places chiefly l)ecause of the light it shed upon them.

It seems strange that the (low of electricity in gases should have
proved easier to interpret than the How of electricity in ntetals, which
in appearance is certainly b\ f,ir the sinijiler. One ai)plies tin- tcrniiiials

112

sOMl- rO.V7/;.UrOA'./A'r .(/)C./.V( /V /.V /7/)S7( V 17 II.!

Ill .1 l>,ittfry to the ends of a wiro, and promptly llu- i-k-ctric potential
(li>triliutes itsflf with a uniform gradient alon^ the win- and a ciirriMit
flows steadiK' down il. So rijiorously is llu- ciirri'iil jiroporlional lo
till' \(illai;e lielween the ends of the wire, over \ er%- wide ranges of
\olta^e .md eurrenl, thai we rejjard the ratio as an essential constant
of the wire: and we regard the ratio of potential-gradient (elertrh-
held) lo current density as an esseiilial characteristic of the metal,
and gi\e it a name — resistivity or specific resistance -and refer to
theories of conduction in metals as theories of metallic resistance.
1 1 all seenis exceedingly simple, and \et in the forejjoing article of this
series I have shown how all the atlempls lo interpret it have ji;one
in vain. Much more complex in appearance is the discharjje throuj^h
a gas. One applies the terminals of a battery to a pair of elect rotles
facing one another in the opwn air, and perhaps nothing happens, or
so minute a current flows that the most delicate of instruments is de-
manded to detect it; and then when the I)attery-\oItagc is very slightly
raised, there may be an explosion with a blaze of light, dissociating the
gas and corroding the electrodes, and draining off the a\'aiiablc elec-
tricity in a moment. Or if one of the electrodes is acutely pointed
there may be glows and luminous sheaths around it or tentacles of
bluish light ramif\ing from it far and wide through the air. Or the
ilischarge may rise to the heat of incandescence, Tind the gas and the
electrodes shine with a blinding radiance, the brightest light that can
tie kindletl on the earth. Or if the electrodes are enclosed in a tube
containing a rarefied gas or vapor, the gas flares up into an extraordi-
nar\' pattern of light and shade, lucent vividly-colored clouds floating
Itetween regions glowing feebly or obscure; and as the gas is gradually
pumped awa>', the pattern changes and fades, a straight beam of
electrons manifests itself by a luminous column traversing the tube,
the glass walls flash out in a green fluorescence, and finalK' all becomes
extinct. As for that e\en gradient, and that constant proportion
between current and field strength distinguishing the metals, we
cannot find them here. There is no such thing as the resistance of
a gas; we had better forget the word, we cannot attach any physical
meaning to the ratio of current and voltage.

I must not give the impression that all these manifold forms of the
electric discharge in gases are understood. Certain of the simplest
of them have been clarified, and as a result still simpler ones have
been realized and comprehended in their turns, and so on down to
the simplest of all, which is the discharge across a vacuum. This
sounds somewhat like a paradox and so it would have seemed thirty
or forty years ago, when electricity was thought to be inseparable

114 DELL SYSTEM TECHNICAL JOURNAL

from matter, and the only known discharges across gases were the
discharges in which the gas plays an indispensable role. It is im-
portant to note the manner of this evolution, for much of the history
of modern physics is dominated by it. We should not be nearly so
far advanced as we are, had we not learned two things; how to reduce
the amount of gas in a tul)e until an electron can fly clear across it with
scarcely any chance of meeting an atom, and how to persuade an elec-
tron to emerge from a metal otherwise than by starting a discharge
in a gas over its surface. We who are so familiar with the idea of
electrons boiling out of a hot wire, or driven out of a cold metal plate
by light shining upon it, or fired as projectiles out of exploding atoms,
find it difficult to imagine the confusion which of necessity prevailed
when all these processes were unknown. In the early stages of
research into the discharge in gases, it was made clear that of each
self-maintaining discharge a stream of electrons flowing out of the
negative electrode is an essential part; the electron-stream maintains
the gas-discharge, and reciprocally the gas-discharge maintains the
electron -St ream. The latest stage commenced when it was made
possible to produce and maintain such an electron-stream inde-
pendently of any gas-discharge, and deal with it at will.

Let me then begin the exposition with this idea, which so many
years of research were required to render acceptable: the idea of a
stream of electrons emerging from a metal wire or a metal plate, at a
constant rate which is not influenced by the presence or absence of
gas in the space surrounding the metal. The reader may think
either of thermionic electrons flowing spontaneously out of a hot wire,
or of photo-electrons fl\ing out of a metal plate upon which ultra-
violet light is shining.'

2. Till. Fi.DW (ir l-"i.i;(TKONs Tiikuk.ii a \i;kv Raricmkd Monatomic
Gas, and Tiikir H.ncolnters with the Ato.ms

Conceive a source of electrons, a negative electrode or cathode,

which is enclosed in a tube. If the tube is highly evacuated, the

' While forming one's ideas it is proferalilc to think of the photoelectric source,
for a variety of reasons; the electron-stream is not very dense, the electrons emerge
with kinetic energies never in excess of a certain sharply-marked limiting value,
the metal is cold and not likely to react chemically with whatever gas surrounds it.
Also several of the clas.sical fundamental experiments were performed in the years
from 180X to I'MV), when the photoelectric elTect had become a reliable instrument
of research and the thermionic effect had not. Nowadays it is sometimes used in
the ho|>e of >ur|>assinK the accuracy of earlier work, or in experiments on compound
(tases which the hot wire might decompose. Still the hoi wire is so much easier
to ins<Tt and handle, its emission so much more convenient and controllable, that
it will no doubt be cmployc<l in the great majority of experiments in the future as
in the past.

SOME roA-/7-.\//'( )/»•.(/>■)• .;/M-.f.V(7:\ IX I'liYsics n iis

electrons enter the vacuum freely; electricity has no liorror of a
vacuum, any more than nature generally. Still there is sometliin^;
which suggests the horror vaciii of the scientists before (lalileo; for
the electrons which arc alreaily partway across the vacuum tend, by
their electrostatic repulsion, to [lush back their followers which are just
emerging from the metal. This is the space-charge effect, which bns
liecome famous since the audion became almost as common an ob-
ject as the incandescent lamp in the American home. I shall presently
have to write down the equations describing this effect; for the time
In-ing we may ignore it, so long as the electron-stream is not more
profuse than a photoelectric current gencralh- is. The electrons of
these scanty discharges enter into the vacuum and pass over without
hindrance.

At this point it is advisable to say what is meant by a "vacuum."
Scientists are growing more exigent year by year in their use of this
term; thirty or forty years ago people spoke of "vacuum tulx;s" mean-
ing tubes so full of gas that they would transmit a big current with
a resplendent luminous displa\', but this self-contradicting usage has
become quite intolerable. At the present day the least density of
gas, or the highest vacuum, commonly attained corresponds to a gas-
pressure about 10" " as great as the pressure ancfdensity of the atmos-
phere. This means that there are about 10~* molecules in a cubic
centimetre of the "vacuum," which may make the name sound absurd.
But the practical criterion for a \acuum is not whether the remaining
atoms seem many or few, but whether they are numerous enough \.o
alTcct the passage of a discharge; and as an electron shooting across a
tulx? 10 cm. wide and evacuated to this degree has 999999 chances
out of a million of getting clear across without encountering a molecule,
the tulx." is vacuJHis enough for any sensible definition.

Next we will imagine that a gas is introduced into the tube, in
quantity sufficient so that each electron going from cathode toward
anotle will collide on the average with one or possibly two atoms on its
way. It is best to Ijegin by thinking of one of the noble gases, of which
helium, argon and neon are the ones in common use; or of the vapour
of a metal, mercury vapour being much the easiest of these to work
with; for their atoms liehave in a simpler and clearer manner toward
the electrons than do the molecules of the commonest gases, particu-
larly the oxygen molecules which are so numerous in air. In fact the
practice of using the noble gases and the metal vapours — that is to
say, the monatomic gases — whcre\er possible in these researches ought
really to be regarded as one of the great advances of the last few years;
our predecessors would certainly have learned more about the dis-

116 BEI.l. SYSTEM Tr.CIIS'lCAL JOCRX.II.

charge in nases than they ever did, if they had not studied it in air
ninet\- limes out of a himdred. and in other diatomic gases most of
the other ten.

Let lis sii|)p()se thai the tiilie contains lieliliin of the extrenieK' small
density I ha\e just defined. 'I'hen so long as the kinetic energ\' of an
electron does nnl exceed lit. 7') Nolts, it will rehoimd from any helium
atom which it strikes, like a vcr\- small perfecth' elastic ball rebound-
ing from a \XTy large one. We might conceive the contents of the
tul)e (for this purjiose and onl\- for this purpose!) asa flock of immense
ivory pushballs floating languidK' about, with a blizzard of etjually
elastic golfballs or marbles darling through the interspiices and occa-
sionally striking and bouncing olT from one of the pushballs. If the
collisions between electrons and atoms are jjerfectly elastic, as I have
s;iid wilhoul giving e\idence, the electron will lose an extremely small
part of its kinetii energy at each collision, owing to the great disparit\-
in masies — a fraction varying from zero up to not more than .0()().").'i7
depending on the direction of rebound.

This wah verified in a prett\- experiment by K. T. ('onipiini AWtl J. M.
Bcnade, who utilized a certain effect- which electrons produce wluii
the\' ha\'e kinetic energ\' exceeding 10.7.") volts at the moment of a
collision with a helium atom. For example, when the pressure of
helium was 4.'M mm. and the electrons were drawn from a cathode to
an anode 0.2().") cm. away, a \()ltage-difference of 20.2.5 (plus an un-
known correction) was required to produce this effect ; when the anode
was 0.90 cm. from the cathode the required voltage-difference was
23.45 (plus the same correction). The extra volts were spent in re-
placing the energ>- lost by the electrons in the collisions with helium
atoms over the extra (\.'.i mm.; they amounted to an average of .0003
of the electron's energy lost in each co'lision. excellenllv in agreement
with the assumption.

.Now as for the transit of the eleclroii-siream fiom cathode to
anode, the helium atoms will simph' thin it down by intercepting
some of the electrons and turning their courses backwards or aside.
The greater the numlier of atoms in the path, the greater the pro-
portion of electrons intercepted; it can easily be seen that, so long
as the gas is not denser than I have s[)ecified, this proportion increases
as an exponential function of the number of atoms between cathode
and anode,'' whether this mnnber be increased by introducing more
gas or by moving the anode farther aw.iy from the cathode. If

' lii<-i|iiiMit i(iiii/;ilion, as (lcs(TilH.-(l hclim.

'The pri>()ortion iiKrcases inort- slowly when dure arc- alrc-adv so many atoms l)f-
twifn ancMJf and rathoili' thai an cicclron is llki'ly to strike two or more on its way

SOI// (O.V// l//M/v'.//x') .;/>/ /.V(/s /V /7/ls/(s (/ 117

till- .iikhIi- ami llir citlioiU- an- two par.illi'l platr^. </ cciiliini'irc^
apart, and tluTt- an- P hfliiim atoms in a rul)ic ci-nlinu-tri' of tlic Ras
iK'twit-n. and Sn i'lirtrons start out in a sirond dirrrtly lowartls the
an(KU' from any area of the ratli<Hie, llie proportion AA' .Vn of elec-
tron^ whirl) .\rc inti'rce|>led before they reach ilic anode is

A.V .Vo=l

(1)

and the niiinlier of electrons reachini; the corresponding; area on the
anode in a second, .V»— A.V, conforms to the e(iu,itioii:

log, (A'o-A.Y)= -.4 A/ + const.

(2)

The coefficient .1 is a constant to be interpreted as the effective cross-
sectional area of the helium atom relatively to an oncoming electron —
that is, the atom behaves towarils the electron like an obstacle pre-
senting the impenetrable area .-1 to it.

In the experiments perfortned to verify these assertions and de-
termine the \alue of .1, the simple geometricifl arrangemeni whicli
I have described is generally modified in one way or another for
greater accurac>- or convenience. Mayer approached most nearly
to the sim()le arrangement; in his apparatus (Fig. 1) the electrons

Fig. 1 — Apparatus for determining the percentage of electrons which go across a
gas of variable thickness without interception. (Mayer, AnnaJen der Physik)

which e.iierge from the hot lllamenl al G, pass througli the two slits
in front of it, and then go down the long tube to the anode A', which
is drawn backward step by step. The logarithinic curves of current
versus distance for various pressures of nitrogen (Fig. 2) are straight.
Unfortunately the current also diminishes as the distance is increased
when the nitrogen is pumped out altogether: this is attributed partly

118

BELL SYSTEM TECHNICAL JOURNAL

to residual \'apors and partly to the electrons striking the walls of the
tube. The other curves are corrected for this ctTect, and then A is
calculated. Vov helium it is 25.10 '^ cm-; the values obtained by
modifications of the method agree well.*

The helium atoms therefore behave as so many minute and yet
appreciab'le obstacles to the passage of the electron-stream, so long
as the electrons are not moving so rapidly that their energies of motion
do not surpass 19.75 volts. Klectrons as slow as these bounce off
from the atoms which they strike. When, however, an electron pos-
sessing kinetic energ\- greater than Id. 75 volts strikes a helium atom,

c2

06

S-^ 04

0.2

0.0

^^.

^

^

^?

..^

^

f^

'"-^'''
"^P"

00000
00026

Nitre

gen

>^

00050
0OO75

mmHg

2.7 5.4 82 (0.9 (3.6 cm

Fig. 2 — Curves illustrating the iiilircupliDii of electrons by nitrogen niuleculcs which
they strike. (Mayer, Annalen der Pliysik)

it is liable to lose 19.75 volts of its energy to the atom, retaining only

the remainder. This energ>- does not become kinetic energy of the

atom, a process which would be incompatible with conservation of

momentum; neither is the atom broken up; it receives the quota of

energy into its internal economy, where some kind of a domestic

change occurs with which we are not concerned for the moment,

except in that it furnishes an exceedingly accurate indirect way of

calculating the exact amount of energy taken from the electron. The

atom is said to be put into an "excited" or sometimes into a "meta-

* The niodifie<l methods are generally more accurate. Ranisauer's device, which
1 described in the first article of this scries, is probably the best. By a magnetic
field he swung a stream of electrons around through a narrow curving channel, and
those which were deviale<l even through a few degrees struck the limiting partitions
and were lost from the beam; he varied the numl>er of atoms in the channel by
varying the gas-pressure. In this way he discovered that A for argon atoms differs
very greatly for different sirixIs of the electrons; it was later found that other kinds
of atoms have a variable ,1, although happily the variations are not great. This
seems strange at first.'but it is probably stranger that A should have nearly the same
value for different 9pec<ls of the oncoming electrons, as for many atoms it does; and
alrangrr yet that it sliould have the s.itnc value for an oncoming atom as for an
oncoming electron, as is often tacitly assumed, and not too incorrectly.

SOME COM F.Ml'OR.IKy . (/'/ '. /.V( /• s IX fllVSUs' II 11''

slal)le" statf, and the ciierny wliiili il lakes up. nRasurid in volts,
is called its resoname-potential. The electron is left with only the
difference between its initial energy and the I!).?") volts whii h it
surrendered.

This loss of ciuTijx- iti .( so-called "inelaslii'" collision ciii lie diin-

8tiChltunigtnde Spannung »

Kig. 3 — Curve displaying resonance-potentials of mercury.
(Einsporn, Z5./. Physik)

onstrated by inserting a third electrode into the path of the electrons,
charged negatively to just such a degree that an electron retaining
its full initial speed can overcome the repulsion of the electrode and
win through to it, while an electron which has lost a quantity of
its kinetic energy in an inelastic collision cannot quite "make the
grade." When the energy of the electrons streaming into the helium

120 HILL sySTf.M TECIIMC.IL JULKS'AL

is raised just past 19.75 \olts there is a sudcien falling-off in llie num-
ber of electrons arriving at the third electrode. The curve in Fig. 3,
obtained by ICinsporn, shows the current into such an electrode in
mercury-vapor rising and falling again and again as the voltage
passes through the values which arc integer multiples of 4.9 volts,
the least resonance-potential of mercur\-. Heliiun has a second
resonance-potential, at 20.45 volts; neon has two, at 1G.65 and 18.45
volts rcspectisely; argon three, at 11.55, 13.0 and 14.0 \olts;' mercury
two, at 4.9 and 0.7 volts. It is almost certain that in each case these
are only the most conspicuous among many, but the lowest men-
tioned is the lowest of all.

Up to this point we find the gas acting as a mere inert obstruction
to the discharge; e\ery collision of an electron with an atom inter-
rupts the progress of the electron toward the anode and to that extent
impedes the discharge. Past the resonance-potential the same action
continues, although the interruption is doubtless less severe when
the electron is depri\ed of part of its energy of forward motion than
when it is flung backward with its motion reversed in direction and
its encrg\' intact. .At the resonance-potential, the gas does begin
to assist the discharge in an indirect way. Atoms which are put
into an "excited state" b\- a blow from an electron revert of them-
selves to the normal stale, some time later; in so doing they emit
radiation, some of which falls upon the cathode; some of this is ab-
sorbed in the cathode metal, and exjjels electrons which go along
with the maintained electron-stream as extra members of it. Thus
the gas hel[)s in increasing and maintaining the discharge; this effect
is of great theoretical importance, and I will return to it later; but
in these actual circumstances it is not \ery prominent.

The really powerful cooperation of the gas in the discharge com-
mences when the electrons are given so great an energy that they dis-
rupt the atoms which they strike, tearing off an electron from each and
leaving a posiliveb-charged residue, an ion which wanders back
towards the cathode while the newly-freed electron and its liberator
go on ahead towards the anode. The onset of this ionization may
be detected by inserting a third electrode into the gas, it being charged
negatively to such a degree that no electrons can reach it, but only
p(»siiive ions; or by the increase in the current between cathode and
ano<le, for the current increases very suddenly and very rapidly
when the energy of the primary electrons is raised past the threshold-
value, the ionhiiiR-poleiiliul of. the gas; 24.5 volis for helium, 21.5 for
neon, 15.3 for argon, 10.4 for mercury. Consider for example the

* I take the wiluex for neon .tnd ,irK<iii (roin Hertz' I.Uesl puliliration.

/

soMi iOM I MroK.iNv .inr.ixcis i\ rinsns ii ui

pri'iipil.ilc upwaril rii.sli ut the lurrfiil-volt.iKi' tiirM- in 1"^. 4, from
the work of Davis aiui Cioucher.'

At this point I will digress to speak very l)riftl\' of thu siuTcssioii of
i'\cnts which oinirs when the eleitron-syeani is much denser than

Fig. 4 — Onset of ionization in mercury vapor at 10.4 volts (preceded by suhsidiary
etTects at 4.*> volts and 6.7 volts; see footnote'). (Davis and Goucher)

we ha\e hitherto imagined. So long as the energy of the electrons
does not attain the resonance-potential of the gas, there is no reason
to expect any novel effects; the collisions will be perfectly elastic,
just as when the electrons were few. But when the atoms are thrown
into the "excited state" by impacts, there will be occasional cases
of an atom being struck twice by electrons in such quick succession
that at the moment of the second blow, it is still in the excited state
provoked by the first. Now, much less energs' is reqtiired to ionize
an atom when it is in the excited state than when it is normal; con-
secjuently when the electrons are so abundant that these pairs of

• The sudden upturn at 10.4 volts is the swift rise of current at the onset of ioniza-
tion. The much less violent upturns at 4.9 and 6.7 volts are due to the electrons
e.xpelled from the metal parts of the apparatus by the radiation from the excited
atoms. In the lower curve, by modifying the apparatus, the latter upturns are
translated into downturns to distinguish them from the upturn which denotes
ionization. This distinction was not realized until I'M/, and in articles published
iK'tween 1913 and 1917 the lowest resonance-potentials of gases are given as their
ionizing potentials. Enormous improvements in the methods and technique of
measuring these critical P'Otentials, and recognizing of which kind they are, have
lieen effected since then.

122 BBLL SYSTEM TECHNICAL JOURNAL

nearly-simultaneous collisions hapf)en often, ionization will begin at
the resonance-potential. In a profuse electron-stream, the threshold
potential for ionization is the lowest resonance-potential. Another
feature of the profuse discbarge is, that when ionization does com-
mence the current leaps up much more suddenly and violently than
it does in the scanty discharge. This is because the electron-current
is depressed at first by the space-charge effect, the repellence which
the electrons crossing the gap exert against the electrons which are
on the verge of starting; when positi\e ions first appear in the gap,
they cancel the action of a great number of the traversing electrons,
and the flow of electrons from the cathode to anode is immensely
increased. I shall speak of this more extensively further on.

We return to the case of the feeble electron-stream. We have con-
sidered various things which an electron may do to a helium atom
which it strikes — bouncing off harmlessly, or putting the atom into
an excited state, or ionizing it; we have mentioned that each of the
two latter actions commences at a critical value of energy, at the so-
called resonance or ionizing potential, respectively; we have con-
sidered the effect of each of these actions upon the discharge. Have
we listed all the possible interactions between atoms of matter and
atoms of electricity, when electrons flow across helium? and if we
knew all the resonance potentials and all the ionizing potentials'
of helium, could we predict all the features of all electrical discharges
in pure helium, whether in rarefied gas or in dense, whether the elec-
tron-stream be scanty or profuse? This is the general belief; whether
justified, it is impossible to say. We e\idently need another Maxwell
or anotJier Boltzmann, somebody e.xceedingly skilful in statistical
reasoning, al)le to take the information we can provide about the
possibility or the probability of various kinds of impacts, and deduce
the slate of affairs in the mixture of atoms, ions and electrons without
getting hopelessly entangled in the frightful maze of equations into
which his very first steps would certainly lead him. While awaiting
him we have to content oursehes with our successes in interpreting
the (low of electrons through very rarefied helium and the other noble
ga.ses and the metal vapors; and as for the discharges in denser gases

' I have simpli(ii.-(J this passage somewhat so as not to retard the exposition. We
know that an electron may "excite" a helium atom if its energy exceeds 19.75 volts,
but this docs not prove that it must do so; it is more reasonable to suppose that it has
a certain chance of exciting the atom, zero when its energy is less than 19.75 volts,
but greater than zero, and a certain function of its energy, when the latter exceeds
19.7S volls. We should know these functions for all the resonance-potentials and for
the ionizing-|K>tential; inde|>endent experiments to determine them have been per-
formed, and no doubt will be multiplied.

SOME CONTEMPOKAKY ADVANCVS l\ I'llVSICSII I.M

we have to take the experimental data as we fwul lliem, and analyze
tlietn as Inist we ntav. not with too jjreat an experlatioii of penetrating
to the properties of the ultimate atoms; and yet, as we shall see, the
analysis does in certain cases penetrate unexpectedly far.

'.\. TlIK KH)\V OK Kl.IiCTRONS A( ROSS UliNSE AlR, XlIROGliN,

Hydrocen and Similar Gases

The celebrated series of researches by Professor Towiisend of
Oxford and by his pupils, commenced in l'.U)2 and continuing through
the present, relate chiefly to such gases as iiydrogen, nitrogen, oxygen
and the familiar mixture of the last two which we breathe; and chiefly
to these gases at densities much greater than we have hitherto con-
sidered— densities corresponding to such pressures as a thousandth
or a hundredth of an atmosphere, therefore so great that an electron
crossing over from a cathode to an anode a few centimetres away must
collide with scores or hundreds of atoms. If a stream of electrons is
poured into perfectly pure helium of such a density, we must not look
for a sudden onset of ionization when the voltage between cathode
and anode is raised just past 24.5, for the reason illustrated by those
experiments of Compton and Benade — the electrons lose energy in
all of their collisions, even the elastic ones, and arrive at the anode
not with the full energ>' corresponding to its potential but with this
energy- diminished by what they lost on the way. In the familiar
diatomic gases, the electrons lose much more energy in their ordinary
collisions. I did not speak of these gases in the foregoing section,
because experiments of the very same type as those which show the
sharp distinction between elastic impacts and inelastic impacts in the
noble gases and give the sharply-defined values of the resonance-
potentials of these gases, yield comparatively vague and ill-defined
data, when they are performed on hydrogen or air. In these gases,
above all in active gases like oxygen or iodine, it is unlikely that any
of the impacts, whether the electrons be moving rapidly or slowly,
are truly elastic'

' However, Foote and Mohler have obtained quite undeniable evidence of critical
potentials, at which the loss of energy by the impinging electron is much greater
than it is just below these potentials. The electron can transfer energy to (and
receive energy from) a molecule in more difTerent ways than to (from) an atom; such
as by setting the molecule into rotation, or putting its constituent atoms into vibra-
tion relatively to one another. There is also the mysterious fact of "electron affin-
ity"— an electron may adhere firmly to a non-ionized molecule. Numerous measure-
ments of the rate at which electrons progress through a gas (a field of research which
I have not space to consi<ler here) indicate that at field strengths such as prevail in
these experiments, adhesion of electrons to molecules is rare and transient.

124 nni.L SVSTBAf TECHNICAL JOURNAL

Now if an electron on its way throuj^h the electric field from cathode
to antKle strikes atoms so often that it rarely has a chance to acquire
more than say half a volt of energy from the field between one impact
and the next, and if in each impact it loses most of the energy it has
just acquired — if this condition prevails, we need not wonder that the
voltage between the electrodes must be raised far be\ontl the ionizing-
potential of the gas before there is the least sign of iniensificalion of
current.

In interpreting the experiments upon such gases and at such pres-
sures as these last, it has been customary to make a more drastic assump-
tion, the opposite extreme from the one which justified itself in dealing
with rarefied helium; it is assumed that the electron surrenders at
every impact all the energy which it has derived from the field since
its last preceding impact. One ma\' be inclined to make mental reser-
vations in accepting so extreme an assumption, and it could almost
certainly be advantageously modified; but as a tentative assumption
it is successful enough to be legitimate. If it is true the electron
can never build up a capital of energy step by step along its path;
the only chances it will have to ionize will come at the ends of un-
usually k)ng free flights.

Let us imagine a specific case pour fixer les idees : supposing the
anode and the cathode to be parallel plates d apart, and representing
the potential-difference between them by V and the field strength
between them by .V (A'= V/d), we will set d = Q cm., F = 300 volts,
,Y = oO volts/cm.; we will imagine that the interspace is filled with
a gas having an ionizing-potential equal to 15 volts, and so dense
that the average free path of an electron between collisions is one
millimetre. I say that the average free path is 1 mm. long; if all the
sixty free paths which the electron traverses in going from cathode
to anoile were equal, it would never acquire more than 5 volts of
energy, and could never ionize an atom; but owing to the statistical
distribution of free paths about the mean value, there will be a certain
number out of the si.xty which will be longer than three millimetres,
and long enough, therefore, for the electron to acquire the 1.5 volts of
energy which are necessiiry to ionize. In this case there will be (iO e'-',
about eight, of these long free paths. In each centimetre tluri' will
be 10, t- of them. I will use the letter a' to designate this latter num-
ber, which is the number of atoms struck by the electron in each centi-
metre of its path, at moments at which it has energy enough to ionize
an atom; a' is therefore the number of chances to ionize vvliiili tiie
elccirnn \\.\- per centimetre. The formula for a' is:

.sou/-: co.\rr.Mi'(yii.iRy .ini.iwis i\ riivsus n \2->

in which lo reprt'si-iils iht- i<ini/iiiK-P"l*^'')'>->' "f 'lif Hi's^: ^ rt-prfsi-nls
the (lUMii fri'e path of thi- rli-ciron; (', its a-ciprocal, is the luimliiT
(if collisions suffered !>%■ the electron in each centitneire of the [latli:
and. since (" is proportional to the pressure of the j;as, it is replaced
l)y Pp in the final foriniilalion.''

It is already clear that the new .issiiniplion leads lo a llieor\ which
re<iiiires a different latii;iiaKe and a different set of ideas from those of
the foregoing section. \ot the ioni/ing-potenlial, Init the niiinlier
of ionizations performed li\ an electron in a centimetre of its |).iih.
is the quantity to he measured ii\ experimental de\ices; not i1h>
voltage between the electrodes, hut the field strength in the gas, is
the factor which controls the phenomena.'" In dealing with gases
which are expected to conform to the theory, the appropriate (iro-
cedure is to measure the nund)er of molecules which an electron ionizes
in a centimetre of its path, for all [)ractical values of the field strength
.V ami the density of the gas (or its pressure p) as independent vari-
ahles. I will designate this numher, following the usual practice,
hy a; if the theory is true it cannot he greater than a', it may he less.
These ciuantities a and a' are statistical quantities, not like tlic ioniz-
ing-potential qualities of the indi\idual atom or molecule, aiul ihi>
is a misfortiuie and disachantage of the theory and of the experiments
which it interprets; we are not, so to speak, in the presence of the
ultimate atoms as hefore, we are one step rem')\'e(l from ihcin, and this
step a difficult one to take.

The measurement of a is effected !)>■ \arying the distance d hetween
anode and cathode, and determining the current as function of d. If
-Vo electrons flow out of the cathode in a second, the ionization com-
mences at the distance rfo= V'X from the cathode, and from that

' Since the nunilier of free paths, out of a total number No, which exceed L in
length is equal to A'o exp ( — L \): and since the potential-difference between the be-
ginning and the end of the path of length L, if parallel to the field, is XL. It may
fx? objected that the electrons fiounre in all directions from their impacts, while the
language of this paragraph implies that they are always moving exactly in the
direction of the field. The rebuttal is, that if they do lose almost all of their energy
in an impact, or all but an amount not much greater than the mean speed of thermal
agitation, they will soon be swerved around completely into the direction of the
field no matter in what direction they start out.

'"The ionizing-potential determines the distance from the cathode at which ioniza-
tion commences; this is ecjual to (/o=''o/A', and within this distance from the
cathode there is no ionization and the theorj- does not apply; beyond this distance
the ionization is controlled entirely by the field strength and by the number of in-
flowing electrons and the voltage between cathode and anode affects it only insofar
as it affects these.

126 BELL SYSTEM TECHNICAL JOURNAL

point onward the electron-stream increases exponentially, so that
the current .Ve arriving at the anode is

.Ve = AV e\p a {d- do) (4)

In Townsend's experiments the cathode was a zinc plate, the anode a
film of silver spread upon a quartz plate; through little windows in
the silver film a beam of ultraviolet light entered in from behind,
crossed over the interspace and fell normally upon the zinc plate,
and drove electrons out of it. The zinc plate was raised and lowered
by a screw; the voltage-difTerence between it and the siher film was
altered pari passu so that the field strength in the gas remained always
the same. The current rose exponentially as the distance between the
plates was increased, and thus a was determined. A typical set of
data (relating to air at 4 mm. pressure, with a field strength of 700
volts/cm.) is plotted logarithmically in Fig. 5, the logarithm of the
current as ordinate and the distance from anode to cathode as abscissa.
The first few points lie close to a straight line, corresponding to an
exponential curve such as equation (4) requires; the value deduced
for a is 8.1G. (The distance d„ is about .35 mm. and has been ignored.)
Of the divergence of the later points from the straight line I will speak
further on.

Such an experiment shows that there is an a — that the theory is
not at any rate in discord with the first obvious physical facts — and
it gives the value of a for the existing values of A' and p. Townsend
performed many such measurements with different field strangths
and different pressures, and so accumulated a large experimental
material for determining o as function of the two variables /» and X.
To interpret these we will begin by making the tentative and tempo-
rary assumjition that whenever a molecule is struck by an electron
having energy enough to ionize it, it is ionized — that is, a' = a.
Rewriting the equation (3) which expresses a' as function of p and A',

we '^(•f lh.lt

a' p = li exp ( - /i I -.p X) =/ (X/p) . (5)

Therefore, if «' = «, the (|uotient of a by /> is a fiiiictiDii of X and p
only in the combination X/p; or, whenever the pressure and the field
strength are varied in the same proportion, the number of molecules
irinized by an electron in a centimetre of its path varies proportionally
with the pressure. I leave it to the reader to invent other wav's of
expressing (.")) in words which illumin.ite various aspects of its physical
meaning.

SOME CONTEMPORARY AlWANCES IN PHYStCS-Vl 127

FiK- 5 — Logarithmic plot of the currents across a gas (air) in which ionization by

collision is occurring, for a constant fieltl strength and various thicknesses of gas

(Data from Townscnd)

Experimentally, the test of (5) is made by dividing each one of
Townsend's values of a by the pressure at which it was determined,
and then plotting all these values of a/ p versus the corresponding
values of X p. All the points for any one gas should lie on or close
to a single curve, and within certain ranges of pressure and field
strength they do; so far, good. The curve should be an exponential

128 nr.l.l. SVSTFSf Tr.CIIXICAL JOVRWAl.

one, and within certain ranges of field strength and pressure it is;
again, good. The next step is to calculate the values of B and Vn
which the curve imposes on the gas to which it relates. I quote the
values of In, the ionizing-potential, which Townsend presents:

.\ir

N:

11:

CO,

11(1

Ii,()

.\

He

2.0

27 . (•)

2f)

2:i . ;<

1(1..')

22 . 4

17.3

12.3

W'luii ihe first of these values were (ielenuiiieil. an more direct way
of measuring ioiiizing-potcntials was known. Xow that we ha\e
some values obtained l)y the direct methods sketched a few pages hack,
and fortified 1)>- indirect but very forcible evidence from spectroscopy,
it is possible and cjuite important to test some of these. The values
for argon and helium, although of the proper order of magnitude, are
certainly too low. This is not in the least surprising, considering how-
many of the collisions between electrons and atoms must be perfectly
elastic. It seems indeed rather nnsterious that the current- voltage
relation in either of these gases should ha\e conformed closely enough
to (4) to make it jiossible to define and ineasure a; but the electrons
no doubt entered into luany of the collisions with energy enough to
put the atoms into excited states, if not to ionize them; and it is
nearly always possible to take refuge in the assertion that the im-
purities may have been sufficient to distort the phenomena. As for
the other gases in the list, all of them diatomic or triatomic, Town-
scnd's values are too high — not ver\- much too high, however; iisiiallv-
a matter of one-third to two-thirds."

It appears therefore that the theory I have just developed is too
sinijile, and must be amended. It seems natural to begin by dropping
the tentative assumption that a molecule is ionized whenever it is
hit by an electron having as much or more energy than is required
to ionize it, and adopt instead the idea once already suggested in
these pages, that it is sometimes but not always ionized by such a
blow; that there is a certain prohubility of ionization by a blow from
an electron having energy U, a probability which is zero wiicn I' < V
and is some yet-to-be-determined fimction of U when {'> V. Tiiis
would leave intact the conclusion that a p should lie a function of
X p, a conclusion which we have already foimd lo be veritied b\'
experiment; but it would relieve us of the necessity of assuming that

" TownsfiKj's v,t1iics of B likewise corrospoiul to values of the effectivT cross-
licction of the niolcriih.-, the (iiLinlity .1 of equation (2), which are of the same order
of magnitude as the directly determined values oi A. '

SOMli ii'\;/ w;i'A'./A'J' .;/)/•. /.V( / s /\ /■//> ^/( ^ i; 1."*

that function is precisely the expoiienli.il runction appearing in (•">).
[•".ssenlially the theory is rejiuced to this postulate: the nuinher of
molecules ionized l>y an electron in a centimetre of its path depends
only u(X)n the eneryj),- it accjuires from the field in its free ni^lil from
one collision to the next. If in this form the theory still cannot
give satisfaction, the next step will he to alter the original assuiyp-
tion that the electron comes practically to a dead stop in e\er>- col-
lision. In dealing; with the nohle gases and the metal \apnurs, the
facts alxiut elastic collisions which I ha\e alread\' oulliiuvl pro\e
that this assumption should not be made at all. It is clear ilial this
is another prolilein for the future Bolt/mann!

Meanwhile, one of the cardinal features of the TowummhI experi-
menis is the fact that the\' display the .gradual advent of the trans-
formation of the maintained currents which we have hitherto con-
sidered, into the self-maintaining discharges which are the familiar
and the spectacular ones; and we now ha\e to examine the agencies
of this transformation.

4. TnK Discn.\R<.F. Begins to CoxTRinuTE to the F,i.ECTRf)N-
Stre.xm Which M.mnt.mns It

(■reatly though the current of primary electrons from the cathode
to the anode may be amplified by the repeated ionizations which I
have described, there is nothing in this process which suggests how
the discharge may eventually be transformed into a self-maintaining
one like the glow or the arc. The free electrons may ionize ever so
abundantly, but as soon as the supply from the cathode is suspended
by cutting ofT the heat or the light, the last electrons to be emitted
will migrate off towards the anode, and whatever electrons they
liberate will go along with ihem, leaving a stratum of gas devoid of
electrons in their wake; and this stratum will widen outwards and
keep on widening until it reaches the anode, and then the discharge
will be ended. Something further must happen continually in the
gas through which the electrons are flowing, something which con-
tinually supplies new free electrons to replace, not merely to supple-
ment, the old ones which are absorbed into the anode and vanish
from the scene.

We have alreacK' noticed one sort of e\ent contiiuialh' hai)peiiing
in such a gas as helimn traversed by not-too-slow electrons, which
might conceivably develop into a mechanism for maintaining the dis-
charge; for, when an atom of the gas is put into the "excited state"
by a blow from an electron, it later returns into its normal state, and

130 PELL SYSTEM TECHNICAL JOURNAL

in so returning it emits a quantum of radiant energy which may
strike the cathode, and be abs<)rl)ed b\- it, and cause another electron
to leap out of the cathofie and follow the first one. There are two
other concei\able processes, which have the merit that they can not
only be concei\ed but also witnessed in operation iiy themselves when
the right conditions are provided. Positive ions flung violently
against a metal plate drive electrons out of it, as can be shown by
putting a positively-charged collector near the bombarded plate and
noticing the current of negative charge which flows into it; and posi-
ti\-e ions flowing rapidly across a gas .ionize some of the atoms in
it, as may be shown by sending a beam of such ions across the inter-
space between two metal plates, with a gentle crosswise field between
them which sucks the freed electrons into the positive plate. The
mechanism of the first process is not understood, except when the
positive ions are so many and so swift that they make the metal hot
enough to emit thermionic electrons, which does not happen in the
cases we are now considering. The mechanism of the second process
is only dimly understood, but it is clear enough that a positive ion
driven against an atom is much less likeh' to ionize it, than an electron
of equal energA- would be.'- Either of these two processes is very
inefficient, at least at the comparatively low speeds with which posi-
ti\e ions move under the circumstances of these experiments; but they
are probably efficient enough to do what is required of them. No
doubt all three of them contribute to the discharge; but the relative
proportions in which they act certainly differ ver>- nuicli from one sort
of discharge to another, and will furnish research problems for years
to come.

Returning to I-'ig. 5, we note once more that as the electrodes are
moved farther and farther apart while the density of the gas and the
fielfl strength arc held constant, the current at first rises exponentially
(linearly in the logarithmic plot) as it should if the free electrons and
onl>' the free electrons ionize; but eventually it rises more rapidly
and seems to be headed for an uncontrollable upward sweep. Town-
send attributed this uprush to the tardy but potent participation of
the i>osilive ions, either ionizing the molecules of the gas by impact
after the fashion iA the negati\e ions, or driving electrons out of the
cathode when they strike it, or both. F^ilher assumption leads to

"If iiKiiiicntuin is rinisorvrd in the iiii|>art liotwoc-n ion and atom, the ion must
retain ,1 larKe part o( its kinetic energy after the cullision, or else the struck atom
must lake a kir^e part iif it as kinetic energy of its own niotiun; it is not possible
for tlie striking partiile to spend nearly its entire energy merely in liberating an
elerlron from the struck one. Conservation of momentum |x'rliaps does not pre-
vail on the atomic scale; but of all the principles of classical ilvnaniics, it is the one
which the reformers of physics most hesitate to lay violent hands upon.

soMr. co.v/r.uroK.iA'K .tnf.iKcrf /.v riivsics- n i.ii

an iHiuation expressing the dal.i e(niall\' well. If we adopt the former,
and desiitnale by (i the niiinher of moleniles ionizetl i)y a positive
ion in a centimetre of its path, and by X,> llie iininhcr of electrons
supplied [wr second at the cathode, we ^;et

Of course, ii must he mnili smaller than <*, or tiic posilixe ions would
have made themseUes felt earlier. Or if we adopt the latter idea,
and tiesiRnate by k the number of electrons expelled from the cathode
(on the average) by each positive ion striking it, we arri\e at the
formula

^^ 1 -*(«•«■'- !)• ^''

N'atur.dl>- k must be imich smaller than unity for the s.iiiie reason.
In Fig. r> the broken curve represents (ti), with the values <S. 1(5 and
.0067 assigned to a and ji; it also represents (7), with the values
S. 10 and .00082 assigned to a and k." (It was expected that the
cur\es representing the two equations would be perceptibly apart
on the scale of Fig. ."); but they were found to fall iiidistiiiguishably
together.)

Fvidently, therefore, the positi\e ions, weak and lethargic as they
are in liberating electrons (one has only to compare 0 with a, or look
at the \alue assigned to k in the last sentence!), can produce a notable
addition to the current when the electrodes are far enough apart; and
more than a notable addition, for when the dis'ance d is raised to the
value which makes the denominator of (6) — or of (7), whichever
equation we are using — equal to zero, the value of .V is infinite! Per-

" The derivations of (6) and (7) are as follows. Represent l)y M (x) the nunil)er of
electrons crossing the plane at .v in unit time (the cathode being at .v = o and the anode
at .v=</); by P (x) the numlwr of positive ions crossing the plane at x in unit time;
by .V,, the numtier of electrons independently supplied at the cathode per unit time,
which is not necessarily equal to the value of M at .x=o (hence the notation); by i
the current, or rather the current-density, as all these reasonings refer to a current-
flow across unit area. We have

Me+Pe = i, hence
making the assumption which leads to (6) we have

dM/dx = aM+0P = (a-/3) M+pi/e

The boundary conditions are: ..V = A'oat .v=oand M = i''eat x=d. Integrating the
equation and inserting these we get (6). Making the assumption which leads to
(7) we have

dM,dx = aM

The boundary conditions are: M = NQ+k(i/e — Af) or (l-|-it;.l/ = iVo-|-At/< at x = o,
and M = i/e at x = d. Integrating the equation and inserting these we arrive at (7).

132 PFJJ- SySTF.yf TECIISICAL .lOVRXAL

liaps llie best way to conceive of lliis is, that as the distance between
the plates is increased toward tliat critical value of d, the value of
.Vo — which is the rate at which we have to supply electrons at the
cathode, in order to keep a preassigned current flowing — diminishes
continuously and approaches zero; so that e\entually the current
will keep itself going (and actually start itself) with the assistance of
the occasional ions which are always appearing spontancousK in
every gas, even though it be encased in an armor-plated shield. ( )l
course, it is rather risky to predict just what is going to happen.
when an e(|ualion whicii has been lised u|j to represent a finite physical
phenomenon over a certain range exhibits an infinite discontinuity
at a point outside of that range. I'sually, of course, the infinite value
which the equation rec|uires is modified into a finite one by the influ-
ence of some factor which was neglected when the equation was
devised. In this case, howe\er, the infinite discontinuity corresponds
to a sudden catastrophic change. If an electrometer is shunted
across the interspace between anode and cathode, its needle is forci-
bly jerked; if a telephone-recei\er is connected in series with the
interspace, it makes a clicking or a banging sound; if the gap is wide,
so that the voltage just before the disruption is high, there is a brilliant
flash, which ma>' bear an uncomfortably strong resemblance to the
liglitiiing-bolt which is the cosmical prototype of all electric sparks.
What goes on after the critical mcjment of transition or transforma-
tion depends on many things; and not only on ob\ious features of the
spark-gap, such as the kind and density of gas and the shape and size
and material of the electrodes, but also on such things as the resistances
and the inductances in series with the discharge, and the qualities of
the Sf)urce of elect romoti\e force and its ability to satisfy the demands
for current and voltage which the new discharge may make. Some-
times these demands are too extravagant for most laboratory sources
or jjcrhaps for an\- .source to meet; probably this is why the spark
between extended plane surfaces in dense air is as ejihemcral as it is
\iolent. But this does not always happen; in a s-ufficienth' rarefied
gas, the sc-lf-mainiaining discharge which sets in after the transforma-
tion re(|uires only a modest current and a practicable \-oliage, and
supports itself with a few thousand \olts ajjplied across its terminals.
The same thing occurs in a dense gas, if either of the electrodes is
I)ointed or shari)l\- curved, like a needle or a wire; the condition, more
exactly, is that the radius of curvature of either electrode should be
distinctly less than the least distance between the two. The trans-
formation, however, is always very sudden, whether the new dis-
charge be transient or |)ermancnt; and there are also sudden transi-

sci// coxir.Mi'ou.iRy .iitixcis- i\ I'livsiis \ i i.u

timis from one sort <>f s«."lf-m.iiiu.iiniiit; (liscli.irno lo iinotlier, r.i;.,
from rIow lo arc or from om- kind of ^;lo\v to anoilu-r when ci-rtain
critiral roiulilions are transi;rrssr(I (criliral coiulitiotis wliirh mav
tlK-msolM's ili'priul on the l>atti'r\' ami ihc rirniit as well as the con-
st.uUs of tin- spark-gap). There are disroiitiniiities of eurreiit and
diseontinuiiies of \oItai;e at these transitions, and al)riipl chanj;fs
in the \ isil>le appearance in the discharge; and at each transforma-
tion there is a rearrangement of the distribution of space-charge in
the gas. Hitherto we have encountered space-charge only in one or
two of its simplest manifestations, retarding tlte How of an electron-
stream across a vacuum, anil suddenly annulletl when positive ions
are mingled with the stream. .Now we ha\e to consider much subtler
and more complicated cases, in which the space-charge varies rapidly
in density and e\en in sign from one part of the gas to another, and
the field and potential distributions are utterly distorted by it; and
these distortions are essential to the life of the discharge. This
distribution of space-charge is indeed dominant; and so I will write
down some formulae which mav be used to describe it.

.'). l)iiiRi:ssi()\ TO W'kiii. Down Somk Sp.\< e-Ch.\rge

I-".gl ATIONS

The fundamental cfiualion of the electrostatic field, known as
Poisson's equation, is

^ -\ = -n-^ + -j-^ + -r^ = - 47rp (8)

a.v- ay- dz- ^ '

in which l' represents the electrostatic potential, and p the xoluine-
density of electric charge.

We consider only the mathematically simplest case in which all
variables are constant over each plane perpendicular to the .r-axis,
and so depend only on the coordinate .v; as for example near the
middle of an exceedingly wide tube with the .v-axis lying al(jng its
axis. In this case Pois.son's equation is

dH' dX

in which A' represents the potential-gradient, or field strength with

sign reversed.'* The value of X is determined at all points when the

" Field-gradient is therefore, proportional to space-charge with sign reversed,
and rice versa. Positive fieUI-graditnt implies negative space-charge; negative field-

134 BELL SYSTEM TECHNICAL JOURNAL

value of A' at any one point and the values of p at all intermediate
points are preassigned. Thus let Ao represent the preassigncd value
of A' at .v=0, and Xj represent the value of A' at .v=(/; wc have

Aj=-4jr/'pr/.v + A'o. (10)

•'0

Consequently the P.D. between an\- two points is also determined;
that between a=0 and x=d is

Vi- Vo= -i^ f (ix Tp dx + Xo(L (11)

Jo Jo

Now we introduce the further assumption that the electric charge
is concenlraled upon corpuscles (electrons or charged atoms) of
one kind, of ec|ual charge E and mass ni, of which there are iidv in a
very small volume dv at .v; n is a function of .v. Then

«£ = p. (12)

Assume finally that the corpuscles are moving with speed u, identical
for all corpuscles having the same A;-coordinate, but depending on x;
represent the current-density by i; we have

ttEu = i (13)

and consequently

p = i/u. (14)

I

Now consider the llow of current between two parallel jjlanes, from
one electrode at x = 0 to the t)lhcr at x=d. If the current is borne
by corpuscles of one kind, and the assumption last made is true; and if
we know the speed of the corpuscles at every point between the plates,
and the field strength at someone point; then we can calculate the field
strength everywhere between the plates, and the potential-difTerence
between them.

The customary convention about the field strength is to assume
it to be xero at the electrode from which the corpuscles start, so that
Xo = 0 in (11). Rewriting (11) to take account of (14), we have

Vd - To = - 4 TTt / dx f'dx/u ( 1 o)

Jo Jo

as the general equation.

Krudiciit iiiiplif!) (xjsilivf space-charge; iinirumi field implies zero space-charge.
It is instructive lo exaniiiie mappings of fielcl-distribiition with this principle in
mind: such mappings, tor example, aslhose in Kig. '>. The uniform fu-ld in a current-
carrying wire nieans th.it |K>sitive and negative charges are distril)ute(l everywhere
in the metal with equ.d density — a conclusion one might forget, but for these more
general cases.

SOMI-: COM F.Mi'iU^'.iKy .inr.ixcrs /.v I'livsus it \y?

If \vi' siipiMisi' lli.it the corpiisili-s .u'(|iiiii' llirii s|hc(1 ii .iI iIr- ili>l.iiu»'
■v ill frir llii;lil Inmi ilir i-lrctrndr wlicir llu-\ si.irl, \vc li>ivr \inir=e\',
.iiul

{Va-V.)"^=^=yj'^id\ (16)

This is till- t(|u,iliiii .ul.ipted to ok-rtrons or other ions llowing acrAss
olht-nvisf enipt\ sp.ur.

If wo supposr that the corpuscles have at each point a speed propor-
tional to tin- titid -trenyjth at that point, we have u= ±k dV/dx, nm\

I'd- V»= .^-^

This equation would be adapted to ions drifting in so dense a gas,
or so weak a field, that they acquire very Utile energy from the field
(in comparison with their average energy of thermal agitation in the
gas) Ix'tween one collision and the next, and lose it all at the next.'^
If we conceive of ions which acquire much energy from the field
between one collision and the next (much, that is, in coinparison
with their average energ>' of thermal agitation) and lose it all at
the next collision, we have u- = {irel/2m) dV,'dx and

{V4-Vof = Cid^'^ (18)

the constant C being equal to vm'El multiplied by a certain numer-
ical factor, and / standing for the mean distance traveled by the ion
between one collision and the next.

The theory- just given is too simple; it is an essential fact of the
actual physical case that the ions emerge, at the surface of the electrode
whence they start, with forward velocities which are distributed
in some way or other about a mean value. These initial forward
velocities, though often small compared with the velocities which the
ions may acquire as they cross to the other electrode, are large
enough so that all of the ions would shoot across the gap if the field
strength were really zero at the emitting electrode and assisted them
ever>where beyond it. In fact the space-charge creates a retarding
field at the surface of the emitting electrode, and a potential minimum
(if the ions are negative; a potential maximum, if the ions are positi\e)
at a certain distance in front of it. Here, and not at the emitting
electrode as we previously assumed, the field strength is zero. Equa-
tion (10) is often valid in practice, because this locus of zero field-
strength is often very close to the emitting electrode. In fact, by

'* .As in electrical conduction in solid metals (cf. my preceding article).

136 Bni.I. SySTIlM TECIIMC.il lOlliX.II.

raising the IM). bfiwccii tlic ])l;ilcs sulVuiciitly, the locus of zero
field can be driven hark into coinridenre with the emitting plate;
beyond whieh stage, the "limitation of current by space-charge"
ceases. But if the P.I), is sufficiently low the potential minimum (or
maximum) is prominent and is remote from the electrode, and in
these cases the equations we have just deduced are inapplicable.

It thus may readily happen that when we apply a certain potential
to one electrode and a certain other potential to another electrode
separated from the first one by gas or vacuum, we may find points
between them where the potential is not ittlerniediate between the
potentials of the electrodes. This is a (jueer conclusion, to an\hody
accustomed to the How of electricity in wires, liul ii is true, and
must be kept in mind.

0. Tiiii Self-M.m.ntai.ninu Disc h.vrcus

The Arc ought to be the easiest to understand among the self-
maintaining discharges, in one rcsjicct at least; for it keeps its own
cathode so inten.sel>- hot that thermionic electrons are supplied con-
tinuously in great abundance at the negative end of the discharge,
and the theorist can begin his labors l)y trying to explain how and
why this high temperature is maintained. Anything which lends to
lower the temperature of the cathode, for instance b>- draining heat
awa>- from it, is \er>- perilous to the arc. Stark uses various schemes
for preventing the cathotle from growing \ery hot, and they all killed
the arc. This alsf) ex()lains why the arc is most difficidl to kindle
and most inclined to flicker out when formed between electrodes of
a metal which conducts heat exceptionally well, and most durable
when formed between electrodes of carbon, which is a comparati\ely
poor conductor for heal. It probably explains why the arc has a
harder time to keep itself alive in hydrogen, a gas of high thermal
conductivity, than in air. While the gas in which the arc has its
being and the anode to which it extends both influence the discharge,
the high temperature of the cathode is cardinal.

The cathode is presumably kept hf)t by the rain of jKhsitive ions
upon it, striking it with violence and yielding up their energy of
motion to it; at least this is the obvious and plausible explanation.
Now the arc is commonly and easily maintained in fairly dense gases,
with a com|)aratively small potential-difference between widely-
si'parated electrodes; and the euerg\- which an ion can acquire from
the field strength prevailing in it, in the short interval between two
collisions with nrnki uUs, ij. so sm.ill lli.it it cannot be made to account

s<mi-: C(K\rr.Mi'(V<.ih'y .-inr.ixcrs tx rinsus ri \m

iur iIr- furious luMt ik-M-Iopi'd ,il tlu- ciilindf wluti tin- inns lin,ill>-
strike it. Just ln-lori' tlu- ions i»rri\o ,it ilu- i.iiIkkIi' thr\ must \k-
t'lulowi'd with a kiiu-lic oniTk;\' which is \i'i\ uinisu.il (lits.i\ ihi- iiMsl )
in tlie miililio of iht- ilisrli.irm-; and it is in fa( i ol)si'rvfd thai just in
front of tlie cathodt- there is a sharj) and sudden jiotenti.d-f.dl, cor-
res|>ondin); to a strong field extending; I)ut a little \va\- outward from
the electrode and then dsing down into the weak lield pre\ailinK
throusli the rest of the arc. This strong lield picks up the ions which
have meanderetl to its outward edge from tiie hody of the discharge
and hurls them against the cathode — not very forcihh , for the energy
they recei\e from that potential-fall is not a great amount by ordinary
standards, and most of the ions probably lose some of it in collisions
on the way; but with much more energy than they would be likeK'
to possess anywhere else in the arc.

This fX)tential-fall immediately in front of the negative electrode,
the cathode-fall of the arc, is measured by thrusting a probe or sound-
ing-wire into the discharge as close as possible to the cathode (gener-
ally about a millimetre away), and determining the P.D. between
it and the cathode. The probe is regarded with some distrust, as it
raises in an acute form the old ciuesiion as to how far the phenomena
we observe in nature are distorted by the fact that wc are observing
them; the wire may alter the potential of the point where it is placed,
or it may assume a potential entirely different from that of the en-
vironing gas; but the general tendency nowadays, I believe, is to
accept its potential as a moderately reliable index of the potential
which would exist at the point where it stands if it were not there.'"
The cathode-fall, as so measured, depends unfortunately on quite
a number of things; the material of the cathode, the gas, the current.
The gas is always mi.xed with a vapour of the electrode-material,
particularly in the vicinity of the electrode; the only way to have a
single pure gas is to enclose the whole system in a tube, evacuate the
tube to the highest possible degree, and then heat it until the vapor-
tension of the metal of which the cathode is made rises high enough
for the vapor to sustain the arc. This is practicable with the more
fusible metals; and with mercury, the arc generates heat enough to
maintain the vapor-tension sufficiently high. In pure mercury-

" On this matter the e.xperiments of Langniuir and Schottky, mentioned further
along in this article, promise new knowledge. The probe automatically assumes
such a potential that the net current-flow into it is nil; for example, if it is immersed
in an ionized gas in which electrons and ionized atoms are roaming about, its eventual
potential is such that equal numbers of particles of the two kinds strike and are
absorlwd in it per unit time. If the electrons are much more numerous or have a
much higher average energy, or both, this potential may be several volts more
negative than the potential at the same point before the probe was put in. The
same may be said about the wall of the tube.

138 BELL SYSTF.M TECHXIC.-IL JOURNAL

\apor, the caili()(k'-f;ill assuniL's tlie value 4.9 \oIts which is the first
resonance-potential of the mercury atom and therefore, as we have
seen, is effecli\ely the ionizing-potential of the free mercury atom when
the electron-stream is as dense as it is in the arc. This suggests a
delightfully simple theory of the whole process: the electrons stream
from the cathode, they acquire 4.9 volts of energy from the cathode-
fall, they ionixe mercury atoms at the outward edge of the region of
high field strength, the positive ions so created fall backward across
the cathode-fall and strike the cathode, surrender their energ>' to it
and so keep it hot, more electrons pour out, and so forth ad infinitum.
It remains to be seen whether so simple a theory can be modified,
by statistical considerations or otherwise, to explain the values of
the cathode-fall in mixed and diatomic gases.

We do not know a priori what is the ratio of the number of electrons
flowing outward across the cathode-fall in a second to the number
of ions flowing inward. It might, however, be very great, and still
the number of ions within the region of the cathode-fall at any instant
could far surpass the number of electrons within it — the electron
moves so much more rapidK' than the ion, and has so much better a
chance of crossing the region in one free flight without a collision.
Even in hydrogen, in which the ions are the lightest of all ions, the
electron current would have to be 350 times as great as the ion-
current if the electrons just balanced the ions in unit volume. It is
therefore legitimate to try out the assumption that the region of
cath(xle-fall is a region of purely positive space-charge, in which some
such ecitiation as (IG), (17),f>r (IS) gives the current of positive ions as a
function of the cathode-fall and the width of the region. K. T. Comp-
ton selected (18). Unfortunately the width of the cathode-fall region
has not been measured, but he assumed it equal to the mean free
path of an electron in the gas. The value which he thus calculated
for the current of jiositive ions was about 1% of the observed total
current; the remaining OlC^'f consists of the electrons.

From the cathode region onward to the anode, the gas traversed
i)y the arc is dazzingly brilliant. In the long c\lindrical tubes which
enclose the mercur\- arcs so commonh' seen in laboratories and studios,
the \apor shines everywhere except near the ends with a cold and
rather ghastly white light tinged with bluish-green. This is the
positive coliMiin of the mercury arc. The potential-gradient along
it is uniform, suggesting the flow of electricity down a wire; but here
the resemblance stops, for when the current-density goes up the
(«)tential-gr;idient goes down. The curve of voltage versus current,
which for a solid metal is as we all know an upward-slanting straight

st>Mi: ci>.\ 1 1 Mfi'K.iio tin .ixu-.s i.\ rilVSICS VI l.io

liiii', is for thf arc a (iDwnw.iril-slaiilinK rur\i' (l-'i^;- •">). Such a curvt'
is ralli'tl a ilianuliristic, ami tin- arr is said lo liaw a ncn'iUvc cliaractrr-
istic. Ii>iiixatii)ii gm-s on roiilimialK witliiii the positive column,
ami ions of l)olh si^ns can Ik; drawn out i)y a crosswise field; hut
recombination of ions, a proccs,>? which we have not considered, also
goes on i-onlimiaily and maintains an cfiuilibrium. Presumably it

Fig. 6 — Voltage-current curves or "characteristics," for arc discharges (lielow) and
glow discharges (above) in air, between gold electrodes. The different curves corre-
s|K)nd to different anofle-cathcKlc distances. (Ives, Journal of the Franklin In^lilute)

is the effect of the field strength on this equilibrium which causes
the current-voltage curve to slant in what most people instinctively
feel is the wrong wa>'; but the theory of the eciuilibriuiii is not yet
far advanced.

Langmuir and Schottky, working independenth' in Schenectady
and in dermany, [)erformcd some very pretty experiments by thrust-

140 flF.LL SYSTEM TF.CIIXIC.IL .lOL'RX.-II.

iii}i n(.Kativul\ -rhargcd wiit-s or plates into ihc i>usili\e column. These
wires and jilales surroundeil themselves with dark sheaths, the thick-
ness of which increased as the potential of the metal was made more
and more hii;hly negative. The explanation is, that the electrons
in the positive column cannot ai)i)i-oach the intruded wire, being
clri\eii back b\- the adverse field; the ilark sheath is the region from
which they are excluded, and across it the positive ions advance to
the wire through a field controlled by their space-charge. The equation
selected by Langniuir to represent the relation between the thickness of
the sheath, the voltage across it, and the current of positive ions into
it, is (16). As the sheath is \ isible and its thickness can be measured,
as well as the other cjuantities, the relation can be tested. This was
done by Schottk)-; the result was satisfactory. When the intruded
electroile is a wire, the sheath is c>lindrical, and expands as the voltage
of the wire is made more negati\e. As the area of the outer boundary
of the sheath is increased by this expansion, more ions from the positi\'e
column touch it and are sucked in, and the density of flow of positive
ifins in the column can be determined. By lowering the potential
of the wire gradually so that the electrons can reach it, first the fastest
and then the slower ones, the velocity-distribution of the electrons
in the column can be ascertained. Their average energy depends on
the density of the mercury vapour, and may amount to several \-olts.

Beyond the posili\'e colimin lies the anode, itself preceded by a
sharp and sudden potential risi-. The electrons are flung against it
with some force, and it grows and remains \ery hot; usually, in fact,
hotter than the cathode. This high temperature does not seem to
be essential to the continuance of the discharge, for the anfxle can
be c<Hjled without killing the arc; yet it seems strange that a quality
so regularly found should be without influence upon th? discharge.
One must beware of underestimating the influence of the anode;
when an arc is formed in air between two electrodes of different
materials, it behaves like an arc formed between two electrodes of
the same material as the anf)de, not the cathode!

The so-called lo'u'-i'ollanc arc, although not a self-niaini, lining dis-
charge, merits at least a paragraph. .A dense electron-sireani poured
into a monatomic gas from an independenth-hcaleil wirr. and ac-
celerated by a P.D. surpassing the resonance-potential of liiu gas,
may ionize it so intenseh- that there is a sudden transformation into
a luminous arc-like discharge. This is a sort of "assisted" arc, its
catlxKle being ke|)t warm for its benefit by outside agencies. Its
history is .i long and interesting chapter of contemporary physics,
whereof the end i> not \et. The most remarkable feature of this arc

Ts/c.v n

^m mwmtmmmmmmmmmmm*

-^ »«««M4tf MM Mlll»>

«r^ •• ' '^ " '"'r<iWir<it«wnnRrrc*«'^

Fig. " — Photographs of the glow-dischnrge in a long narrow rvlintlcr. showing chiclly

the sulHJivision of the positive column into striations. (De la Rue and Muller,

Philosophical Transactions of the Royal Socifly)

142 BELL SYSTEM TECHMC.IL JOURNAL

is that it can siir\ ive even if tlie voltage between anode and cathode
is far below the resonance-potential of the atoms of the gas, which
seems impossible. A year ago it seemed that this effect could always
be ascribed to high-voltage high-frequency oscillations generated in
the arc. This explanation was presently confirmed in some cases and
disfjualificd in others, and now it appears that when there are no
oscillations an astonishingly strong potential-ma.ximum de\elops
within the ionized gas. Potential-maximum and oscillations alike
are pr(»l)ably to be regarded as manifestations of space-charge.

The Glow in a rarefied ^as is a magnificent sight when the gas is
rarefied to the proper degree, not too little and not too much; divided
into luminous clouds of di\'crse brightnesses and diverse colors, re-
calling Tennyson's "fluid haze of light," yet almost rigidly fi.xed
in their distances and their proportions, it is one of the most theatrical
spectacles in the repertoire of the physical laboratory-. The grand
divisions of the completely-de\eloped discharge are four in number,
two relalix'eK' flim and two bright; beginning from the cathode end.

ODD

Fig. 8— The Crookcs dark space between the cathode (thin line at left) and the
negative glow. See footnote ". (.Aston, Proeerdings of the Royal Society)

they are the Oookcs dark space, the negative glow, the I'aiada\ dark
space, and the positive column. .Additional gradations of color and
brightness can often be seen very close to the cathode and \-ery close
to the an(Kje. Photographs of the glow which give anything ap-
proaching a true idea of its appearance to the e\e are hard to find.
I repHKluce in Fig. 7 some photographs taken nearly fifty years ago by
de la Rue, which have re.ip|RMred in many a text; they show chiefly
the striking flocculent cloudlets into which the positive column some-
limesdivides itself. In Fig. 1) there are tw.) sketches made by Graham.

soMF. coNrr.MPOR.im- .iDr.iscr..^ tx /-//rv/i v r/ i-u

The Cr»K)kcs dark space (or catluxle dark spare, or Mitlorf dark
space as it is called in (ierinaiu) extends from the cath<Mle to the
boundary of the bright luminous cloud which is the ncRatise glow.
The boundary is generally so well-defined and distinct that an observer
finds it easy to juilgc when a soundinj;-wirc just touches it, or the
cross-hair of a telescope coincides with its image; "in the case of oxy,--
gen," Aston s;ud, "the sharpness was simply amazing; even with so
large a dark space as 3 cm., the sighter coukl be set (to the boundary)
as accurately as to the cathode itself, i.e., to about 0.01 mm." I re-
produce some of Aston's i)hotograplis in Figure 8, although ho says
that for reasons of perspective the boimdary of the negative glow ap-
pears more diffuse than it really is." The electric field strength within
the CrcMikes dark space is greater, often very much greater, than in
any of the other di\'isions of the discharge; almost the whole of the
voltage-rise from cathode to ancnlc is comprised within it, and the re-
mainder, although spread across all the brilliant parts of the glow, is
inconsiderable unless the tube is made unusually long. The behavior
of the dark space when the current through the tube is varied (by
varjing a resistance in series with the tube) is curious and instruc-
tive. If the current is small and the cathode large (a wide metal
plate) the negative glow overarches a small portion of the cathode
surface, lying above it like a canopy with the thin dark sheath be-
neath it. When the current is increased the canopy spreads out,
keeping its distance from the metal surface unaltered, but increasing
its area proportionally to the current; the thickness of the Crookes
dark space and the current-density a'cross it remain unchanged. If
the experimenter continues to increase the current after the cathode
is completely overhung by the glow, the dark space thickens steadily,
and the current-density across it rises.

The changes in the voltage across the Crookes dark space which
accompany these changes in area and thickness are very important.
The voltage is measured with a souniling-wire, like the cathode-fall
in thq arc; but since the boundary of the dark space is so sharply
marked, the experimenter can set the sounding-wire accurately to it
instead of merely as close as pnjssible to the cathode. So long as the

"Adjacent to the cathode a thin perfectly dark stratum can be distinguished
(especially in the picture on the right l. The P.D. across this thin black space is, as
nearly as it can be guessed from the width of the space, of alK)Ut the magnitude of
the ionizing-potential of the gas. In fact .-Xston estiniatc<l it for helium (to which
the pictures refer) as 30 volts, a good anticipation of the value 24.5 assigned years
later to the ionizing potential. It seems therefore that the outer edge of the very
dark space is at the level where the electrons coming from the cathode first acquire
energy enough to ionize.

144 BEI.L SYSTEM lECIIMCAL JOL'RXAL

negative glow does not overarch the whole cathode, and the thickness
and current-density of the dark space keep their fixed mininunn
values, the voltage across it remains constant likewise. This is the
normal ralliode-fall of the glow. It is an even more thoroughgoing con-
stant than the thickness or the current-density of the dark space, for
these \ary with the pressure of the gas (the dark space shrinks both
in depth and in sidewisc extension, if the current is kept constant
while the gas is made denser) while the normal cathode-fall is iniiiuine
to changes in pressure. It depends both on the gas and on the ma-
terial of the cathode; the recorded values extend from about (iO \-olts
(alkali-metal cathodes) to about 400 volts. Attempts have been made
to correlate it with the thermionic work-function of the cathode metal,
and there is no doubt that high values of the one tend to go with
high values of the other, and low with low. When the cathode is
entirely overspread by the negati\c glow and the dark space begins
to thicken, the \'oltage across it rises rapidly; the cathode-fall is said
to become anomalous, and ma\' ascend to thousands of volts.

Almost the whole of the voltage-rise from cathode to anode, as I
have stated, is generalh' comprised in the cathode-fall; the remainder,
although spread o\er all of the brilliant divisions of the discharge, is
inconsiderable unless the tube is unusually long. The field strength
in the Crookcs dark space is also much greater than anyw'here else in
the glow. This is illustrated b\' the two curves in Fig. 9, representing
the field strength in the discharges sketched above them. (For the
region of the (Vookes dark space, however, the curves are defective.)
In the luminous clouds the electric force is feeble, and the>- in fact
are not essential to the current-flow; if the anode is pushed inwards
towards the cathode, it simply swallows them up in succession with-
<iut interfering with the current; but the moment it invades the
Crookes dark space, the discharge ceases unless the electromoti\'e
force in the circuit is hastily pushed up. The mechanism wliiili keeps
the glow ali%'e lies concealed in the dark space.

One naturally tries to in\enl a mechanism re.seml)ling llie one
suggested for the arc: the cathoile-fall serves to give cnerg\- to tJU'
electrons emerging from the cathode, so that they ioni/e molecules at
the e<lge of the neg.iti\e glow; and the ions fall .igainsl the cathode
with energy enough to dri\e out new electrons. But the details are
more difficult to ex|)lain. The cathode-fall gives much more energy
to the electrons than they need to ionize any known molecule, so that
apparently its high \-.ilue is what the ions require to give them enough
energy to extract electrons from the cathode. We can hardly argue
that the electrons are thermionic electrons; the cathode does not

.V(».u/-: COM r.Mi'oK.uo' .inr.ixci-s ix rnvsics vi 145

i;nnv liol fni>ii>;li; if it docs, tlic callnHlf-l'.ill MuMi-iiK- Cdll.ipsrs. and
till- ^;lt)\v is liaMf to turn into an arc. Mxpiilsion of t.-lfrlrons from cold
metals l)y ions strikini; tlu-m lias hccn separately studied, l)iil not
siilTicientK'.

On the other haiul, there is good e\ idenci- ill, it the (rookis d.irk
space, like those tlark sheaths scooped out in the i)ositi\i' cohm;:!

Faraday Crookes

dark space Negative glow dark space

V

—

—

■^

^J

v

2 4 6 8 10 12 14 16 18 20
d

Negative
Uniform positive coljmn. Faraday darl< space, glow

u

'^

k.

V

^- — .

'V

12 K 16 18 20

Fi^. 9 — Sketches of the (,'li)W in rarefud nitrogen ,it two pressures (the higher below)

with curves showing the trenri of field strength along the discharge. (Grahnni,

Wiedemanns Annalen)

of the mercur>- arc by intruding a negatively-charged wire, is a region of
predominantly positive space-charge, in which positive ions advance
towards the cathode in a manner controlled by some such equation
as (16) or (17). F"or example, (iunther-Schulze proposed (16) to de-
scribe the state of affairs in the Crookes dark space in the condition
of normal cathode-fall; that is, he assumed that the ions fail unim-
peded from the edge of the negative glow to the cathode surface. Xo

146 DELL SYSTEM TECHNICAL JOURNAL

doubt this assumption is too extreme, yet it leads to unexpectedly
good agreements with experiment. Thus when the thickness of the
Crookes dark space is altered (by altering the pressure of the gas)
lea\ing the voltage across it constant, the current-density varies in-
versely as the square of the thickness, as it should by (16). And when
Gunther-Schulze calculated the thickness of the dark space from
(10), using the observed values of cathode-fall and current for six
gases and two kinds of metal, and substituting the mass of the mole-
cule of the gas for the coelTicient m in that equation, the values he
obtained agreed fairly well (within 40^0 with the observed thick-
nesses. Long befoie, J. J. Thomson had proposed (17), and Aston
tested it by a scries of experiments on four gases, in the condition
of strong anomalous catho<le-fall. As k of that equation should be
inversely proportional to the pressure p of the gas, the product id^V--
{V standing for the cathode-fall) should be constant at constant
pressure, and the prfxluct id'V'-p should be constant under all cir-
cumstances. These conclu>i<>ns were fairK- well confiniicr! for large
current-densities.

Several attempts to test the theory by actuall\- dcterniiiiing the
potential-distribution in the Crookes dark space were made with
sounding-wires and by other methods; but the>' have all been super-
seded, wherever possible, by the beautiful method founded on the
discovery that certain spectrum lines are split into components when
the molecule emitting them is floating in an intense electric field, and
the separation of the components is proportional to the strength
of the field. This was established by Stark who applied a strong
controllable electric field to radiating atoms, and by LoSurdo who
examined the lines emitted by molecules rushing through the strong
field in the Crookes dark space, in the condition of anomalous cathode-
fall. Now that the effect has been thoroughly studied it is legitimate
to turn the experiments around and use the appearance of the split lines
as an index of the field strength in the i)lace where they arc emitted.
Brose in Cermanx' and l-'oster at \'ale did this. In the pholograjihs
(Fig. 10, 11) we see the components merged together at the top, wiiicii
is at the edge of the negati\'e glow, where the field is \-ery small;
thence they diverge to a maximum separation, and finally approach
one another very slightly Ix-fore reaching the bottom, which is at the
cathode surface." This shows that the net space-charge in the Crooke

" The (lisplarcmcnts nf (crlnin coiniioiicnts arc not rigorously proportional to the
fii-ld, and sonictinicsi'ntiri-lv new lines make their appearance at hitherto unoccupiecl
places when a sironK fielil i> applied. Holh of these anomalies can lie delected in
Ihc pictures. l-"or the original pl.itc from which l-'ig. 11 was made 1 am iiideliled to
Ur. l"o8tcr.

soMr cnxTr\rrnn 1RV .tnr.ixrrs- rx rnv'^rc'^ vi i-»7

A4388:P
PARHELIUM

HYDROGEN

A4026:P
HELIUM

Kig. 10 — S|)octriim lines siiUlivided and spread out in the Crookes dark space by
the strong and variable field. See lootnote ". (J. S. Foster, Physical Review)

Fig. 11 — A group of lines near X43S8 Cparlielium s|x?ctruni) resolved and spread
out in the Crookes dark space. See footnote ".

148 BF.IJ. SVSTF.if TF.CIIXICAL JOURNAL

dark space is positive from the edge of the negative glow ahiiost but
not quite to the cathode; there is a thin region just above the cathode
where there is more negative charge than positive. This is splendid
material for the theorist, and it is deplorable that the method cannot
be applied excciit when the rathode-fall is anomalous and exceedingly
large.

When a narrow straight iiole is pierced in the catliode, the positive
ions making for it shoot clear through, and can be manipulated in
a chamber provided behind the cathode. In particular the ratios of
their charges to their masses can be measured, and thence their masses
can be inferred. This is Thomson's "positive-ray analysis," which
.Aston developed into the most generally available of all methods for
analyzing elements into their isotopes. If the density of the gas is so
far reduced that the Oookes dark space extends to the anode, the
electrons can be stutlied in the same way and their charge-mass ratio
determined. Hence the mass of the electron can be deduced, and
its dependence upon the speed of the electron ascertained, yielding
precious evidence in su.pporl of the special or restricted theory of rela-
tivity. These are among the simple phenomena which I mentioned
at the beginning of this article, in which the properties of the ultimate
atoms of electricity and matter are revealed.

The positive column, which is the lirilliant, colorful and CDiispicuous
part of the glow, resembles in some ways the positive ccjlumn of the
mercury arc. In it the ]X)tential-gradient decreases with increasing
current, and the characteristic of the glow is negative (Fig. 6).
Often the jjositive column subdivides itself into a regular procession of
cloudlets or slriations, all just alike and equally spaced (Fig. 7). The
potenlial-flitTerence f)etween two consecutive striations has the same
value all along the procession, and everyone feels instinctively that it
ought to be the i(»nizing-p(ttential or the resonance-potential of the
gas; but this is evidently too simi)le an interpretation for the general
case, although striations at potential-intervals of 4.9 volts have been
realized in mercurv' va|)or. deneralK', if not always, the striations
appear when the gas is contaminatetl with a small admixture of
another. In this fact the key to the jiroblem of their origin probably
lies.

The (ilo'iC in a dense jias (as dense as the atmosphere, or more so)
is visible only when the surface of either or both electrodes is curved,
with a radius of curvature smaller than the minimum distance between
the two. In these circumstance.s the field strength varies very greatly
from one point to another of the inters|)ace, at least before the space-
charges Ix-gin to distort the field, and presumably afterwards as well;

S()Mn coNiEMi'OK.iRv .ii>r.i.\ii:s i\ rinsus ii i-w

it attains values just in front of the riir\i(l I'li-iMrtiile (or elci'trotk's,
if liolh arc iiirvi"<l) so ^real that if thi'\ prevaik'il over an equal inter-
space Iiotween flat electrodes they would instantly provoke an explosi\e
sp.irk. In some cases the glow in a diiise gas reseinhles a very ron-

Fig. 12 — The glow in air at atmospheric pressures, near a curved electrode (ihe
otlicr electrorie is a plate beyond the top of the picture). In 1, 4 the curved electrode
is the anode; in 2, 3, 5, 6 it is the cathode. (J. Zelcny, Physical Review)

tracted and reduced copy of portions of ilie ylow in a rarefied, gas.
Thus in the photographs (Figs. 12, 13) of the luminosity surrounding a
very ctirved cathode, it is possible to discern two dark spaces and two
h)right ones, the first dark space lying just outside the cathode, the last
bright region fading off intcj the darkness which extends away towards
the Hat anode (far above and out of the picture). In the pictures of the
glow surrounding a very curved anode, we see only a luminous sheath

150 BELL SYSTEM TECHNICAL JOURNAL

spread over the metal surface (Fig. 12)." Mathematically the simplest
case (at least before the space-charjje l)egins to afTect the field) is
realized by a slender cylindrical wire stretched along the axis of a

Fig. 13 — Mjyiiiln .itiDii ■il one (it ilic pliitircs in l-'i^. H. (The lowest bright spot
is a rcllotlioii in the cathode surface)

much wider hollow cylinder, the wall of which may be imagined
to recede to infinity in the limiting case. In this case the glow bears
the euphonious nxime of corona, and has been intensively studied
l)ccause it wastes the power transmitted over high-tension lines.

"I am indelileil to I'rofessor J. Zcleny (or plates from which these figures were
made.

\<>.w/: ((i.v// .u/'oA'./AT .U'l.i.wis IX rinshs ri im

Ufti'H tlu-ri- is .1 luiniiuuis (-yliiitlrit.il sluMtli i-iic.isin^; the wire, and
from the lioundary of tlie sheatli outwards to the outer cylinder the
^as is dark. It is customary to assume that tlie dark region, like the
(itluT dark spaces we have considered, is traversed by a procession of
inns of one sign, positive or negative as the case may Iw, moving at a
speed pro(Mirtional to the field and controlled by their own space-
charge according to the ecjuatioii in cylindrical cnorilinates corre-
sponding to {\7); and the ex|)erinicnls suppcjrt this assumption to a
certain extent.

I must use my last paragraph to erase the impression — inevitably
to Ik.' given by an accoimt so short as this, in which the understood
phenomena must be stressed and the mysterious ones passed over —
that the flow of electricity through gases iss to be set down in minds
anti lx)oks as a perfected science, organized, interpreted and fin-
ished. Quite the contrary! there are as many obscure and mysterious
things in this tield of physics as there are in any other which has been
explored with as much diligence. Its remarkable feature is not that
most or many of the phenomena in it have been perfectly explained;
but rather, that for those few which have been explained, the ex-
planations are ven,- simple and elegant; they are based on a few funda-
mental assumptions about atoms and electrons which are not difficult
to adopt, for they arc not merely plausible but actually demonstrable.
Perhaps as time goes on all the phenomena will be explained from
these same assumptions. There will be experimenters who modify
the apparatus and the circumstances of past experiments so that all
of the avoidable complications are avoided and the phenomena are
simplified into lucid illustrations of the fundamental principles; and
there will be theorists, who take the complicated phenomena as they
are delivered over to us, and extend the power of mathematical analy-
sis until it overcomes them. They may find it necessary to make other
and further assumptions, beyond those we have introduced; at present
it is commonly felt that ours may be sufficient. Whether posterity will
agree with us in this, must be left for posterity to decide.

Carrier Telephony on High Voltage
Power Lines

Bv W. V. WOLFE

Introulctiun

Till", use of |)()\ver from hydro-electric generating stations and
central steam ]>lants has increased until single companies serve
a territory of many thousands of s{|uare miles and the problem of
coordinating the distributing centers with the generating stations
has steadily increased in compIexit\-.

One of the essentials of this coordination is obxiously an adequate
system of communication and until the recent advent of high frequency
telephony, this ser\'ice was secured over privately owned telephone
lines and over lines of public service telephone companies.

The advent of the power line carrier telephone system now offers a
highly reliable and satisfactory means of communication in connection
with the operation of power systems. This equipment has been
designed to employ the power conductors as the transmission medium
and to provide service as reliable as the power lines themselves with
a low initial cost, a small maintenance charge, increased safety for
the operating personnel and transmission comparable in quality
and freedom from noise with that obtained on high grade commercial
toll circuits.

Preliminarv Prohlems

In proceeding with the development of the Western Electric Power
Line Carrier Telephone System three major problems were encount-
ered. It was first necessary to learn from field tests and close contact
with power companies tiie characteristics of power lines and asso-
ciated apparatus at high fretjuencies and the operating requirements
for such a telephone system; second, it was necessary to develop a
safe and efficient method for coupling the carrier ap|)aratus to the
power conductors and third, to select and dewlop circuits and i(iui[)-
ment suited to this .ser\ ice.

The superiorit\- of the full-metallic over the grouiui return high
frefjuency circuit was easily established l)y comparati\e measure-
ments of attenuation, noise and interference, and therefore the experi-
intntal work was largely confined to the former circuit.

i.iKh^ii-R riii.iii-iioxy ox iih.ii ii.>i.i.h:e uses i5J

llii.ii KKi\>riM V Ai II MA riuN oi I'i>\\i k I.im ■-

Siiui- till' miM^lirrim-iil i>l tlu' .itlriHi.ition of ;i circilil (irdin.iriK
ri(|iiiri's that tlu- ririuit l)r uriuinali'd in its mitj^i- imped. hkc ' In
avoid rt-UfCtion i-UVrts, tlu- first step in deliTiiiiiiinK tlie altiiniation
of the power line was to measure its siirj^'e impedanre. After con-
sidering se\eral methods for measuring this impedance, a siil)sti(iiti(»«r

Fig. I — Open Circuit iZ,) and Short Circuit (Z.) Iinpcdance as Measured at
Carrier Frequencies on a 110,000 \'olt I'owcr l.inc \1 Miles Long

methml was adopted lx?causc of its simplicity and the rapidity with
which measurements could be made. This method depends upon the
fact that the apparent or measured impedance of a uniform line
terminated in its surge impedance is equal to that surge impedance
and it consists in terminating the line in a known resistance and
determining the value of current supplied to the line by an oscillator

' Surge or characteristic impedance may be defined as the measured impedance of
a uniform line of infinite length or in the case of a finite line it may Ix; expressed
mathematically as Z = VZ„-„„ X 2,i,„,,

154 BELL SYSTEM TECIISUAL JOLKX.-IL

and then substituting for the line a non-inductive resistance until
the same value of current is drawn from the oscillator. In employing
this method for determining the surge impedance it was assumed that
the oscillator output was constant, and that the phase angle of the
surge impedance was small.

A study of the curves on Fig. 1 shows that the apparent impedance
of the line will change with the impedance in which the line is termi-
nated in different ways, depending upon the frequency used. (1) If

MEASURED IMPEDANCE - OHMS

Kig. 2 — Graphical Solution of Substitution Methotl for Determining the Surge
Impedance of a Power Line

a frequency mid-way between the quarter wave lengths* is used,
the open circuit and short-circuit impedances are the same. (2) If
a fre(|uency corresponding to an e\en quarter wave length is used,
an increase in the terminating impedance will produce an increase
in the ajiparent im()edance f)f the line. (3) If a frequency corre-
sponding to an cxid quarter wave length is usetl, an increase in the
terminating impedance will produce a decrease in the apparent impcd-

' Whenever the length of the line Ixjcomes equal to, or some multiple of, one
quarter o( the length of the eli-ctric wa\e of the corresponding frequency, it is referred
to as a quarter wave length fre<|uency, or, for short, a quarter wave length.

c.tHKiiK ii:ii.riioxy ox high i"i.,.i<,i. ii\,^ \"->

aiirc i)f the liiu-. If tlic appari-nt inipt.'(laiui' of the line is plollcd
against the tcrniinatini; iniprdaiui-, in (I) tlic iiirvc will he hori-
zontal; in (,2) the curve will have a positive slope a|)|)roa(hinK ■♦•''°
anil in (3) the curve will have a negative slope of approximately
45°. Kach of these curves will intersect a 45° line drawn through the
origin at a (loint where the terminal inipeilance is ecjual to the surgj.
itn|X"dance of the line. This intersection can he determined with the

FCEQUENCY IN OUAETte WAVE LENC.TH3 IM168

Fig. 3 — Frfr|ucncy vs. .Attenuation and Frequency vs. Surge Impedance'as Measured
on the Tallulah Falls-Gainesville 110,000 Volt Power Line

greatest ease and accuracy when the curve crosses the 45° line at
right angles or under condition (3), that is, when the determination
is made at a frequency corresponding to an odd quarter wave length.
To determine the surge impedance at a given frequency all that was
neccssiiry was to terminate the line at the distant end in an impedance
which it was anticipated w-ould he just helow the surge impedance
and measure by the substitution method the apparent impedance
of the line, and then to terminate the line at the distant end in an
impedance which would just exceed the surge impedance and deter-
mine the corresfKinding apparent imfwdance. The intersection of
a straight line through these points with the 45° line determined the
correct terminating impedance. In Fig. 2 is shown a determination

156

BF.Ll. SYSTEM TECHKICAL JOIRSAL

of the characteristic imix-chince of the Tallulah F"alls-Gainesville
line of the Georgia Railway and Power Company at three different
frequencies.

The attenuation of the line was then measured by terminating it
in its characteristic impedance and measuring the current in to the
line and current out of the line.'' The results of the attenuation
measurements made on the Tallulah Falls-Gaines\ille line are shown
on Fig. 3. The irregularities in the attenuation shown by the Idwvr

racQvtHct- MLOCrCLfS

I'ig. 4 — In)|K>(laiue Cliaraclerislirs at Carrier Frequencies of a Typical (i()00:l KHMH)
\'olt Transformer Bank

cur\e are |)robal)l\' caused !)>• ihe error in assuming that the phase
angle of the surge impedance was small and that the surge impedance
was a straight line function of fre(|uency. Frt)m these and other
data it .was evident that for frequencies as high as l.")0 K.(", the
attenuation is not excessisi'.

IIk.II I'KKyfEXCY C"lI.\KA( THklsrUS Ol- I'()\V1:k Tr.wsiormkks

In order to determine the effect of power transformers on the use
of the power line as a transmission medium for high frequenc>- currents,

• .Attenuation expressed in transmission units is equal to 20 logic t'- where /i is

the current mto the network and /> is the current received from the network and
measured in a circuit whose impc<hince corresponds to the characteristic impedance
of the network.

c.iik'kiik ri:i.rriii>xy ox men jiw/.m,/ iim^ i.v

the iin[K'<laiui' of t>pir.il transformer l)anks was im-asiiri-d. In
Fig. 4 is shown the ini(K'(lanre versus fre(|iK'nr\' characteristic of a
thrif phase, llO.OtM) titKM) \\. 12.(MK) K.V.A. transformer hank con-
nccte<l "star" on the lii^h side wiiii ilie neutral ^numded and "delta"
on the low side. As shown l)>' the diajjrani, these measiirentents
were made l)etween phases on the high side with the low side optyr
circuited and short circuited. The coincidence of these curves for
frequencies aliove 50 K.C". indicates that at these fre(|uencies the
dominant characteristic is the distributed capacity of the \\\g\\ windinjj
and the iniptnlance is probably unaffected by changes on the low
p<itential side of the transformer. Below .')() K.C, however, the
impedance changes rapidly both with lre(|ueiuv- and with the low
potential termination.

A study of Figs. 3 and 4 and other data shows that the dtsirabk-
frequency range in which to operate a power line carrier telephone
circuit is that from ."lO K.C. to 1.10 K.C. In this range the attenua-
tion is not excessive, it is very little affected by the associated power
apparatus, and it is independent of the conditions on the low potential
power circuits. The curve shown in Fig. 3 indicates that, contrary to
the common l)elief, the attenuation in this range is a relatively smooth
function of freciucncy. This conclusion is supported by the fact that
in the various installations of power line carrier telephone equip-
ment which have liecn made since the attenuation measurements on
Fig. 3 were obtained, no [X)vver Imes have been encountered where the
attenuation was a critical function of frequency. Another important
argument for the selection of this frcquencv' range lies in the fact tnat
it is well above the range emplovcd for midtiplex telephony on com-
mercial telephone svstems and therefore precludes any interference
with such systems.

Coii'i.iNc; Bi;r\vi;iiN C.arrikr Hoi'i'^'iiNr and Powkk Line

Probably the most ililficult problem to solve was that of providing
a satisfactory method for connecting the carrier eciuipment to the
power line. The u.se of power transformers has not been found prac-
ticable for if frequencies low enough to be efficiently transformed were
employed, the attenuation of the circuit would be a function of the
conditions in the distributing network and a change in the number or
arrangement of transformers would result in an appreciable change
in the attenuation. Such a method of coupling to the power line
would also have the objection that communication would not be
possible when the p<jwer transformers were disconnected from the line.

158 BELL SYSTEM TECIISICAL JOURNAL

Since it did not seem practicable to (le\eiop a carrier frequency
transformer suitable for conneclinj; between phases of a high voltage
power line it was decided to cou|ile to the power line by means of
capacity. Two general tyjies of condensers are possible, first, a con-
centrated capacity condenser and second, a distributed capacity
condenser. A concentrated caiiacity condenser suitable for direct
connection to a high voltage power line was not available, but its
development has been successfull>- undertaken by the Ohio Brass ("o.

^ FI?EOUENCy IN KILOCYCLES

c ioco)o«o»oMio8090iooiioiui3ai40iaciurro

Fig. 5— Xoltagc .Viiiplifiiation Characteristic of High Frequency Transformer

The distrilnited rapacity was obtaiiietl by suspending a wire ixiralle!
to the power conductor and employing this wire as one plate of the
condenser and the conductor as the other plate. Both of these meth-
CKJs of connecting to the power line have been developed and are
described later.

Dksicn ni- Tiiic C'akkikk Moiipmknt

.■Mtiiough the "carrier suppressed" system has nian\' ad\antages
over the "carrier transmitted" system, the dilTftcullN- of securing filters
suitable for suppressing the unwanted products of the modulation
prevented the use of the carrier suppressed system.

Several general characteristics of the electrical and mechanical
design of this carrier e(|uipmcnt are worthy of note. The \'arious
stages of vacuum tubes in both the transmitting and receiving cir-
cuits are coupled b\- transformers. These transformers are closed
iron core coils using the standard core employed for audio-frequency
transformers. Kig. .") shows the characteristic of one of these traiis-
formers, and it is e\'ident from this figure that the variation in am-
plification from '\i\ K ( " |M I "id K (\ Is only a fraction of a trans-
mission unit.

CARKir.R TF.i.i.riioxy on high roi.r.icn uxrs

159

.\lth(>Uk;h till' froquenck's employed by this e(|uipinent are fairly
hinh. it was [)raotieal)le to inoiiiU all of the apparatus on standard
steel relav rack plates. In order to niinimi/e the inaintenanre on tliis
equipment no "C" batteries ha\e been emplosed, the ^;rid potentials

Fig. 6 — -Front \'icw of Transmitter Panel with Cover Reniovecl from Tuning
Condensers

being obtained from filament drop, "H" battery drop and a com-
bination_of these two.

l_^The transmitting unit shown in Figs, (i and 7 is divided into two
parts, the transmitting circuit proper and the power amplifier. The
first is a circuit comprising a 101-D tube functioning as a Hartle\-

160

BELL SYSTEM TECHSICAL JOURNAL

oscillator with indiulixc fied-back, a 223-A tube operating as a
speech am])lifier or modulator and a 223-A tube operating as a high
frequency anii)lifier. The |)latc or constant current system of modu-
lalinn is emploxed but dilTers somewhat from the usual practice in

I'ig. 7 — Rear View of Trdnsmiiu-r I'diiel with C"o\tT Kcmovcd

that the ouljiut of the high fie(|uency amplifier is modulated ralher
than the output of the oscillator itself. This scheme was found to
delixer more modulated jxiwer than the usual arrangement since it
is not limited to the same extent by the oxerloading of the higii fre-
(|uency amplifier. This circuit has a power output of one watt, which
has i)ro\e(l to be ample f(jr normal o|)eration (jf the carrier system.

c.ikHiiK Ti:i.i.i'ii()\y (K\ iiiaii i-oLucr. i.ixi.s \m

To providi- Inr (>|H'r,iti(iii dI tlii' s\>trm wlu-n ilu- .iiU'iiu.iti<iii on the
powiT liiu- has hoi-ii inati-rialK' iiicrfasi-tl 1)\- liiii' fault conditions a
power ann>lifier is pro\i(lf(l. This aniplilii-r employs a 50 watt tula-
1211-A) and is placed in the eircuit i)y a simple swiichinjj o()eration.
When this amplifier is operated, the output of the iransitiitlinji circuit
is impressed upon the j;rid of the 50 watt tuhe and ampiilu'd to aj)-
proximately fift>- times its normal power output.

In the present ty[X' of carrier system duplex or two way operation
is secured by the use of two dilTerent carrier frecpiencies, one for
transmission in each direction. .\s will he |)i)inted out later in llu-

Fig. 8^ Rear View of Receiver Panel

section on signalint; the lower fre(|uenc\- is always assigned to the
calling station. The transmitting circuit must therefore operate at
two different frequencies. This change is accomplished by the auto-
matic operation of the relay shown in Fig. (i. The operation of this
relay changes the capacity in the oscillating circuit, thereby changing
its frequency. The values of the two frequencies at which the trans-
mitting circuit operates are determined by the variable condensers
Fl and F2, Fig. 6, and certain fixed condensers which are connected
in parallel with the variable condensers.

The receiving unit shown in Fig. 8 is extremeh- simple. It is not
tuned and the only control is the filament rheostat. It consists of
three 101-D vacuum tul)es operating respectively as a carrier fre(iuency
amplifier, a negative grid potential detector and an audio freciuency
amplifier.

Two way operation is secured In- operating tiie transmitting and
receiving circuits at dilTerent fretiuencies and separating them by
means of filters. In the single channel systems this separation is
secured by a high pass filter and a low pass filter although in the mul-

162

BELL SYSTEM TECHNICAL JOURNAL

tiple channel system band pass filters will be employed. Fig. 9 shows
attenuation versus frequency characteristics of the high and low pass
filter combination. A study of these curves shows that the trans-
mission loss or attenuation in the high pass filter to frequencies trans-
mitted by the low pass filler is never less than 90 T.U., which corre-

I'ig. 9 — Transmission Characteristic of llinh Pass anil Low Pass Filters

ponds to a current ratio of approximately 30,000 or a power ratio
of appro.ximalely 9x 10", and the attenuation in the low pass filter
to the frequencies transmitted b\' the high pass filter is also equal to
or greater than 90 T.U.

The characteristics of these filters are remarkable when it is con-
sidered that the frequency range in which they operate is higher
than that employed for multiplex carrier telephone systems, the
attenuation secured is higher than that ordinarily required for such
systems, and a power of 50 watts has to be transmitted through them
thereby introducing special problems in the design of the coils and
condensers. I'igs. 10 and 11 are fnmt ami l>ack \iews of one of these
filters.

One of the uiuisii.il featines in the use of these lillers is the f.u I that
the position of the filters in the circuit is changed from time to time

C.IRKir.R TELEPHONY ON HIGH lOl.TAC.E LINUS IM

1)\- tin.' ()|M'rati()ii of the ri-l.i\' slmwiinii l-ii;. II, ili.it is to s.i\-, wlu-n
the transmitting circuit is oporatini^ at a fri.(incnc\- lower than 80 K.C.
the low pass filter is connected to it and when the transnuttinj; circuit
is operating at a frequenc\- higher th.m 1(H) K.C. the high pass filter
imist l)e connecleil to it.

SlUNAI.INd SVSTKM • '

Signaling or rinj^in.;; is acconiplisiuMl at tlie Iransniitling end l)y
changing the fre(|uenc>- of the oscillator frttiu a fre(|uenc\- helow 80 K.C.
to a fre(iuency ahove 100 K.C. without changing the fiUors. This is

Fig. 10 — Front \'ie\v of Low Pass Filter with Cover Removed

Fig. 11 — Rear View of Low Pass Filter with Cover Removed

accomplished by operating and releasing the relay in the oscillator
circuit. Since the filter connected to the transmitting circuit will
pass only one of these frequencies, pulses of the carrier frequency are
sent out on the line. At the receiving end these pulses are ampli-
fied and rectified and the change in the space current of the detector
operates a marginal relay. The number and arrangement of these
pulses is controlled by a spring-operated selector key of the type com-
monly employed for telephone dispatching on railroad lines. At the
receiving end these pulses operate a train dispatching selector relay

164

ni:i.L sysriiM ii:ci ixic.il joirwil

(see Fig. 12) which responds to 17 impulses. This selector relay will
respond to only two arrangements of these 17 pulses. The first
arrangement is 17 consecutive pulses in which case these pulses must
follow one another at the correct speed and must be of the correct
duration. This makes it possible to ring all stations at the same time
as may be desirable in issuing general orders. The selector relay
will also respond to 17 pulses broken up into three groups in which
case the correct number of pulses must occur in each group and the
total of the three groujjs must be 17. This makes it possible to

Fig. 12— Ki-.ir \ iew ol Sij;iKilinK anil Low Frcfjiicncy Pant'l Sliowiii^ llii- Sigiialiiii;
.-\pparatus

select one station from a grouj) of more than 50 stations without dis-
turbing the others. In addition to these desirable characteristics a
single selector relay will provide selective ringing on four low fre-
quency extensions from the carrier terminal.

The carrier ecjiiipment may be operated with complete control and
talking facilities from either a telephone located at the carrier terminal
or a telephone some distance from the carrier terminal but connected
to it by a ph%sical telephone circuit. In any event the control is
aMlt)maiic, the transmitting circuit operating only when the receiver
is off the switchhook, while the rccei\ing circuit operates continuously

Designating the carrier fre(|uenc>' which is below 80 K.C as Fi
and the carrier freciuenc\' which is above 100 K.C. as Fn, the opera-
tion of a carrier system com|)rising three carrier terminals designated
as /I, /J and C with a remote control station designated as .-1 1 located
at the load dispatcher's office and separated from the carrier terminal
by several miles of physical telephone circuit is as follows. Each of
these stations may communicate with any of the other stations.
Communication between A, B and C is carried on over carrier cir-
cuits; communication between ,1 and .1 1 is carried on oxer the jihysical

C.IRKIF.R Tl:l.r.l'llO.\y O.V ///(,// rOl.T.IGE I.IM-.S l(.5

(irriiit wliilt- (■oinmimicKion lutwirii .li, li and C is rarrird on i>\vr
cimiits whifh arr idiiiposi'tl of a cirrit-r cirriiil ami a pinsical cir-
ruit <)|H'ratiiij; in taiuU-in. W'lu'n in llu- nnrni.il or iiDn-oiK-rali-d
conditions, earli of tlu'si' carrier tiTniin.ds is set ii)) lo reci-i\e a sij^nal
on fri'(]iifncy Fu lint wlit-n tlie rert-ivcr is reinmed from the swilcli-
hiH)k at any station to initiate a call, the carrier tenninai corre-

Fig. l^ — 110 K.W Coupling Condensers Used for Coupling Carrier Circuit to a
110 K.V. Power Line

sjiondini; to that telepiione is autonialicalK' set up to transmit on
frecjuency Fi and receive on frequency F«. When the ringing kc\' is
operated, pulses of frequency Fi are sent out and received at all of the
other carrier terminals. At the called station these pulses operate
a selector relay and ring the l>ell, and when the operator removes
his receiver from the switch-hook to answer the call, his carrier terminal
is automatically set up to transmit on frequency F> and recei\e on

166 BELL SYSTEM TECHNICAL JOURNAL

frequency Fi. This switching of the transmitting and receiving cir-
cuits from one frequency to another is necessary where more than
two stations arc operated on the same system and it is desirable for
every station to \k> able to call every other station without routing
the call through a central point.

If station .4i is connected with station A by means of two or more
pairs of telephone wires which are not exposed to high voltage power

fREQUENCY IN KILOCVCUS

on 20 30 40 50 60 70 eO 90 WO 110 IfO 130 KO ISO 100 170 180 190

Fig. 14 — Transmission Characteristic of Coupling Band Pass Filter

lines, a simple D.C. remote control circuit may be emplo\cd. How-
ever, if only two wires are available or if tiie telephone lines to be used
arc exposed to high voltage power lines and must therefore be equipped
with insulating transformers and drainage coils, it is necessary to
emi)lo\- a somewhat more complex alternating current control circuit,
in this circuit the 135 cycle interru|itcrs and rcla\s familiar to the
telephone plant are employed.

The voice frequency circuits used in connection with this carrier
equipment are the standard two wire and four wire circuits used in
commercial tele|)hone practices.

ColI'I.INfi HV Co.NDF.NSFRS AND BY DlSTRIHUTED CAPACITY

Fig. 13 shows two of the 120 K.V. coupling condensers developed
by the Ohio Brass Co. Each, of these condensers has a capacity of
.003 fii although similar condensers ha\ing a capacity of .007 /if are
also available. These condensers are ajjproximately 5 ft. in diameter
and 12 ft. high over the bushing and weigh about 8,000 pounds. The

i.ih-iaih' 1 1 1 1 riinxy ox nu.n j -'//./(,/ //.\/\

lf>7

i(iii(l»n>«.r cliiiK'tit is m.ulc up of a large inmibcr of small coiuluiiscrs
ii) par.illi-l, (ho ass<'mi)ly iK'iiig immorsed in tr.insforiner oil.

At pnsint llioso coiuloiisirs arc oiiiploNcd as the scries capacity
cleiuciil of a single seetion, conllueiil lyi)e, Camphell hand pass filler
as shown by I"ig. 22, the general attenuation characteristic being
shown by Fig. 1 L This filter is intended to transmit etVicienlly the
carrier fre<iiiencies, and to exclude power frequency currents.

Fig. 15 — Typical Layout of Power Line Carrier Telephone System, Using Hij;h
Voltage Condensers for Coupling to Power Line

In Fig. 15 is shown a typical layout of a condenser coupled power
line carrier telephone system.

In employing the distributed capacity type of condenser for coupling
to the power line, two coupling wires (sometimes incorrectly called
antennae) are suspended parallel to the power conductors for a dis-
tance of approximately 1,000 ft. Pig. 10 shows the last tower sup-
porting the coupling wires in an installation at Anniston, Alabama.
This is a twin circuit 110 K.\'. power line and in order to secure
coupling to both lines, the coupling wires are suspended midway

I6S /?£/,/, SYSTEM TECHNICAL JOURNAL

between tlic tup ami hoUuni i)liases. Tlio box shown on tlic lower
in Kig. Hi is ilu- i'oiii)ling wire liniini; unit shown in lii;. 17. The
conplint; wires are lerniinaled in this lunini; iniil. In l-'ii;. IS is

liK. l'> Hi'

11 I'.ii'l "I l'\|iii,ii (.Duplinj; Wire liiblallaliun Sliowiiig Coupling
U ire Tuning L'nil

shown the schematie diagram of the wire eoupling circuit and Fig. 19
illustrates the character of the resonant peaks secured In- this circuit.
The series inductances L\ and tlie lenninaiinn inductance Li are
\arial)Ie and by adjusting liuni iht- points of resonance may be

CANKirR ir.i.fu'iioxy (h\ men roi.i.icr. i.ixi.s kw

sliil'ti'd Id lorirct lor wiri.itioiis in iIr- rmipliiii; win- iiKliuM.iiui' and
rap.uiiN Inr ililTiri-nt iiisl. illations. \"\\:,. 20 illiisiiati-s a tspical
farruT ti'iiniiial installation rmplox inn ''h- win- coupling,' nu'thod.

The onK point in l.uor of tlir wire couplini; as coniparrd with the
condenser coiiplini; is the lad liiai for power line^ ol \oltai;e> liii;her

l-"ig. 17 — Coupling Wire Tuning Unit

than '.i'.i K.\'. it is somewhat cheaper. On the other hand condenser
coupling is much more etiticient, thereby increasing the range and
reliability of the system. It also permits high quality transmission,
the transmission through it is not affected by small variations in
frequency, and the component parts are of constant value determined
at the time of manufacture and require no adjustment at the time
of installation. In addition to these advantages the inspection and
maintenance of the condenser is easier than for the coupling wires.

Pr()Ti;( TivE Mk.\sires

In considering the problem of safety to the operating personnel
and the equipment from the power line voltage, the normal insulation

170 BELL SYSTEM TECHNICAL JOURNAL

supplied by tlie high voltage coiulenser where it is employed or by
the air separation where the coupling wires are employed, is dis-
regarded, since this insulation ma\- fail, thereby apiiKing the power
line voltage to the line terminals of the coupling circuit shown in

I — nnsw^

I — npppr^

/T?RJF|— iihn

—■\H

Fig. 18 — St'hematic of Wire Coupling Circuit

Fig. 21. The circuit shown in this figure is the same both for con-
denser and for wire coupling instiiUations. The first element of
protection is the horn gap, which is mounted outside of the building
and serves to limit the voltage to ground which tlie drop wire fuse,

CfiCPlEP FPECUENCY IN KILOCYCLES

Fig. 19 — Charaitt-r of Resonant Peaks secured with Wire Coupling

constituting the second element of protection, will ha\'e to break.
This fuse consists of an element inside of a jjorcelain tube the ends
of which are closed by lead caps. This fuse is about 5 inches long
and } 2 i'leh in diameter and is supported by the wire itself. When it

CARRIER TEl.EPllOXr OX IIIC.II rOl.T.ICF. US'ES

171

faiU, the arc ostaMislud williiii llic ixirilaiii tube causes tlic liiliu
to l)rcak ami [K-rmils the wires to fall apart. In power line c.irrier
telephone practice this fuse is so installed that a clear droj) of at least
20 ft. is obtained. The tliird element of (protection is the shunt coil
with the mid-point grounded. In many respects this elcnuni i^ I lie

l.iiK- Cirritr Telephone System Using Wire
Coupling

most important one, since it provides a low impedance path to ground
for power frequencies, thereby draining ofT the 60 cycle potentials
which are ccjUected by either the coupling wires or the condensers
in normal operation.

As will be noted from Fig. 27 the line series inductances and this
shunt inductance coil comprise a unit (the upper panel) which is
known as the filter coil unit. The coils on this unit are insulated
for 20,000 volts on the line terminals and are constructed of edgewise
wound copper ribbon large enough to carry heavy momentary currents
without damage. The fourth element of protection is a fused switch
and surge arrester such as is commonly emplo\ed for the protection of
private telephone lines exposed to power lines. This device consists of

172

Hr.l.L SYSTEM Tf.CHXIC.IL JOURX.IL

fuses in series with the line ami fonniny the blades of a switch. These
fuses ha\e been found satisfactory for tiie inf,erruption of voltages as
high as 25, 000. Following this fused switch is a l,oOO volt breakdown
static spark gap to groinid and a oOO volt breakdown vacuum gap

■^TRRT^h

®

©

^l^W^h

TO CAPPlER

Kig. 21 — Srheniatic of Protertion Circuits

across the line. l-Oliow ing these there are two series capacity elements
which are high Noltage mica condensers. These condensers ha\e a
capacity of .007 fit. and a breakdown voltage in excess of 7,oOO. FinalK',
there is proxided a rei)eatiiig coil with the mid-point of the line side

Cftl?l?ICI? FI?E(3UENCV IN KILOCYCLES

40 W 80 100 lEO 140 IfcO

Fig. 22 — Change in the Attenuation of the High Frequency Line Necessary to

Maintain a Constance X'oice Freciuuncy Level with \'ariation in the Frequency of

the Carrier

winding groimded and protected 1)\ .j(K) \(ilt \acuiim gaps to groimd.
This repeating coil is also provided with a grounded shield between
the windings and has a breakdown voltage from the winding to the
shiekl of 1,000 volts. The operation of this protective circuit has
been demonstrated se\eral limes in the field by connecting one phase

c.iKRii H ri.i.i.i'iioxy ox men roi.i.iar. i.ixi.s i7,i

of ,1 III) K.\'. pnwrr liiir (liri'C(l>- to oili- of llic line trriiiiii.ils of llii-
protectivf circuit. In every case tlu- circuit lias operated satis-
factorily. Ill no case has any of the standard apparatus lieeii <lani-
aj;e<l nor has there heen any evidence tliat the elements of protection
beyond the third, th.it is, tlie slunil coil with the mid-point grounded,
h.i\e lieen c.dled upon to fmiction.

Transmission I.kvki, CiiARACTF.RtsTrcs

Fij;. 22 shows the attenuation (expressed in transmission units) of
the hi^h frecjuency line versus the carrier frec|iienc>- of K.C. It will
Ih- noted that o\er the rani;e from .'lO K.C". to l-")0 K.C the vari.uion

HIGH F;?E0UENCY line (T.U.)
JO iO 50 bO

Kig. 13 — \'ariation of Overall ('.a!ii with llu- .\ltemiation of the \Ug,h f-'requeiicy Line

in attenuation is less than o T.l'. This curve was made with a constant
audio frequency input of 3.35 mils and an output of 3.35 mils from
the carrier circuits, the audio frcfjuency being 1,000 cycles. The
\ariation of audio frequency level with the attenuation of the high
frequency line is shown in Fig. 23. The observations given in Fig. 24
were made on an artificial transmission line in which the line constants,
and therefore the attenuation, could be readily changed without
changing the carrier frequency. The shape of this curve is a function
of the receiving circuit since the audio input, carrier frequency- and
the mtxlulated output of the transmitting circuit are maintained
constant. It shows that for audio frequency levels lying between
— 10 and +10 T.U. the equivalent is appro.ximately a straight line
fimction of the attenuation of the high freciuencN' line, and ihat
therefore the receiving circuit is not overloaded.

Fig. 24 shows the audio frequency load characteristic. This curve

174 BELL SYSTEM lECllSICAL JOVRNAL

is principally a funclion of the load characteristic of the modulator
and it shows that for inputs greater than 1 mil, the modulator is
overloaded. In practice the overloading of the modulator is pre-
vented by increasing the average low frequency line equivalent to an
attenuation of 10 T.L'. bv means of a resistance artificial line. This

Fig. 24 — Tniiismilting Ciriiiit Load Characteristic

arrangement is desirable in order that the balancing of the low fre-
quency hybrid coil may not be complicated when operating over very
short physical circuits.

The curve in Fig. 25 is a single frequency quality characteristic
and shows that where the method employed for connecting to the

AUDIO FREOUENCY IN CYCLES

tOOO 2M0 3000 IMO lOOC

Fig. 25 — Single F'reqiieiuy Quality Cliaractcristic

power line will permit, remarkably true voice transmission may be
secured. The \ariation in the e(]ui\alent o\er the range from 100
cycles to 5,000 c\-cles is only 51^ T.U., while the variation from 300
cycles to 5,000 cycles is only 2 T.U. Reference to Fig. 10 will indi-
cate, however, that less satisfactory quality characteristics are ob-

c.tRRir.R Ti-iri'iioxv o.v ifiaii roi.r.ian i.ixr.s 175

t.iiiinl wlii-n till" wire niii|>liiii; mu-iIhhI is i-iiipliiyc'd, Ix-caiiM' of llir
sli.irpnrss of a'sonaiicc ul (Ik- rnupliiii,' circiiit.

Alabama PowI'.r Company Installation

I'i^s. 2ti ami 27 are [)lu)l(ii;ra[»hs of the installalioii of pnwir line
carrier telephone equipment at tlio Amiiston sulislatimi of the Alalianu'

Kig. 20 — Typical I'ower Line Carrier Telephone Installation

176 IIBLL SYSTEM TllCflXlCtL .lOLRX.II.

Power Company. Fig. 2(5 illustrates the simple character of the
assembled units and freedom from controls. The right hand l)a\'
is devoted to power control apparatus with space reser\ed for the
135 cycle remote control f(|uipnienl when it is employed. The left

I in. 17 I ypical Installation of Coupling Panels

liand bay iiicludes the transmitting and receiving circuits, the higli
and low pass carrier freijuency filters and the voice frequency and
D.C control circuits. Ik'ginning at the top of this bay, the first
panel, which is blank on front, carries the system terminal, block
to which all wiring except the power supply is ct)nnecled. The second
panel is the high pass filter; the third panel is blank. The fourth

C.IKKIIR TlU.r.l'IlOW r).V ///(,// VOLTAGE I. IMS 177

p.im-1 is till" Iransinittin^j e(|iiipiiH-i)t, \»>[\\ low powrr and IukIi power.
Tin- tifih paiu'l is {\w reruivinn rirniit; \hv sixth paiu-l ojiitains (ho
\oicf frefiiu'iiry and signaling i-ciuipim-nt. Tlir si-vonlh panel contains
D.l". control i'(iuipnu'nt, and the bottom panel is the low pass filler.
On the wall to the rijjlu of the carrier panel assembly are shown the
tilter coil unit and the filter and [irotector iniit. These imits are yn)re
clearly shown in Fig- 27 and diagrammaticalK- in Fig. 21 . Returning to
Fig. 2(i, the desk staiul which the operator is using is that associated
with the carrier eciuipment, while the key moimled on the table im-
mediately to the left of the desk stand is the selector key employed for
ringing. Fig. 1(> shows the coupling wire installation at this station.

The power line carrier telephone eciuipment which has been briefly
tlescrit)ed in the foregoing article is in successful operation today on
se\eral power systems in this country. Its reliability, simplicity- of
operation and maintenance have been well established.

The large number of variables which are involved in line failure
conditions make it impossible to predict what effect these emergency
contlitions may have on the operation of the carrier equipment.
The fact remains, however, that under many simulatefl and actual
trouble conditions successful operation of the carrier equipment has
been obtained.

With the growing need of power companies for communication
facilities, it is probably only a question of a very short time before
multiple channel carrier, systems will be in operation on the large
power systems of this country.

Abstracts of Bell System Technical Papers

Not Appearing in the Bell System

Technical Journal

Photomechanical Wave Analyzer Applied to Inharmonic Analysis}
C. F. Sacia. This type of Fourier Analysis deals with wave-forms
which are not strictly periodic, since they are of finite duration and
of varying cyclic forms. Hence in a finite frequency range they have
an infinite number of infinitesimal components (shown by the Fourier
Integral) as contrasted with the finite number of finite components
at regular intervals (shown by the Fourier Series).

This analyzer utilizes the continual repetition of the aperiodic
wave, deriving therefrom a periodic wave, the infinitesimal compo-
nents neutralizing except for frequencies which are integral mul-
tiples of the frecjuency of repetition; here the components build up
to finite magnitudes. The simple relation between these components
is seen from the corresponding Fourier Integral and Series identities
for the unrepeated and repeated waves respectively. By increasing
the period of repetition a new set of components can be similarly
derived.

The wave form is represented as a black profile on a transparent
strip whose ends are joined to form an endless belt. Driven at con-
stant speed past a transverse illuminated slit, it generates light fluctu-
ations which are converted into electrical fluctuations by means of a
selenium cell. A tuned circuit, amplifier, rectifier and microammeter
are used to select and measure the components, while the frequencies
are determined by the speed of the strip, the frecjucncy of tuning,
and the time scale of the original wave form.

"Demagnetization and Hysteresis Loops.'"- L. W. McKeehan and
P. P. CiOFFi. The fact that permalloy shows its maximum initial
permeability in the absence of external magnetic fields is used to
check the exact compensation of the earth's magnetic field or other
stray fields by measurement of the initial permeability of a strip or
wire of permalloy placed parallel to the field component to be com-
pensated. Increased accuracy is obtained by the use of somewhat
greater fields than those which approximately give the initial permea-
bility. The effect of demagnetization by an alternating current field
is sluflied with samples of the same sort, the apparent permeability
varying as the external field at the time of magnetization is \-aried.
The dissymmetry in hysteresis loops where the upper and lower limits

' J. O. S., K. S. I., Vol. 9, pp. 487-494, 1924.

» J. O. S., K. S. I., Vol. 9, pp. 479-485, 1924.

178

.tnsTR.icTs or pull system technical p.-wi-L'S 179

an- iiiis\innu'trir.il with rfspoot l<> tlio /i-ro of maniu'tic fii-ld is illiis-
tratwl ami the (li'tfctii)n of such dissyinnictrj' is discussetl.

.1 Classijifd List of Published fiibliog,raphies in Physics, 1!)IQ-1!)22}
Kari, K. Darrow. This work, uncicrtaken at tlic request of the
National Research C"ouiicil, represents an attempt to cope with tlic
proMeni of providing a con\enient and adequate hihlionraphy of
physics, not by actually writing a complete classified hiiiliograplA'
(which would fill a huge volume and retjuire the prolonged lalK)r of
sc\eral men), but b\- listing the very numerous partial bibliographies
under a detailed subject-classification. Many of the accounts of
research publishetl in scientific journals contain short histories of the
previous work in the subjects which they treat, many others contain
lists of references, and there are also a number of critical or uncritical
reviews of particular fields with thorough documentations. The
Classified List of Published Biblioiiraphies refers to all of these which
appeared in any of the familiar physical journals between 1910 and
1022 inclusively, and a numlxr of books as well; it is believed that
almost every article upon a physical subject, which has ever been cited
or reviewed in another article, can be traced through the List. The
system of classification, in which the field of physics is divided into
seventy-five classes with numerous sulxlivisions, is much the most
detailetl and elaborate which has been made out for the science of
physics in a score of years. An adequate system of classification is of
great value in any science, for researches which are clasified under
it are not only made easy to trace, but their various aspects and their
mutual relations can be emphasized. Because of the rapid growth
and evolution of physics, the earlier systems have mostly become
inadequate; but it is hoped to make and keep this system effectiv^e
by constant attention and revision, and to e.xtend the use of it.

Transmitting Equipment for Radio Telephone Broadcasting.*
Edw.vrd L. Nelson. The general transmission considerations apply-
ing to any system for the high quality transmission of speech or music
are outlined briefl\-, and the specific requirements to be met by the
various apparatus uniti in a radio broadcasting equipment are dis-
cussed in some detail. The standard Western Electric 500-watt
broadcasting equipment, which has found application in some fift>' of
the larger stations in this country and abroad, is described. Its per-
formance capabilities are illustrated and it is indicated that a standard
of performance has been attained which renders possible reproductions
not substantially different from the original.

' Bulletin of the .National Research Council, No. 47.

• Proc. of The Inst, of Radio Engineers, Vol. XII, page 553, 1924.

ISO BELL SYSTEM TECIIXICAL JOURNAL

" The Vapor Pressures of Rochelle Sail, the Hydrates of Soiiiiim and
Potassium Tartrates and Their Saturated Solutions."' H. H. Lowry
and S. O. Moriian. The vapor pressures were determined by a static
meth(Kl at several temperatures between 15° and 40°. Tempera-
tures were controlled to ±0.1° and the pressures read to ±0.1 mm.
The measurements on the saturated solution of Rochelle salt show
that the solid phase in such a solution is unstable above 40°, in agree-
ment with other investigators.

Minimal Length Arc Characteristics.^ H. E. Ives. This paper is a
stu(i\' of the electrical discharges which occur between opening con-
tacts. It is found that the discharge occurring when currents below
a certain \alue are broken are atmospheric sparks corresponding to a
definite breakdown voltage, which in the case of air is about 300 volts.
Above a critical value of current, which is different for every material,
the discharge is an arc, in which the voltage corresponding to the
discharge varies with current. Spectograms taken in the two regions
show only the air spark spectrum for all materials below the critical
current and the arc spectra of the materials above the critical current.
The characteristic equations of the arcs caused by the opening con-
tacts are deri\-ecl and are used to obtain expressions for the cinrent
\s. time relations at the opening contact.

The Dependence of the Loudness of a Complex Sound Upon the Energy
in the Various Frequency Regions of the Sound.'' H. Fletcher and
I . (". STEiNBERfi. Two complex sounds were studied, one with a con-
tinuous energy frec|uency spectrum corresponding to connected speech,
the other a test tone ha\ing discrete frequency components. B>'
means of filters the energy was removed from all frequencies either
above or below a certain frequency, and the resulting decrease in
loudness was measured b>- attenuating the original soimd without
distortion imtil equal in loudness to the filtered sound. Taking the
average results for six observers, this decrease was found to depend
on the absolute values of the loudness. For a loudness of 22 units
alxne threshold, each frequency region contributes to loudness in
proportion to the energy in that region weighted according to the
threshold energy for that frequency. For a loudness above 30 units,
however, this is no longer true, because of the non-linear character of
the response of the ear. B\' assuming each frequency region con-
tributes in proportion to a fractional power of the weighted energy
of that region, values of the total loudness in agreenu'til with ob-

'Joiir. Am. Cliciii. Soc, \ol. 4.S, pp.' 2192-2196, 1924.

•Journal of the Franklin Institute, \'ol. 198, pp. +37-474, 1924.

' Physical Kcvicw, \dI. 24, page 306, 1924.

.iPSTR.icrs ()/• /{/;/./. svsTr.M rr.cfixic.ir. r.ii'fiRS isi

siTveil values ari- ohtaiiicil if prn|H'r \aliirs an- taki-ii for the fractioii.il
|x)\ver, tIeiTcasiiijj to one tltiril as tlio IoikIiicss iiicn-ases to JOO units.

Correlation BchiCin Crack Dnrlopnti-nt in Class While Condtuling
Electrieity ami the Chemical Composition of the Glass.^ Karlk K.
StillMAUlKR. A stu(i\' was made of tiie susceplil)ility to craok
ilevelopnient shown l)y live ilitTerent kinds of glass when they were
suhjectctl to the action of an electric current. The results indicated
that the tendency to crack increased with increasing alkali content
of the glass and with increasing electrical con(lucti\it\'.

Report of the Chairman of the Telegraphy and Telephony Committee
of the American Institute of Electrical Eni^ineers.^ O. B. Blackwki.i,.
This report gives a brief summary of the advances which have been
niatle or which have come into prominence in the communication
art during the year. Pajx-rs which have been presented before the
Institute and which, in general, lia\e recorded such advances are
reviewetl.

Selective Circuits and Static Interference}" J. R. Carso.v. This
paper is an application of a general mathematical theory to the ques-
tion as to the possibilities and limitations of selective circuits when
employed to reduce "Static" interference. In the case of static
interference and random disturbances in general the random and
unpredictable character of the disturbances makes it necessary to
treat the problem statisticalh' and express the results in mean values.
In spite of the meagre information a\ailable regarding the character
and frequency' distribution of static, this treatment of the problem
yields general deductions of practical significance. The conclusion
is reached that for given signal requirements there is an irreducible
residue of static interference which cannot be eliminated. This
limit is closely approached when a filter of only two or three sections
is employed as the selective circuit, and only a negligible further gain
is made possible by the most elaborate circuit arrangements. A
formula is also given for calculating the relative figures of merit of
selective circuits with respect to random interference.

The Guided and Radiated Energy in Wire Transmission}^ J. R.
C.VRSOX. This is a mathematical analysis of wave propagation along
guiding wires from the fundamental equations of electromagnetic
theorj-. It is shown that the engineering theory of wire transmission
is incomplete, and that, in addition to the transmitted wave of en-

» Jour. .\ni. Chcm. Soc., \ol. XL\"I, No. 8, -August. 1924.

'Journal of the .American Inst, of Elec. Engineers, \'(>l. 4.^, pas;o lOS.?, 1924.

'° Trans. .A. I. E. E., 1924.

" Jour. -A. I. E. E., Oct., 1924.

182 BELL SYSTEM TECHNICAL JOURNAL

ginecring theory, an infinite series of complementary waves exist. It
is through these waves that the phenomena of radiation are directly
accounted for. E.xcept for the phenomena of radiation, however, the
complementary waves are of theoretical rather than practical interest
in present-day transmission practice, and except in extreme cases they
may be ignored in practice without appreciable error.

Sound Magnification and Its Application to the Requirements of the
Deafened.^- Harvkv Fletcher. A general description of the gen-
eration and projiagation of sound waves was given and experiments
performed to illustrate the principles involved. The general require-
ments for aiding persons ha\ing various amounts of deafness were
outlined. The relation between the loudness of speech received by
the ear in a room of average acoustic characteristics and the distance
the speaker is away from the ear was illustrated by a chart. Also,
a chart showing the characteristic frequency regions and loudness
levels of the fundamental speech sounds, and one showing the interpre-
tation of speech at various loudness levels by persons having various
degrees of hearing, were exhibited. By means of these three charts
it was shown how one could predict the amount of intelligibility which
would be obtained by a person having a definitely measured amount
of hearing. In particular it was pointed out that such sounds as
th,f, and v will be the first sounds to be lost as the hearing decreases.
These sounds are the easiest ones to detect by lip reading so that
hearing aids and lip reading go hand in hand in aiding one wlio is
hard of hearing to obtain the proper interpretation.

Abstract of a Telephone Transmission Reference SyslemP L. J.
SiviAN. The subject is dealt with in four parts: A — The function of
a transmission reference system; B — Requirements to be met by the
reference system; C — Work done on the construction and calibration
of a preliminary model of the new reference system; D — Proposed
future development of the new reference system in its final form to
be adopted as the standard for the Bell System.

A brief discussion of the methods and apparatus entering into the
general problem of rating telephone transmission is given. It is

" Lecture given before the .\nnii;il Conference of the .American Federation of
Organiziitions for the Hard of Hearing, Washington, U. C, Thursday, June S, and
published in Volta Review, Septenilwr, 1924.

A large number of the audience who listened to this lecture were hard of hearing.
A rough measurement of the amount of hearing of each of those present was made
and groups arranged according to the degree of hearing. The amplification was
then adjusted to each group to suit their i)articular needs. The results seemed
to bo most gratifying, as nearly everybody said that it was the first time they ever
heard a public lecture of this sort without difficulty since they had become hard of
hearing.

" Klcctrical Communications, Vol. Ill, pp. 114-126, 1924.

.lli.<^rR.lCTS <■! I'll I. sVWTTA/ TECIIS'ICAI. I'JIT.RS IS.l

nnuluilid that a phxsical rifirriuo system is essential, anil that a
mere siH-eilication of its plnsiial ()|H>ratinK chararteristirs is insuni-
eiciit. The inaile(|iiaeN' of the refireiice systems now in use is pointid
out.

The conditions to bo aimed .it in the new reference s>stem are:
I — 'llie performance of the s>stcm and of its component parts mi^irt
be specitiai)le in terms of quantities admitting of definite physical
measurement; II — The performance of the reference system, under
specified njKTating and atmospheric conditions, must remain constant
with time; III — The reference system must be free from non-linear
distortion over the range of acoustic and electric amplitudes which
it must handle; IV' — The frequency response over the range of speech
frequencies must be as nearly uniform as possible.

Uf the above, conditions I ami II are regarded as the most im-
jKtrtant. It is also proposed to build auxiliary reference systems
which will meet conditions I and II while falling short of III and IV.
These are needed for purposes of ready comparisons with the com-
mercial circuits commonly in use.

Contributors to this Issue

F. L. Riiouiis, S.B., Massaclui^cits Institute of Technology, 1892;
American Bell Telephone Company; Outside Plant Engineer, Ameri-
can Telephone and Telegraph Company, 1900-19; Outside Plant
Development Engineer, 1919 — . Mr. Rhodes has had an active part
in the development and standardization of materials, apparatus and
practices employed in the underground and overhead wire plant
of the Bell S\stcm. He has written many articles, among which
may be mentioned those on "The Telephone" in the EncNclopedia
Americana and Nelson's Encyclopedia.

Gkorgk Crisson, M.E., Stevens Institute of Technolog\-, 190G;
instructor in Electrical Engineering, 1900-10. American Telephone
and Telegraph Company, Engineering Department, outside plant
division, 1910-14; transmission and protection division, 1914-19;
De\elo[)ment and Research Department, transmission development
division, 1919—.

\V. II. II.\Ki)i:.\, B.E.E., University of Michigan, 1912; Engineering
Department, American Telephone and Telegraph Company, 1912-
1919; Department of Operation and Engineering, 1919 — . Mr.
Harden has been engaged in the development of transmission main-
tenance testing methods and in the preparation of routines and
practices rer|uire(l for ai3[)l\ing these nielhods in the telephone plant.

K. S. Joii.xsoN, A.B., Harvard University, 1907; Graduate School
of Applied Arts and Sciences, 1907-09; Engineering Department of
the American Telephone and Telegraph Company, 1909-13; Engi-
neering Department, Western Electric Co., Inc., 1913-24; Bell Tele-
phone Laboratories, Inc., 1925 — . Mr. Johnson's work has related
especially- to the theoretical aspects of telephone and telegraph trans-
mission.

TiMOTiiv E. SiiE.\, S.M., Massachusetts Institute of Technology-,
1919; instructor in Electrical Engineering and Physics, 1918 20;
Manufacturing Deixtrtment, Western Electric Comi:)any, 1920-21;
luigineering Deiiarlment, 1921 24; .Apparatus Development Depart-
ment, Boll Telephone Laboratories, 1925 — . Mr. Shea has been
principall)' engaged in the development of electric wave filters and
allied apparatus.

184

(.OXIKIKl /('A'V /(' I Ills /ssr/. 18.1

Kaki. K. Dakrow, S.B., riii\iTsit\ of ("hiciijo, I'.MI; I iii\rrsily
of I'aris, l!)ll 12; liiivcrsity of Ikrliii, litI2; I'll. I)., in physics and
mathi'Miatii's, rnivcrsity of t'hicajio, I'.MT: lliiniiu-i'riii^; Di-p.irl-
mi-nt, W'l'stiTii Kk-rlric Cimipany. 1*.M7 '_M. lUll 'IVli'plioiu- I.abor.i-
tories, Inc., 1925 — . Mr. Harrow luis been ciijjancd lar^'ly in pri;-
pariiig studies anil analyses of published research in \arious fields wf
plusics.

W. \'. Woi.Ki:. B.S.. Carnegie Insiiuite of Technolojjy, 1!)1H; Sij^nal
Corps, 1918 19; tJcneral Klectric Company, 1919; Standard Under-
ground Cable Compan\-, 1920; Engineering Department, Western
Klectric Compan\-, 1920 24; Bell Telephone Laboratories, Inc.,
1925 — . Mr. Wolfe has been engaged in the dexelopmenl of \-arious
types of carrier systems.

r tclcphuiic lint, as thrif sivaratc Mack
s|iun(ling to one primary i. .lor

The Bell System Technical Journal

April, 1925

The Transmission of Pictures Over
Telephone Lines

By H. E. IVES and J. W. HORTON. Bell Tel. Lab. Inc.
R. D. PARKER and A. B. CLARK. Amer. Tel. » Tel. Co.

Introduction

THli probltMii of directly transmitting drawings, figures and
photographs froni one point to another iiy means of electricity
has long attracted the attention and curiosity of scientists and engi-
neers.' The broad principles of picture transmission have been
recognized for many years. Their reduction to successful practice,
ho\ve\er, required, among other things, the perfection of methods
for the faithful transmission of electrical signals to long distances,
and the develwpment of special ai)paratus and methods which have
liecome a part of the commimication art only within the last few
years. Prominent among the newer developments which have facil-
itated picture transmission are the photoelectric cell, the vacuum
tube amplifier, electrical filters, and the use of carrier currents.

None of the .systems heretofore de\'ised have been sufficiently
developed to meet the requirements of modern commercial service.
The picture transmission system described in this article has been
designed for practical use over long distances, employing facilities
of the kind made a\ailable by the network of the Bell System.

The desirability of adding picture transmission facilities to the
other communication facilities otTered b\' the Bell System seems now
to be well assured. \'arious engineers of the System have made
suggestions and carried out fundamental studies of the possibilities
for picture transmission otTered by the telephone and telegraph
facilities in the Bell System Plant which have aided materially in the
development of the method to be described.

' .A comprehensive account of earlier work in Picture Transmission will be found
in "Telegraphic Transmission of Pictures," T. Thome Baker, Van Nostrand, 1910,
and the "llandbuch der Phototelegraphie und Telautographie," Korn and Glatzel,
Leipzig, Nemnich, 1911.

187

188 BELL SYSTEM TECHNICAL JOURNAL

The account of the picture transmission system which follows is
intended to give only a general idea of the work as a whole. A num-
ber of engineers ha\e collaborated in this work, and it is expected
that later publications will describe various features of the system
and its operation in greater detail.

Gkneral Scheme of Pictlre Tr.vnsmission

Reduced to its simplest terms, the problem of transmitting a pic-
ture electrically from one point to another calls for three essential
elements: The first is some means for translating the lights and
shades of the picture into some characteristic of an electric current;

Fig. 1 — Sending end optical system in section: (L) light source; (D) condensing lens;
(A) diaphragm; (S) projection lens; (C) transparent picture film in cylindrical
form; (P) photoelectric cell

the second is an electrical transmission channel capable of trans-
mitting the characteristic of the electric current faithfully to the
required distance; the third is a means for retranslating the electrical
signal as received into lights and shades, corresponding in relative
values and positions with those of the original picture.

Analyzed for purposes of electrical transmission, a picture consists
of a large number of small elements, each of substantially uniform
brightness. The transmission of an entire picture necessitates some
method of traversing or scanning these elements. The method used
in the present apparatus is to prepare the picture as a film trans-
parency which is bent into the form of a cylinder. The cylinder is
then mounted on a carriage, which is moved along its axis by means
of a screw, at the same time that the film cylinder is rotated. A
small spot of light thrown upon the film is thus caused to traverse
the entire film area in a long spiral. The light passing into the

PICTURE TRANSMISSION Oll-.R TELEPIIONF. LINES 189

inti'rior of the cylinder then varies in intensity with the transmission
or tone value of the picture. The optical arrangement by which a
small spot of linht is projectetl upon the pholn^r.ipiiic transparency
is shown in section in Fig. 1.

The task of transforming this light of varying intensity into a
variable electric current is (H?rfornK'<l by means of an alkali metal

Kig. 2 — Photograph of photoelectric cell of type used In picture transmission

photoelectric cell. This device, which is based on the fundamental
discovery of the photoelectric effect by Hertz, was developed to a
high degree of [>erfection by Elster and Geitel. It consists of a
vacuum tube in which the cathode is an alkali metal, such as potassium.
Under illumination, the alkali metal gi\es off electrons, so that when
the two electrodes are connected through an external circuit, a cur-
rent flows. This current is directly proportional to the intensity

190

BELL SYSTEM lECUMC.IL JOi'RXAL

of the illumination, and the response to variations of illumination
is practically instantaneous. A photograph of a photoelectric cell
of the type used in the picture transmission apparatus is shown in
Fig. 2. This cell is placed inside the cylinder formed by the photo-
graphic transparency which is to be transmitted, as shown in Fig. 1.
As the film cylinder is rotated and advanced, the illumination of the
cell and consequently the current from it registers in succession the
brightness of each elementary area of the picture.

Assuming for the moment that the photoelectric current, which is
a direct current of varying intensity, is of adequate strength for suc-
cessful transmission, and tliat the transmission line is suitable for

Fig. 3 — Light valve details: (R) riblxin carrying picture current; (P) pole piece of
magnet; (j) jaws of aperture behind ribbon

carrying direct current, we ma>- imagine the cuneiil Irom tiie [iholo-
electric cell to traverse a communication line to some distant point.
At the distant point it is necessary to have the third element above
mentioned, a device for retranslating the electric current into light
and shade. This is accomplished in the present system by a de\ice,
due in its general form to Mr. E. C. Wenle, termed a "light valve."
This consists essenlialK- of a narrow ribbon-like conductor lying in a
magnetic field in >urh a position as to entirely co\er a small aper-
ture. The iiuiiniing current passes through this ribbon, whicli is in
conse(|uence detlecled to one side l)y the inter-action of the rurreiit
with the magnetic fielil, thus exposing the aperture beneath. Light
passing through this aiierttire is thtis varied in intensity. If it then
falls upon a photographic sensitive film bent into cylindrical form,
and rotating in exact synchronism with the film at the sending end,
the film will be exposed b\- amounts var\ing in proportion to the
lights and shades of the original picture. The ribbon and aperture
of the light valve are shown diagraminatically in Fig. 3. F"ig. 4

/■/( /7A-/. iK.ixsMissiox ori.R iri.i.fiioxi- i.ixr.s

191

>h<>\vs a st'ction of tin- riTt'i\iii)L; riul of a systi'in of (lii- sort |)oslulal(.-(|,
with its liuhl xiiinv, tfu- lij;hl \al\i', ami the ri'ffi\iiii; rylindtT.

.\i>\i-i.\ HON i>i S< III MK ID TiiiiiriioM. I.IM-: Tkansmissiux

The simple stiieine of picture Ir.iiisiiiissiou jiisl outlined must be
miHlitieii in order to adapt it for use on commercial electrical coni-
iiumication systems, which have heen developed |)rimarily for other
puriMtses than picture tr.msmissiou. Of existing electrical means of
communication, which include land wire systems (telegraph and
telephone), submarine c.iMe, and radio, ihe wire s\stem, as developed

III rLcei\ ing ciul optical system: (l.j ll^ht source; (I)) condensing
lens; (V) light valve; (S) projection lens; (Cj sensitive film

for the telephone, offers great advantage when all factors are con-
sidered, including constancy-, freedom from interference and speed.
The picture transmission system has accordingly been adapted to it.
In the simple scheme of picture transmission outlined in the pre-
ceding section, the photoelectric cell gives rise to a direct current
of varying amplitude. The range of frequency components in this
current runs from zero up to a few hundred cycles. Commercial
long distance telephone circuits are not ordinarily arranged to transmit
direct or very low frequency currents, so the photoelectric currents
are not directly transmitted. Moreover, these currents are very
weak in comparison with ordinary telephone currents. On account
of these facts, the current from the photoelectric cell is first amplified
by means of vacuum tube amplifiers- and then is impressed upon a
vacuum tube modulator jointly with a carrier current whose fre-
quency is about 1,300 cycles per second. What is transmitted over

' For a very full description of the standard telephone repeater the reader is
referred to "Telephone Repeaters," (iherardi and Jewett, Trans. A. I. E. E., .Nov.,
1919. Vol. 38, part 2, pp. I287-1J4S.

192 BELL SYSTEM TECHNICAL JOURNAL

Fig. 5 -Portion of transmitted pirturc of variable width line type, enlarged

fUllKI. I l<.l.\sMlsMi'\ ('//./? TF.I.r.rilONE I. IMS

IW

till' ti'lt'phone line is, then, the carrier wave ' inodulatet! by the photo-
eierlric wave s«) that the currents, in fre(iiiency range and in ampli-
tude, are similar to the currents corresponding to ordinary speech.

When the carrier current, modulated according to the lights and
sJKules of the picture at the sending end, traverses the ribbon of the
light vahe at the receiving end, the aperture is o|iened and closed
with each pulse of alternating current. Tlu- envelope of these pulses
follows the light and shade of the pii tiirc. Imt the actual course of

LU

PICTURE CHANNEL

SYNCHRONIZING CHANNEL

Kig. 6 — Diagrammatic representation of the picture and synchronizing currents.

(P) photoelectric cell; (.AM) amplifier modulator; (A) amplifier; (V) light valve;

(M) phonic wheel motors; (T) tuning forks; {.\K) amplifier rectifier

the illumination with time shows a fine structure, of the pcrio(licit\'
of the carrier. This is shown by the enlarged section of a picture.
Fig. 5; in this the black lines are traces of the image of the light valve
aperture. Superposed on the larger variations of width, which are
proportional to the light and shade of the picture, small steps will
be noted (particularly where the line width varies rapidly); these are
caused by the carrier pulses.

Syn'chroniz.ation

In oriler that the light and shade traced out on the receiving c\lin:ler
shall produce an accurate copy of the original picture, it is necess.iry
that the two cylinders rotate at the same uniform rate. This, in
general, demands the use of accurate timing devices. The means
employed in the present apparatus consist of phonic wheels or impulse
motors controlled by electrically operated tuning forks.'' Were it

'A description of electrical communication by means of carrier currents will be
found in "Carrier Current Telephony and Telegraphy," Colpitis and Blackwell,
Trans. A. I. E. E., 1921, Vol. 40, pp. 205-300. A discussion of the relations between
the several components of the signal wave employed in carrier is given in "Carrier
and Sidebands in Radio Transmission," Hartley, Proc. I. R. E., Feb., 1923, Vol. 11,
No. 1, pp. 34-55.

* .A detailed description of the construction and operation of the impulse motor
and its driving fork is given in "Printing Telegraph Svstems," Bell Trans, .\. I. E. E.,
1920, Vol. 39, Part 1, pp. 167-230.

194 BELL SYSTEM lECIISICAL JOLRXAL

possible to have two forks at \viclel>' separated points running at
exactly the same speed, the problem of synchronizing would be
immediately solved. ActualK' this is not practical, since variations
of speed with temperature and other causes prevent the two forks
from operating closely enough together for this purpose. If the two
cylinders are operated on separate forks, even though each end of
the apparatus runs at a uniform rate, the received picture will, in
general, l)e skewed with respect to the original. The method by
which this difficulty has been overcome in the present instance is due
to Mr. M. B. Long. Fundamentally the problem is solved by con-
trolling the phonic wheel motors at each end by the same fork. For
this purpose it has been found desirable to transmit to the receiving
station impulses controlled by the fork at the sending end. The prob-
lem of transmitting both the fork impulses and the picture current
sinuiltaneoush- could be solved by the use of two separate circuits.
If this were done the currents going over the two lines would be
substantially as shown in Fig. 6, where the upper curve represents
the modulated picture carrier for two successive re\olutions of the
picture cylinder, and the lower curve shows the synchronizing carrier
current modulated by the fork impulses.

It would iioi, liowcwT, lie economical to use two separate circuits
for the picture and s\nchronizing channels, consequently the two
currents are sent on the same circuit. In order to accomplish this,
the picture is sent on the higher frequency carrier, approximately
\,'M)() cycles per second, and the synchronizing pulses are sent on
the lower frequency carrier, approximately 400 cycles per second,
both l>ing in the range of frequencies readily transmitted by any
telephone circuit. These carrier frequencies are obtained from
two vacuum tube oscillators.^ The two currents are kept separ-
ate from each other by a system of electrical filters at the sending
and receiving ends, so that while the current on the line consists
of a mixture of two modulated frecjuencies, the appropriate parts of
the receiving apparatus receive only one carrier frecjuency each."

' The vacuum tube oscillator as a source of carrier current is described in Colpitis
and Blackwell, Loc. Cit. .\ general discussion of the vacuum tube oscillator is
given in the ".Xudion Oscillator," Heising, J(yur. A. /. E. E. .April and May, 1920.
.\ discussion of the arrangement of the particular oscillator used with the picture
transmission equipment is given in "Vacuum Tube (Jscillalor," Morton, Belt System
Tech. Jour. July, 1924, \'ol. 3, .\o. \ pp. 508-.S24.

•The application of wave filters to niulli-channel communication systems is
discussed in Colpitis and Blackwell, Loc. Cit. More complete discussions are to
be found in: "Physical Theory of Electric Wave Kilters," Campliell, Bell Sysleni
Tech. Jour. Nov., 1922, Vol. 1, No. 2, pp. 1-32.

I'liUKIl TR.IXSMISSIOX (U//v' lll.iriloM I.I MS l«»i

ni:SCRII'TIO\ OV .\l'l'ARAH.S

Mfchanical A rraii'^emciits

Till' i-ssi-iiti.il p.irls 1)1' ilu- iiu'cli.iiiiMn iisimI for mi.iiini; .md .idv. lur-
ing the cylinder at the sending statiDii, and for holding tin- |)liolo-
tlfctric ci'll and the aniplif\inj; and niodiilatin); sNsttni are shown
in the photograph, Fig. 7. At the extreme left is llie |)hoiiic wlieil
impulse motor, which drives the lead screw through a spiral gear.

Kig. 7 —Sending end apparatus showing motor, tilni carriage, optical system and
amplifier modulator

The spiral gear ordinariK- turns free of the lead screw, hut may be
engaged with it by a spring clutch. The lamp housing, whic h pro-
\ides the illumination for the photoelectric cell, is in the foreground
at the center of the photograph. The photoelectric cell is in a
cylindrical case at the left enti of the large box shown on the track
and projects into the picture cylinder on which a film is in process
of being clamped. The amplifier and modulator system is carried in
the large box to the right, which is mounted on cushion supports to
eliminate disturbances due to vibration.

196

DELL SYSTEM TECHXICAL JOURNAL

The receiving eiui mechanism for turning and ad\ancing the
cylinder is similar to that at the sending end. The parts peculiar to
the receiving end are shown in Fig. 8. They consist of the light
valve, which is in the middle of the photograph, and the lens for pro-
jecting the light from it upon the cylinder. The metal cylinder

F^ig. 8 — \'ic\v of receiving end apparatus showing light valve and observation
microscope

around wliicli the st-nsitixe photngraphic film is wrajJiX'd, appears at
the extreme right. The microscope and prism shown are used for
inspecting the light valve aperture for adjusting purposes.

Electrical Circuits

The essential parts of the electrical circuits used are shown in the
schematic diagrams, Kigs. 9 and 10, in which the various elements
which ha\e hecn dcscrilitMl |)ri\iously are sIkiwii in their relations to
each other.

Certain portions of the electrical circuits deserve somewhat detailed
treatment. One of these is the amplilier-modulator system for the
picture channel, the other is the filter system cmplowd for separat-
ing the picture and synchronizing channels.

\j}m

19S

BEI.I. SYSTEM TECIIXICAI. JOl'RXAL

III l"i^. 11 i> >li()\\n (at the to])) a diagram of ilic liirici currfiu
aini)litier and the modulator used for the picture cliamiel, together
with diagrams (at the bottom) showing the electrical characteristics
of each element of the system. Starting at the extreme left is the

Fig. 11 — Circuit schematic of aiiiplifiiT-modul.ilor with characteristics of
each clenifnt

photoelectric cell, the current from which passes ihr(iui;li a liii;!)
resistance. The potential tapped off this resistance (of ilie order of
'M) or 40 millivolts) is applied to the grid of the first \acuum ttihe
amplifier. The second vacuum tube amplifier is similarly cotijiled

I'lciiKii ih'.ixsMissiox orr.R ii:i.i.i'iii>\n i.ims

iw

with the first, aiul thi- vaniiim tiitic mocluhuor in nirii to ii. The
relationship between illuniinalioii and current in the |)h()l()eleclric
cell is, as shown in diagram No. 1, linear from the lowest to the highest
values of illunuti.ition. The vojiaije-currcnt (/•'. \-er-us /) ciiaracler-

^l-

T . T

SYNCHRONIZING CHANNEL FILTER

PICTURE CHANNEL FILTER

1 1 1 1 r

0 4 8 IZ 16 20 24 28 32 3G 40
FREQUENCY- HUNDREDS OF aCLES PER SECOND

Fig. 12 — Circuit st-heniatics lal)Ovc) and attenuation characteristics (l)clow) of
picture (full line) and synchronizing (dashed line) channel filters

istics of the amplifying lubes and the modulating tube circuits are
shown in the figure by the diagrams which lie immediately below
these tuljes. They are not linear o\er their whole extent. It
becomes necessiiry, therefore, in order to preserve the linear char-
acteristic, which is essential for faithful picture transmission, to locate
the range of \-ariation of current in each of the latter tubes on a linear

2()0 BEU. SYSTEM TECHNICAL JOURNAL

portion of their characteristics. This is accomplished by appro-
priate biasing voltages {Eg), as shown. As a consequence of this
method of utilizing the straight line portions of the tube character-
istics, the current received at the far end of the line does not vary
between zero and finite value, but between two finite values. This
electrical bias is exactly matched in the light valve by a mechanical
bias of the jaws of the valve opening.

Fig. 12 shows diagrammaticall>' the form of the band pass filters
used for separating the picture and synchronizing channels, together
with the transmission characteristics of the filters. The synchroniz-
ing channel filter transmits a narrow band in the neighborhood of
400 c. p. s., the picture channel filter a band between 600 and
2,500 c. p. s.

In addition to the main circuits which have been discussed, arrange-
ments are made for starting the two ends simultaneously and for the
transmission of signals. These functions are performed by the inter-
ruption of the picture current working through appropriate detectors
and relays. Testing circuits are also provided for adjusting the
various elements without the use of the actual transmission line.

Tnii Tr.\nsmission Line

In \'iew of the fact already emphasized, that the currents used in
picture transmission are caused to be similar both as to frequency and
amplitude to those used in speech transmission, it follows that no im-
portant changes in the transmission characteristics of the telephone line
are called for. With regard to the frequency range of the alternating
currents which must be transmitted and also the permissible line
attenuation, the transmission of pictures is less exacting on the tele-
l>hf)ne line than is speech transmission. In certain other respects,
however, the requirements for picture transmission are more severe.
For speech, the fundamental requirement is the intelligibility of the
result, which ma\' be preserved e\-en though the transinission varies
somewhat during a conversation. In the case of picture transmission,
variations in the transmission loss of the line, or noise appearing e\'cn
for a brief instant during the several minutes required for trans-
mission are all recorded and presented to view as blemishes in the
finished picture. Picture transmission circuits must, therefore, be
carefully designed and operated so as to reduce the possibility of such
liisturbances. In transmitting pictures o\er telephone lines, it is also
necessary to guard against ccrt.iiii other elTects, iiuluding transient

flClURli IK.LXS^MISSION OILU ILLLl'llONL LINUS

201

1~1=#

A

J \ I 1 r

C

D

-W\/y\AA-~w\/|/|/V^^

8 S

mm K

Fig. 13— Diagram illustrating' performance of systeii

202 BELL SYSTEM TECHSICAL JOURNAL

effects and "echoes" caused hy reflections from impedance irregular-
ities. A high degree of l)alance between the lines and their balancing
networks at repeater points is also required. These conditions can be
satisfactorily- met on wire telephone lines. Radio communication
channels are inherently less stable and less free from interference,
and special means lo overcome their defects are required in order to
secure high-grade pictures.

("llARACTICRISTICS OK Rli( ICIVED PICTURES

\\\ elect rically transmitted i)iclures Ikuc, as a result ot iJu- processes
of scanning at the sending and recei\ing ends, a certain amount of
structure, on the fineness and character of which depends the detail
rendering of the result.

The origin and nature of the microscopic structure characteristic
of pictures transmitted b>- the present process is illustrated by the
diagrammatic presentation of Fig. 13, which may serve at the same
time to give a re\'iew of the whole process. We will assiune that the
original picture consists of a test object of alternating oi)aciue and
transparent lines. Such a set of lines is shown at .4. The lines are
assumed to be moving from left to right across the spot of light fall-
ing on the film. The width of the sjxit of light (corresi)onding to the
pitch of the screw) is represented b>' the pair of ilashed lines. If
the spot of light were infinitely narrow in \\w diiection of motion
of the picture film, the photoelectric current would l)e represented
in magnitude in the manner shown at B. AclualK- the spot must
have a finite length, so that the transitions lietween the maximum
and minimum \alues of current are represented by diagonal lines as
shown at C. Due to the una\'oidable reactances in the amplifying
system, there is introduced a certain rounding off of the signal so that
the \'ariation of [lotential impressed on the modulator tube follows
somewhat the course shown at D. The alternating current intro-
duced by the vacuum tube oscillator is, then, given the character-
istics shown at K, the envelope being a close cop\' <if D. i^assing
out to the transmission line, the fact that the band nf frequi'ncies
transmitted by a telephone line is limited in extent results in a certain
further rounding olT of the i-iuelope of the |)icture current as shown
in /•'. The ribbon of the light \alvc when traversed 1)\- the alter-
nating current from the line performs oscillations to either side of the
center of the ajx-rture, consef|uently opening first one side of the
aperture and then the other. The two cur\cs of sketch (i repre-
sent the exctirsions of the light \al\e ribbon, ■rtith time, jiast the

riCTVKli TK.tXSMISSlOX OILK I l.Lhl'IIOSL I.ISLS 203

204 BULL SYSTEM TECHNICAL JOURNAL

edges of the aperture, which lattiT are indicated by parallel straight
lines. Owing to the fad that the light valve aperture must have a
finite length in the direction of rotation of the cylinder (indicated by
the small rectangle in the center of the sketch), there is a certain
overlapping of the light pulses on the film. (This is, in fact, neces-
sary' for the production of solid i)lacks.) These are indicated dia-
grammatically at //. In sketch I are shown, from an actual photo-
micrograph, the variations in the image of the light valve as traced
out on the moving photographic film. Here the dashed lines repre-
sent the limits of the image as formed by one rotation of the receiving
cylinder. It will be noted that the images due to the opening of the
light \'alve in each direction form a double beaded line. These
double lines are juxtaposed, so that the right hand image due to one
rotation of the cylinder backs up against the left hand image due to
the next rotation, thus forming on the film a series of approximately
symmetrical lines of variable width. These are exhibited clearly
in the enlarged section of a picture, Fig. 5. It will be understood
that for purposes of illustration, the grating used as the test object
in the [^receding discussion has been represented as traversing the
spot of light at the sending end at such a high speed that the final
picture is close to the limit of the resolving power of the system.
Thus the photomicrograph shown in I must be viewed from a con-
siderable distance in order that its difference in structure from the
original object A will disappear. A practical problem in the design
of picture transmission ai)paratus is to so choose the speed of rota-
tion of the c\linder with reference to the losses in resoKing power
incident to transmission that definition is sul)staiitiall\- the same
along and across the constituent picture lines.

There are, in general, two methods by which a transmitted picture
ma\' lie recei\'ed. One of these is to form an image of the light \-aIve
aperture on the sensitive photographic surface. When this is done,
in the manner described in connection with l-'ig. 13 the picture is
made up f>f lines of constant density and \ar\iiig width. .\ jiicture
of this sort is shown in Fig. 14. A merit of this kind of picture (when
recei\'ecl in negative form) is that if the structure is of suitable size
(()() to fio lines to the inch) it may be used to print directh- on zinc
and thus make a t\pogra|)hic printing plate similar to the earlier
forms of half tone, whereby the loss of time usualh' incident to
copying a picture for reproduction purposes may be a\-oided. A
disad\antage of this form of picture is that it does not lend itself
readily to retouching cr to change of size in reproduction.

Another method of pictin-e reception is to let the light from the

I'iciuRr. Th'.ixsMissiox orr.R ir.i.F.i'iioMi ijats 2ns

Kin. 15 — Portion of transmitted picture of variable density line type, enlarged

2()C BELI. SYSTEM THCIIMC.IL JOURNAL

ricrcKi: in.ixs.missiox oiek rrirriioM- lis is 207

Fig. 17 — Variable density line picture — Portrait of Michael Faraday

208

BELL SYSTEM TECHNICAL JOURNAL

lij^lu v.iKf fall upon tlii' film in a dilTusfil tnaniu-r through an aper-
ture of lixi'd k'Ugth so llial liius of constant width (exactly juxta-
posetl) hut of varying density are produced. A phototnicro(<raph
of a variable density picture of the opaciue line test object pre\ iously
discussed is shown at J, Fig. IH. Prints maiie from film negatives
receivetl in this way, if the structure is chosen fine enough (100 I^iK-s
to the inch or more) are closely similar in appearance to original
photograpliic prints and may be reproduced through the ordinary
half-tone cross-line screen. They may be retouched or subjected to
s(K'cial photographic procedures in any way desired. An enlarge-
ment of a jX)rtion of a variable density picture is shown in Fig. 15
and exam|)les of complete pictures so received are shown in Figs.
If.. 17 and 18.

Klectrically transmitted pictures are, in general, suitable for all
purposes for which direct photographic prints are used. Such uses
include half-tone reprotluction for magazines and newspapers, lantern
slides, display photographs, etc. Among these uses may be men-
tionetl, as of some interest, the transmission of the three black and
white records used for making three-color printing plates. The
frontispiece to this article is an example of a three-color photograph
transmitted in the form of three black anfl white records, each corres-
ponding to one of the primary colors, from which printing plates
were made at the receiving end.

Some practical details of the procedure follow-ed in the transmission
of pictures by the apparatus described may serve to clarify the fore-
going description. The picture to be transmitted is usually pro-
vided in the form of a negative, which is apt to be on glass and of
any one of a numl)er of sizes. F>om this a positive is made on a cellu-
loid film of dimensions 5" x 7", which is then placed in the cylindrical
film-holding frame at the sending end. Simultaneously an unexposed
film is placed on the receiving end. Afijustments of current values
for "light" and "dark" conditions are then made, over the line;
after which the two cylinders are simultaneously started by a signal
from one end. The time of transmission of a 5" x 7" picture is, for
a 100 line to the inch picture, about seven minutes. This time is a
relatively small part of the total time required from the taking of
the picture until it is delivered in the form of a print. Most of this
total time is used in the purely photographic operations. When
these are reduced to a minimum by using the negative and the send-
ing end positive while still wet. and making the prints in a project-
tion camera without waiting for the received negative to dry, the
overall time is of the order of three-quarters of an hour.

210

BELL SYSTEM TECHSICAL JOLRKAL

t

'^)

e — -B

I'ig. 19 — Electrical transmission of cartoon

I'lCrURf: TR.IXSMISSIOX Oll-R ir.lJ.I'IIOM-. I.IM.S

I"li;i.l>S ()!■ I'SKFULNKSS

211

Thf tieUls in wliirli iliitrirall\ transmittfcl piiluris may l)f of
greatest service are those in whirli it is desired to transmit informa-
tion which ran only t)e conve>ed eUcctively, or at all, by an ap[H'a!
to vision. Illustrations of cases where an ade(|uate verbal descrip^
tion is almost impossible, are portraits, as, for instance, of criminals

'^:^?.^»«

Fig. 2() — Electrically transinittod fingerprint

or missing individuals; drawings, such as details of mechanical parts,
weather maps, military maps, or other representations of transient
conditions.

The value of electricalK- transmitted pictures in connection with
police work has been recognized from the earliest days of experi-
ments in the transmission of pictures. Besides the transmission of
portraits of wanted individuals to distant points, there is now pos-
sible the transmission of finger prints. Some of the possibilities of
the latter were demonstrated over the New York-Chicago picture
sending circuit at the time of the Democratic Convention, July,
1924. The Police Department of New York selected the finger-
print of a criminal whose complete identification data were on file
in the Police Department in Chicago. This single fingerprint,
together with a code description of the prints of all the fingers, was

212 BF.LL SYSTEM TECHNICAL JOURNAL

transmitted to Chicago and identified by the Chicago experts almost
instantl>-. This method of identification will be, it is thought, of
value in those cases where difficulty is now experienced in holding a
suspect long enough for identification to be completed. Fig. 20
shows a transmitted fingerprint.

The fact that an electricalK- transmitted picture is a faithful coi^y
of the original, offers a field of usefulness in connectinn witii the

^

f

>

^

A

V\g. 21- IVaii'iniissinn iif .iiilniir.iph in.itrrial — I'irsl st'clion of Japaiiese-Aiiicricaii
Irealvof 185,i

transmission of original messages or documents in which the exact
form is of significance, such as autographed letters, legal papers,
signatures, etc. It would appear that this method might under
certain circumstances save many days of valuable legal time and
the accumulation of interest on mone>' held in abeyance. For these
reasons, it is thought that bankers, accountants, lawyers, and large
real estate dealers will find a service of this kind useful. Fig. 22
illustrates the transmission of handwriting.

ricruh'ii TK.ixsMissiox ori.ii telei'iionf. lines 2\i

Mi'ss.igi-s iti fori'imi l;uij;iiagi-s, t'mplti\iiiK alph;il)ets of forms not
siiitfil for ti'lfuraphir riKliii^;, an- haiullcd lo advaiUagf. Thus,
V\^. 21 sliows the hrsi strtion of the origin. il Japanese-American
treaty in Japanese script, as transmitted from New \'ork to Cliicano.

Advertising material, parliciilarly when \\\ ihe lUrm of special
t\|H>graph\- and drawings is often dirt'icuit and (i^ily to gel lo dis-

^lAAUyYL

' (Jriritfyi

'<S-<.

'^?^

^^r^s^"^^^:^

Fig. 22 — Transmission of signatures

tant piil)lishers in time for certain issues of periodicals and maga-
zines. A wire service promises to he of considerable \alue for this
purpose.

.A very large field for electrically transmitted pictures is, of course.
The Press. Their interest in the speedy transpcjrtation of pictures
has been indicated in the past by the employment of special trains,
aeroplanes, and other means for quickly conveying portraits and
pictures of special events, to the large news distributing centers. The
use of pictures by newspapers seems at present to be growing in

214 BELL SYSTEM TECHNICAL JOURNAL

favor, and main- are now rimning daily picture pages as regular
features.

Some of the possibilities in this direction were demonstrated by
the picture news service furnished to newspapers, especially those
in New York and Chicago, diiring the 1924 Republican and Demo-
cratic National Conventions at Cleveland and New York. During
these conventions several hundred photographs were transmitted
between Cleveland and New York and between New York and
Chicago, and copies furnished the Press at the receiving points.
Photographs made shortly after the opening sessions, usually about
noon, were transmitted to New York and Chicago and reproduced
in afternoon papers. A demonstration of picture news service on a
still larger scale was furnished on March 4th, 1925, when pictures of
the inauguration of President Coolidge were transmitted from Wash-
ington simultaneously to New York, Chicago and San Francisco,
appearing in the afternoon papers in all three cities. Illustrations of
t\pical news pictures are given in Figs. 14 and 18. The transmission
of timely cartoons offers another field for service. Fig. 19.

Other news-distributing agencies can also use electrically trans-
mitted pictures to advantage. Among these are the services which
make a specialty of displaying large photograjihs or half-tone repro-
ductions in store windows and other prominent places. Electrically
transmitted pictures of interesting events, about which newspapers
have published stories, appear suited to this service, and have already
been so used by some of these picture service companies. They
may also be used as lantern slides for the display of news events
of the day by projection either upon screens in front of newspaper
offices or in moving picture theaters.

Miscellaneous commercial uses have been suggested. Photographs
of samples or merchandise, of building sites, and of buildings for sale
may be mentioned. The quick distribution of moving picture
"stills" which is now done by aeroplane is one illustration of what
may prove to be a considerable group of commercial jihotographs
for which speedy distribution is of value.

Propagation of Electric Waves Over the Earth

By H. W. NICHOLS and J. C. SCHELLENG

S\ Mii-.|s: Thf lomiMMlivi-ly |K)or lr,iiismis.sii)n of r.iilin waves of Iwo or
ihri'f luindrt'il iiifttTS iiulicatcs soino sort of selective elTect in the alinos-
pluTe. Siith .111 etTcel is foiiiul to result from the cxisterue of free electrons •
ni the .itniosphere when the niaKnetir field of the earth is taken into airount.
In the earth's niasnetie tielil, which is alioilt one-half gauss, this selective
etiect will ixcnr .it a w.ive leUKth of approxintalelv 200 meters. Ionized
hydrogen nioletules or atoms result in resonant effects at frequencies of
a few hundritl cycles, this Ix'ing outside of the radio range. The pa|K'r,
however, takes into account the eflfects of ionized molecules as well as
ekitrons.

The result of this coml)ination is that the electric vector of a wave travel-
ing ikirallel to the magnetic field is rotated. Waves traveling (wrpendicular
to the magnetic field undergo doul)le refraction. Critical elTccts are
observeil in rotation, bending of the wave and absorption at the resonant
frequency. The paper develops the mathematical theory of these phe-
nomena and gives formulas for the various etTccts to be expected.

THE problem of the propagation over tlie earth of electromagnetic
waves such as are used in radio communication has attracted
the attention of a niimher of investigators who have attacked the
prnlilein along somewhat different lines, with the purpose of offering
an explanation of how electromagnetic wa\'es can affect instrimienis
at a great distance from the source in spite of the curvature of the
earth. N'o attempt will be made here to describe adequately the
various theories, but we remark that the theories of diffraction around
a conducting sphere in otherwise empty space did not give satisfactor>-
results and led to the necessity for the invention of a hypothetical
conducting layer (Heaviside layer) whose aid is invoked to confine
the wave between two concentric spherical shells. In many cases
this Heaviside layer was considered to have the properties of a good
conductor and it was supposed that a beam of .short waves, for ex-
■iinple, might be more or less regularly reflected back to the earth.
The high conductivity of this layer was supposed to be due to the
ionizing action of the sun f>r of particles invading the earth's atmos-
|)here from outside and producing in the rarefied upper atmosphere a
high degree of ionization. The differences in transmission during
day and night and the \'ariations which occur at sunrise and sunset
were supposed to \)C due to the different ionizing effects of the sun's
rays appropriate to the different times of day. The explanation of
the phenoment)n of "fading" or comparatively rapid fluctuations in
the intensity of received signals could then be built up on the assump-
tion of irregularities in the Heaviside layer producing either inter-
ference between waves arriving by different paths or reflcrtion to
different points on the earth's surface. The principal difiticully in

215

216 BHLL SYSTEM TECHNICAL JOURNAL

tliis explanation is the necessity for rather high conductivity to account
for the propagation of \va\cs to great distances without large ab-
sorption.

In 1912 there appeared an article by Kccles ' in which the bending
of waves around the surface of the earth was explained on the basis
of ions in the upper atmosphere which became more numerous as
the vertical height increased and thereby decreased the effectixe
dielectric constant which is a measure of the velocity of propagation
of the wave. In this case the velocities at higher levels will be sliglith-
greater than the velocities at lower levels, which will result in a bend-
ing downward of the wave normal and a consequent curvature of the
vva\e path to conform to the curvature of the earth. In order to
produce this effect without absorption the ions must be relatively
free. If they suffer many collisions during the period of a wave,
energy will be absorbed from the wave and pass into the thermal
agitation of the molecules. Thus absorption of the wa\'e can be
computed provided the nature of the mechanism is luuierstood
thoroughh'.

Sommcrfeld and others luivc worked nut the ctTcct of the iiniK'rfecl
conductivity of the grouml uijon the wa\e front and such computa-
tions lead to a prediction that the electric vector in the wa\'e near
the ground will be tilted forward and thus have a horizontal com-
]ionent. This effect of imperfect conductivity is usualh- given as
the cause of the large electromotive force which is induced in the
so-called "wave antenna." This effect, however, apparenth' does
not lead to an e.vplanation of the bending of waves around the earth.

There has recently appeared an article by Larmor - in which the
idea of a density gradient of ions or electrons is developed further to
explain the bending of waves around the earth without a large absorp-
tion. This paper, as well as that of Hccles, leads to the conclusion
that long radio waves will be bent around the earth, and that the
effect increases as the scjuare of the wave length, becoming vanishingK-
small for very short waves.

The large amount of data now available from both qualitative
and quantitative observations of radio transmission shows that the
|)hcnomena may be more complicated than would be indicated !)>•
these theories. It is found that very long waves possess a considerable
degree of stability and freedom from fading and that as the wave
length decreases the attenuation antl the magnitude of fluctuations
increases until for a wave length of (he orcjcr of two or three hundred

' IVoc. Roy. Soc., June, 1912.
> Phil. Mag., Dec., 1924.

rKor.ic.mox or electric tr.irrs orEU run eaktii 217

meters there is Rrcat irrcKnIarity in transmission so that rcliaMe
rommunication over land for distances as short as 100 miles is not
always (lossiMe even with larjje amounts of power. With decreasinR
wave length we tnul also variations in apparent direction of the wave.
On the other hand, as the wa\e length is decreased still further we
luul, sometimes, rather surprising increases in range and stability.
The nature of the fading changes, becoming more rapid, and the
absorption in many cases seems to decrease. This peculiarity of
wa\e transmission must be explained in a siitisfactory theory. In
addition to the apparent selective effect just mentionetl, some observa-
tions indicate that there are often differences between east and west
and north and south transmission at all wave lengths.

The various irregularities in radio transmission, and particularly
the apparently erratic and anomalous behavior of electromagnetic
waxes occurring in the neighborhood of a few hundred meters wa\-e
length seem to indicate that as the wave length is decreased from a
value of several kilometers to a value of a few meters some kind of
selective effect occurs which changes the trend of the physical phe-
nomena. These considerations have suggested to us the possibility
of finding s<ime selective mechanism in the earth's surface or in the
atmosphere which becomes operati\e in the neighborhood of 200
meters. A rather superficial examination of the possibility that
such a selective mechanism ma\' be found in a possible distribution
of charged particles in the atmosphere has resulted in the conclusion
that a selective effect of the required kind cannot be produced by
such a physical mechanism. There is, however, in the earth's atmos-
phere— in .iddition to distributions of ions — a magnetic field due to
the earth, which in the presence of ions will have a disturbing effect
upon an electromagnetic wave. As is well known, a free ion moving
in a magnetic field has exerted upon it, due to the magnetic field,
a force at right angles to its velocity and to the magnetic field. If
the ion has impressed upon it a simple periodic electric force, it will
execute a free oscillation tf)gether with a forced oscillation whose
projection on a plane is an ellipse which is traversed in one period
of the applied force. The component velocities are linear functions
of the components of the electric field and at a certain frequency,

depending onlv upon the magnetic field and the ratio — of the ion.

Ill

become very large unless limited by dissipation. This critical fre-

Ile . .

quency is ec|ual to if // is measured in electromagnetic units

Zittnc

and e in electrostatic units. It is the same as the frequency of free

218 BELL SYSTEM TECHNICAL JOURNAL

oscillation. For an electron in the earth's magnetic field (assumed
to have a value of 1/2 gauss) this resonant frequency is 1.4 X 10' cycles,
corresponding to a wave length of 214 meters.' We thus ha\e an
indication that some at least of the phenomena of transmission at
the lower wave lengths may be explained by taking into account the
action of the earth's magnetic field upon electrons present in the
earth's atmosphere and acted upon by the electric field of the wave.
This frequency occurs at appro.ximately the position in the spectrum
at which the peculiar effects already mentioned occur. The next
resonant frequency which would be encountered would be due to the

e 1

hydrogen ion which has a ratio, — , equal to 7^777; that of the electron.

ni 1 oUU

The resonant frequency of this ion is only 800 cycles and certainly
can have no sharply selective effect in the propagation of electro-
magnetic waves over the earth. We have, therefore, worked out the
consequences of the assumption that we ha\'e in the upper atmos-
phere two controlling factors influencing the propagation of electro-
magnetic wav-es in the radio range, namely, free electrons and ions
together with the earth's magnetic field. The electrons will be
dominant in their effects in the neighborhood of the resonant frequency
and perhaps above, while the heavy ions will affect the wave at all
freciuencies and, if much more numerous, may be controlling at
frequencies other than the critical one. In working out this theory
it is assumed that there are present in the earth's atmosphere free
electrons and ions. At high altitudes these are capable, on the
average, of %-ibrating under the influence of the electromagnetic
field through several complete oscillations before encountering other
ions or neutral atoms. At low altitudes this assumption will not
hold, the collisions being so numerous that the importance of tiie
resistance term in the equations of motion becomes much greater.
In either case the ions ha\'e no restoring forces of dielectric type.
The motion of the electron or ion constitutes a convection current
which reacts upon the electromagnetic wa\e and changes the \i'l()rit\-

^ This frequency does not depend upon ifu' direction of the field, and is practically
constant over the earth's surface.

f)n March 7, after this paper had been written, the February 15 issue of the Pro-
ceedings of the Physical Scxiety of 1-ondon arrived in New York. In this journal
there was a discussion on ionization in the atmosphere in which Prof. K. V. .Appleton
suggested, in an appendix, that the earth's magnetic field acting upon electrons
would change the velocity of a wave and produce rotation. A calculation of the
critical frequency was given in which, however, only the horizontal com|X)nent
of the earth's field was used, resulting in an incorrect value for the critical frequency,
namely less than half the actual value. If the complete equations are written
down it is evident at once that the total field is involved in the critical frequency,
no matter what may be the direction of propagation.

I'Kor.tGATIOS OF Ll.ix iiui i/.»/7;.V OITR THE li.tHTII 2n>

of propa^^alion of the wa\c. This is, in fact, thv l)asis for the explana-
tion of the optic.il pro|H'rties of transparent and absorhinK media
and also of nu-di.i which show magnetic or other rotatory |M)wers.
Due to collisions aiul recomhinations, energy will pass continuously
from the electromagnetic held and increase the energy of agitation of
neutral molecules. Since this prcness is irreversible it accounts fyi
absorption of energy from the wave.

Asiiume an electron or ion of charge e and mass m moving with
velcH-ity V and acted u|)on !)>■ an electric lield E and the earth's mag-
netic held H. The etpialion of motion of the free ion will be

e c

or av = E + vxh (1)

in which h is written for — and a for w; e. (When we come to consider
c

absorption it will be necess<irv to generalize </ into*/ (l — i — ) to in-

dude a resisting force. n.\ proportional to the velocity.)
The total current is given by

4irI = E+'^A7TXcv. (2)

In these equations and the following we are using Gaussian units
.ind the summation refers to different kinds of ions.

In order to avoid a complicated mathematical treatment, which,
however, is not difficult to carry through if necessary, it will be as-
sumed that the magnetic field H is along the axis of s. When more
general results are required, they will be stated. All time variables

are assumed periodic with a frequencv - , so that =in.

Solving equation (1) for the coniixuH-nts of v we find, for each
type of ion :

inaX+hY

11

h^--a'-n-

— hX + ina

Y

t'l

h^-a'-n^

t'3

ina

220 BELL SYSTEM TECHNICAL JOURNAL

from which it appears that a resonance frequency occurs for

h

n = — =Wo.

a

Since e/m for the electron is — 1.77c X 10', the earth's magnetic field
of about 1/2 gauss will produce a resonance frequency at l.-tXlO^
corresponding to a wave length of 214 meters, while all heavier ions
have resonance frequencies far outside the spectral region to be
considered.

The assumption that the components of the ionic motion are simple
harmonic, in spite of the fact that the motion of the ion is rather com-
plicated, is justified as follows. From (1) we find that the velocity
of an ion (r), say v, is made up of the complementary solution, V,'
and the particular solution Vr"=J{E). The latter depends upon the
impressed force E, while the former has constants of integration
determined by the position and motion of the ion at the last collision.
The complete current is thus

I^^E+y^eVr' + NefiE).
■iir ■*"'

The second term, however, a\-erages out over a large number of ions
since the initial conditions are random;* hence, as far as the effect
upon wave propagation is concerned, we may treat all quantities
as periodic.

Following the usual i)n)cedure for the investigation of the propaga-
tion of waves in media of this kind, we shall rewrite equation (2) in
terms of the com|K)nents of the electric field, tinis for each t\ pe of imi :

., <T.\ - -

47r/, = f 1 -f r .\ X - i -^r-^, y=uX - ia Y,
\ 11^- — 11- J iio' — n-

T.V-"

Wo — M" V Wo" — KV

in which =ci, or 3.2X10' for an electnui and o.2 . 10' ,- for

a .1/

an ion of mass ^1/. In order to avoid complicated formulas, the

summatif)ns which must be carried in equations (3) to lake account

• It is luTC iis-sunud ih.il the iman lime lntWTcii collisions is large compared to — .

rRor.iG.-tih'.s ('/■ i-.i.iAiKii II III s (II I Ik iiir. i..ii<iiiii\

of the efTcct of ions of different kinds have heen nniitled, l)ul it is to
he understocxl that the dielectric constants «, «, etc., are Ixiilt up
from the contriluitions of all t\pes of ions. Tlius for an ion of mass

.1/ we nuist put a for a, «„ for w,„ in e(iii.ilions (.5).

The etTective dielectric constant, instead nl Ixinv; unity, lias thus
the structure:

0 «2 /

and we may write ecination (2) as

4jr/= (t)E

which has the significance of the scalar equations (3). Thus / is a
linear vector function of E and the operator («) is skew symmetric,
indicating a rotator>' effect about the axis of z.

(The general case in which h has the three comjionents (li\ //; hi)
residts in a dielectric constant ha\ing the structure

(«i — /Ss — /as —^i + iof. \

— /3j — taj — /3| + ;'ni «3 '

of which the above is a special case. With tiiis \aiuc of (e) the equa-
tion (4) below contains the general solution of our problem.)

Let H\ be the magnetic force associated with E in the wa\e so that

ccurl f/, = (f) E
ccurl E=-Hi.
Kliminating Hi from these equations we get

-V^£+rdivE = 4'(0E (4)

or in scalar form

-^'^4-:^ div E=4'(ei X-iaY),

222 BELL SYSTEM TECHNICAL JOURNAL

_ V= r + 1- di V E = ^' {iaX + 6 , F) , (5)

oy c-

02 C-

These ecjuatioiis for the propagation of light in magnetically active
substances have been given by \'oigt, Lorentz, Drude and others
and form the basis of the explanation of optical phenomena in such
substances. As applied to optics, they are worked out, for example,
in Drude's "Optics" (English translation), page 433. As applied
to this problem, they assume either that the motion of the ions is
unimpeded or that the resistance to the motion may be expressed as
a constant times the velocity, which, as explained later, may be done
in this case. We shall work out some comparatively simple cases
and point out the conclusions to be drawn from them.

Consider first a plane polarized ray having its electric vector pardllf]
to the magnetic field and moving in the xy plane; for example parallel
to X. In this case the electric vector is a function of x and / only
of the form

Z = Zo

H'-t)

in which - is the \'elocit\' of the wa\e. Sutistituting in the general

M
equations (.')) wc find that

M- = l-l^. (6)

The \el(>cit\ of projiagation is thus a fiuution of tlie frequency and
of the density A'. This particular case corresponds to that treated
by Eccles and Larmor in the papers cited. It will be noted that the
velocitj' is greater for long waves than for short waves and that if A^
is a fimction of distance from the surface of the earth, the velocity
will \ary in a vertical direction, causing a curvature of the rays as
worked out by the authors mentioned. In this particular case, how-
ever, which corresponds completely in practice to conditions obtaining
over only a limited area of the earth's surface, the greatest effect is
produced on the longer wa\-es. Since electromagnetic waves are in
general radiated from vertical antennas so that the electric vector
is vertical, this case would correspond to the condition of transmitting
across the north or south magnetic poles of the earth.

The second ca.se to be considered is that of propagation along the
direction of the magnetic field. In this case X and Y are functions

FKOr.tC.ITKKW or ELECTRIC U'AIES OVER THE E.lRTIl 223

of s and / and ilu- .ippropri.Ki- soliiiions of ilio fimd.inuiit.il (•(|iialii>iis
(5) are

A-' = .la.s.(/-^;.^).

r= -.4 sin «(/-— V Mr = fi + a,

A'" = ^l cos w (l-y-)'

Y" = A sin /; ('-^'"-)' m/ = «i-".

whirli rt-pri'si-nt two opposilcK- circularK' polari/ed components
traNclinj; with the different \elocities — and —. The plane of poiar-
ization is rotated through an angle of 2 tt in a distance given by

The third case to be considered is that of propagation at right
angles to the magnetic field, say in the direction of x. For this case
equations (5) become:

X = ^Y

-„^>>'-("-f>

n-
of which the solutions are

A = — Fo f ^ 'I
«i

.-(,-'^) , a'

Z = Zo

ll 1-^"

The first of these is merely the (usually small) component of field
required to make the total current solenoidal, that is, to balance the

224 BELL SYSTEM TECHNICAL JOURNAL

convection of electrons. The last two show that the plane polarized
ray whose electric vector is parallel to // will travel with the velocity

—'while the one whose electric vector is at right angles to this direction

and to the direction of propagation will travel at a dilTerent speed,

c

— . There is thus doiililc refraction.
Ml

Bending of the rays. If m is the index of refraction, which is a

function of the space variables, the curvature of the ray having this

index is where s is taken perpendicular to the direction of the

II ds

ray. Since n is practically unity except at the critical frequency,

this curvature is 1/2 d fr/ds. In order that the ray should follow

the curvature of the earth it is clear that n must decrease at higher

altitudes; that is, '-^ must be negative.
ds

We shall workout the curvatures for the special cases considered.

(The first case has been given above and was worked out in the papers

cited). For the case of propagation along //, tlie two ciriii!arl\-

polarized beams have indices given by

Mr = ei + a = l + ^ j^. (0

n" o}-\-\'

(-=?)•

We are interested in the \alues of 1/2—— in which .V and /; are fiinr-

ds

lions of distance s and also of the time. These conic out to be

N dir

(9)

_ (T r <«'^ dX 0}-' i\ rf/;~j

'"wLiii^ 'ds~ {u>-iyirdsj'

^^ ~ 2n6'Lw+l ds ^ {oi+iyhdsS ^ '

.\ striking fact shown by tlicse formulae is that the curvatures of
tlie two rays are in general difTerent. A limited beam entering an
ionized medium along a magnetic meridian will be split into two
which will traverse different paths. Thus we should expect to find,

rR(U'.n:.iTi(>\ ()/• i-i.r.CTNic u.irns ornn riir. F.iRrii 22-^

orrasionalK', a ciriularl\' pnlari/i-d l>fam .it the riTfiver due to the
fact that the reteiving insirumfiU is locati-d at a iK)int toward which
oiu- of the Iwams is diverted after lia\iiin ()assed lhroii)^h an iip|HT
ioni/til layer. This is now hein^; investijjaled experimentally. It
is clear that, although the two components do not in general travel,
over the siune path, hoth ma>' e\enlually arrive at the same receivei'.
The first ray, however, ma\- iiave pi'netrated iniicli higher in the

atmosphere than the other, that is, to a level at wiiich — has the

(is

prof>er negative value to cause it to return to earth.

For long waves, these curvatures become:

-f-?a.

<:■,-, -J

2«„-L (is h (is J

Hence a limited beam of long waves entering this medium would tend
to split into two of opposite polarization and traverse different paths.

In the special case for which ^.~- = -, — r~ throughout the medium,
.\ (is h ds

there will be no such separation of the beam.

F~or verv short waves

" 2no=L

Hence if the most effective cause of refraction is the variation in the
ionic density both components tend to remain together and to travel
with a rotation of the plane of polarization. If variation in the
magnetic field is appreciable the two components tend to diverge as
in the case of long waves.

F'"or propagation at right angles to //, sav along .v, we have

Mr =«•.!= 1- -.7. (!•■>)

(16)

226 BELL SYSTEM TECHXICAL JOURNAL

The bending of tlic plane polarized comixmriit lia\in,i; the index ixi
shows no selective effects, being simply

In' as

and is appreciable only for long waxes unless .V is \er\- large. For
the other component we find :

wtiere, in onlcr lo simplify ilic furnuila, oiiK' liii' lerni cmitaining

—;— has l)een iiirliifled. Tiiis api)lies to ions of one kind.
as

I'or long wa\es those two curxatiires become

2«o-v Wo^ / as

These formulas show that the first curvature is alwa\s in the same

(LX
direction for a given value of -^, while the second curxature, which is
lis

that of the electric vector perpendicular to the magnetic field, is, for
very long waves, in the same direction as Ci but, as the wave length
is decreased or N increased, reverses in sign and becomes opposite
to Ci. As an example, if N= 10, for 6 kilometer waves the curva-
tures are opposite, so that if the first component tends to bend down-
ward the second will tend to bend upward; while if .V=100, for the
same wave length both cur\atures ha\e the same sign and the second
is five times as large as the first.

For extremely short waves the two curvatures are equal as they
ob\iously should be, since the magnetic field can then ha\'e no effect.

In transmitting from New 'S'ork to London, for example, waves
travel approximately at right angles to the magnetic field, which in
this latitude has a dip of about 70°. If we assume a plane polarized
ray starting out with its electric \ector \ertical, the component
parallel to the magnetic field will be the larger and will be subject
to the curvature C\ abo\e, while the smaller component will be affected

PROPAGATIOS Ol- l-.I.ECTRIC If.iriiS OfLR TUE EARTH 227

!•%• the iii.i^;nclic fivM .uul will lia\e the curvature t';. The two com-
(xtnents into whioli tiie original \va\e is resf)lve(i will travel with
different \elocities. It is clear that when the distrihution of ions
in the up|H'r atmosphere is changed by varying sunlight conditions,
the resulting effect at a receiver is likely to \ary considerably. Sorae
of the possibilities will In.' discussed later.

Rotation of the plane of polarization. It has been shown that in
the second case, namely transmission along the magnetic fiekl, there
will Ih; a rotation of the plane of polarization of the wave. This
rotation is such that the wave is rotated through a ii)ni()lfit' iiirn in a
distance given by

" Mo <jN or' ^ '

«o- ur — \

It is interesting to note that the distance in which a long wa\e rotates

through 2 V approaches the constant value — ^ as the wave length

(jN

increases and that for very short waves the rotation of the plane of
polarization tends to vanish with the wave length.

Absorption. When an electron strikes a massive neutral atom the
a\erage persistence of velocities is negligible and in the steady state
of motion of electrons and neutral molecules the element of convection
current represented by an impinging electron will be neutralized, so
far as the wave is concerned, at every collision. Of the energy which
has been put into this element of convection current since the last
collision, a part will l)e spent in accelerating neutral molecules, part
will go to increase the average random velocity of the electron and a
part will appear as disordered electromagnetic radiation. Thus, as
far as the wave is concerned, the process of collision with massive
neutral molecules is irreversible even if the molecules are elastic,
and all the energy picked up by the electron from the wave between
collisions is taken from the wave at the next collision. Exactly the
same state of affairs would exist if at each collision the electron recom-
binerl with a molecule and a new electron were created with zero or
random velocity. Thus for massive molecules for which we can
neglect the persistence of electron velocities the effect upon the wave
is exactly the same whether the collision is elastic or inelastic.

These conclusions are verified by the results of two different com-
putations which we have made of the resistance term, re, in equation

228 BELL SYSTEM TECHNICAL JOURNAL

of motion of the electron. Consider in the hrsi place a mixture of
electrons and massive neutral molecules, assumed perfectly elastic,
in which the persistence of velocities of the electrons after collision
is negligible. If an electric field A'*'"' operates in the x direction and
if the state of motion is a steady one, we can compute the energy w
taken from the wa\e by a single electron at any time after a collision
at the time t\ and before the next collision. Let this time after /i be
T. If the mean frequenc\' of collisions is/, the time r between colli-
sions will be distributed according to the law

/*

-fr

and we shall obtain the mean energy taken from the wave per collision
by multiplying w by the above expression, integrating from zero to
infinity with respect to r and then performing an average o\er all the
times /,. The result of this is that the mean energy loss per col-
lision is sini[)ly

'^~ 2mn- P + n^

and consequently the loss per second is / times this. If we equate
this to rv^, which is also the rate at which energy is being dissipated,
we find that r = nif, which is therefore the resistance term to be inserted
in the equation of motion of the electron.

If the convection current is carried partly by heavier ions, it will
not be annulled at each collision and all the energy derived from the
field will not be lost on impact.

The foregoing computation assumes as ob\ious that energy is lost
from the wave at a rate equal to the number of collisions times the
average energy which the electron takes from the wave between
collisions. The second method is somewhat more general. The
mean velocity at a time / is found for electrons which collided last
in an interval at /i. This is evidently- a function of the velocity
persisting through the last collision and hence of the average velocity
before the impact; so that if the average velocity before collision
was V, that after impact would be 5 v, in which 5 is a number less
than unity, depending on the relative masses and the nature of the
collision. Averaging for all values of /, before / and using the same
law of distribution assuiTied above, the mean velocity of the ions
since the last collision is obtained. \i\ comjjarison with the solu-
tion obtained for the velocity of forced oscillation in which the re-
sistive force is rv, we find that r = ;w/(l— 6). For the special case of
electrons, B may be taken equal to zero, hence' r = w;/. For the case

PROPAGATIOS or ELFXIKIC W.illiS OVER THE EARTH 22!^

of MTN' heavy iims colliding wiili liglil lu-iilral molecules, r=o, since
6 = 1. I'or e(|iial masses & would lie about one half, hence r = .', mj.

Since the resistance factor r is eciual to ;;//, in order to include the
i-lti'it of .iiii-iui.iiioii of the wave, we mii-ii icpl.Mc n li\-

./

..(-.■:-)

If, as usual, we assume a wave proportional in

I c t ^ c '

the eiiuations (.')) show that, in ortler to calculate the \ahie of the
absorption constant k, we must put

in which t is the generalized dielectric constant appropriate to the
case considered. We have worked out in this way the absorption
for the various cases treated above with the f(jllowing results.

In the case in which there is either no magnetic field or the magnetic
held is parallel to the direction of the electric \ector, we find

2no^ l+P/n"'

This formula for absorption applies (for electrons) for any value
of / or H. Thus near the surface of the earth where the collision

fretiuencv/ is of the order of 10", the fraction -^—will be large even for

n

rather short waves. As we go higher in the atmosphere this ratio

decreases for a given wave frequency until at a height for which

f
= 1 we encounter the ma.ximum absorption per electron. Above

thi^. Ie\el ^^ and consequenth- the absorption per electron decreases.

For ions other than electrons the resistance will be somewhat different
from mf, depending upon the ratio of the masses, and a corresponding
change must be made in the above statement.

In this paper we are considering only the effects which take place
at heights above that for maximum absorption so that, generally

speaking, ^ will be small or at least less than unity. This approxima-
tion will be used in computing the absorption constants which follow.

230 BHU. sysrrM teciisical jovrxal

As an example of tlie iialuie of this approxiination. at a height of
about 100 kilometers, we may expect an atmospheric pressure of
10~' standard and a corresponding collision frccjuencx' of the order
of 10''. Thus for \er\' long \va\es of frequency 40,000 cycles per

second we still have •- =.4, while at the critical frequency — is only
n ' n

1/100.

The computation of the collision frequency for electrons is rather
invoked because of the peculiar nature which such a collision may
ha\c and because it probably is not permissible to assume thermal
equilibrium with the molecules of the gas. The processes of ionization
and recombination will also lead to complications. Probably the
most significant information would be the number of electron free
paths per second for unit \'olume.

The question of the behaxior of waxes in or below the la\er of
maximum absorption per ion is a somewhat tlifferent one and belongs
projjerly in another paper.

Kor the case of transmission along a magnetic meridian the oppo-
sitely circularly jx)larized rays have the absorption constants '■

, _ aN (j}-f/n , _ <rN o)^ /

Ii will be noted that, at the critical frequency, the first of these waves
lias till' lii.uli .ibsorption .y j ' ,■ and is therefore extinguished in a

short (li^Iall(■c■, wliik' the other \va\e has a normal alisorption const. ml

aN f

— ^ • ^. Thus lor the case ol traiisniission along a meridian at the

8w„- H

critical frequency we might expect a receiving station, sufiiciently far
al)ove the ground, to recei\e a circularly polarized beam. This would
mean that if a loop were used for reception, the intensity of the
received signal would be independent of the angle of setting of the
loop, pro\ided one diameter of the loop was set parallel to the direction
of propagation of the wave. In general, of course, this ideal condi-
tion could not be realized due to the disturbing action of the ground
and of other conducting or refracting bodies and the most we should
expect to receive in practice would be an elliptically polarized beam.
In the third case, namely, that of propagation perpendicular to
the ilirection of the magnetic lield. we find that the wave polarized
with its clcciric \ccior parallel to the magnetic field has the same

I'Koi'.iG.irtos or i.u.ciKic ir.irns o\er tiii: earth 2i\
'->>■■ .. ,'"

al)sori)ti<iii .IS hrlorc, ii.iiiu'l\- x- "■' .. .mil tin- hIIht r.iv wliosi- cdiii-

* ■ O .\ ft

pli-\ iiiili'X cif rcfr.utioii is «i— " has the .ihsorptioii coiistiml J (/fri + ztj)

ill whirh k\ and kt are the abs<irpti()n constants j^Im-ii aliove for
prop.iij.uion alons a nuiKnetic meridian.

.\l llu- rritir.il freqiieniA we tind, tlierefore, lli.it tlie absorption

constant is abnorm.ili\' hiuh and equal U^ ,' . ■ . which is one-half

4 «„- /

that obtained for the first ray of case 2.

One very striking fact is brought to light by these equations. Thus,
referring to the two values of absorption constants for transmission
along the magnetic field, we find that for \ery long waves (for which
(ji is large) the ionic absorption is very much less with a magnetic
field present than without it. This means that in this case and in
the next the presence of a magnetic field assists in the propagation of
an electromagnetic wave by decreasing the absorption. This reduc-
tion in absorption may amount to a rather large amount, as may be
seen from an inspection of the formula for ^i. For example, if in
this case ui is 20, corresponding to 4,000 meter w'aves, we find
that under corresponding conditions the absorption due to electrons
only is reduced by the magnetic field to 1 /400th the value it
would have for no magnetic field. Of course, these cases are not
directly comparable because the path chosen by the wave would be
different in the two cases. It is plausible, however, that the propaga-
tion of long waxes along the magnetic field ma>' go on with much
less attenuation than propagation from Kast to West omt ,i region
in which the magnetic field is nearly vertical, in which case the effect
of the magnetic field is largely absent. This conclusion, however,
cannot be made in general since a number of other causes are influen-
tial in determining the propagation, for example, the bending of the
rays, so that it is not certain that transmission oN^er a region in which
the magnetic field is vertical is always more difficult than in the
other cases.

The reason for the decreased absoriitioii of long wa\es wlien the
magnetic field can operate (that is, in all cases in which the electric
vector is not parallel to the field) is that the velocities acc|uired by
the free electrons are much less for small \alues of // wiien the magnetic
field is present.

Fading. By this is meant a variation with time of the strength of
a received signal at a given point. It is clear that a wave starting

2i2 BELL SYSTEM TECHNICAL JOURNAL

originalK- with constant amplitude and frequency can be recei\ed as
one of variable amplitude only if certain characteristics of the medium
are variable with the time. So far as the atmosphere is concerned,
these characteristics may be the distribution of electrons and heavier
ions and the intensity and direction of the earth's magnetic field.
If these are functions of the time, the velocities, bending, absorption
and rotation of the plane of polarization will all be variable,
the amplitude of variation depending upon the variations of A^,

-r-, //, — J-, as well as the frequencv of the wave, the effects being in
as as

many cases magnified greatly in the neighborhood of the critical fre-
quency. These effects are obviously sufficiently numerous to account
for fading of almost any character and suggest a number of experi-
ments to determine the most effective causes. The question of rota-
tion of the plane of polarization, fading and distortion is now being
examined experimentally.

From the formulas it is clear that the velocity, curvature and absorp-
tion of an electromagnetic wave as well as the rotation of its plane of
polarization can all be affected by a time variation in the intensit\'
and direction of the earth's field. An examination of the probable
time and space variations of each, however, lead us to the conclusion
that these are not of primary importance in determining large ampli-
tude fading except, perhaps, during magnetic storms. One result of
the last two years of consistent testing between New York and London
at about GO, 000 cycles has shown that sexere magnetic storms are
always accompanied by corresponding \ariations in the strength of
received signals. Thus, although the earth's magnetic field can
well exercise a large influence upon the course and attenuation of
radio waves, it does not seem likely that its time variation is ordi-
narily a large contributing cause to fading.

This leaves as the probable principal cause of time variations the
number and distribution of ions in the earth's atmosphere. It is
impossible in this paper, which is devoted primarily to a development
of a theory of transmission involving the earth's magnetic field, to
consider adequately all the possibilities resulting from changes in
ionic distributions, but some general remarks may be made. Imagine
a wave traveling from the source to the receiver. At a short distance
from the source the wave front will be more or less regular but as it
progresses, due to the irregularities in ionic distribution, the wave
front will develop crinkles which become exaggerated as the wa\e
goes on. These crinkles in the wa\e front will be due to irregularities
in the medium and can be obtained by a Huyghen's construction at

rROP.tGATlOX OF ELECTRIC WAVES OVER THE EARTH 2.13

.my point. If we consider the wave a short distance before it reaches
the receiver, we will tind regions in which the wave front is conca\e
to the recei\er and regions of opposite curvature. Thus at certain
portions of the wa\e front energ>- will be concentrated toward a point
farther on and at other parts will be scattered. The location of these
convex or concave F«)rtions of the wave in the neighborhood o{ a
given receiving point will be very sensitive to changes in ionic dis-
tribution along all the paths of the elementary rays contributing
to the effect at the receiver. Hence, if we knew the location and
movement of all the ions between the transmitter and the receiver,
it would be possible, theoretically, to predict the resultant eflfect at
the latter point.

To explain fading it is essential that there be a time variation in
this distribution. It is clear that effects of this kind should be more
marked at short waves than at long waves since a region of the medium
comparable in dimensions to a wave length must suffer some change
in order to produce an effect upon the received signal. If, for example,
there were space irregularities in the medium comparable to the wave
length, a kind of diffraction effect would be produced at the receiver
which would be ver>' sensitive to slight changes in grating space.

A possible cause of irregularity may be found in the passage across
the atmosphere of long waves of condensation and rarefaction, each
of which results in a change in the density and gradient of the ions,
even though the average density remains constant throughout a
large %olume. If, as seems plausible, the upper atmosphere is
traversed by many such atmospheric waves of great wave length,
the resulting effect at a given receiving point would be fluctuations
in signal strength due to a more or less rapid change in the configura-
tion of the wave front near the receiver.

For radio waves whose length is of the order of a few hundred
meters, fading experimentally observed occurs at a rate of the order
of one per minute (of course, it is not implied by this statement that
there is any regular periodicity to the fading). The pressure wave
referred to would travel in the upper atmosphere with a velocity of
the order of 300 meters per second at lower levels or 1,000 meters in
the hydrogen atmosphere, so that the wa\e length of these "sound"
waves would be of the order of 50 of the radio wave lengths. The
irregularities of the medium would thus be of sufficient dimensions
with respect to the electromagnetic waves so that one of the char-
acteristics referred to above might be developed. In this way we
might explain variations in intensity of the wave at the receiver re-
curring at intervals of a minute or so.

234 BELL SYSTEM TECUSICAL JOURNAL

These effects, of course, might be produced even without a magnetic
field but the results of this paper indicate that conditions in the wave
front will l)e complicated still further by a rotation of the electric
vector and by the existence of bending and double refraction due to
the magnetic field, these effects being exaggerated in the neighbor-
hood of the critical frequenc\-. Due to the magnetic field we have
also the possibility of summation effects between components of the
wa\e which were split off by the action of the field and consequently
had traveled by different paths at different speeds. It is obviously
impossible to make any general statement concerning the nature of
the effects which will be produced by this complicated array of causes
but future experimental work will, we hope, allow us to estimate
the relative importance of the various elements.

Open Tank Creosoting Plants for Treating
Chestnut Poles

By T. C. SMITH
iMKKDUniON

Tj^Olv ,1 mimlicr of years rlu'stiuit tinila-r, lieraiisc of its many
■I (li'sirahle cluiracti'risfirs, has served a broad field of usefulness
in telephone line construction work, not only in its native territory,
the eastern and southeastern part of the United States, but also in
neighboring states. In fact, as an average, about 200,000 chestnut
poles are set annualK- in the Bell System plant as replacements and
in new lines.

In areas which are gradually being extended from the northern
part of the chestnut growing territory into the southern sections,
blight is ra()idly making serious inroads into this class of pole timber.
North of the Potomac Riser practically all chestnut territories have
been visited by the blight anil it has in a major sense crossed into
areas south and southwest of this river, where it is de\-eIoping from
scattered spots. While many pj)les are yet secured in the blighted
areas, they must be cut within a very few years after becoming afifected,
in order to save them from the fleca\' which destroys blighted poles
after they are killed.

.A chestnut pole lasts satisfactorily above the ground line but
decays at and within a few inches below the ground, thus weakening
it at a critical location. In order to protect the poles from decay
at this lf)cation. the open tank creosote treatment seems to be the
most satisfactory-, where the facilities for applying the treatment
are available. In general this treatment consists of standing the
[>oles in an ofK'n tank and treating them in a creosote bath which
covers them from the butt ends to a point about one foot above
what will l)e the ground line when the poles are set. The method
of appKing the treatment will be explained in more detail further
along in the paper.

Due to the scattered locations of the cliesiTUit timber .ind also to
the fact that in many places this timl>er is rapidly being depleted
by the blight, it has required cf)nsiderable study to establish loca-
tions for ofH'U tank treating plants which would be convenient for
applying the treatments anti would also have a sufficient available
pole supply to permit the oi)eration of the plants long enough to

235

236 BELL sySTEM TECIlStCAL JOURNAL

warrant the necessary investment in them. However, suitable
locations have been established and plants have been constructed
which will, when operating to their planned capacities, treat about
139,000 chestnut poles per year, and these plants may easily be
enlarged to treat additional quantities as the demand for treated
poles develops.

These plants have been designed by our engineers and are being
operated for applying preservative treatments to poles used by the
Bell System.

LOC.VTING THE TREATING PLANTS

It might be interesting to bring out the governing considerations
in locating the chestnut open tank treating plants, as compared with
commercial plants for treating cedar poles, which are operating in
the north central and northwest portions of the Uhited States. Due
to the geographical locations in which the cedar poles grow, in rela-
tion to the centers of distribution en route to the locations where
they will be used, treating plants of large capacities can be supplied
for many years with poles which pass them in the normal course of
transporting the poles from the timber to their destinations. Com-
mercial pole treating companies seem to have had no difficulty in
establishing locations for handling 100,000 or more cedar poles per
\ear through a single plant; whereas the scattered locations of the
chestnut poles, as outlined above, make it more economical to build
the chestnut treating plants in units \'arying between 10,000 and
36,000 poles per year capacity.

Several factors were considered in deterniiiiing tiu' jiropor loca-
lioiis for the seven Bell System treating plants which have been
l)nili. It was often possible to select a location which was admirabl>-
adajjled to the purpose when considered from two or three view-
pi)iiits but which was foimd imdesirable when considered from all
(if I he necessary angles. The principal points considered were:

1. yuantitN' of poles of liie desired sizes axailable locally wliicli
could be ilelivered to a proposed plant b\- wagons, mnicir \flii(les,
etc.

2. Qiianli(\' of poles wliicli coiiM he con\ cnienlK- routed past the
plant during the rail sliipmenis iVoin tlu> tiniher lo their desti-
nations.

3. Quality of the available timber.

CRr.osorixc i'L.ims iok tri.iiixc iiiisixri nu.r.s 2i7

I. TIk' k'ligth of tiini" diiriiij; wliiili a pi, ml of ilu- dfsirfil si/r
cniiKI 1)0 supplied with liininT for trfalmciil. This rstimati'd
li>;urc would, of loursc, diicrminf tin- liiiijili i>\ lifi> nf ilu' |)rn-
posi'd pl,mt.

."). K,iilro.id farilitics .iiui frrii;hl di^t.uucs fnuii liir propoMd pi.uit
to points wluTi' till" poU's would hi- used.

ti. Avail.djilitx' of l,d»>i" for opir.iliiit; liu' pi. nil.

7. Locating a suilahle site for tlu' pi.mt.

I-".x(H.'rifiu-c of the Western l-llectrie ("ompain's Purcii.isinj^ I )e[)art-
nieiii and the loeal .Associated Tele[)hone {\impany representatives,
tni;eiher with inform, itioi) from ( "inxrrnment re|)orts, |iro\ ided the

I'i^. 1 — I. ami ii|)<)H which S\l\-,i I'l.uit w.i> Duill

answers to the first hve items. Studies upon the j;round were made
to settle the remaining two items after a preliminary survey of the
situation had iiidirated what locations seemed to w'arrant consid-
er.ilion.

The une\enness of the hind >is siiown 1)\- l-ig. 1, wliicii is l\|)ical
f)f the many avaihiblc locations studied, made it difficult to secure a
comparatively level tract of the proper area and dimensions adjoining
a railroad siding or at a location where a siding could conveniently

238

/?/:ll system technical journal

be established. In fact it soon became evident in making the pre-
liminary studies, that it would be necessary to design the various
treating plants to fit the best of the available tracts.

As a result of these studies, seven plants were established and
placed in operation in five states as outlined below:

Total .Annual Pole

Date when Plant

Capacity When

Location

Was Placed in

.Annual Pole

.Additions .Now

Operation

Capacity Now

I'lanned Are
Completed

Shipiiian, \'a

Oct. 1922

10,000

l.S,000

Dec. 1922

10,000

10,000
18,000

N.iliiral Bridge, Va

Apr. 1923

10,000

Williiuantir, Conn

Aug. 1923

10,000

10,000

Svlva. .\. C

May 1924

18,000

25,000

Nashville, Tenn

July 1924

18,000

25,000

Ceredo, W. Va

Sept. 1924

23,000

36,000

Total?

99,000

139.000

It will be noted from the above table that several of the plants
are not yet working to their capacities as now planned. In designing
the plants, the plans were made to provide for the total annual capac-
ities shown above. However, when they were built the initial capaci-
ties were made somewhat lower as indicated by the table, by omitting
in some cases tanks and in other cases pole handling equipment
which could readily be added in conformity with the plans, later
when the additional capacities would be required.

Y.VRD Sizes

It might not .seem necessary to occupy a very great area in the
operation of a pole treating plant. However, experience with some
of the earlier plants indicated that a reasonably large yard was \er\-
desirable because of the number of poles necessarily carried in piles
on skids in the yard both in the untreated stock and in the treatetl
stock. In so far as practicable the poles in the various treating
plants are arranged in such a manner that each length and class is
piled -separateK'. This greatly facilitates handling the poles, but
re(iuires considerable sjjace. Ordinarily about <S0 pole ()ilcs are
necessary in a yard.

From four to ten acres of land has been used for each of the various
pole treating yards. Fig. 2, which includes about half of a com-
paratively small capacitN' \ar<!, sliows the necessity for plcnt\- of
room for the pole piles.

CKEOsorixG rL.i.\is fOR ■nir..irjM; ciii.srxur roi.ES 2i<)

\*.\kl) I.AVOl IS

Sinfi' tlu" pi>li- tiiMtiiiji >ar<l l,i\c>iits ari' iH-ri-ss.iriK' Imili around
the railroad sidinjjs whirl) haiulli- the |M)Ii's in and out of the yards
and transfer them from one location to another inside I he \-.irds, it is
di'sirahle to Imild the >ards lonij and narrow.

Fig. 2 — I'ortioii of I'olc Yard at One of the Smaller Plants
Creosote Storage Tank at Right)

(Tool House and

Of course, the sharper the railroad cur\es can be made in la\ing
out a siding from the railroad into the pole treating yard, the easier
it is to accommodate the siding to cramped yard conditions or to
spread out the tracks over a short, wide yard. However, due to the
use of heavy locomotives on the main lines and the desirability of
having switch curves suitable for the locomotives ordinariK- used,
it has been necessary to use 12 degree railroad curves in planning
most of the yard entrances, and in no case has a cur\c Iwen used
which is sharper than 18 degrees.

It will be noted from Fig. 3 that the pole treating apparatus is so
located that the work of hantiling poles to and from the treating
tanks will not interfere in any way with loading outgoing cars of
treated poles from the skids. It will also be noted that the poles
which are received from the river are treated during the natural
course of their passage to the "treated" skids.

240

BELL SYSTEM TECIISICAL JOURNAL

■"k-

±33ais Nivi^

cKiiosori.xc i'i..iMs roK iia-..iii\c ciir.srxur roi.ns 24\

Car loads of polrs which an- ri-ci-iwd l)y rail may In- backed into
ilu- track Icadini; to the ()olc Ircatiny; (ilaiil for treatment or may Ik-
unloaded u()<in the "untreated" skids if desired. In any event, there
>liould l>e a mininuim of cotifiision in the pole moving operations.

l-ig. I shows the skids at one enil of the Sylva yard before (>oU's
had been (liled upon ihem. It illustrates tin- desirability- of havitii; a

\>K- 4 -Skill l.,iy<)iU .11 Dm- l-.ml ul >\ Iv.i ^ .ird

long, narrow \ard and also shows that the switch track is the backbone
of the |)olc yard.

It will also be noletl from Fig. 4 that in the Sylva yard the enils
of the skids are brought up close to the track. This is because the
jK)le handling in the Sylva yard is done by means of a locomotive
crane which runs on the track and works from the ends of the cars.

In the Natural Bridge yard, which is show'n in Fig. 5, a tractor
crane is used for p:)lc handling. This unit has crawlers and wheels
which operate on the narrow roadways at either side of the spur
tracks. The tractor crane runs up to the side of a car to unload it.
iiy operating at the sides of the cars a much shorter boom is required
by the tractor crane than for the locomotiv'e crane working at the
ends of the cars handling the same lengths of poles.

Delivery of Poles to Pi-\xts

\'arious methods are used for delivering poles to the treating plants,
from the locatit)ns where the>' are cut. In adtlition to the use of
automobile trucks with their trailers, and to the use of horse-drawn

242

BELL SYSTEM TECHSICAL JOURNAL

wagons which may be seen along the road in Fig. 4, poles are tlelixered
by railroad cars, river rafts and ox-teams.

In the timber the poles are ordinarily loaded on cars for shipment
to the treating [jlants b>' means of a logging loader shown in Fig. G.

Fig. 5— ^'ard l,a\i)Ul at One liiul of .Natural Bridge Vanl, \ irwiil Irui
Derrick

Mast of

lig. 0- I'lucing Poles on Logging Car !)>■ .Means of Logging I,oailer

CKEOSOIlMi I'UIMS /OA' TKF.ATISG CIIF.SIXUT POLES 243

Although it has a short Ihmhii, it is al)U- lo handli- vi-ry long poles
iH'faiisi- of till- nu'tluHl it) whirh it lifts iht-in. One end of the [lole,
either to|) or l>utt, is rested against the middle point of the iiooni
and the |x>ie lifted 1)\- the winch line which nia>' he attached only
one-third or one-fonrth of the (list.incc fmin ilie Io.kUt end lo the

Fig. 7 — Gearctl LcKomotive in Use on Logging Road Which Supplies I'oles to
Treating Plant

free enil of the pole. In lifting long [loles by this nietluKl. they spring
considerably, and brash timber usually breaks under this treatment.
Thus in handling poles by this method, they are given a test before
they leave the timln-r.

The winch line is attached to the pole b\- means of hooks which
resemble ice tongs. From long experience in handling these tongs,
the pole men are able to throw them several feet and catch a pole at
any point they ficsirc, to pull it from the pole pile. This operation
is ver>' fast. In fact, under favorable conditions, 'Sit foot chestnut
p<iles have been loaf led on a car at the rate of two per minute.

The pole piles along the logging road are usually disorderly, re-
sembling a lot of giant tooth-()icks which might have been carelessly
dropped in a heap.

244

BBLL SYSTEM lECllMC.ll. JOURNAL

Steep grades on the logging roads make it very desirable to use
locomotives which have a maximum amount of traction. For this
reason, a geared type locomotive is used which [x^rmils a big reduc-
tion between the engine and drive wheels, and also transmits the
drixing torque to all wheels of the engine and coal tender which is
shown, and also to the wheels of the water tender which is not shown
in Fig. 7.

From one to ten car loads of poles in a grouj) arri\'e at the trealini;
plants. A car load varies between 40 and 65 poles depending upon

l-'iy. X -tar Load of Poles Arriving at the Danljury Treating Plant

ihe sizes of the |)oles. They nia\- be unloaded by a locomotive crane
or a tractor crane or b\ the iiuiliod shown in Fig. !).

At the Shijjman \'cU(i liie jxiies are unloaded b\- cutting the stakes
and permitting the poles to roll down an embankment into piles
from which they are drawn to the treating plant by means of a steel
rope from a tractor winch.

Utilization of the cheajiest method of delivering poles to the treat-
ing plants is possible at Ceredo and Nashville where the plants are
located on the river banks. These poles are si-curely tied in rafts of
about 100 poles each and either floated down tin- rixcrs or handled
b\- stern wheel. ri\tT steamboats.

I

CREUSOIIW: /7../.V/.V /■■('A' Ikl-.tllXC Clir.STMl I'OI. lis 24S

--

mm

"^-^1

Ml

,'*i

V

i^^^^^iii^^

11-^

^^i^M

^^jp

♦*«'

"^1

I^Bw^K^^

y

^^^^^m

^^K^^— <

^^

BhI

Kig. *> — Inloadini; I'uli-^ it thi- Shipiuan ^'ar(l

I i^' In I Miir K.,11- i.l r,,l., ,,t Ccredo I'laiil

246

HELL SYSTEM TECHNICAL JOURNAL

It m.i\ \>v (.f iiiirrt'st to note thai the i)liotograph shown in Fig. 10
was takfii from the West Virginia l.ank of the river, while the Ohio
bank is seen across the river and ilir Keniiickx hills are xisihle beyond
the bridge.

Particularly in ihe Cirolinas, ox-teams are used tt) draw pole
loads down from ilu' mountains.

I iii. 11 ruK' l)<li\cry liy ()x-Tcams

Fig. 12 Ucrrlik (or HaiulliiiK Poles from River Rafts to I'ilcs or Pole Cars
in the Yard

CRF.OSOIINC PLINTS roR TKIIAIISC CHESTNUT POLES 247

Mandi.inc. Poi.ks in riiK Yard

W'luTi- till' (liTrifk is iist-d for lifting i><)lfs out of the ri\tT it is
ne«-fss;iry to set it at a distanco from ttu- watrr's i-(li;r which, of course,
apf)roaches and rcceiics dciH'ndiuR upon the height of I he river.
Because of this distance, the poles are dragged as well as lifted u;j
the siopiiiv; si<le of the hank.

1 IK- 14— liuilor Cr.iiif Haiitiliiix I'olc, Iruiii Kail I Ulu

It has been found that wherever it is po.ssiWe to eliminate the
handling of poles by nian-p<iwer, a considerable economy can he

248

PELL SYSTEM TECHNICAL JOURNAL

realized. Less men are required for crane or derrick operation, and
the cranes and derricks do the work much more rapidh'.

In order to move the poles about the yard it is not necessary to
retain a freight car to carry them, since small rail dollies have been
provided for this purpose. The two dollies shown in Fig. 14 are
separate and can be located under the poles at any distance apart
tlepcnding upon the lengths of the poles.

The tractor crane which is used for poll.- lianilling in ilie smaller
plants is operated !)>• a hea\\- duty gasoline engine and it is able

I'ig. 15 — Stiff lAg IX'rrick Removing Poles fromyrrcating Tank anil Loading Them
on Flat Car

to handle a 1,01)0 11). load at .i !•') font radius tiudugh an arc of about
270 degrees. It has a 30 fool liooni. Since a very large percentage
of the chestnut poles handled, wiigh less than one ton each, this
tractor crane has sufficient capacity for the ser\ ice.

In the smaller plants where it has been found tlesirai;le to increase
the pole treating capacities aboxe what could be handled b\- means
of the tractor cranes, stilT leg derricks ha\-e been installed. Thesi-
derricks are of 6-tons capacitN', ha\ing 4.5-foot booms. They are
operated by steam from the ireatint; plant boiler, which fi-eds the
H H.P. hoisting engines. In- these Inst, ill. itioiis tlu' swingers are
operated by the hoisting I'ligiiies.

Where the treating plant is of large enough cap.icitX' to warrant

ch!i-.(>sonxi; i'i..is'Ts /(i/v* iKiLtiixa ciir.srxcT roi.t:s 2V)

thi- invcstrnont in a limimotivi" crane, this ts|)r of unit has proven
to In- the njost satisfactory in oi>eralion. The cranes which are
suitable for this t> pe of work have a oO foot lxM)ni and are rated at
17'-_> tons capacity. ActualK' tltey can safely handle a :<-lon load at
"lO feet radius from tlie kinjj pin of (he crane, perpendicular to the

I :.

:iijin iliL liiMtiiiK Tanks tu tlic Dullu.
Locoiiiotivf Crane

track, without tipping the car hotly of the crane. Of course, with \hv
lK)om in a position above the track the ma.ximum safe load is con-
-iderably greater.

The method of handling poles most commonly used is illustrated
in Fig. 17 where the poles are lifted in a balanced condition, swung
to one side of the track and piled parallel to it.

.Another method which is applicable, particularly lo handling a
lO-foot and longer pole, consists of butting the pole end against the
lHK>m of the locomotive crane and swinging it to a pile which lies
perpendicular to the track. This method of handling poles is similar
to that shown in use with the logging outfit in l-'ig. (i.

When the poles are piled either parallel or f)erpendicular to the
track as shown by Figs. 17 and 18, respectively, there should be
•rf(iuent breaks in the piles in order to permit the air to circulate
around the pf.les and keep them dry, and to reduce the fire
hazard .

w

Fig. 17 — llaiulliiig I'lili's b>- H.ilanrcd Mclliud with l.iiiomcitni- ( ranc

!•'!«. KS— IliinilliiiK Pole with laid United Against Room of l.ci. oniotive Ciaii

CREOSOTING PLANTS FOR TREATING CHESTNUT POLES 2S1
Preparing Poles for Treatment

AIiIioukIi efforts were originally made to clean and prepare the
|H)Ies on the cars at the time the\' were received at the plant, in order
to bi- able to unload them from the cars directly into the treating
tanks, it was found to be more satisfactory to first imload them
upon skids where tlu-\- would In- more accessible for the removal

1 i^. 1'-' rrcp^ialiuu bkidi Upiji

rruuling I'aiiki ul b>l\a I'luiU

of all bark and foreign matter from the area to be treated and where
any defective poles could be culled out before treatment.

The preparation skids are ordinarily not used for storage purposes.
When a load of poles is placed upon them it can be spread in such a
manner that every pole will be accessible.

In Fig. 20 the load of poles from the dollies has just been laid on
the preparation skids where they will be cleaned for treatment in the
far tank which is shown empty. Due to the desirability of having a
continuous supply of poles for treatment, also of having the poles
seasoned for several months before treatment, it is not practicable
in a very large percentage of cases to ship the poles direct from the
timber to the yard and unload them on the preparation skids for
immediate treatment. For this reason it is necessary first to pile
them in the untreated section of the pole yard and later to bring
them to the preparation skids on dollies as illustrated in Fig. 20.

252

BELL SYSTEM JECILMCAL JUL KX.U.

Treatmknt

The following is a very brief outline of tlie nuiliod pur?
treating the poles and also of the results obtainetl.

In so far as practical >lr the poles are seasoned (i niontiis (
before being treated. Tiic niciliod of treatment coiisisis
mersing llic butts to a U'\il nf .ihout 1 fool alioxc what will

r more

of ini-
\<v ihc

Fig. 20 — IVe[)aralion Skids Opposite Treating Tanks in Nashville N'ard

ground line nf liic |)oles, for not less than 7 hours in crcosoic at a
temperature between 212° and 2;^0° Fahrenluil. .\l the end of the
hot treatment, the hot oil is ciuickK- removed irnni tiu' lank and cold
oil at a temperature of from 100° lo 11()~ Fahrciiiicii is perniitled to
flow quickly into the treating tank lo liu' lc\cl [)it\iously readied
by the hot oil. The cold oil trealincMl hisls for al least I hours.

Heat is absorbed b\- the p<<\v Initts in the iiol oil bctlii tiiilil the
moisture contained in the sa|)wood is either e.\i)anded into steam or
entirely driven out. DiUMUg the short interval while the oil is being
changed, the surfaces to be treated remain covered In- oil from the
hot treatment. The oil change is made so C|uickl\ tiiit tin- pole
butts cof)l verv' little before it is completed. Then, as soon as the
cold oil is admitted, these surfaces are covered by the creosote which
reuKiins until the pole butts become cool. In the sapwood, from
which the moisture has been driven by the hot treatment, the cooling
[)rocess condenses the steam, thus forming a partial vactium in the

CKLositiixu fi..i.\is /o/v' iNi:.iii.\a ciii:si.\ri roi.ns 2^i

254

BELL SYSTEM I ECIIMC.IL JOLKSWL

wood. This causes the oil, in which these surfaces are inimersfd,
to be forced into the wood by atmospheric pressure.

During the treatment, tiie creosote is absorbed b\- the pole to such
an e.xtent that as an average, about 95 per cent, of the sapwood in
the treated section of the pole is saturated. This requires from
2 to 4 gallons of oil per pole, dejiending upon the size and condition
of the |)ok' heiii^ irt-aled.

Assii.MBLY Lav()i:t

The same general features of design were followed in all the pole
treating plant layouts in so far as i)ractical)le. However, the number

Fig. 12 — \'k-w of Treat iiiK I'.quipmcnt at SyKa Plant

of the different units ii-ed \\a> xaricd tn |)ni\iilr llii- plant capacities
re(|uire(l.

In designing the i)lants it was found desirable to separate the
p<jles into two or three treating tanks in order that the treating gang
could be contiiuiotisty emj)loyed in either preparing or handling poles
from or to one of the tanks while the treatment would be in progress
in other tanks. B>- dividing the tanks it was also possible to use a
smaller (juantity of hot creosote, since the hot oil could be used in one
tank and when that treatment was fmished, i^timped to another
tank containing iresh poles ready for treatment. Cutting down the
hot oil capacit\', of course, reduced the amount of radiation in the
heating tank and also the amount of radiation in use at any particular

CREOSOTIXG ri..lMS FOR TREATING CHESTNUT I'Ol.ES 2?<S

time in tlu- IriMtiiiK tanks, thus rtsultinj; in lonsidirably li-ss steam
hoiler capacity thin would l>c necessary with a very lar^e single
treating tank unit.

HandHnK poles .il smaller tanks is nuicli f,i>ier liec.ni>c less
l)<M)in action of the derrick is required and the men at the tanks can
reach all |)oles more easily for attaching and removinR the derrick
winch line.

It was found that a \eriic.il c\ lintlric.il I. ink served hetter ih.m a
horizontal one for the storage of hot oil, while the horizontal c>lindrical

,1 I'uK- R.ick

tanks were preferable for cold oil storage. The radiation from a
vertical hj)t tank is i-onsitierably reduced l)y the jacket of hot air
rising ak)ng its side.

Particularly during the summer months care must l)e taken to
keep dowi\ the temperature of the c(jld oil. It has been found that
the long cylindrical steel tanks when lying horizontally radiate heat
frf)m the oil to the atmosphere satisfactorily and thus keep the oil

CCX)1 .

Care has been taken in the design, to locate the various units so
that all hot oil leads would be as short as possible in order to minimize
radiation. Wherever jjossible, both the hot and cold oil are handled
by gravity. The steam boiler is located as near as practicable to
the heavy banks of steam radiators.

Fn all cases, careful study has been gi\'en to facilitating the handling
of poles, since a considerable part of the cost of the pole treating
process is due to pole handling.

256

/}/•/./. sy.si EM rr.cHxiCAL jovrnai.

Pom; R \( ks

For supporting the poles standing in the treating tanks, it is neces-
sary to have a very strong rack siirroinuiing each of the tanks. Fig. 20
shows a \ie\v at (mc- end and the front side nf tiie two-tank rack in
the \asliville jilant. i'lie poles shown, >tand <S'2 feet heinw iIk'
ground level. They are supported at the ends and middle of the
rack by timbers under the rack platform at a height of 12 feet abo\e

iIk- ijniund. .\l the i).ick, liic poles are siipp:)rled 1)\ ,i linihcr w hi<li
i> Hi feel alin\c liic i;r(iiin(l. This arrangement prrniils llir treal-
iiH'iit ni any size- of |)i)le iij) to and including (>") tcil in Iciiglh.

It will be noted in Fig. 23, which shows the rack al)()\e one lank,
that the |)oles in each lank are di\ide(l at the middk' l)\' the platform
of the pole rack. This feaiiirc nf ilu rack has prmcd id in' \er\-
desirable in that it j)ermils liie plalforni ni.iii to rcacii an\ |)i)le in
the rack during the loading and imloading process, so thai ilure is
no delay and no ha/artl in attaching the winch line sling lo, or de-
taching it from the poles. The taper of the poles is such that ample
space is pro\ itletl for holding ihe sections of the poles at the platform

(A-/ i)\i)//V(, ri.txis i>>i< I ly'i-.iiixt; (iirsixfi i-oi.is 2?7

lf\rl v\vi\ [hi<uy}\ tlir ari-a i>l' llu' oix-iiiii^ ,it lliis Irvrl is soiiu-wImI
snialliT than llu- ari'a of tlu- huttoiii of ilu- Iri-.ilin^; tank.

SiiitaMi' railiiij^s havi' l)irn prnvidcil arotiiul all parts of tin- [iLilfonn
III proti'i't till- platlonn ni.m. 'I'hry arc siihslantial i-iu)iii;li to proltTt
till- i)()frat(ir and \i'l lU-xilik- i-noiiijli to coinpi'iisate for the irri'^iiiar
sections of poll's which niav lie aji.iinsi ilicin.

I

TVNKS

As was nu'ntiorH'd al)o\c, in so far as practicahlc the tanks for the
various plants are made in nuiitiples of standard units. The treatinj^

KIk- i^ -("onrretc Foundation and I'rotecting Walls for Treating Tanks

tanks for the smaller plants are 11 feci long and 5 feet G inches wide
with t) inches in each end of the tanks taken up by the vertical radia-
tors. These tanks are of proper size to treat y^ carload of poles each.

The larger plants are provided with treating tanks, each of which
will easily handle one carload of poles. These tanks are 1.") feet
long. 8 feet wide and 9 feet 8 inches deej) in the clear.

Some idea of the sizes and arrangement of the treating tanks can
be had from the excavation for them shown in Fig. 24. Kach of the
raised levels shown, will su|)port the bottom of a tank while the jiits

258

BELL SYSTEM TECHNICAL JOURNAL

between will contain the steam and oil piping, oil handling machinery,
etc. This is a three-tank pit with space for two tanks shown.

In order to provide dry pits for the equipment below the treating
tank bottoms and also to facilitate removal of a tank from the ground
in case it might need repair, it has been found desirable to build
concrete foundations and walls around the treating tanks.

I'ig. 26 — TriMliiiH Tanks in Plac

A few inches of space is left between the concrete retaining walls
and the sides of the treating tanks. This space serves two purposes:
it permits placing or removing the tanks with ease and it also pro-
vides air spaces around the sides of the tanks, which tend to insulate
them from the ground. As has been mentioned, it is necessary to
change the temperature of the oil in the tanks quickly from about
220° to about 105° Fahrenheit. There is very little lag in making the
tem]>erature change due to heat retained by the tank walls. However,
if the ground around the tanks were wet and in contact with them,
considerable lag would be e.xperienced in making the temperature
change of the oil because of heat which would be retained by the
ground.

The poles in the tanks as shown by Fig. 2G rest in a position
inclined slightly back toward the racks so that they remain in this

CREOSOriNC f7.WiV7.S- /'OW V/v'/T. / / /A'C; CHESTNUT I'Ol.ES 259

(xisttioii without iH'iiiR tii-tl. Iiu-liiiiiiK ihr tank Im>I loins iDw.inl
the roar facilitati-s tlie draiiia.m" of oil from tluiii.

The Ixjttom of ihc tank is practiralK- |HT(H'ii(liriiiar to the ()<)ies
as they stand on it, which niiniini/es llu- lendenry for the butts to
slip on tlie tank liottoni. In order to further pre\ent any danger
front this hap|K'ning, the Inittom of each lank is covered l>y extra
heavy Ir\ing grids similar to those used at subway ventilating open-
ings. These grills are supported by a suitable I-beam framework in

lioHuTii 111 Trialiiii; lank Showing Horizontal Radiators anci (Iriil^
Covering Them

which the steel pipe radiators are placed. The grids do not inter-
fere with the circulation of the hot oil and form a good protection
for the radiators.

Kach of the horizontal cold oil tanks has a capacit\' of about 14, ()()()
gallons. Tanks of this size will easily take a tank-car load of creosote
each, lea\ing some reserve capacity for residual ('il which may be in
the tanks at the time the additional cars of oil ;ire received. The
tank cars ordinarily carry from 8,000 to 12,000 gallons of oil.

The hot oil tanks vary in capacity between 3,000 and 13,000 gallons
each, depending upon the sizes of the plants. One hot oil tank

260

BEl.L SYSIEM TECIISICAI. JOURNAL

suffict's for each installation. In orticr to conserNO the heat, these
tanks are co\ereci by a li-^inch coat of magnesia block heat insulating
material, the outside of which is covered by }i inch of asliestos ci-inc-nt
and 'i inch of half and half asliestos and Portland cement.

Boii.KKs, Kauiatoks, PkicsstkI'; Ri,(.i i.atoks and Othkk Sti;a\i
l*j.)iii'Mi':Nr

I'or these iiisiallaiiniis, a self-contained t\'pe of steam boiler was
used because of its c(ini|)arati\el\- high etificiencN' in the sizes icquired
and alMi i)ccausc of iIk- case of installation. 'I'iic boilers userl \arv

liw.

1 loi i/oi,i.,l ( -,,1,1 ( )il r.Liilis ,111,1 \ 111 ir.il lid Oil r.ink

from 3U to 80 horsepower cap.iiiix dcpcmlinL; iipni ilic >i/cs ol the
plants. These b:)ilers are of the iciurii iiihuLif i\pr with tlir tire
bo.xes and sm:)ke b.).\es lined with kc\cil-iii lire brick.

The boilers are opi-rated at ,t pressuic ol .ihoiit 100 llis. which is a
suitable pressure for tlic steam turbine ,mil for liie steam hoisting
engines in the plam> \\ iierc these are used. Tliis bniler steam pressure
is too high for the cast iron radiators which are usi'd lo heal oil in the
hot and cold tanks and, for the smaller plants, in the treating tanks.
Steam for these radiators should l)e sujiplied at a pressure of about
40 pounds. Ill order to meet this* recjuiremenl a pressure reducer is
iiMtl to convert the steam from the boiler pressure, whate\er it may
be, to a pressure of alxnit 40 pounds, before it enters the radiators.

The water condensed from the \arioiis radiators is ret iiiiud to the
boiler in order lo conser\'e its hi'. it. Small .iiitoiii.itii sUmiu traps

u<ij>si>ii\(; /7../.V/.S /<'/v' ii<r..irixa ciir.siM i rm.iszM

pass thi- w.iIiT otndi'iisi-d in tin- r.uli.ilors as last as it is iiiadf, l)iil
do not permit tlu- stoam to pass. On tlu' water side of tlu'si- small
steam traps, tlu- pipiiii; Ironi the \arioiis radiators is hroiijjht lonelher
^\w\ led to a point alio%e tlie steam l)oiler where it is connected lo a
iarj;e tillini; trap. 'I'hi- traps ailtom.ilically raise the water lo a

1 .^. :■) \irlu.il II.. I !hl l.iuL uiih luMil.iU-a ( u\LTiii.i;

receiver above the boiler and the tilting trap injects it into ihe boiler
as fast as it is deli\ered to the water pipe lines by the small ir,ip>.

It is very desirable in the operation of the steam turbines that
they be supplied with dry steam in order that slugs of water cannot
enter the turbine chambers at high velocities and injure the \anes.
.A large water trap is located above the treating tank (lit at each
|)lant to insure dry steam for the iiirbiiu- wliicli is iiKumied in the
pit rlirectly below it.

'ri;.MI"KK.\Tl RIC ("o.NTROL

A continuous record is kei)t of the temperature of the oil in the
treating tanks by means of recording thermometers mounted in the
l)oiler r»H)m and cf)nnected bv flexible thermometer tubes to the bulbs

262

BELL SYSTEM TECHNICAL JOURNAL

which are immersed in oil along the inside of the tanks after the poles
are in place. In the cold and hot tanks the temperature does not
change rapidly, so their temperatures can be read by means of station-
ary- indicating thermometers mounted on the sides of the tanks and
ha\ing bulbs which project into the insides of the tanks through
suitable fittings. The oil temperatures, of course, are controlled by
the steam valves to the radiators in the \arious tanks.

l-'ig. M) — Steam Boiler During [nslallalioii

Oil. II.WDMNG

The heart of the oil handling apparatus, of course, is the centrifugal
pump which has been mentioned and which is direct connected to the
20 H.P. steam turbine. In some of the smalU-r i)lants ilie centrifugal
pumps are ofierated by .5 H.P. gasoline engines.

lioth cold oil and hot oil are fed from the storage tanks to the
treating tanks by gravity. The centrifugal pimip is used for returning
the oil from the treating tanks to the proper storage lank, for moving
it from one storage tank to another or for delixering oil from the tank
cars to the storage tanks.

Since the creosote which is used in pole treating ma\' solidify at
any temperature below 100° Fahrenheit, even in comparatively warm
weather it is sometimes necessiiry to provide a steam connection to

CKLOaoriNG I'l^-INIS l-OR TRli.lllSG CltliSTNUT I'OLl-S 2bi

ilu- radiators iiisidi- tin- t.mk car in order to inaki' tlu- oil fluid i'iiourIi
to tlow throuj;li tlu- tli-\il)if hoso and ])i|H-s to the ci-ntrifiinal [)iiinp.
A'hv soiidif\iii^ of tlu- rri-osotc at i'omparati\i'K' hi^li ti-in|HTatiirfs
.dso rf(iiiir(.-s a small l)ank of radiators in i-ai-h cold tank.

'I"lu- sicani |ii|H- riuis, hctwi-i-n the steam lioiler and the vari'iiis
tanks, and the oil |)i|K' lines between the various tanks and the pump,

Fig. .51 — ^Gener.il \ im ul .\.aui,i! Ijiulgc I'lant in Operation

lire grouped so that both the steam lines and oil lines can be enclosed
in boxes. The heat radiated from the steam lines warms the air in
the Ixjxes to such an extent that the oil remains liquid.

The valve controls for the oil and steam lines which arc led through
the bo.xes, are grouped so that several can be reached by opening
the door of each of the boxes.

In the smaller plants which have the one-half-car pole capacity
of treating tanks, the centrifugal pump handles the oil at a rate of
alx)Ut 200 gallons jx^r minute. In the larger plants, howe\er, where
the treating tanks have one-car capacity of poles, the oil is handled
through the centrifugal pump at the rate of about 600 gallons per
minute. As mentioned in the above section describing the treat-
ment, the high rate of oil movement is necessary in order to accom-
plish the change from hot to cold oil in the treating tanks in such a

264 BELL SYSTEM TECIIXICAL JOIRSAL

short liiiiu that the lu'ated pole butts will not he permitted to cool
when not immersed in oil. The oil change ordinaril\- is made in from
7 to 12 minutes from the time the pump starts to remove the hot oil
until the cold oil is up to the proper le\'el.

Experience indicates that no material loss in penetration of the
creosote into the poles is experienced by having the treated section
imcoN'ered for this short length of time. Practically the same pene-
tration is obtained as would be secure<l by keeping the poles in hot
oil for the same length of time and then permitting the hot oil to
remain aroimd them until its temperature had ;j;racliiall\' fallen b\-
radiation to that specified for the cold oil bath.

Changing the oil instead of permitting it to cool in the treating
tanks greatly expedites the treatments and conseciuently increases
the plant capacity, which, of course, results in a corresponding economy
in the cost of treating the poles.

COXCI.U.SION

In this paper an endeaxor has been made to co\'er in ,i i;cn(.ral way.
the principal engineering and operating features in\'ol\eil in building
creosoting plants designed specially for applying open tank treatment
to chestnut poles. It has, of course, been necessar\- to omit practically
all of the details of construction, which were followed in building
the various plants.

These treating plants ari' valuable .ismIs lo iho Hell System in
providing concentration points where preser\ati\e treatment can
be economically applied to the chestnut poles, thus becoming an
important factor in the general program for the conser\-ation of
natural resources, by making possible the utilization of this valuable
and rapidly diminishing type of timber over a considerably longer
period.

Selective Circuits and Static Interference*

By JOHN R CARSON

SvNovsi-.: riu- protiit i>.i|H'r has its iiui-ption in the iummI of ,i corrcri
imilcrst.iiKliiij; of the Itchavior of selective circuits when siil>jeileil to ir-
roRiilar and random interference, ami of devisiiiK a practically useful
figure of merit for conipiiring circuits desiKne<l to reduce the effects of this
type of interference. The problem is essentially a statistical one and the
results must Ix; expressed in terms of mean values The mathematical
theory is developed from the idea of the spectrum of the interference and
the res|Hinse of the selective circuit is expressed in terms of the mean
square current and mean power al>sorlK-(l. The application of the formu-
las deduce<l to the case of static interference is discussed and it is shown
that deductions of practical value are possible in spite of meagre informa-
tion regarding the precise nature and origin of static interference.

The outstanding deductions of practical value may be summarized as
follows:

1. Even with absolutely ideal selective circuits, an irreducible minimum
of interference will Ix; absorbed, and this minimum increases linearly
with the frequency range necessary for signaling.

2. The wave-filter, when properly designed, approximates quite closely
to the ideal selective circuit, and little, if any, improvement over its present
form may be expected as regards static interference.

3. .As regards static or random interference, it is quite useless to employ
extremely high selectivity. The gain, as compared with circuits of only
mo<lerate selectivity, is very small, and is inevitably accompanied by
disadvantages such as sluggishness of response with consequent slowing
down of the [wssible speed of signaling.

4. .A formula is developed, which, together with relatively simple ex-
jwrimcntal data, provi<lcs for the accurate determination of the spectrum
of static interference.

5. An application of the theory and formulas of the paper to repre-
sentative circuit arrangements and schemes designe<i to reduce static
interference, shows that they are incapable of reducing, in any substantial
degree, the mean interference, as compared with what can be done with
simple filters and tuned circuits. The underlying reason lies in the nature
of the interference itself.

I

' I ^ H f-1 selecti\e circuit is an e.xtremely important flenieiii of e\er\'
-*• radio receiving set, and on its efficient design and operation
depends the economical use of the available frequency range. The
theory and design of selective circuits, particularly of their most
conspicuous and important type, the electric \va\'e filter, ha\'e been
highly de%'eloped, and it is now possible to communicate simultane-
ously without undue interference on neighboring channels with a
quite small frequency separation. On the other hand too much has
been expected of the selective circuit in the way of eliminating types
of interference which inherently do not admit of elimination by any
form of selecti\e circuit. I refer to the large amount of inventive
thought devoted to devising ingenious and complicated circuit ar-

• Presented at the Annual Convention of the .A. I. E. E., Edgewater Beach, Chicago,
III., June 23-27, 1924.

265

266 BELL SYSTEM TECHNICAL JOURNAL

rangements designed to eliminate static interference. Work on this
prolilem has been for the most part futile, on account of the lack of a
clear anahsis of the problem and a failure to perceive inherent limi-
tations on its solutions by means of selective circuits.

The object of this paper is twofold: (1) To develop the mathe-
matical theory of the behavior of selective circuits when subjected
to random, irregular disturbances, hereinafter defined and designated
as random interference. This will include a formula which is pro-
posed as a measure of the figure of merit of selective circuits witk respect
la random interference. (2) On the basis of this theory to examine
the problem of static interference with particular reference to the ques-
tion of its elimination by means of selective circuits. The mathe-
matical theory shows, as might be expected, that the complete solu-
tion of this problem requires experimental data regarding the fre-
quency distribution of static interference which is now lacking. On
the other hand, it throws a great deal of light on the whole problem
and supplies a formula which furnishes the theoretical basis for an
actual determination of the spectrum of static. Furthermore, on
the basis of a certain mild and physically reasonable assumption,
it makes possible general deductions of practical value which are
certainly qualitatively correct and are believed to involve no quanti-
tatively serious error. These conclusions, it may be stated, are in
general agreement with the large, though unsystematized, body of
information regarding the behavior of selective circuits to static
interference, and with the meagre data available regarding the wave
form of elementary static disturbances.

The outstanding conclusions of practical value of the present
study may be summarized as follows :

(1) Even with absolutely ideal selective circuits, an irreducible
minimum of interference will be absorbed, and this minimum in-
creases linearly with the frequency range necessary for signaling.

(2) The wave-filter, when properly designed, approximates quite
closely to the ideal selective circuit, and little, if any, improvement
over its present form may be expected as regards static interference.

(3) As regards static or random interference, it is quite useless to
employ extremely high selectivity. The gain, as compared with
circuits of only moderate selecli\ity, is \'ery small, and is inevitably
accompanied by disadvantages such as sluggishness of response with
consequent slowing down of the possible speed of signaling.

(4) By aid of a simple, easily computed formula, it should be pos-
sible to determine experimentally the frequency spectrum of static.

SF.LECTIIE CIRCUITS AND STATIC INTERFERENCE 267

(5) Formulas given below for comparing (he relative efficiencies
of selective circuits on the basis of siRnal-to-interference cnerRV ratio
are believed to have considerable practical value in estimatinR the
relative utilit\- of selective circuits as regards static interference.

II

Discriinin.ition between signal anil inlcrfcrcnce liy means of selec-
tive circuits depends on taking advantage of differences in their wave
forms, and hence on differences in their frequency spectra. It is
therefore the fimction of the selective circuit to respond effectively
to the range of frequencies essential to the signal while discriminating
against all other frequencies.

Interference in radio and wire cotnmunication may be broadly
classified as systematic and random, although no al)solutely hard and
fast distinctions are possible. Systematic interference includes those
disturbances which are predominantly steady-state or those whose
energy is almost all contained in a relatively narrow band of the
fre(|uency range. For example, interference from individual radio-
telephone and slow-speed radio telegraph stations is to be classified as
systematic. Random interference, which is discussed in detail later,
may be pro\isionally defined as the aggregate of a large number of
elementary disturbances which originate in a large number of un-
related sources, vary in an irregular, arbitrary manner, and are char-
acterized statistically by no sharply predominate frequency. An
intermediate type of interference, which may be termed either quasi-
systematic or quasi-random, depending on the point of view, is the
aggregate of a large number of individual disturbances, all of the same
wave form, but having an irregular or random time distribution.

In the present paper we shall be largely concerned with random
interference, as defined above, because it is believed that it repre-
sents more or less closely the general character of static interference.
This question may be left for the present, however, with the remark
that the subsequent analysis shows that, as regards important prac-
tical applications and deductions, a knowledge of the exact nature
and frequency distribution of static interference is not necessary.

Now when dealing with random disturbance, as defined above, no
information whatsoe\-er is furnished as regards instantaneous values.
In its essence, therefore, the problem is a statistical one and the
conclusions must be expressed in terms of mean values. In the
present paper formulas will be derived for the mean energy and tnean
square current absorbed by selective circuits from random interfer-

268 BELL SYSTEM TECHNICAL JOVRN.IL

ence, and their applications to the static problem and the protection
afforded by selective networks against static will be discussed.

The analysis takes its start with certain general formulas gi\en by
the writer in a recent paper', which may be stated as follows:

Suppose that a selective network is subjected to an impressed
force 0 (0- We shall suppose that this force exists only in the time
interval, or epoch, o^t^T, during which it is everywhere finite and
has only a finite number of discontinuities and a finite number of
maxima and minima. It is then representable b\' the Fourier Integral

4,{t) = \;-,rf i/(ai)|-COsM + e(a))lf/a) (1)

1/(0,) \- = \f <i>(t) COS co/f//T+ r /* <p{n sin ojtdt'X. (2)

where

Now let this force 0 (/) be apiilied lo the network in tiie drrcing branch
and let the resulting current in the receiving branch be denoted by
I (t). Let Z {i w) denote the steady-state transfer impedance of the
network at frequency w/2ir: that is the ratio of e.m.f. in driving
branch to current in receiving branch. Further let z (i u) and cos
a (a,) denote the corresponding impedance and power factor of the
receiving branch. It ma\' then i)e shown that

f\nr>Vdi = V.fl^,d. (3)

and that ilie total energy IF absorbed by the reccix'iiig i)rancli is
giV'Cn by

W=l/w r 1^1^ I z{io,) 1 cos a{co) ■ da,. (4)

To apply the formulas given above to the problem of random
interference, consider a time interval, or epoch, sa\- from l = o to t=T,
during which the network is subjected to a disturbance made up of a
large numljer of unrelated elementary disturbances or forces, <t>i {(),
<t>t (t) ... 4>,, it).

If we write

*(/)=<^,(/)-t-</,2(0+ . . . +<i>nU),

then i)y (1), <!>(/) can be represented as

*(/)

= 1/V f ' I F(a)) 1 • cos M + 0(co)h/a
•/(I

' Transient Oscillations in KIcctric \\a\o I^'iltcrs, Carson and Zohcl, Hell Syslen
Technical Journal, July, 1923.

SELECTirr. ciKci'irs .ixn sr.cnc ixrnRiERF.Ncr. zt^

and

.'il Jo I Z(Jui) ,-

W'f now intnxluci- tlu- fmulion /? (w), wliirh will In- ii-rnifd the
energ^y spectrum of the random interference, and which is analyticijHy
detined !>>■ the equation

/?(co) = y|F(w)|» (5)

Dixiding both sides of (H) and (4) l)y T wc get

/- = I , IT / ^ — -. — ., rfo), (b)

P=\ T^ I , „, ■ ,,.,1 s(t"a))| • cos a ((i)) ■ rfto. (7)

^0 lZ(la))|-

/-. P and /? (oj) become independent of the T provided the epoch is
made sufficiently ^reat. /- is the mean square current and P the mean
power absorbed by the receiinng branch from the random interference.

In the applications of the foregoing formulas to the problem under
discussion, the mean square current /- of the formula (6) will be
taken as the relative measure of interference instead of the mean
power P of formula (7). The reason for this is the superior sim-
plicity, both as regards interpretation and computation, of formula
((i). The adoption of /- as the criterion of interference ma\' be justified
as follows :

(1) In a great many important cases, including in particular ex-
perimental arrangements for the measurement of the static energy
spectrum, the receiving device is substantially a pure resistance. In
such cases multiplication of I- by a constant gi\'es the actual mean
p<iwer P.

(2) It is often convenient and desirable in comparing selective net-
works to have a standard termination and receiving device. A three-
element vacuum tube with a pure resistance output impedance sug-
gests itself, and for this arrangement formulas ((i) and (7) are equal
within a constant.

(3) We are usually concerned with relative amounts of energy
absorlwd from static as compared with that absorbed from signal.
X'ariation f)f the receiver impedance from a pure constant resistance
would only in the extreme cases affect this ratio to any great extent.
In other words, the ratio calculated from formula (6) would not
differ greatly from the ratio calculated from (7).

270 BELL SYSTEM TECIIXICAL JOURXAL

(4) While the interference artually appercei\ed either \isuall\' or
by car will certainly depend upon and increase with the energ\- ab-
sorbed from static, it is not at all certain that it increases lincarK-
therewith. Consequently, it is believed that the additional retine-
ment of formula (7) as compared with formula (6) is not justified
by our present knowledge and that the representation of the receiving
device as a pure constant resistance is sufficiently accurate for present
purposes. It will be understood, however, that throughout the
following argument and formulas, P of formula {!) may be sub-
stituted for /- of (G), when the additional refinement seems justified.
The theory is in no sense limited to the idea of a pure constant resist-
ance receiver, although the simplicity of the formulas and their ease
of computation is considerabK' cnhanred ihcrebN'.

The problem of random interference, as formulated by equations
(6) and (7) was briefly discussed by the writer in "Transient Oscilla-
tions in Electric Wave Filters" ' and a number of general conclusions
arrived at. That discussion will be briefly summarized, after which a
more detailed analysis of the problem will be given.

Referring to formula (6), since both numerator and denominator
of the integrand are everywhere ^o, it follows from the mean value
theorem that a value w of w exists such that

TT .'11

z{/a>) r

(8)

The apijroximale location ol a; on the fre(itieni\' scale is ba.-^ed on the
following considerations :

(a) In the case of efficient selective circuits designed to select a
continuous finite range of frequencies in the interval toi^co^ojo,
the important contributions to the integral (0) are confined to a finite
continuous range of frequencies which includes, but is not greatly
in excess of, the range which the circuit is designed to select. This
fact is a consequence of the impedance characteristics of selective
circuits, and the following properties of the spectrum R (oj) of random
interference, which are discussed in detail subsecjuently.

(b) R (ci)) is a continuous finite function of co which converges to
zero at infinity and is everywhere positiv'e. It possesses no sharp
maxima or minima, and its variation with respect to oj, where it exists,
is relatively slow.

On the basis of these considerations it will be assumed that w lies
within the band wi^u^toj and that without serious error it may be

si.i.iciiri iiKcriis .txn si.iin i\ 1 1 i,-i r.Ri sen 271

lakfii .IS thf iiii(l-frt'<iiit'tu'\' Wm of llu' h.md wliicli iii.iy In- (li'l'mcd
fitluT .IS (wi+w.) 2 or as wlu^^. C"onso(nu'iitK-

It Jo I Z(lw) ,-

l-'nim (,!•) it follows tli.il tlir iikmii sciu.irc ruiiHiil I', due to r.iiidom
intfiffrfiui', is nunlu up of two factors: one R {w,,,) which is propor-
tion.il to thecnerny level of the interference spectrum at mid-frequency
u)« '2 k: anil, second, the intej^ral

which is independent of the ch.iracter antl intensity- of the interference.
Thus

l- = pR(icJ. (11)

I'ornuil.i (11) is of considerable practical importance, because by its
aid the spectral energy level R (w) can be determined, once /- is
e.\i)erimentally measured and the frequency characteristics of the
receiving network specified or measured. Il is approximate, as dis-
cussed above, but can be made as accurate as desired by emplo\ing
a sufficiently sharply selective network.

The formula for ihe Jigti re of merit of a selective circuit 'witli respect
to random interference is constructed as follows:

Let the signaling energy be supposed to be spread continuously
and uniformly over the frequency interval corresponding tooji^co^wj.
Then the mean square signal current is given by

£- /•W5 d u

I Ziiw) 1^
or, rather, on the basis of the same transmitted energy to

^rT7?7Tr=^^-^- (^2)

£»

7r(a)2 — 0)1

The ratio of the mean square currents, due to signal and to interfer-
ence, is

^^ ' " (13)

R{li}„) 0)2 — 0)1 p'

E-
The first factor "- depends onlv f)n the signal anfl interference

A(o)b,)

energy levels, and does not involve the properties of the network. The
second factor depends only on the network and measures the

272 BELL SYSTEM TECIIXIC.IL JOrRXAL

efficienc\- with which it excludes encrg>- outside the signaling range.
It will therefore be termed the figure of merit of the selective circuit and
denoted by S, thus

0)2 — oil p 0)0 — COiJj^i /C[lu))- Jo \jC(tU)\'

Staled in words, the figure of merit of a selective circuit with respect
to random interference is equal to the ratio of the mean square signal and
interference currents in the receiver, divided by the corresponding ratio
in an ideal band filter which transmits without loss all currents in a
"unit" band (ojo- o)i = l) and absolutely extinguishes currents outside
this band.

Ill

Before taking up practical applications of the foregoing formulas
further consideration will be given to the h\[)othesis, fundamental
to the argument, that over the frequency range whicii includes the

important contributions to the integral / . „ . . ^ ,., the spectrum i?(a))

^0 I Z(ia)) l"

has negligible fluctuations so that the integral

r

— dw
Z(lcc) (■

ma\ , without ap|>reciable error, be replaced by

Ju I Z(toi) \i

where Um 2 ir is the "niifl-frec)uenc\" of the selective circuit.

The original arguniciU in support nf this lu'pothesis was to ilie
effect that, since tlie interference is made uj) of a large number of
unrelated elementar\- disturbances distributed at random in time,
any sharp maxima or minima in the spectrum of the indi\idual di-
turbances would be smoothed out in the spectrum of the aggregate
disturbance. This argument is still bclicNcd to be (|iiite sound: the
importance of the question, ho\vi\cr. ctrlainK calls tor the more
detailed anaK'sis which follows;

:V

Lei <\'{l)=^(t:r(t-tr) (15)

1

where /, denotes the time of incidence of the r"' disturbance (t>r (/)• The
elementary disturbances 0i, <t>2 . . . (t>s are all i)erfectly arbitrary, so

sii.ixiirr. ciKcriis .ixn >/.///( i.\ 1 1 kii ki m i. m

that * (/) as (li'hiK'tl l)y (1")) is tin- most ni-iicral typo of (lisliirl)ance
|)ossil)lf. Thi- only assiim|)tion made as yi't is that thi- instants of
inciili-nit' t\ . . . t^ are (listril)iilc(l at random ii\tr ilio epoch o^t^T;
an .issumplion vvhicli is dearly in aicorilanc c wlili the facts in the
case of static interference. If we write

(V(,w) = / (/>,(/) COS wt (It,

Sr{<ji) = / </>,(/) sin wl (It. (16)

•'O

it follow^ from (2) and (15), after some easy rearrangements that

.V .V

l-\^) ;■-•= N^ N^cosa)(/,-/,)(G(<.))C(a,) + 5,(a,)5.(w)] =

r-l i-\

V^G» + 5,=((o) (17)

+ ^ ^,nsa>(/,-/,) [G(u,)G(a.)+5r(u)) 5,(0,)], r?t«.

The first summation is .-impl\- ^ |/r(a,) ]-. The double summa-
tion in\ol\es the factor cos a, (t, — li). Now by virtue of the assump-
tion of random time distribution of the elementary disturbances, it
follows that /, and /,, which are independent, may each lie anywhere
in the e()och o^t^T with all values equally likely. The mean value
of j F (u>) |- is therefore gotten by a\eraging- with respect to tr and fj
o\er all possible values, whence

1 FM 1== ^l/,(a,) ;.+2/T'^~^"^

X ]^ ^ [CMC,M+Sr{(^)S,M] (18)

and

/- ' \^ /•°° |/r(fa)) i' J , 2 \^ \^ /•°° l-cosoirf^, ^ .

+5»5,(co)li '^'"

1 Ziico)

' The averaging process with respect to the parameters /,. and /, employed above
logically applies to the average result in a very large number of epochs during which
the system is ex()ose<l to the same set of disturbances with different but random
time distributions. Otherwise stated, the averaging process gives the mean value
corresponding to all possible ecjually likely times of incidence of the elementary
disturbances. The assumption is, therefore, that if the epoch is made sufficiently
large, the actual ctTect of the unrelated elementary disturbances will in the long
run be the same as the average effect of all possible and equally likely distributions
of the elementary disturbances.

274 BELL SYSTEM TECHNICAL JOURNAL

Now in the double summation if the epoch T\s made sufficiently great,

the factor -^^ ^ ^ vanishes everywhere except in the neighbor-

hood of 0) = 0. Consequently, the double summation can be written as

■G(o)G(o)

2 r°° 1 -cos 0)7- , ^. \^ \^ G(o)G(o) l\p^rA(

I 2(0) I

Finally if we write A7 7' = » = average number of disturbances per
unit lime, and make use of formula (2j, we get

N ^—1 Jo I Z(itxi) Y

which can also be written as

when ir = ir (t) is the current due to the r"' disturbance <(>, (/).

Now the double summation vanishes when, due to the presence of a
condense or transformer, the circuit does not transmit direct current
to the receiving branch. Furthermore, if the disturbances are oscilla-
tory or alternate in sign at random, it will be negligibly small com-
pared with the single summation. Consequently, it is of negligible
significance in the practical applications contemplated, and will
be omitted except in special cases. Therefore, disregarding the double
summation, the foregoing analysis may be summarized as follows:

RM = ^^\frM\' = n-r{.>), (21)

J. «V,.rM^,„ (22)

A ^^ Jn I Z{tw) p

=;;^v^,,=„.^. (25)

In these formulas n denotes the average number of elementary dis-
turbances per unit time, Wm the energy absorbed from the r'* disturb-

SEl.r.CTiri- CIRCUITS .iXD ST.iTIC ISTERFERF.NCE 275

.line 4), (/), aiul P tlu- nu-aii power absorln-d from tlu- angrcRatc
ili>turl)aiu-e. r (ui) is ileliiifil by formula (21)) .iiid is the mean spec-
trum of (he a!ii;ren.ile dislurbaiice, lluis

rM = 1 .V V \frM {■ = K(o>),.\. (26)

We are now in a [wsition to discuss more precisely ilie ai)pro\ima-
lions, fundanu'iUal lo formulas (D) (14),

•'0

\Z{iw)[-" "^-""\/„ \Z(io>)-\

riie approximation involved in this formula consists in idenlif\ing
u'm, 2 ir with the "mid-frequency" of the selective circuit, and is based
on tile hypotiiesis tiiat over tlie range of frequencies, which includes
the important contribution to the integral (22), the fluctuation of
R (u)) may be ignored.

Now it is evident from formulas (21) -(22) thai the theoretically
complete solution of the problem requires that R (oj) be specified
over the entire frequency range from oi = o to co = ^. Obviously, the
required information cannot be deduced without making some addi-
tional hypothesis regarding the character of the interference or the
mechanism in which it originates. On the other hand, the mere
assumption that the individual elementary disturbances <^i . . . 0j,
tlifTer among themselves substantially in wave form and duration, or
that the maxima of the corresponding spectra |/r(a)) | are distributed
over a considerable frequency range, is sufificient to establish the
conclusion that the individual fluctuations are smoothed out in the
aggregate and that consequently r (oi) and hence R (oj) would have
negligible fluctuations, or curvature with respect to oi, over any
limited range of frequencies comparable to a signaling range.

It is admitted, of course, that the foregoing statements are purely
qualitative, as they must be in the absence of any precise information
regarding the wave forms of the elementary disturbances constituting
random interference. On the other hand, the fact that static is en-
countered at all frequencies without any sharp changes in its intensity
as the frequency is varied, and that the assumption of a systematic
wave form for the elementary disturbances would be physically
imreasonable, constitute strong inferential support of the hypothesis
underlying equation (27). Watt and Appleton (Proc. Roy. Soc,
-April 3, 1923) supply the only e.xperimental data regarding the wave
forms of the elemcntarj' disturbances which they found to be classifi-
able under general types with rather widely variable amplitudes and

276 BELL SYSTEM TECIIXIC.U. JOrRX.-IL

durations. Rough calculations of r (oj), based on their results, are
in support of the hypothesis made in this paper, at least in the radio
frequency range. In addition, the writer has made calculations
based on a number of reasonable assumptions regarding variations
of wa\e form among the individual disturbances, all of which resulted
in a spectrimi R (a;) of negligible fluctuations over a frequency range
necessary to justify equation (27) for efficient selective circuits.
Howe\-er the problem is not theoretically solvable by pure mathe-
matical analysis, so that the rigorous %'erification of the theory of
selecti\ity developed in this paper must be based on e.\perimental
e\idencc. On the other hand, it is submitted that the hypothesis
introduced regarding static interference is not such as to \-itiate
the conclusions, qualitatively considered, or in general to introduce
serious quantitative errors. Furthermore, even if it were admitted
for the sake of argument that the figure of merit 5 was not an accurate
measure of the ratio of mean square signal to interference current,
nevertheless, it is a true measure of the e.vcellence of the circuit in
e.xcluding interference energy outside the necessary frequency range.

W

The practical applicalioii;, of the foregoing analysis depend upon
ihe fornuilas

-, R(w„) C^ do,

ir Jn Zilui) r

(11)

c_ 1 /*"' dw /*" do) _ 1 ^ ,.^.

W2 — Wl.(j| |Z(fa))P' Jo \Z(ioj)\^ 0)2 — wi p

which contain all the information which it is possible to deduce in the
case of purely random interference. They are based on the prin-
cii)le that the effect of the interference on the signaling system is
measured by the mean square interference current in the receiving
branch, and that the efficiency of the selective circuit is measured
by the ratio of the mean square signal and interference currents. As
stated above, in the case of random interference results must be
expressed in terms of mean values, and it is dear that either the mean
square current or the mean energy is a fundamental and logical
criterifjn.

Referring to formula (11), the following important proposition is
deducible.

SF.I.F.CTIIF. CIRClirS .IXH SI.ITIC IXrr.RFF.RENCE 277

// the sigmiling system requires the transmissions of a band of fre-
quencies corresponding to the interval uj — coi, and if the selective circuit
is efficiently designed to this end, then the mean square interference

current is proportional to the frequency hand width

This follows from the fad that, in tho c.isi- of ctlk-ifiitlj- designed

liaiid-tiliors. (Ii>ii;iu<l to si-li'ct tlif frii|m'iicy ran^je "„ ~i- and

2ir

I'Mludf otliiT fri'(iui'niius, tlic inloi;ral / i-;^/-:— r,.; is proportional to

Jo I Z (Joj) I'

uij — uji to a high degree of approximation.

The practical consequences of these propositions are imijortaiit and

immediate. It follows that as the signalintj speed is increased, the

amount of interference inevitably increases practically linearly and

that this increase is inherent. Again it shows the advantage of

single vs. double side-band transmission in carrier telephony, as

fx)inted out by the writer in a recent paper.' It should be noted

that the increased interference with increased signaling band width

is not due to any failure of the selective circuit to exclude energy

outside the signaling range, but to the inherent necessity of absorbing

the interference energy lying inside this range. The only way in

which the interference can be reduced, assuming an efficiently designed

band lilter and a prescribed fre(iuenc\' range — =-r — -, is to select a

2?r

carrier frequency, at which the energy spectrum R (w) of the interfer-
ence is low.

Formula (11) proi'ides the theoretical basis for an actual determination
of the static spectrum. Measurement of P over a sufficiently long
inter\al, together with the measured or calculated data for evaluating

, _ . . , ,„, determines R (ojm) and this determination
- i ^ ('") I"

can be made as accurate as desired by employing a sufficiently sharply

tuned circuit or a sulihciently narrow band filter. It is suggested

that the experimental data could be gotten without great difficulty,

and that the resulting information regarding the statistical frequenc\'

distribution of static would be of large [practical value.

The selective figure of merit S as defined by (14) is made up of two

factors, which is inversely proportional to the re^iuired

(0)2 — OJi)

signaling frequency range; and the ratio of the integrals <r/p. This

' Signal-to-Static-Interference Ratio in Radio Telephony, Proc. I. R. E. £.,
June, 1923.

278 BELL SYSTEM TECHNICAL JOURNAL

ratio is unity for an ideally designed selective circuit, and can actually
be made to approximate closely to unity with correctly designed band-
filters. Formula (14) is believed to have very considerable value in
comparing various circuits designed to eliminate interference, and is
easily computed graphically when the frequency characteristics of
the selective circuit are specified.

The general propositions dediicihle from ii ina\' be briefiy listed
and discussed as follows:

With a signaling frequencv range -^ - — ' specified, the upper limiting

Ztt

value of S ivilh a theoretically ideal selective circuit is , and the

(a>2 — o)i)

excellence of the actual circuit is measured by the closeness with 'which

its figure of merit approaches this limiting value.

I'ormula (14) for the figure of merit S has been applied to the study
of the optimum design of selective circuits and to an analysis of a
large number of arrangements designed to eliminate or reduce static
interference. The outstanding conclusions from this study may be
briefly reviewed and summarized as follows :

The form of the integrals a and p. taking into account the signaling
requirements, shows that the optimum selective circuit, as measured
by S, is one which has a constant transfer impedance over the signaling

frequencv range ^^ — '-, and attenuates as shar[)lv as possible

currents of all frequencies outside this range. Ncnv this is precisely
the ideal to which the band filter, when properly designed and termi-
nated, closely approximates, and leads to the inference that the wave
filter is the best possible form of selective circuit, as regards random
interference. Its superioritv' from the steadv-state viewpoint has, of
course, long been known.

An investigation of the effect of securing extremely high selectivity
by means of filters of a large number of sections was matle, and led
to the following conclusion:

In the case of an efficientl>' designed Inmd-tilter, terminated in the
proper resistance to substantially eliminate reflection losses, the
figure of merit is given to a good approximation by the equation

5=_J_ __i

(j>i — W\ 1-|-1/H)M-

wliere n is the number of filter sections and -^- ^ tlu' transmission

band. 1 1 follows that the selective figure of merit increases inappreciably
with an increase in the number of filter sections beyond 2, and that the

SEI.ECTIIE CIRCUITS .1X1) STATIC IXTERI-ERENCE 279

band filter of a fnv sections can be designed to have a fisurr of merit

iloselv approximating the ideal limiting value, ,

(wj — Ul)

This prop<isition is merely a special case of the general principle
that, as regards static interference, it is useless to employ extremely
hijih select i\ity. The gain obtainable, as compared with only a
mcKlerate amount of selectivity is slight and is inherently accom-
panied by an increased sluggishness of the circuit. That is to say, as
the selectivity is increased, the time required for the signals to build up
is increasetl, with a reduction in (|iiality and possible signaling speed.

Another circuit of practical interest, which has been proposed as a
solution of the "static" problem in radio-communication consists of a
.series of sharply tuned oscillation circuits, unilaterally coupled through
amplifiers.* This circuit is designed to receive only a single frequency
to which all the indi\'idual oscillation circuits are tuiu'd. Tlu' figure
of merit of this circuit is approximately

^-^-^ (2«-2)!

where n denotes the number of sections or stages, and L and K are
the inductance and resistance of the indi\idual oscillation circuits.
The outstanding fact in this formula is the slow rate of increase of 5
with the number of stages. For example, if the number of stages is
increased from 1 to 5, the figure of merit increases only by the factor
."i.titi, while for a further increase in « the gain is very slow.^ This gain,
furthermore, is accompanied by a serious increase in the "sluggish-
ness" of the circuit: That is, in the partciular example cited, by an
increase of 5 to 1 in the time required for signals to build up to their
steady state.

The analysis of a number of representative schemes, such as the
introduction of resistance to damp out disturbances, balancing
schemes designed to neutralize static without affecting the signal,
detuning to change the natural oscillation frequency of the circuit,
demodulation through several frequency stages, etc., has shown that
they are one and all without value in increasing the ratio of mean
square signal to interference current. In the light of the general
theory", the reason for this is clear and the limitation imposed on the
solution of the static problem by means of selective circuits is seen
to be inherent in the nature of the interference it.self.

'See r. S. Patent No. 1173079 to .Xlexanderson.

' When the number of stages n is fairly large, the selective figure of merit liecomes
proportional to /n and the building-up time to n.

Some Contemporary Advances in Physics — VII
Waves and Quanta

By KARL K. DARROW

THV. in\;ilual)lc agoiit of c)iir best knowledge of the ciniroiiiiisj
world, aiul \et itself unknown except by inference; the inter-
mediary between matter and the finest of our senses, and yet itself not
material ; intangible, and yet able to press, to strike blows, and to recoil ;
impalpable, and yet the \ehicle of the energies that fiow^ to the earth
from the sun — light in all times has been a recognized and conspicuous
feature of the ph\-sical world, a perpetual reminder that the material,
the tangible, the palpable substances are not the only real ones. \c{
its apparent importance, to our forerunners who knew only the rays
to which the eye responds and suspected no others, was as nothing
beside its real importance, which was realized \-ery gradually during
the nineteenth century, as new families of rays were disco\cred
one after the other with new detecting instruments and with new
sources. Radiation is not absent from the places where there is
no eye-stimulating light; radiation is omnipresent; there is no region
of space enclosed or boundless, vacuous or occupied by matter, which
is not pervaded by rays; there is no substance which is not perpetu-
ally absorbing rays and giving others out, in a coniiiuial interchange
of energy, which either is an equilibrium of equal and opjiosite ex-
changes, or is striving towards such an equilibrium. Radiation
is one of the great general entities of the physical world; if we could
still use the word "element," not to mean one of the eight\- or ninei\
kinds (if material atoms, but in a deeper sense and somewhat as liu'
ancient^ used it, we niiglil describe radiation and in, hut. or possiiiK-
radiation and eieclricily, as coec|ual elements. Also the problem
111 ilie nature and structure of radiation is of no lesser importance
than the jiroblem of the structuri' and nature of matter; and in fact
neither can be treated separateK-; tiu'\' are so inextricably inter-
twined that whoever sets out to expound the jire.sent condition of
one soon finds liimself outlining the <iilui-. One cannot write a
discourse on the nature of radiation alone nor on the structure of liie
atom alone, one can iuit \ary the relative emphasis laid u|)on these
two subjects, or rather upon these two aspects of a single subject;
and in this article I shall restate main- things about the atom which
were stated in former articles, but the emphasis will be laid tipon light .
Speaking very generall>' and rather \-aguel\-, light has been much
more tractable to the theorists than most of the other objects of

280

SOME COS'ir.MI'Ok'.IRV .1l>r.lXCLS IN I'llYSlCS-ni 281

ftuiiiiry in physirs or choniistr%'. Over .» rathi-r lonjj prridd <if yt-ars,
it was iiKlffil m'iu"rali>' rojianlrd as |)rrfi'cll\' iiili-lliv;il)ir. Tlu-
famous haltli- ln-lweon tlu- rorpusnilar tlu-ory adopitd 1)\ Xrwion,
and the vvavt-lhooiA' foundod In- Disrartrs and Hiiyniuns. dird out
in the earher \ears of the nineteenth century witli ilie ^radiial ex-
linrtion of the former. The history of optics in the nineteenth cc'h-
tur\-, from Fresnel and V'oiinu to Michelson and Ra\kMj;h, i> liie tale
of a brilliant series of beaiitiftii and strikinj; demonstrations of the
wave-theory, of experiments which were founded upon liie wave-
theory as their basis and would have failed if the basis had not been
firm, of instruments which were designed and com]X'tent to make
ditlicult and delicate measurements of all sorts — from the thickness
of a sheet of molecules to the diameter of a star — and would ha\e been
useless had the theory been fallacious. The details of the bending
of light around the sides of a slit or the edge of a screen, the intricate
pattern of light and shade formed where subdivisions of a beam of
light are reunited after separation, the complexities of refraction
through a curved surface, are represented by the theory with all
verifiable accuracy; and so are the incredibK' complicatefl phenomena
attending the progress of light through crystals, [jhenomena which
have slipped out of common knowledge because few are willing to
undertake the labour of mastering the theory. The wa\e-lheor\- of
light stands with Newton's in\erse-st|uare law of gra\itation, in respect
of the many extraordinarily precise tests which it has undergone with
triumph; I know of no other which can rival either of them in I his
regard.

By the term "wave-theory of light" I have meant, in the foregoing
paragraph, the conception that light is a wave-motion, an undulation,
a perifxlic form ad\ancing through space without distorting its shape;
I have not meant to imply any particular answer to the question,
what is it of which //?/// is a wave-motion.^ It may seem surprising
that one can make and defend the conception, without having answered
the question beforehand; but as a matter of fact there are certain
properties common to all undulations, and these are the properties
which have been verified in the experiments on light. There are also
certain properties which are not shared by such waves as those of
sound, in which the vibration is confined to a single direction (that
normal to the wavefront) and may not vary otherwise than in ampli-
tude and phase, but are shared by transverse or distortional waves
in elastic solids, in which the \'ibrati(3n may lie in any of an infinity
of directions (any direction tangent to the wavefront). I-ight pos-
sesses these properties, and therefore the wave-motion which is

282 BELL SYSTEM TECHNICAL JOURNAL

radiation may not be compared with the wave-motion which is sound;
but a wide range of comparisons still remains open.

Of course, very many have proposed images and models for "the
thing of which the vibrations are light", and many have belie\-ed
with an unshakable faith in the reality of their models. The fad
that light-waves may be compared, detail by detail, with transverse
vibrations in an elastic solid, led some to fill universal space with a
solid elastic medium to which they gave the sonorous name of "lum-
iniferous aether". It is not many years since men of science used to
amaze the laity with the remarkable conception of a solid substance,
millions of times more rigid than steel and billions of times rarer
than air, through which men and planets serenely pass as if it were
not there. Even now one finds this doctrine occasionally set forth.'

In that image of the elastic solid, the propagation of light was
conceived to occur because, when one particle of the solid is drawn
aside from its norma! place, it pulls the next one aside, that one the
next one to it, and so on indefinitely. Meanwhile, each particle
which is drawn aside exerts a restoring force upon the particle of
which the displacement preceded and caused its own. Set one of the
particles into vibration, and the others enter consecutively into
vibration. Maintain the first particle in regular oscillation, and
each of the others oscillates regularly, with a phase which changes
from one to the next; a wave-train travels across the medium. One
particle influences the next, because of the attraction between them.
But in the great and magnificent theory of light which Maxwell
erected upon the base of Faraday's experiments, the propagation
was explained in an altogether different manner. V^ary the magnetic
field across a loop of wire in a periodic manner, and you obtain a
periodic electric force around the loop, as is known to ever\'one who has
dabbled in electricity. \'ary the electric field periodically, and you
obtain a periodic magnetic field — this a fact not by any means so
well known as the other, one which it was Maxwell's distinction to
have anticipated, and which was verified after the event. In a
traveling train of light-waves the electric field and the magnetic
field stimulate one another alternately and reciprocalh', and for this
reason the wa\'e-train tra\els. Since the periodic electric field may
point in any one of the infinity of directions in the plane of the wave-
front, the wa\e-motion possesses all the freedom and variability of

' Apparently the image of the elastic solid was never quite perfected; one recalls
the question as to whether its vibrations were in or normal to the plane of polarization
of the light, which required one answer in order to agree with the phenomena of
reflection, and another in order to agree with those of double refraction. ProbabK
a modus t'ivendi could have been arranged if the whole idea had not been superseded.

MM// i (i.\ I l:Mn>l<.IRy .//'/JAi / s l.\ /•//) s/( s ill 2R3

Inrm which .in- rt'qiiiri'd to .iccoiint for the ()l)srr\i'(l proptTlii's f)f
liy;l>i.

Ma.wvrll'ri ihrorN iiniiUHliati-l>' arliii-xol ilu- si milling success of
prfscntinj; a valiif for the six-ifl of the iina^iiu-d elect roniannetir
waxes, determined e\chisi\ely from measurements upon ilie maKnelic
lields of electric currents, and a^;reein>; precisely with the observed
s(H'e<l of linlit- Two suppose<lly ilislincl jirovinces of jiliysics, each of
which li.id In-en organized on its own particular basis of experience
•md in its own particular manner, were suddenh' iniited i>y a stroke
of synthesis to which few if any parallels can be foimd in the history
of ihoui^ht. An<I this is l)\- no means the only achievement of the
electromagnetic theory of linht; there will shortly be occasion to
mention some of the others.

Now that there was so much evidence that light travels as a wave-
motion, and that its speed and other properties are those of electro-
magnetic waxes, it became urjjentlx' desirable to inquire into the
n.iture of the sources of lijjht. Granted that light en ronle outxvards
from a luminous particle of matter is of the nature of a combination
of xvaxe- trains, what is taking place in the luminous particle? To this
((uestion all our experience and all our hal)its of thought suggest one
sole obvious answer — that in the luminous particle there is a xibrating
something, a vibrator, or more likely an enormous number of \ibra-
tors — one to each atom, possibly — and the oscillations of these vibra-
tors are the sources of the xvaves of light, as the oscillations of a
xiolin-string or a tuning-fork are the sources of waves of sound.
This analogy draxvn from acoustics, this picture of the vibrating
xiolin-string and the vibrating tuning-fork, has been powerful —
indeed, it begins to seem, too powerful — in guiding the formation of
our ideas on light. It is profitable to reflect that the exolution of
thought in acoustics must hax-e traveled in the opposite sense from
the exolution of thought in optics. Whoexer it xx'as xvho was the
first to conceixe that sound is a xxave-motion in air, must certainly
haxe arrixed at the idea by noticing that sounding bodies vibrate.
One feels the trembling of the tuning-fork or the bell, one sees the
xiolin-string apparently spread out into a band by the amplitude
of its motion; it is not difficult to build apparatus which, like a slowed-
down cinema film, makes the vibrations separatelx' visible, or, like
the strolmscope, produces an equix-alent and not misleading illusion.
This was not possible in optics, and never will be. In acoustics,
one may sometimes accept the x'ibrations of the sounding body as
an independently-gix-en fact of experience, and reason forxvard to the
wave-motion spreading outwards into the enx-ironing air; in optics,

284 BELL SYSTEM TECHNICAL JOURNAL

this entrance to the path is closed, one must reason in the inverse
sense from the wa\e-motion to the qualities of the shining body.
Inevitably, it was assumed that when the path should at last be
successfully retraced, the shining body would be found in the sem-
blance of a viljrator.

For a few years at the end of the nineteenth century and the begin-
ning of the twentieth, it seemed that the desired vibrator had been
found. Apparently it was the electron, the little corpuscle of nega-
tive electricity, of which the charge and the mass were rather roughl>-
estimated in the late nineties, although Millikan's definite measure-
ments were not to come for a decade yet. Maxwell had not con-
cei\'ed of particles of electricity, his conception of the "electric fluid"
was indeed so sublimated and highly formal that it gave point to
the celebrated jest (I think a French one) about the man who read
the whole of his "Electricity and Magnetism" and understood it all
except that he was never able to find out what an electrified body
was. H. A. Lorentz incorporated the electron into Maxwell's theory.
Conceiving it as a spherule of negative electricity, and assuming
that in an atom one or more of these spherules are held in equilibrium-
positions, to which restoring-forces varying proportionally to displace-
ment draw them back when they are displaced, Lorentz showed that
these "bound" electrons are remarkably well adapted to serve as
sources and as absorbents for electromagnetic radiation. Displaced
from its position of equilibrium by some transitory impulse, and then
left to itself, the bound electron would execute damped oscillations in
one dimension or in two, emitting radiation of the desired kind at a
calculable rate. Or, if a beam of radiation streamed over an atom
containing a bound electron, there would be a "resonance" like an
acoustic resonance — the bound electron would vibrate in tune with
the radiation, absorbing energy' from the beam and scattering it in
all directions, or quite conceivably deli%ering it over in some way or
other to its atom or the environing atoms. There were numerical
agreements between this theory and experience, some of them very
striking.' Apparently the one thing still needful was to produce a
plausible theory of these binding-forces which control the response
of the "bound" electron to disturbances of all kinds. Once these
were properK- de.scribed, the wa\es of light would be supplied with

' Nolal>ly, the trend of the dispersion-curves for certain tran.sparcnt substances,
recently extended by Bergen Davis and his collaborators to the range of X-ray fre-
quencies; the normal Zeenian effect; Wicn's observations on the exponential dying-
down of the luminosity of a canal-ray beam, interpreted as the exponential decline
in the vibration-amplitudes of the Ixjund electrons in the Hying atoms; the de|)en-
dencc of X-ray scattering on the number of electrons in the atom.

SOME CONTEMPORARY ADVANCES IN PHYSlCS-VIl 285

tlu'ir vibrators, the electromagnetic theory would receive a most
valuable supplement. And. much as a competent theory of the
binding-forces was to be desired, a continuing failure to produce one
would not impugn the electromagnetic theory, which in itself was a
coherent system, self-sustaining and self-sufficient.

This was the state of affairs in the late nineties. The wave-con-
ception of light had existed for more than two centuries, and it was
se\'enty-five years since any noticeable opposition had been raised
against it. The electromagnetic theory of light had existed for about
thirty years, and now that the electron had been discovered to serve as
a source for the waves which in their propagation through space
had already been so abundantly explained, there was no effective oppo-
sition to it. Not all the facts of emission and absorption had been
accounted for, but there was no reason to believe that any particular
one of them was unaccountable. Authoritative people thought
that the epoch of great discoveries in physics was ended. It was
only beginning.

In the year 1900, Max Planck published the result of a long series
of researches on the character of the radiation inside a completely-
enclosed or nearly-enclosed cavity, surrounded by walls maintained
at an even temperature. Every point within such a cavity is tra-
versed by rays of a wide range of wave lengths, moving in all direc-
tions. By the "character" of the radiation, I mean the absolute
intensities of the rays of all the various frequencies, traversing such a
point. The character of the radiation, in this sense, is perfectly
determinate; experiment shows that it depends only on the temper-
ature of the walls of the cavity, not on its material. According to
the electromagnetic theory of radiation, as completed by the adoption
of the electron, the walls of the cavity are densely crowded with bound
electrons; nor are these electrons all bound in the same manner, so
that they would all have the same natural frequency of oscillation—
they are bound in all sorts of different ways with all magnitudes of
restoring-forces, so that every natural frequency of oscillation over a
wide range is abundantly represented among them. Now the con-
clusion of Planck's long study was this:

// the bound electrons in the walls of the cavity (i.e., in any solid body)
did really radiate while and as they oscillate, in the fashion prescribed
by the electromagnetic theory, then the character of the radiation in the
cavity would be totally different from that which is observed.*

' The belief that the character of radiation within a cavity could not be explained
without doing some violence to the "classical mechanics" had already been gaining
ground for some years, by reason of extremely recondite speculations of a statistical
nature. It is very difficult to gauge the exact force and bearing of such considerations.

286 niiLL SySTEM TECIIMCIL JOURX.IL

Howe\er, if the bound electrons do not radiate energy while they
oscillate, but accumulate it and save it np and finally discharge it in a
single outburst when it attains some one of a certain series of values
hv, 2hv, 'Shv, etc. (// stands for a constant factor, v for the frequency
of vibration of the electrons and the emitted radiation) — then the
character of the radiation will agree with that which is observed, pro\'ided
a suitable value be chosen for the constant //.

The \alue recjuired ' ff>r // in C.Ci.S. units (erg seconds) is (1. .■).'{. 10-'.

Here, llii'ii. was a phenonirm in which ilie eleclroniagnctic Hu'cirx-
seemed to be fundamentall\ incapaljle of explaining, hor this
notion of a bound electron, which oscillates and does not meanwhile
radiate, is not merely foreign to the classical theory, but very dan-
gerous to it; one does not see how to introduce it, and displace the
opposed notion, without bringing down large portions of the structure
(including the numerical agreements which I cited in a foregoing foot-
note). Howe\er, Planck had arri\ed at this conclusion by an intricate
process of statistical and thermod>namical reasoning. Statistical
reasoning is notoriously the most laborious and perplexing in all
physics, and many will agree that thermodynamical reasoning is not
much less so. Planck's inference made an immense impression on
the most capable thinkers of the time; but in spite of the early ad-
herence of such men as Einstein and Poincare, I suspect that e\'en to
this day it might practically be confined to the pages of the more
profound treatises on the philosophical aspects of physics, if certain
experimenters had not been guided to seek and to discover phenomena
so simple that none could fail to apprehend them, so extraordinary
that none could fail to be amazed.

Honour for this guidance belongs chielh- lo liinstein. Where
Planck in lilOO had said simply that bound electrons emit and absorb
energy in fixed finite quantities, and shortly afterwards had softened
his no\el idea as far as possible by making it apply only to the act
of emission, Einstein in IflOo rushed boldly in and presented the idea
that these fixed finite quantities of radiant energy retain their iden-
tity throughout their wanderings through space from the moment
of emission to the moment of absorption. This idea he offered as a
"heuristic" one — the word, if I grasp its connotation exacth-, is an
apologetic sort of a word, used to describe a theory which achieves
successes though its author feels at heart that it really is too absurd to

* I take the numerical values of the constant /; scattered through this article from
Gcrlach. The weighted mean of the exix;rimental values, with due regard to the
relative rclialiility of the various methods, is taken as 6.55 or 6.56. 10~". None of
the individual values cited in these pages is definitely known to differ from this
average by more than the experimental error.

SOME coxrnMroK.iRV .//>r./.vr/:.<r /.v rnvsics^ni 287

Ih' prost'n table. Tin- impliiatioii is, that iIr- i-xpi-rinifnliTs should
pnu-ftil to verify the pre<lietioiis liased upon the idea, cjiiite as if it
were aiieptahle, while remeinherinji always that it is ahsiiril. If the
siircesses continue to nioinit up, the absurdity may lie contideniK'
exjH.'Cte<i to fade uradu.iIK- out of the piililic mind. Sucii was the
destiny of this heuristic idea.

I will now descrilfe some of these wonderfulK- simple [ihenomena -
wDiulerfulK- simple indeed, for they stand out in full simplicity in
domains where the classical electromajjnetic theory would almost or
unite certainly impose a serious coni()lexit\-. If Planck's inference
from the character of the radiation within a cavity had been deferred
for another fifteen years, one or more of these phenomena w'ould
assuredK' ha\e been discovered independent h-. What would have
happeneil in that case, what course the e\(»lntion of theoretical physics
would have followed, it is interesting to conjecture.

The photoelectric effect is the outflowing of electrons from a metal,
occurring when and because the metal is illuininated. It was dis-
covered by Hertz in 1S89, but several years elapsed before it was
known to be an efflux of electrons, and several more before the electrons
were pro\ed to come forth with speeds which vary from one electron
to another, upwards as far as a certain detinite maximum \alue, and
never lieyond it.

Here is a rather delicate point of interpretation, which it is well to
examine with some care; for all the contro\ersies as to continuity
\ersus discontinuity in Nature turn upon it, in the last analysis^.
What is meant, or what reasonable thing can be meant, when one
saNs that the speeds of all the electrons of a certain group are con-
tmed within a certain range, extending up to a certain limiting top-
most value? If one could detect each and every electron separately,
and separately measure its speed, the meaning would be perfectly
clear. For that matter, the statement would degenerate into a
truism. The fact is otherwise. The instruments used in work such
as this perceive electrons only in great multitudes. Suppose that
one intercepts a stream of electrons with a metal plate connected by
a wire to an electrometer. If a barrier is placed before the electrons
in the form of a retarding potential-drop, which is raised higher and
higher, the moment eventually comes when the current into the
electrometer declines. This happens because the slower electrons
are stopped and driven back before they reach the plate, the faster
ones surmount the barrier. As the potential-drop is further magni-
fied, the reading of the electrometer decrea.ses steadily, and at last
becomes inapprecial>le. Beyond a certain critical value of the retard-

BELL SYSTEM TECHNICAL JOURNAL

ing voltage, the electrometer reports no influx of electrons. Does this
really mean that there are no electrons with more than just the speed
necessary to o\erpass a retarding voltage of just that critical value?
Or does it merely mean that the electrons flying with more than that
critical speed are plentiful, but not quite plentiful enough to make
an impression on the electrometer? Is there any topmost speed at

/^DVLE^E: VOLT/qGL

Fig. 1 — Curves showing thfrniioEiic flfitri)n-ciiircnt \er.sus opposing voltage, ileinon-
st rating a distribution-in-specd extending over an unlimited range of speeds. Multiply
the ordinates of the middle cur\e by 100, those of the right-hand curve by 10,000, to
bring them to the same scale and make them merge into a single curve. (L. H. Gernier)

all, or should we find, if we could replace the current-measuring
de\'ice with other and progressively better ones ad infinitum, that the
apparent maximum speed soared indefinitely upwards?

Absolute decisions cannot be rendered in a question of this kind;
but it is possible, under the best of circumstances, to pile up indica-
tory evidence to such an extent that only an imusually strong will-
to-disbelieve would refuse to be swayed by it. Tiie judgment depends
on the shape of the curve which is obtained by plotting the electro-
meter-reading vs. the retarding potential — in other words, the fraction
y of the electrons of which the encrgj' of motion surpasses the amount
X, determined from the relarding-voltage by the relation x = eV.
Look for example at the curves of Fig. 1, which fefer to the electron-

SOMF. COtWTEMl'OR.IRV .IIH\IXCr.S IX rUVSICS III 280

msmm

^ig. 2 — Curves showing pliotoclwtric ckti riiii-( urrciit versus opposing voltage,

demonstrating a ilistribution-in-spoerl extcndinx over a range limited at the top.

(R. A. Millikan, Physical Review)

29() BELL SYSTEM TECIISICAl. JOIRS.U.

slreani flowing sp()iuancniisl\' out <it an intaiulrsri'ni wire-; \\\v\ are
three segments of one single cur\e, plotted on dilTerent scales as the
numerals show. This curve bends so gradually around towards
tangency with the axis of abscissae, that one can hardly avoid the
inference that it is really approaching that axis as if to an asymptote,
and that if the electrometer at any point ceases to declare a current,
it is because the electrometer is too insensitive to respond to the
smaller currents, and not because there are no faster electrons. Look
instead at the curves of Fig. 2, which refer to the electrons emerging
from an illuminated surface of sodium. These curves slant so sharjily
towards the axis of abscissae, they bend so slightly in the portions of
their courses where the data of experiment determine them, that the
linear extrapolation oxer ihe Utile interval into the axis commends
itself as natural and ine\ilable. Because the curves for the thermi-
onic electrons approach the axis so geiitK-. it is agreed that their
\elocities are distributed continuously o\er an unlimited range; be-
cause the curves for the photoelectrons cut into it so acuteK', it is felt
that their \elocities are confined below a definite maximum \alue.

This therefore is the photoelectric efl'ect : waves of light inundate
the surface of a metal, and electrons pour out with \arious velocities,
some nearly attaining and none exceeding a particular topmost
\alue. I will designate this maximum speed, or rather the corre-
sponding maximum kinetic energy, by £max- Analyzing the process
in the classical manner, one must imagine the waves entering into the
metal and setting the indwelling electrons into forced oscillations;
the oscillations grow steadily wider; the speed with which the electron
dashes through its middle position grows larger and larger, and at
last it is torn from its moorings and forces its way through the surface
of the metal. Some of the energy it absorbed during the oscillations
is spent (converted into potential energ>') during the escape; the
rest is the kinetic energy with which it flies away. Even if the electron
were free within the metal and could oscillate in response to the
waves, unrestrained by any restoring force, it wdiild still ha\e to
spend some of its ac(|iiired energy in passing out through the l)oimdar\-
of the metal (the laws of thermionic emission furnish evidence enough
for this). It is natural to infer that £,„ax 's the energv' absorbed by
an electron originally free, minus this amount (let me call it P) which
it must sacrifice in crossing the frontier; the electrons which emerge
with energies lower than /Jnmx nM\\ be supposed to ha\e made the same
sacrifice at the frontier and others in addition, whether in tearing
themselves away from an additional restraint or in colliding with
atoms during their emigration. This is not the only conceivable

SOMF. CO.V77:,U/'()A'./A'r . //)r. /.V(T.V IX rilVSlCS- III JQl

interprt'tatioii, IniC it si-rms iinprDtitaMi* to i-nltT into ilio oilicrs. It
is tluTt-fori' /i,„.,x whii'li apiH-ars to nu'rit llu- most .iiti-ntinn.

Now the miTo fact that then- is a ina\iiiuin) M-liuitN- of thi- i-sraprd
I'kvlrniis, that there is an /i,„„,. is not in itself of a nature to snyjuest
that the classical theory is ina(le(|iiate. It is tiie peculiar depeiiden^-e
of this quantity on the two most important controllable (lualities
of the lijiht — on its intensity and on its frecpienc}*- wliidi awakens
the hrst faint suspicions that something has at last been disco\ered.
which the classical theor\' is ill adapted to explain. One would
pretlict with a k'xxI tli'jd <'f confidence that tiie greater the intensity
of the light, the i^reater the energy acfjuired by the electron in each
cycle of its forced oscillation would be. the greater the energy with
which it woukl finally break away, the greater the residuum of energy
which at the end would be left to it. F3ut /i|„;,x '^ found to be inde-
j)endent of the intensit>' of the light. This is strange; it is as though
the waxes beating upon a beach were doubled in their height and the
powerful new waxes disturbed four times as many r>ebbles as before,
but did not displace a single one of them any farther nor agitate it
any more violently than the original gentle waves did to the pebbles
that they washed about. As for the dependence t)f £niax "" tht> fre-
quency of the light, it would be necessary to make additional assump-
tions to calculate it from the classical theory; in any case it would
probably not be ver\' simple. But the actual relation between £ma.x
and V is the simplest of all relations, shf>rt of an absolute proportion-
ality; this is it :

E,„..^ = bv-P (1)

Fig. 3 shows the relation for sodium, obserxetl l>y Miliikan.

The maximum energy of the photoelectrons increases linearly with
the frecjuency of the light. P is a constant which varies from one
metal to another. In the terms of the simple foregoing interpreta-
tion, P is the energy which an electron must spend (more precisely,
the energy which it must invest or convert into potential energy-)
when it passes through the frontier of the metal on its way outward.
Comparing the xalues of P for several metals with the contact poten-
tials which they display relatix'ely to one another, one finds powerful
evidence confirming this theory. Having discussed this particular
aspect of the question in the fifth article of this series, I will not
enter further into it at this point.

The constant // is the same for all the metals which ha\e been
use<l in such exfieriments. The best determinations have been made
upon two or three of the alkali metals, for these are the only metals

292

BELL SYSTEM TECHNICAL JOURNAL

SilOA 4-

S410A-

Kig. 3 — Curve showing the linear relation between the maximum energy
electrons and the frequency o( the light which excites them. (Millikan
Review)

of |)hoto-
Phyiical

SOME CONTEMPORARY .inf.lXCES IN I'HYSICS- VII 293

which rt'liMso electrons when illiiininaled with hulit of wi<le C()n\eii-
ient ranges of fre(|Ueiiry and color. Most nielals must l)e irradiated
with ultraviolet light, and the cxiK'rinieiits heconie very dilViciilt if
they nuist be (K-rforiued with lii;ht of frequencies far from the visible
spectrum. The values which Millikan obtained for sodium and for
litiiium agree within the experimental error witii one another and
with the mean value /, =0.')7.1() ■' (2)

The maximum energy of the electrons released by light of the
frequency v is therefore equal to a quantity hv which is the same,
whatever metal be illuminated by the light — a ([uantity which is
characteristic of the light, not of the metal — minus a cjuanlity P
which, there is ever\' reason to belie\e, is the cjuota of energy sur-
renilered by each electron in passing out across the boundar\-surface
of the metal. 1 1 is 05 i/ each of the released electrons had received
a quantity hv ol energy from the light. I will go one step further,
and la>' down this as a rule, with another cautioush-inserted us if to
guard against too suddenly daring an inno\ation:

Photoelectric emission occurs as if the energy in the light icere concen-
trated in pHtckets, or units, or corpuscles of amount hv, and one whole
unit were delivered over to each electron.

This is a perfectly legitimate phrasing of equation (1), bin I doul)!
whether anyone would e\er have emplo\'ed it, e\en with the guarded
and apologetic as if, but for the fact that the \alue of // given in (2)
agreed admirably well with the value of that constant factor involved
in Planck's theory, the constant to which he had given this very
symbol and a somewhat similar role. Deferring for a few pages one
other extremely relevant feature of the photoelectric effect (its "in-
stantaneity") I will proceed to examine these other situations.

An effect which might well be, though it is not, called the inverse

photoelectric effect, occurs when electrons strike violently against

metal surfaces. Since radiation striking a metal inay elicit electrons,

it is not surprising that electrons bombarding a metal should excite

radiation. Electrons moving as slowly as those which ultraviolet or

l)lue light excites from sodium do not have this power; or possibly

they do, but the radiation they excite is generally too feeble to be

detected. Electrons moving with speeds corresponding to kinetic

energies of hundreds of equivalent volts, '^ and especially electrons

'One equivalent volt of energy' = the energy- acquired by an electron in passing
across a potential-rise of one volt=e/300 ergs= 1.591.10 " ergs. This unit is
usually called simply a "volt of energy", or "volt", a bad us^ige but ineradicable.
.Also "sijcefi" is used interchangeably with "energy" in speaking of electrons, and
one finds (and, what is worse, cannot avoid) such deplorable phrases as "a speed
of 4.9 volts" ! ! !

294 BF-LL SYSTEM TECHXIC.IL JOCRX.IL

with energies amounting to tens of tiioiisands of c(iiii\'aienl \'olts, cio
possess it. Tiiis is in fact liie process of excitation of X-ra\s, wliich
are radiated from a metal target exposed to an intense bombardment
of fast electrons. The protagonists of the electromagnetic theor>^
had an explanation ready for this effect, as soon as it was discovered.
A fast electron, colliding with a metal plate, is brought to rest by a
slowing-down process, which might be gradual or abrupt, uniform or
satcade, but in any case must be continuous. Slowing-down entails
radiation; the radiation is not oscillator^', for the electron is not
(jscillating, but it is radiation none the less; it is an outward-spreading
single pulsation or pulse, comparable to the narrow spherical shell of
condensed air whidi diverges outward through the atmosphere from
an electric spark and has been photographed so often, or to a transient
in an electrical circuit.

One may object lh.it the pulse is just a i)ulse and nothinj; niori'. w liile
the X-rays are wa\e-trains, for otherwise the X-ra\' spectroscope
(which is a diffraction apparatus) would not function. The objection
is answered by pointing out the quite indubitable fact that any pulse,
whatever its shape (by "shape" I mean the shape of the curve repre-
senting the electric field strength, or whatever other variable one
chooses to take, as a function of time at a point tra\ersed by the
wave) can be accurately reproduced by superposing an infinity of
wave-trains, of all frequencies and divers properly-adjusted ampli-
tudes, which efface one another's periodic variations, and in fact
efface one another altogether at all moments except during the time-
interval while the jiulse is passing o\er — during this interval they
coalesce into tiie pulse. Thence, the argument leads to the con-
tention that the actual [Hilse is made up of just such wa\'e-trains,
and the sa|)ient diffracting crystal recognizes them all and diffracts
each of them dui\' along its proper path. The problem is not new,
nor tlie answer; white light has long been diagnosed as consisting of
just such pulses, and the method of anahzing transient impulses in
electrical circuits into ilu-ir et|ui\,ilent sums of wa\e-irains has been
strikingly successful.

The ajiplication of the mellKid to liiis case nf X-ra\' excitation
eiijo>ed one qualilati\e success. The spherical pulse tli\erging from
the place where an electron was brought to rest should not be of etjual
thickness at all the points of its surface; it should be broader and
flatter on the side towards the direction whence the i-leitron came,
thinner and sharper on the side towards the direction in which the
electron was going when it was arrested. Analyzing the jjulse, it is
found that at the point where it is broad and low, the most intense of

SOME CONTEMfOK.lRV AIHASCI.S IX rilYSUS III 295

its c(iiiivali-tu \v;ivf-trains an- on i\\v vvhcilr of a Iowit fri'<|iii'iuy than
ilu- most iiiti'iisi- of thi- \va\e-irains wliicli lonstituti- it wlu-ri- it is
narrow and hinh- By i-xaininin^j and rcsol\inj; tlu- X-rass radiated
frotn .1 t.ir^;i't , at \arious inclinations to tlu- diriTlion of tlu- Iximhardinn
rli-itrons, this was vorilicd -Acrilk-d in part, not altont-'llur. Thi' X-
ra\s radiated nearly towards the .source of tlie electron-stream inciiiHe a

/

■

/

/

/

/

/

/

/
/

/

/

/

/

/

1 '

l».A

/

y /

..«'

*.•>•

m M«M MOW ■»•••

/
MM* noee moot >

/ ..

MO 1I«W MOM M^ J19M MM<

' V.

wSm 400«0 «.«M

otrrcRCNCf or pottntui Am.co to tubc in volts

Fig. 4 — Curves ("isochromatics") each representing the intensity of X-radiation

of a very narrow range of frequencies, plotteil versus the energy of the bomljartling

electrons. (Duane & Hunt, Physical Review)

lesser proportion of high-frequency wave-trains, the\' are softer as
the phrase is, than the X-ra\-s radiated nearly along the prolongation
of the electron-stream. In the spectrum of each of these beams of
X-rays, there is a wave length where the density of radiant energ>-
attains a ma.ximiim, and this wave length is longer in the former
beam than in the latter one. .So much is implied in tiie classical
theoi>'.

But it is nowhere implied in the cl.issical theor\' that the spectrum
of an X-ray beam, produced when electrons of a constant energy
rain down upon a metal, should extend upwards only to a certain

296 BELL SYSTEM TECHNICAL JOURNAL

maximum frequency, and then and there come to a sudden end; yet
apparently it does. There is a high-frequency limit to each X-ray
spectrum, and wave-trains of frequencies exceeding that limit are
not detected; whereas the spectrum of the hypothetical pulses ought to
include wa\e-trains of everj' frequency low or high, the amplitudes
indeed declining to infinitely low values as one goes along the spectrum
to infinitely high frequencies, but certainly declining smoothly and
gradually. To demonstrate this high-frequency limit is a delicate
experimental problem, quite like that other problem of demon-
strating a sharply definite topmost value for the energies of photo-
electrons. That question whether the curves of photoelectric current
vs. retarding voltage, the curves of Fig. 2, cut straightly and sharply
enough into the axis of abscissae to prove that there are no photo-
electrons with velocities higher than the one corresponding to Xo,
returns again in a slightly altered form.

The most reliable of the methods actually used to demonstrate
the high-frequency limit depends on the fact that the high limiting
frequency (which I will call ;',nax) varies with the energy of the bom-
barding electrons, increasing as their velocity increases. Therefore,
if the radiant energy' belonging to rays of a certain fixed wave length
or a certain fixed narrow range of wave lengths is separated out from
the X-ray beam by a spectroscope, and measured for various veloci-
ties of the impinging electrons, passing from very high \'elocities step
by step to very low ones; it will decrease from its first high \'alue
to zero at some intermediate velocity, and thereafter remain zero.
But according to the classical theory also, it must decrease from its
first high value to an imperceptibly low one; the descent however will
be gradual and smooth. Thus the only question which can be settled
by experiment is the question whether the descent from measurable
intensities to immeasurably small ones resembles the gentle quasi-
asymptotic decline of the curve of Fig. 1 or the precipitate slope of
the curve of Fig. 2. The data assembled by Duane and Hunt are
shown in Fig. 4 plotted in the manner I have described; there is little
occasion for doubt as to which sort of cur\'e these resemble most.*

Fach of the curves in Fig. 4 represents that portion of the total
intensity of an X-ray beam, which belongs to rays of wave lengths
near the marked value of the frequency v. This frequency is the high

• Three simple cur\'es of the intensity-distribution in the X-ray spectrum are
shown in Figure 5. The abscissa is neither frequency or wavelength, but a variable
which varies continuously with either (it is actually arc sin of a quantity propor-
tional to wavelength) so that the acute angle between each curve and the axis of
abscissae, at the point where they meet, corresponds to and has much the same
meaning as the acute angles in Figure 2 — not so conspicuously.

SOME CONTEMPORARY ADVANCFS IN PHYSICS- I'll 297

limiting freqiii-nry >-„,;„ for that \.iliie of llic energy E of the hotii-
f)arcling elcrlrons, which corresponds to the point on the axis of
abscissae where the curve (extrapolated) intersects it. Ihe relation
between ««„„, and E is the simplest of all relations:

E = constant • v,,,.!, = //

or

The const. ml h is the saiiU' for all the nictais on which liic cNiu'rinii'iit
has been performed- a few of the least fusible ones, for metals of a
low melting-point would be melted before E. could be lifted far enough
to give an adct)uatc range for determining the relation between it and

H%ti09 of in(tn9it>49 oflin*3

*t400kv to Utoat dt iiSkv,

^>Ot gtmrtJ rtdiition lublracttd), tre

j5> jJ* jSj

Vilu*3-of h giv*n by th^e curwa,

tttaokv, ff6X-l0"»rg ate.

- »ia •. h'ssf/o" - • ;

" I3t ■■ . h-e33-o" - -

Mu/i 0/4// h dUtrminttJOns on rhodi/m,
wiih tha vt/ue o/t 13 SSi-to" trgaee

Fig. 5 — The continuous X-ray spectrum for three v.ihics of the energy of the bom-
barding electrons, intensity being plotted versus a quantity varying uniformly
with frequency. Ignore the peaks. (D. L. Vsc\is,lcr,\J'liysical^Review.) Sec footnote 6

298 HELL SYSTEM I ECIISICAL JOIRX.IL

"max- The \alue' given for il by Gerlacli, after a critical stii(i\- of
all the determinations, is

/z=().53.10-=' (4)

The highest frefiiiency of radiation which electrons moving with
the energy E are able to excite, when they are brought to rest b\-
colliding with a metal target, is therefore equal to E divided by a
constant indei)endent of the kind of metal. So far as this high lim-
iting frequency is concerned, it is perfeclK' legitimate to express
equation (3) in these words.

Excitation of radiation by electrons stopped in their flight by collision
with a metal occurs as if the energy in the radiation were concentrated in
units of amount hv, and one such unit were created out of the total energy
which each electron surrenders when it is stopped.

As for the radiation of frequencies inferior to the high limiting
frequency, it is very easily explained by asserting that most of the
electrons come to rest not in one operation, but in several successi\e
ones, dividing their energy up among several units of frequencies
inferior to ^nuix or £ /;; or possibly they lose energy in \arious sorts
of impacts or various other ways before making the first impact of
the sort which transforms their energy into energy of X-rays. Xoihins.;
about il contradicts the italicized rule. Still it is not likely tli.it ,iii\-
one would have formulated e(|ualion (3) in such language, if the \alue
of the constant /; which appears in it were not identical with the value
which we have alread\' once encountered in anaKzing the jihoto-
electrir effect, and with the \'alue at which Planck earlier arri\-ed.

I think it is too early in this discourse to fuse these italicized Rules
for the release of electrons by radiation and the excitation of radiation
by electrons into a single Rule; Inn by cnniomplaiing the two Rules
side by side one arrives without niucli labor ,u an inference which
could be tested e\en though we had no wa\' of measuring the fre-
quency of a radiation, and in fact was \-erified before any such wa>'
existed. For if electrons of energ\- E can excite radiation of fre(iiienc\'
E/h, ami radiation of frequency E, h striking a piece of metal can
elicit electrons of energy // (/i, h)—P; then, if a target is bombarded
with electrons, and another metal target is exposed to the radiation
which emanates from the first one, the fastest of the electrons which
escape from the second target will mo\e with the same velocity and

■ tii-rlaih ri-(;ar<ls this as the most arcuratc of all ihf methods for (Iclcrmhiiiig //,
un upliilon in which probably \vA all would concur. Il has been nialntaine(l that
the hiKh-fre(|uency limit, like the wavelength of niaxinuini intensity in the X-ra\-
siH-ctrum, deiH-nds on the inclination of the X-ray beam to the exciting electron-
stream. I do not know whether the exi>erimenls adduced in support of this claim
h-n.- 1 n -mI.- K ,,.„t, ,..■.!

SO^fE CONTEMl'ORAHY .IIH-.-IXCFS IX PIIVSICS I'll 2^9

thf siiinc energy as the electrons which strike the first one (minus the
((iiantiiy P which, howexer, is iinnieasural)l\- small anti jwrfectly
iu'nli>;''»'<" in comparison with the energ>' of the electrons which
excite or<linar>' X-rays). This fact emerged from a series of experi-
ments which were performeti by various people in the first decatlc
of this century, the results of which were generally phraseti soirte-
wh.il in this way, "the energy of the secondary electrons depends
only on the energy of the primar> electrons, not on the nature (.f the
material which the primary electrons strike or on that frf)m which
the secondary electrons issue, nor on the distance over which the
X-rays tra\el." I'pon these results Sir William Bragg based his
corpuscular thet)ry of X-rays; for (he argued) the most sensible
interpretation of the facts is surely this, that some of the electrons
striking the first target rebound with their full energy, and rel)f)und
again with their full energy from the second target, each of them
carr>ing with it from the first to the second target a positive particle
which neutralizes its charge over that part of its course, and so defeats
all the meth(xls de\ ised to recognize a flying electron. Not many
years later, Sir William cooperated in the slaying of his own theory,
by developing the best of all methods for proving that X-rays are un-
dulatory and measuring their wave-lengths; but it was only the im-
agerv' of the theory that perished, for its essence, the idea that the
energ>- of the first electron travels as a unit or is carried as a parcel
to the place where the second electron picks it up, had to be resur-
rected. All the mystery of the contrast between wave-theory and
quantimi-theory is implicit in this phenomenon, for which Sir William
found an inimitable simile: "It is as if one dropped a plank into the
sea from a height of 100 feet, and found that the spreading rip()Ie was
able, after tra\elling 1,000 miles and becoming infinitesimal in com-
parison with its original amount, to act upon a wooden ship in such a
way that a plank f)f that ship flew out of its place to a height of 100
feet."

Among the radiations excited from a metal by electrons of a single
energy E, there are many of which the frequencies differ from the
interpreted frequency E h, being lower. Among the electrons ex-
pelled from a metal by radiation of a single frequency v, there are
many of which the energies differ from the interpreted energy-value
liv, being lower. These were accounted for by supposing that the
electrons are troubled by repeated encounters with closeK-crowded
atoms. If then a metal \apor or a gas were bombarded with electrons
or ex[X)sed to radiation, would all the excited radiation have a single
frequency conforming to equation (3), would all the released electrons

300 BELL SYSTEM TECHNICAL JOURNAL

ha\c a single energj' conforming to equation (1)? One could not
affirm this a priori, for a solid metal is not a collection of free atoms
close together as a gas is an assemblage of free atoms far apart, but
rather a structure of atoms which interfere with one another and are
distorted, and there are many electrons in a solid of which the bonds
and the constraints are very different from those by which the elec-
trons of free atoms are controlled and vice versa. When a plate of
sodium or a pool of mercury is exposed to a rain of electrons, not
exceeding say 10 equivalent volts in energ>', nothing apparent hap-
pens." When the vapor of either metal is similarly exposed, the atoms
respond in a manner from which they are inhibited, when they are
bound together in the tight latticework of a solid or the promiscuous
crowding of a liquid; and light is emitted.

The phenomena are clearest when the bombarded \apor is that of
a volatile metal, such as mercury, sodium, or magnesium. The atoms
in such vapors are not usually bound together two by two or in greater
clusters, as they are in such gases as oxygen or hydrogen, of which
the response to electron-impacts or to radiation is not quite under-
stood to this day; and the first radiations which they emit arc not
in the almost inaccessible far ultra-violet, like those of the monatomic
noble gases, but in the near ultra-violet or even in the visible spectrum.
Dealing with such a vapor, I will say mercury for definiteness, one
observes that so long as the energy' of the bombarding electrons
remains below a certain value, no perceptible light is emitted; but
beyond, there is a certain range of energies, such that electrons pos-
sessing them are able to arouse one single frequency of radiation
from the atoms. Ordinarily, as when a \apor is kept continuously
excited by a self-sustaining electric discharge throughout it, the
atoms emit a great multitude of different frequencies of radiation,
forming a rich and complicated spectrum of many lines. But if the
energy of the bombarding electrons is carefully adjusted to .some value
within the specified range, only one line of this spectrum makes its
appearance; under the best of circumstances this single line may be
exceedingly bright, so that the absence of its companions— some of
which, in an ordinary arc-spectrum, are not much inferior to it in
brightness — is decidedh' striking. The one line which constitutes
this single-line spectrum is the first line of the principal series in the
complete arc-spectrum of the element; its wave length is (to take a
few examples) 2o3GA for mercury, .'jSOO for sodium (for which it is a
doublet), 4.571 for magnesium.

' According to a vcr>' recent paper by C. H. Thomas, radiations from iron excited
b>- electrons with as low an energy as some two or three equivalent volts have been
detected.

SOME CONTEMPORARY AinWSCES IS PUYSICS~yn m

Docs this single line appear suddenly at a precise value of the
enerR>' of the iinpinRing electrons? This ()uesli(in suggests itself,
when one has already studie<l the excitation of X-rays from solids by
electrons and the excitation of electrons from solids by light. Here
again we meet that tiresome but ineluctable problem, as to what
constitutes a sudden appearance, and how we slundd recognize it if it
really occurretl. The only consistent way to meet it (consistent, that
is, with the wa>s already employed in the prior cases) would be to
measure the intensity of the line for various values of the energy of
the electrons, plot the cur\e, and decide whether or not it cuts the
axis of abscissae at a sharp angle. This is in principle the same
method as is used in determining whether a given X-ray frequency
appears suddenly at a given value of the energy of the electrons
boml)arding a solid; the curves of Fig. 4 were so obtained. Attempt-
ing to apply this same method to such a radiation as 2, .536 of mer-
cun.', one has the solitar>" advantage that the frequency of the light
is sharp and definite (it is not necessary to cut an arbitrary band of
radiations out of a continuous spectrum) and two great counteracting
disadvantages: the intensity of the light cannot be measured accur-
ately (one has to guess it from the effect upon a photographic plate)
and the impinging electrons never all have the same energy. Owing
probably to these two difficulties, there is no published curve (that I
know of) which cuts down across the axis of abscissae with such a
decisive trend as the curves of Figs. 2 and 4. Still it is generally
accepted that the advent of the single line is really sudden. The
common argument is, that one can detect it on a photographic film
exposed for a few hours when the energy of the bombarding electrons
is (say) 5 equivalent volts, and not at all on a plate exposed for hun-
dreds of hours when the bombarding voltage is (say) 4.5 volts. In
this manner the energy of the electrons just sufficient to excite 2.536
of mercurj- has been located at 4.9 equivalent volts. Dividing this
critical energy (expressed in ergs) by the frequency of the radiation,
we get

(4.9e/300) / (f /.00002536) =6.59 • lO"" (5)

It agrees with the values of the constant which I designated by h
in the two prior cases, and the data obtained with other kinds of
atoms are not discordant. Gerlach arrives at 6.56- 10~" as the mean
of all values from experiments of this type upon many vapours. The
evidence is not quite so strong as in the prior cases, but fortunately
it is supplemented and strengthened by testimony of a new kind.
When electrons strike solids and excite X-rays, it is impnassible to

302 BELL SYSTEM TECHNICAL JOLRXAL

follow their own later history, or the adventures of a Ijeam of radia-
tion after it sinks into a metal. We have inferred that the electrons
which collide with a piece of tungsten and disappear into it transfer
their energ>- to X-rays, but the inference lacked the final support
which would have been afforded by a demonstration of these very
electrons, still personally present after the collision but deprived of
their energ>'. Now when electrons are fired against mercury atoms,
this demonstration is possible, and the results are very gratifying.
I have already several times had occasion to remark, in this series of
articles, that when an electron strikes a free atom of mercury, the
result of the encounter is very different, according as its energy of
motion was initially less than some 4.9 equivalent volts, or greater.
In the former case, it rebounds as from an elastic wall, having lost
only a very minute fraction of its energ>', and this fraction spent in
communicating motion to the atom; but in the latter case, it may and
often does lose 4.9 equivalent volts of its energ>' eti bloc, in a single
piece as it were, retaining only the e.xcess of its original energy over
and above this amount. Thus if electrons of an energy of 4.8 equiva-
lent volts are shot into a thin stratum of mercury vapor, nothing
but electrons of that energy arrives at the far side; but if electrons
of an only slightly greater energj', say 5.0 equivalent volts, are fired
into the stratum, those which arrive at the far side will be a mixture
of electrons of that energy, and very slow ones. The very slow
ones can be detected by appropriate means, and the particular \alue
of the energy' of the bombarding electrons, at which some of llicni
are for the first time transformed into these very slow ones, can be
determined. Once more we meet that question as to whether the
transformation does make its first appearance suddenly, but in this
case the indications that it does are rather precise and easy to read.
Furthermore it is possible to measure the energy of the slow electrons,
and one finds that it is equal to the initial energy of the electrons,
minus the amount 4.9 equivalent volts. (These measurements are
not so e.xact as is desirable, and it is to be Impi'd ilial sdmobody will
take up the task of perfecting them.)

We, therefore, see both aspects of the transaiiicui wliich occurs
when an electron whereof the energy is 4.9 equivalent \olis, or greater,
strikes a mercury atom. It loses 4.9 equivalent volts of energy, and
we measure the loss; the atom sends forth radiation of a certain
frequency, and no other; the atom does not send forth even this
frequency of radiation, if none of the electrons fired against it has at
least so much energy. We have already compared the energy trans-
ferred with the frequency radiated, and as in the case of X-rays

SOME COMF.MPOR.IRV .-IDr.-tNCF.S IN PHYSICS— III 303

fxiitfil from a soliti targi-t by very fast fUrtrons, it is legitimate to
Siiy for these radiations which form the single line s()ectra of metallic
atoms, that

Exiilution oj the ray forming a single-line spectrum, by the collision
of an electron against an atom, occurs as if the energy in the radiation
were concentrated in units of amount hv, and one such unit were createa
out of the total energy which the electron surrenders.

There are yet se\eral phenomena which I might treat by the same
inductive methcx.!, arriving after each exposition at a Rule which
would resemble one or the other of those which I have thus far written
in italics; but it is no longer expedient, I think, to pass in each instance
through the simie elaborate inductive detour. These three phe-
nomena which I have discussed already combine into an impressive
and rather fornudable obstacle to the classical manner of thinking.
Here is a mercury atom, which receives a definite quantity of energy
U from an electron, and distributes it in radiation of a definite fre-
quency U/h. Here again is a multitude of atoms locked together
into a solid, and when an electron conveys its energy U to the solid,
it redistributes that energy in radiation of a definite frequency U/h.
(It is true that many other radiations issue from the solid, but they
are all explicable if one assumes that the electron may deliver over
its energy in stages, and there is no radiation of the sort which would
controvert the theory by virtue of its frequency exceeding U/h.)
And when that radiation of frequency U/h in its turn strikes a metal,
it is liable and able to release an electron from within the metal,
conferring upon it an energy which is apparently equal to U. Ap-
parently there is some correlation between an energy U and a fre-
quency U, h, between a frequency ;' and an energy hv. Apparently
a bl(xk of energy of the amount U tends to pass into a radiation of
the frequency U/h; apparently a radiation of the frequency v tends
to deliver up energy in blocks of the amount hv. The three italicized
Rules coalesce into this one:

Photoelectric emission, and the e.Kcitation of A'-rav5 from solids by
electrons, and the excitation of single-line spectra from free atoms, occur
as if radiant energy of the frequency v were concentrated into packets,
or units, or corpuscles, of energy amounting to hv, and each packet were
created in a single process and were absorbed in a single process.

If the neutralizing as if were omitted, this would be the corpuscular
theory rediviva. It is good policy to leave the as if in place for awhile
yet. But conservatism such as this need not and should not deter
anyone from using the idea as basis for every prediction that can
be founded upon it, and testing every one of the predictions that

304 BELL SYSTEM TECHNICAL JOURNAL

can be tested by any possible way. Just so were the three phenomena
cited in these Rules discovered. All of them involve either the
emission or the absorption of radiation, and so do all the others which
I could have quoted in addition, if this account had been written
three years ago. Reserving to the end the one new phenomenon
that transcends this limitation, I must explain the relation between
this problem and the contemporary Theory of Atomic Structure.

The classical notion of a source of radiation is a vibrating electron.
The classical conception of an atom competent to emit radiations of
many frequencies is this: a family or a system of electrons, each
electron remaining in an equilibrium-position so long as the system
is not disturbed, one or more of the electrons \-ibraling when the
system is jarred or distorted. A system with these properties would
have to contain other things than electrons, otherwise it would fly
apart; it would have to contain other things than particles of posi-
tive and particles of negative electricity intermixed, otherwise it
would collapse together. One would have to postulate some sort
of a framework, some imaginary analogue to a skeleton of springs
and rods and pivots, to hold the electrons together in an ensemble
able to vibrate and not liable to coalesce or to explode. This would
not be satisfying, for in making atom-models one wants to avoid
the elaborate machinery and in particular the non-electrical com-
ponents; it would be much more agreeable to build an atom out of
positive and negative electricity associated with mass, omitting all
masses or structures not electrified. Nevertheless, if anyone had
succeeded in devising a framework having the same set of natural
frequencies as (say) the hydrogen atom exhibits in its spectrum — if
anyone expert in dynamics or acoustics had been able to demonstrate
that some peculiar shape of drumhead or bell, if anyone \ersed in
electricity had been able to show that some particular arrangement
of condensers and induction-coils has such a series of natural vibrations
as some one kind of atom displays — then, it is quite safe to say, that
framework or that membrane or that circuit would today be either
the accepted atom-model, or at least one of the chief candidates for
acceptance. Nt)body e\er succeeded in doing this; it is ilu' consensus
of opinion today that the task is an impracticable one.'*

' It is difficult to put this statement into a more precise form. Rayleigh was of
the opinion that the hydrogen sjX!i-trum could not be regarded as the ensemble of
natural freciucncies of a mechanical system, because it is the general rule for such
systems that the second power of the frequency conforms to simple algebraic formulae,
while in the hydrogen s|)cctruni it is xhe first power for which the algebraic expression
is simple. He admitted, however, that it was possible to find "e.\ccplional " mechan-
ical systems for which the first power of the frequency is given by a simple formula;
which goes far to vitiate the conclusion. Another aspect of the formula (6) for

SOME coxTr.Mi'oK.tKy .inr.ixcr.s i.\ riivsics ni m)?

This st't of natural fri-(|Ufiuii>s whitli hartled all the etTorls to
fxplaiii it, the set oonstituliiiK the two siiu[)iest of all spectra (the
siH'ctriini of atomic hyiIro^;eii .iiul the spectrum of ioni/ed heliumV
is given by the formula

. = r('\-\) .-(6)

the different lines being obtained by assigning different integral
values to the parameters in and n; lines corresponding to values of m
ranging from 1 to 5 inclusive, and to values of n ranging from 2 to 40
inclusive, have already been obser\ed, and there is no reason to doubt
that lines corresponding to much higher values of m and n actually
are emitted, but are too faint to be detected with our apparatus.
The constant R has one value for hydrogen, another almost exactly
four times as great for ionized helium.

Here, then, is the problem in its simplest presentation : How can a
model for a hydrogen atom be constructed, which shall emit rays of
the fretpiencies given by the formula ((>), only these and no others.''
The obvious answer "By constructing a mechanical framework
having precisely these natural frequencies" is practically excluded;
it seems infeasible. Something radically different must be done.
The achievement of Niels Bohr consisted in doing a radically different
thing, with such a degree of success that the extraordinary divergence
of his ideas from all foregoing ones was all but universally condoned.
I do not know how Bohr first approached his theory; but it will do
no harm to pretend that the manner was this.

Look once more at the formula for the frequencies of the h\drogen
spectrum. It expresses each frequency as a difference between two
terms, and the algebraic form of each term is of an extreme sim-

the hydrogen spectrum is this, that it specifies infinitely many frequencies within
finite inter\'als enclosing certain critical values, such as R, 4H, 9R, and so forth.
I'oincari' is said to have proved that the natural frequencies of an clastic medium
with a rigid Ixjundary cannot display this feature, so long as the displacements are
governed by the familiar equation (ftfr rf/- = *V-«. For a membrane this equation
is tantamount to the statement that the restoring-force acting upon an element
of the membrane is proportional to the curvature of the membrane at that element.
Kitz was able to show that the natural frequencies of a square membrane would con-
form to the formula (6), »/ the restoring-force upon each clement of the membrane,
instead of l)eing profmrtional to the curvature of the membrane at that element,
delJended in an exceedingly involved and artificial manner ui)on the curvature of
the membrane elsewhere. He ajjologized abundantly for the extraordinary character
of the pro(x-rties with which he had l)een obliged to endow this membrane, in order
to arrive at the desired formula: but his procedure might have proved unsuspectedly
fruitful, if Bohr's interpretation had not supplanted it.

306 BELL SYSTEM TECHNICAL JOURNAL

plicity. Multiply now each member of the formula by h, that same
constant /: which we ha\e encountered three times in the course of
this article; and rc\erse the signs of the terms.'" The formula becomes

hv = {-h R/n-)-{-h R'm-') (7)

In the left-hand member there stands hv. The reader will have
become more or less accustomed to the notion that, under certain
conditions and circumstances of Nature, radiant energy of the fre-
quency V apparently goes about in packets or corpuscles of the amount
hv; now and then, here and there, energy is absorbed from such radia-
tion in such amounts, or energy is converted into such radiation in
such amounts. Suppose that this also happens when a hydrogen atom
radiates, whate\er the cause which sets it to radiating. Then the
left-hand member of the equation (5) represents the energy which
the hydrogen atom radiates; so also does the right-hand member; but
the right-hand member is obviously the difference between two
terms; these terms are respectively the energy of the atom before it begins
to radiate, and the energy oj the atom after it ceases J rom radiating.

The problem of the hydrogen atom has now experienced a funda-
mental change. The proposal to make a mechanical framework,
having the natural vibration-frequencies expressed by (6), has been
laid aside. The new problem, or the new formulation of the old prob-
lem, is this: how can a model for a hydrogen atom be constructed,
which shall be able to abide only in certain peculiar and distinctive
states or shapes or configurations, in w'hich various states the energy
of the atom shall have the xarious \alues —hR, —hR 4, —hR it,

— hR/\ii, and so forth?

Bohr's own model has become one of the best-known and most-
taught conceptions of the whole science of ph>sics, in the twelve
years of its public existence. He based it upon the conception, then
rapidh- gaining ground and now generally accepted, that the hydrogen
atom is a microcosmic sun-and-planet system, a single electron revolv-
ing around a much more massive nucleus bearing an electric charge
ec|ual in magnitude and opposite in sign to its own. This is really
a most unpromising conception, very ill adapted to the modification
we need to make. We want an atom w^hich shall be able to assume
only those definite values of energy which were listed above: —hR,

— hR A, —hR !) and the rest. Now the energy of this sun-and-
planet atom depends on the orbit which the electron is describing.

'"For tlif explanation of this rather confusing reversal, see my third article (page
278; or page 11 of the reprint).

SOME CONlE.XfPOR.-IRY .tPr.lXCCS IX niYSICS- I'll 307

If thf ciKTRV may assume only those dofiiiitf v.iliics, the electron
may tlescril>c only rertain defmite orbits. But there is no obvious
reason why the electron should not describe any of an infinity of
other orbits, circular or elliptical. To consider only the circular
«)rbits: if the atom may have no other \alues of energy than —liR,
and —liR 4, and —liR it, and the rest of the series, then it may not
revolve in any other circular orbits than those of whi»-h the radii are
f' 2hR. and e- '2(liR 4), and e-, 2(liR !»), and so forth; but why just
these? What prevents it from revolving in a circular orbit of radius
f- '2(hR 2). or any other value not in the series.-* And for that matter
how can it revolve in a closed orbit at all, since accoriling to the
fundamental notions of the electromagnetic theor\' it must be radiating
its energy- as it revolves, and so must sink into the nucleus in a gradu-
ally narrowing spiral?

Bohr did not resol\-e these difficulties, and no one has e\-er resolved
them except by ignoring them. The customary procedure is to
select some common feature of these permitted orbits, and declare
that it is this feature which makes these orbits permissible, and
forl)ids the electron to follow any other. For example, there is the
fact that the angular momentum of the electron in any one of the
permitted circular orbits is an integer multiple of the constant quan-
tity h 2?r, /) being the same constant as we have met hitherto, which
is hardly an accidental coincidence. If one could only think of some
plausible reas<5n why an electron should want to revolve only in an
orbit where it can have some integer multiple of // 2w for its angular
momentum, and should radiate no energy at all while so revolving,
and should refuse to revolve in an orbit where it must have a frac-
tional multiple of /; 2r, the model would certainly be much for-
tified. Failing this it is necessary to put this assertion about the
angular momentum as a downright a.ssumption, in the hope that its
value will be so great and its range of usefulness so widespread that
it will commend itself as an ultimate basic principle such as no one
thinks of questioning. So far this hope has not been thoroughly
realized. On the one hand, Sommerfeld and VV. Wilson did succeed
in generalizing it into a somewhat wider form, and using it in this
wider form they explained the fine structure of the lines of hydrogen
and ionized helium, and Epstein explained the effect of an electric
field upon these lines. These are truly astonishing successes, and
no one. I think, can wf)rk through the details of these applications
to the final triumphant comparisons of theory with experiment, and
not experience an impression amounting almost or quite to con-
viction. Vet on the other hand this generalization does not account

308 BELL SYSTEM TECHNICAL JOURNAL

for the frequencies forming tiie spectra of other elements." There is
the spectrum of neutral helium, for example, and the spectrum of
sodium, and the spectrum of mercury; in each of these there are
series of lines, of which the frequencies are clearly best expressed
each as the difference between a pair of terms, and these terms should
be the energies of the atom before and after radiating. But we have
not the shadow of an idea what the corresponding configurations of
the atom are; it may be that the outermost electron has certain
permissible orbits, but we do not know what these orbits are like nor
what common feature they possess.

Is it then justifiable to write down a Rule such as this: the frequencies
of the rays which free atoms emit are such as to confirm the idea that
radiant energy of the frequency v is emitted in packets or corpuscles of
the amount hv? V'ery few men of science, I imagine, would hesitate
to approve this. However one may fluctuate in his feelings about
Bohr's model of the atom, there always remains that peculiar relation
among the frequencies emitted by the hydrogen atom, which is so
nearly copied by analogous relations in the spectra of other elements.
When one has once looked at the general formula

/ hR\ ( hR\ ,_,

and has once inter|ircted the first term on the right as the energy
of an atom before radiating, the second term on the right as the
energy of the atom after radiating, and the quantity hv as the amount
of the packet of energy radiated, it is very difiicult to admit that this
way of thinking will e\er be superseded; particularly when one re-
members the auxiliary facts, such as thai fact about the electrons
transferring just 4.9 equivalent volts to tiie mercury atoms which
they strike, no more and no less. Analyzing the mercury spectrum
in the same way as the h>drogen spectrum was anahzed, we find
the frequencies expressible as differences between terms; interpreting
the terms as energy-values, we find that between the normal state
of the mercury atom and the next adjacent state, there is a difference
in energy of 4.9 equivalent volts, and between this and the next
adjacent state there is a further difference of 1.8 volts. This then
is the reason why an electron with less than 4.9 equivalent \()lts of

" The mathematical experts who have laboured over the theory of the Iieliiiiu
atom (two electrons and a nucleus of charge +.^<') seem to have convinced them-
selves that the features which distinguish the permitted orbits of the electrons in
this atom, whatever they may be, are definitely not the same features as distinguish
the permitted orbits of the electron in the hydrogen atom. This cannot be said
with certainty for any other atom.

SOML CONIluMI'OR.IRV ADVANCIIS IN I'HYSICS-lll 309

energy can i-otjununii-aU" no encr>;y at all to a merrury atom; and an
electron with ") or () et|uivalcnt volts of energy can transfer only 4.0
of them. It is conceivable that other conditions may he found to
j{o\ern the orbits of the electrons, so that the atoms shall have only
the prescribed enerj^y-Nalues and no others; it is even conceivable
that the conception of electron-(jrbits may be discarded; but 'the
interpretation of the terms in the formula (7j as energies will, in all
human probability, be permanent.

The foregoing Rule is thus very strongly based; but let us neverthe-
less rephrase it in a somewhat milder form as follows: The idea that
radiant energy of frequency v is emitted in packets of the amount hv,
and the contemporary theory of atomic structure, between them give a
attractive and appealing account of spectra in general, and a convincingly
exact explanation of two spectra in particular.

But what has happened meanwhile to the Vibrator, to the oscil-
lating electron, to the postulated electrified particle of which the
vibrations caused light-waves to spread out from around it like
sound wa\es from a bell? It has disappeared from the picture; or
rather, since the attempt to account for the frequencies of a spectrum
as the natural frequencies of an elastic framework was abandoned,
no one has tried to re-insert it. But there are some who will never be
quite happy with any new conception, until the vibrator is estab-
lished as a part of it.

Ionization, the total removal of an electron from an atom, affords
another chance to see whether radiant energy beha\es as though it
could be absorbed only in complete packets of amount hf. That
it requires a certain definite amount of energy to deprive an atom
of its l(X)sest electron, an amount characteristic of the atom, may
now be regarded as an experimental result quite beyond question,
cUid not requiring the support of any special theory. Thus, a free-
Hying electron may remove the loosest electron from a free mercury
atom which it strikes, if its energy amounts to 10.4 equivalent volts, not
less; or the loosest electron from a helium atom if its energy amounts
to at least 24.6 equivalent volts. If radiant energy of frequency v goes
about in parcels of magnitude hv, the frequency of a parcel which
amounts just exactly to 10.4 equivalent \olts is j'o = 2.5.3. 10'*, corre-
sponding to a wave length of 1 188A. Light of inferior frequency should
be unable to ionize a mercury atom; light of just that frequency should
just be able to ionize it; light of a higher frequency v should be able
to ionize the atom, and in addition confer upon the released electron
an additional amount of kinetic energy equal to h (v—Vo). The same
could be said, with appropriate numerical changes, for every other

310 BULL SYSTEM TECHNICAL JOURNAL

kind of atom. Of all the [jlieiioinena which might serve to illuminate
this difficult question of the relations between radiation and atoms,
this is the one which has been least studied. The experimental
material is scanty and dubious. There is no reason to suppose that
light of a lower frequency than the one I have called Vo is able to
ionize; but it is not clear whether perceptible ionization commences
just at the frequency Vo, although it has been observed at frequencies
not far beyond. The energy of the released electrons has not been
measured.

The removal of deep-lying electrons, the electrons lying close to
llic nuclei of massive atoms, is much better known; and the data
confirm in the fullest manner the idea that radiant energy of the
frequency' v is absorbed in units amounting to hv. When a beam of
X-rays of a sufficiently high frequency is directed against a group of
massive atoms, various streams of electrons emanate from the atoms,
and the electrons of each stream have a certain characteristic speed.
The kinetic energy of each electron of an>' particular stream is equal
to //;', minus the amount of energy which must be spent in extracting
the electron from its position in the atom; for this amount of energy
is independently known, being the energ>' which a free-flying electron
nnist possess in order to drive the bound electron out of the atom,
which is measurable and has been separately measured. Here again
I touch upon a subject which has been treated in an earlier article
of this series — the second — and to prevent this article from stretching
out to an intolerable length, I refrain from further repetition of what
was written there. The analogy of this with the photoelectric effect
will escape no reader. Here as there, we observe electrons relea.sed
with an energy which is admittedly not hv, but hv minus a constant;
the idea that this constant represents energy which the electrons
have already spent in escaping, in one case through the surface of the
metal and in the other case from their positions within atoms, is
fcirtified by independent measurements of these energies which give
\alucs agreeing with these constants.

We have considered various items of evidence tending to sliow
that radiant energy is born, so to speak, in units of the amount hv,
and dies in units of the amount hv. Whether energy remains sub-
divided into these units during its incarnation as radiation remains
unsettled; to .settle this question absolutely, one would have to de\ise
some way of testing the energy in a beam of radiation, otherwise than
by aljsorbing it in matter; and such a way has not yet been di.sco\ered.
There is, however, another quality which radiant energy possesses.

Conceive a stream of radiation in the form of an extremely long

SOME CONrEMPOR.IRy .iDr.iXCIlS IX PHYSICS— Vn 311

train of plain- waves, flowiiii; against a blackened plate facing normally
at;ainst the tlirection in which they advance, which utterly absorbs
them. This wave-train shall have an intensity /; by which it is
meant, that an amount of energy / apf)ears, in the form of heat,
in unit area of the blackened plate in unit time. I'nrtherniore, the
radiation is found to exert a pressure p against the blackened plate;
by which it is meant, that imit area of the plate (or the framework
upholding it) acquires in imit time an amount of momentum p.
According to the classical electromagnetic theory, verified by ex-
|x?rience, /> is equal to / V. I'nit area of the plate acquires, in unit
time, energy to the amount / and momentum to the amount / r.

Where is this energ>", and where is this momentum, an instant
before they appear in the plate? One might say that they did not
exist, that they had vanished at the moment when the radiation left
its source, not to reappear until it arrived at the plate; but such an
answer would be contrary to the spirit of the electromagnetic theory,
and we have long been accustomed to think of the energy as existing
in the radiation, from the moment of its departure from the source
to the moment of its arrival at the receiver; the term "radiant energ\"
implies this. Momentum has the same right to be conceived as exist-
ing in the radiation, during all the period of its pas.sage from source to
receiver. In the system of equations of the classical electromagnetic
theor\', the expression for the stream of energy through the electro-
magnetic field stands side by side with the expression for the stream of
momentimi flowing through the field. If the second expression is not
so familiar as the first, and the phra.se "radiant momentum" has not
entered into the language of physics together with "radiant energy,"
the reason can only be that the pressure which light exerts upon a sub-
stance is ver>- much less conspicuous than the heat which it communi-
cates, and seems correspondingly less important, — which is no valid
reason at all. Radiant energy and radiant momentum deserve the
same standing; it is admitted that the energy / is the energy which is
brought by the radiation in unit time to unit area of the plate which
blocks the wave-train, and with it the radiation brings momentum I/c
in unit time to unit area of the plate. The density of radiant energy
in the wave-train is obviously /, c, the density of radiant momentum
is / f=. '

Now let that tentative idea, that radiant energ\' of tiie fretjuency v
is emitted and absorbed in packets of the amount hv, be completed
by the idea that these packets tra\el as entities from the place of
their birth to the place of their death. Let me now introduce the
word "quantum" to replace the alternative words packet, or unit, or

312 BELL SYSTEM TECHNICAL JOURNAL

corpuscle; I have held to these alternative words quite long enougli,
I think, to bring out all of their connotations. Then the energy' /
is brought to unit area of the plate, in unit time, by I/hv of the quanta;
which also bring momentum amounting to I fc. Shall we not divide
up the momentum equally among the quanta as the energy is divided,
and say that each is endowed with the inherent energy hv and with the
inherent momentum hv/c ?

The idea is a fascinating one, but not so easy to put to the trial
as one might at first imagine. None of the phenomena I have de-
scribed in the foregoing pages affords any means of testing it. In
studying the photoelectric effect, we concluded that each of the
electrons released from an illuminated sodium plate had received
the entire energy of a packet of radiation; but this does not imply
that each of them had received the momentum associated with that
energ)'; the momentum passed to the plate, to the framework support-
ing it, e\entually to the earth. The same statement holds true
for the release of electrons from the deep levels of heavy atoms, such
as de Broglie and Ellis observed. Even if the same experiments
should be performed on free atoms, as for example on mercury vapor,
no clear information could be expected; for the momentum of the
absorbed radiation may divide itself between the released electron
and the residuum of the atom, and this last is so massi\'e that the
speed it would thus acquire is too low to be noticed. Only one way
seems to be open; this is, to bring about an encounter between a
quantum of radiation and a free electron, so that whatever momentum
aiul whatever energy are transferred to the electron must remain
wiiii it, and cannot be passed along to more massive objects where
the momentum, so far as the possibility of observing it goes, is lost.
A priori one could not be certain that even this way is open; radiation
might ignore electrons which are not lightly bound to atoms.

Arthur H. Complon, then of Washington University, is the physicist
whose experiments were the first that clearly and strikingly disclosed
such encounters between quanta of radiation and sensibly free elec-
trons. Others had observed the effect which reveals them, but his
were the first measuremenls accurate enough for inference. Unaware
al the moment of the meaning of his data, he realized it almost imme-
diately afterward, and .so established the fact and the explanation
both — a twofold achievement of a very unusual magnitude, whence
the phenomenon recei\ed the name of "Compton effect" h\ a universal
acceptance, and deser\edly.

What Complon obscr\ed was not ihe pre.sence of electrons pos-
sessed of momentum acquired from radiation — these electrons were

soMi- co.wir.Mi'Oh'.iRv .u>r.ixci:.s ix I'livsics rii .11.1

however to Ik? discovered Liter, as I sliall presently mention Imi llu'
presence of radiation of a new sort, come into beinp hy virtue of tlie
encounters between tlie original radiation anrl free electrons. We
have not encoinitered an>thinK of this sort heretofore. When a
qiiantiuii of radiant energy releases an electron from an atom, it dies
completely and confers its entire energy upon the electron. The
disposal of its momentum gives no trouble, for as I have mentioned
the atont takes care of that. When the electron is initialK' free.
and there is no atom to swallow up the momentum of the radiation,
it c.innot be ignored in this simple fashion. For if the quantum did
utterly disappear in an encounter with a free electron, the velocity
which the electron acquired would have to be such that its kinetic
energy and its momentum were separately equal to the energy and
momentum of the ciuantum; but these distinct two conditions would
generally be impossible for the electron to fulfil. Hence in general, a
quantimi possessed of momentum cannot disappear l)y the process of
transferring its energy to a free electron, whatever may be the case
with an electron bound to a massive atom. This reflection might
easily ha\e led to the conclusion that radiation .md free electrons can
have nothing to do one with the other.

What actually happens is this: the energy and the momentum
of the quantum are partly conferred upon the electron, the residues
of each go to form a new quantum, of lesser energy' and of lesser
and differently-directed momentum, hence lower in frequency and
deflected obliquely from the direction in which the original quantum
was tiioving. The encounter occurs much like an impact between
two elastic balls; what prevents the analogy from being perfect is,
that when a moving elastic ball strikes a stationary one, it loses
some of its speed but remains the same ball, whereas the quantum
retains its speed but changes over into a new and smaller size. It
is as though a billiard-ball lost some of its weight when it touched
another but rolled off sidewise with its original speed. I do not
know what this innovation would do to the technique of billiards,
but it would at all events not make technique impossible; the result
of an impact would still be calculable, though the calculations would
lead to a new result. The rules of this microcosmic billiard-game
in which the struck balls are electrons and the striking balls are
(|uanta of radiant energy are definite enough to control the conse-
(juences. The rules are these:

Conservation of energy requires that the energy of the impinging
quantum, hv, be equal to the sum of the energy of the resulting
quantum, hv , and the kinetic energy K of the recoiling electron. For

314 HELL SYSTEM TECHNICAL JOURNAL

this last quantity the expression prescribed h\ tlie spetiai relativity-
theorv '- is usefi, \iz.

.( 1
V-v/1-

in which m stands for the mass of the electron and cfi = v for its speed.
The equation of conservation of energy is then

liv = lii'' + mc-( ,i-, -l). (8a)

Conservation of momentum retiuires iliat ilu' numu-niuni of the
impinging quantum t)e ccjual to the suin of the momenta of the result-
ing quantum and the recoiHng electron. Momentum being a vector
quantity, this rule requires three scalar equations to express it, which
three may be reduced to two if we choose the .T-a.\is to coincide with
the direction in which the impinging quantum travels, and the y-axis
to lie in the plane common to the paths of the recoiling electron and
the resulting quantum. Designate b>' 0 the angle between the paths
of the impinging quantum and the recoiling electron; by 6 the angle
between the paths of the two quanta. The magnitude of the momen-
tum-vector is, by the special relativity-theory, »/t'/\/l — /3^- Con-
ser\ation <>f nKiniciilum then recjuires:

niv

llV C = (llv' f ) cos 9H ;^r : COS A,

(8b)
()= (hv ■ c) sin 0-\ , sin <^.

Kliminating <t> and v between these three ecjuations, we arrive at
this relation between v and v' , the frequencies of the impinging quan-
tum and the recoiling quantum — or, as I shall hereafter say, between
the frequencies of the primary- X-ray and the scattered X-ray -and
the angle 0 between the dircitinns (if liic piimar\' X-ra\' and the
scattered X-ra>- :

. (9)

" l-|--'^,(l-cos9)
mc-

" If the reader prefers to use the familiar expressions \mv' for the kinetic energy
and »n< for the magnitude of the momentum of the electron, he will arrive at a
formula for v' which, while apparently dissimilar to (9) and not so elegant, is ap-
proximately identical with it when v is not too large — or, which comes practically
to the same thing, when hv is small in comparison with mc'; a condition which is
realized for all X-rays now being profluced.

SOME CONTE.\fPOR.IRy .'tnr.tXCRS IN PItVSICS-ril 315

The relation between X' and X, the wavelengths of the primary
l>eani and of the scattered beam, is still simpler, heiii^

X'-X=-^(l-cose). (10)

mc

•

The intrusion of this anijle 6 into the final equation may seem to
contradict my earlier statement that the results of the impact are
calculable; for it is true that there are not equations enough to elimi-
nate 6. and yet I have offered no additional means of calculating it.
In fact it cannot be calculated with the data at our command. All
that we are able to say is that if the resulting quantum goes ofT in
the direction 6, then its frequency is given b>- (9). What deter-
mines 6 in any particular case? Re\ erting to the image of the billiard-
balls, it is easy to see that the direction in which the rebounding ball
rolls away depends on whether it gave a central blow, or a glancing
blow, or something in between, to the initially stationary ball. If
we knew just which sort of a blow was going to be giv-en, we could
calculate B; otherwise we can only apply our conditions of conservation
of energ^y and conservation of momentum to ascertain just how much
of its energ>- the rebounding ball retains when 8 has some particular
value, and then produce — or, if we cannot produce at will, await — a
collision which results in that value, and make our comparison of
experiment with theory. So it is in this case of the rebounding quan-
tum. When a beam of primary electrons is scattered by encountering
a piece of matter, some quanta rebound in each direction, and all the
values of 9 are represented. We cannot know what determines the
particular value of 6 in any case; but we can at least select any direc-
tion we desire, measure the frequency of the quanta which have
rebounded in that direction, and compare it with the formula. Fig. 6
is a diagram illustrating these relations."

The comparison, which has now been made repealedU' b\- Compton,
repeatedly by P. A. Ross, and once or oftener by each of several other
physicists — notably de Broglie in Paris — is highly gratifying. The
value of the frequency-difference between the primar\- X-rays and
the scattered X-rays, that is to say, between the impinging quanta
and the rebounding quanta, is in excellent accord with the formula,
whether the measurements be made on the quanta recoiling at 45°,
at 90° or at 135°, or at intermediate values of the angle 6. The
method consists in receiving the beam of scattered X-rays into an
X-ray spectroscope, whereby it is deflected against an ionization-
chamber or a photographic plate at a particular point, of which the

Jib HLI.L SYSTEM TECIIMC.U. JOIKX.U.

location is the measure of the wave-length. An image can be made
on the same plate at the point where the beam would have struck it,
if it had retained the frequency of the primary beam. The two
images then stand sharpK- and widely apart. Indeed it is not neces-
sary to make a special image to mark the place on the plate where
a scattered beam of unmodified wave-length would fall, for there

Fig. 6 — Diagram sliowing the energy-relations ensuing upon an impact between a
riuanlum and a free electron. {.After Uebye.) See footnote 13

nearly always is such a beam aiui such an image. .\ plausible ex-
planation is easy to find; one has onh' to assume that the ciuania
composing this beam have rebounded from electrons so rigidK' bound
into atoms that they did not budge when the impinging quanta struck
tiuiu. ,uid liusi' were reflected as fnnii an inimoxabli' wall."

" The iliagrani in I'ig. 6 is designed to illustrate the relations between the energy
of the primary' quantum (radius of the dotted semicircle), the encrg>' of the re-
bounding (juantum (radius of the upper continuous curve), and the energy of the
recoiling electron (radius of the lower continuous curve). Thus the two arrows
marked with a .S are proportional respect i\el\' to the energies of the secondary
quantum and of the recoiling electron, when the encounter has taken place in such
a fashion that the angle 9 is equal to the angle lietween the arrow 10 and the upper
arrow .S. In the same case, the angle between arrow 10 and_ lower arrow 5 is equal
to tp of the ecpiations (9).

" .\s a matter of fad we have no Independent mc.ins of knowing that the recoiling
electrons are initially free, or that t-lie scattered be.im with the modified frequency
originates from collisions of primary quant. i with initi.dly free electrons; we know
<>nly thai the frequency of the scattered (pianta is such as would be expected if
little or no energy is s|H-nt in freeing the electrons, and little or no momentum is
transferred otherwise than to the electrons — which, of course, is not quite the same

soMi: COM i:Mi'OK.iKy .ii>i .ixcis i\ I'livsns ni .Ji7

In ilif |>lu>i(ii;raphs whirh I rcpnuliice," the imprints of tlu-si' two
Ih-.uiis st.md side l)y side. In tlu' tirst of them, l-"ij;. 7. the spectriini
of the primary rays is s|x-iially depicted on the upper lialf of the
plate: one sees the n, d, and ■> hnes of the A'-series of molyhdenuin.
three hnes (the first a tloiihlet ) of wliirh the \va\eleiii;th> ,iro respec-

%

Fig. 7 — At)ove, the A.'-siK>ctrum of niolylKienum (a-doublct, /S-liiic. v-line from left

to right); below, the s[)cctruni of this same radiation after scattering at 90° from

aluminum (each line doubled). (P. .■\. Ross)

tively .710— .7l4.\. .()33A, .(ilSA. Below, the spertnini of the
sec«>ndary rays scattered at the angle 9 is sprearl out: to each of the
primary rays there correspmnds a scattered ray of the same wave-
length, and beside it another ray of which the wavelength exceeds
that of its companion by the required amount.

thing. The Compton effeit has lieen demonstratetl only where there are electrons
associated with atoms. It may lie that the rebound occurs only from an electron
which is connectefl to an atom by some [K-culiar liaison, weak so far as the energy
required to break it is concerne<l, but able to control the rcs|>onse of the electron
to an impact. Something of this son may have to be assumed to explain why the
effect is apjjarcntly not greater for conductive substances than for insulating ones
and is certainly feebler for massive atoms with numerous loosely-liound electrons
than for light atoms with few.

" I am indebtcti to I'rofessor Ross for thcsf photographs.

318

BELL SYSTEM TECHNICAL JOURNAL

Another series of photographs, in I'"ig. 8, shows the two scattered
rays produced when a beam of the A'a-radiation of inoK bdenum falls
upon various scattering substances: carbon (the sixth element of the
periodic table), aluminium (the thirteenth), copper (the twenty-ninth),
and silver (the forty-seventh). The relative intensity of the two
rays — that is to say, the proportion between the number of quanta
which rebound as from free electrons, and ilie nuinlier of quanta
which recoil as from immobile oiistacles — varii'^ in .1 curious manner

Fig. 8 — Above, the A' a-line of molybdenum; below, the same radiation after scatter-
ing at 90° from carbon, aluminium, copper and silver. (P. A. Ross)

from one of these elements to .mother. Mo^~i ol the (|uanta scat-
tered by lithium undergo the alter, ilion in wa\e1eni;th which we have
calculated; nearly all of the quanta scatlcreil by lead emerge with
the same frequency as the incident quanta. Apparently, the heavier
the atoms of a substance are, the less conspicuous does Compton's
effect become. Further, the relative intensity of the two rays as-
sumes different values for one and the same substance, depending
on the direction of scattering. This is illustrated in Fig. 9, the curves
of which may be interpreted as graphical representations of photo-
graphs like those of the foregoing Figure, the ordinate standing for
the density of the image on the photographic plate. (Actually, the
ordinate stands for a quantity which is much more nearly propor-
tional to the true intensity of the rays — that is, the amount of ioniza-
tion which they produce in a dense gas.) These cur\es show, in the
first place, that the separation between the two scattered rays has
the proper theoretical values at the angle 45°, at i)0°, and at 135°; in
the second place, among the quanta scattered at 45°, those that

SOMR CONTF.MPOR.lRy .IIU\IXCl:S IX riiySICS ril .110

rfl.iiii ilu- primary wavclcnutli are inore aluinil.ml ihan tlic allerfd
(luanta. whik- amonn the <inanta scattered at 13")° the modified ones
liavf the pritlominanee. Why tlie relative (-ommnnncss of ihc-^c \\\i<
kinds of Malleriiiif, of these two modes of iiiUr.iriinii liciwccii (|ii,irM.i

t

I

1 1

»OU'SDi.-<l,r«

' 1 M LI!.-t

T M11.J11

,-Ji L , . . ,

' "^^w\ "^

B ^\

1

1 SC»tTC-.<!ti BT

y ORArUITC AT

i

\ "•

•^It

^.sL

. . 1 , . ,

e

7 11 3C*-.-TKniD

i\I \ -'

' il

>.

J

1 , , 1

0 i
.fl\ f

, • , \v 1

to«

•"*>' CALCITl »* ♦°«0

IL Fi,.4

I'ig. 9 — The modified and iinnicKlitied scattered rays, at various inclinations, recorded

l)y the ionization-chamber method. The vertical line 7" represents the position

calculatetl from {')) lor the modified ray. (A. H. Compton, Physical Revinv)

and matter, should depend on the substance and on the angle 6 is a
deeper question than any we have considered.

The recoiling electrf)ns also have been detected; and Figs. 10 and 1 1 .
which are photographs of the trails left by flying electrons as they

^"5

o £

«s

.5 2

'5 "rt

s«>\// COM I uroh'.iKv inrixcis i\ riiysits in ,iji

priHi-i-tl tlii'DUKii .lir Mii)i'i>.iliir.iif«l willi w.id-r vapor, shows f\i(lciu-e
lor ilu'sc.'* 'V\\v long sinuous trails an- those of fast i-IiTtrons, which
wiri' liht-ralfd from their atoms l>\ hinli-fre(iuen(>- (jnanta proceeding
across the gas; each of these electrons possesses the entire energy
of a \ai)islu'i| ((uantuni (minus sue!) |>arl of it .1^ w.i^ v^irriticci! when

l-ig. II — Trails of rciMiillng C'livlrons (C.T. R. Wilson, Proreeiliiie,s of Ihe Royiit Society)

the electron emerged from its atoni). The small sligliilv -clotigated
comma-like "blobs", the "fish tracks" as t\ '1'. R. Wilson called
them, are the trails of very slow electrons — these are the electrons
from which quanta rebounded, transferring in the reboimd a little of
their energy and a little of their momentum. These appear only when
the frequency of the X-ray quanta exceeds a certain minimum amount
— a circumstance which, combined with others, shows that the com-

'• I am inilcl)tc<l to Professor C. T. R. Wilson and to the Si-crctary of the Royal
Society for permission to repriKluce these photographs.

322 BELL SYSTEM TECHNICAL JOURNAL

monness of the Compton effect depends not merely on the nature of
tlie atoms and on the angle at which the scattering is observed, but
also upon the frequency of the radiation. High-frcciiicncy quanta
are liable to rebound in the manner prescribed 1)\' Compion's assump-
tions, but low-frequency quanta are not. Light of the visible spec-
trum suffers no change in wavelength when it is scattered.

Must we now concede that radiant energy travels about through
space in the form of atom-like units, of corpuscles, of quanta every
one of w'hich, for a radiation of a specific frequency v, possesses always
the same energy hu and always the same momentum hv, c? How
indeed can we longer avoid admitting it? The phenomena which
1 have cited do certainly seem to close the case be>ond any possi-
bility of reopening it. Vet they might be interpreted in another
way — a way which will probably seem e.xtremely elaborate and artificial
to the reader, a way which will seem like a mere e.xcuse to avoid
a simple and satisfying explanation; and yet this would not be
sufficient to condemn it utterh'. We might lay the whole blame and
burden for all these "quantum" phenomena upon the atom. We
might say that there is some mysterious mechanism inside every
atom, which constrains it never to emit radiation of a frequency v
unless it has a quantity of energy hv all packed up and ready to deliver,
and never to absorb radiation of a frequency v unless it has a special
storeroom ready to receive just exactly the quantity of energy bf.
This indeed is not a bad formulation of Bohr's theory of the atom.
It would be necessary to go much further, and to say that not only
e\ery atom, but likewise every assemblage of atoms forming a liquid
or a solid body, contains such a mechanism of its own; for the phe-
nomena which I have called the "photoelectric effect" and the "inverse
photoelectric effect" are qualities not of individual atoms, but of
l)ieces of solid metal." And it would be necessar\- to go much funlRi
yet, and make mechanisms to account for the transfer of nionuntuin
from radiation to electrons.

\ (.1 i\cii ill is would not be sufficient; for the most surprising and
inexplicable fad of all is still to be presented. Here is the crux of
the great dilemma. Imagine radiation of the frequency v emerging
from an atom, for a length of time determined by the condition that

" It was formerly contended that this explanation, while applicable to the be-
havior of free atoms which respond only to certain discrete frequencies, would not
avail for a solid substance like sodium which delivers up electrons with energy hv,
whatever the frei|uency v may be. This contention, however, is probably not
forcible, as it can be supposed that the solid has a very great number of natural
frequencies very close together. This in fact was the inference from Epstein's
theory of the photoelectric elTecl.

soMi: coxi r.Mi'ou.ih') .ii'i'.i.Xiis i\ riivsics rii 323

the total energy radiated shall be hv exactly. ArrordiiiK to tiic wave-
theory, it einerKes as a spherical wave-train, of which the wave-
fronts are a series of expanilinj; spheres, widening in all liirections
away from the atom at their common centre. Place another atom
of the same kind some little tiistance away. Apparently it can
absorb no radiant energy at all, unless it absorbs the whole anioiiiu
Ity radiated from the first atom. But how can it do this, seeing that
only a very small portion of each wavefront touched it f)r came any-
where near it, and much of the radiant energy went ofl from the first
atonj in a diametrically opposite direction? How can il reach and
suck up all the energy from the entire wavefront, so little of which it
actually intercepts? And the difficulty with the momentimi is (•\cn
greater.

But, of course, this experiment is unreaii/able. In any laboralor\-
experinient, there are always great multitudes of radiating atoms
close together, and the atoms exposed to the radiation are bathed in
myriads of wave-trains proceeding from myriads of sources. Does
then the atom which absorbs the amount liv of energy take it in little
bits, one from this wavetrain and another from that, until the proper
capital is laid up? But if so, it surely would reciuire some appreciable
time to gather up the separate amounts. According to the classical
electromagnetic theory, a bound electron placed in a wavetrain of
wavelength X will gather up energy from an area of each wavefront.
of the order of magnitude of the quantity X-. Hence we should not
expect that the exposed atom would finish the task of assembling the
amount of energy hv from the various wavetrains which pass by it,
until the lapse of a time-interval sufificient for so much energy to flow
against a circle of the area X-, set up facing the rays at the point
where the atom stands. Set up a mercury arc, or better still, an
X-ray tube, and measure the intensity of the radiation from it at
various distances. You will easily find a position sufficiently near
to it for convenience, and yet sufficiently far from it, so that if a
circular target of this area were set in that position, the radiant energy
falling upon it would not mount up in one minute — nor in one day
— nor in one year, to the amount hv. Yet cover the source of rays
with a shutter, and then put a piece of matter in that position, and
then lift the shutter; and you will not have to wait a year, nor a day,
nor a minute, for the first electron which emerges from the matter
with a whole quantum of energy; it will come out so quickly that no
experimenter has, as yet, demonstrated a delay. What possible
assumptions about the structure of the alom can account for this?

More and more the evidence is piled up to compel us to concede

324 BL/J. SVST/IM TECIISICAL JOLRNAL

that radiation traxi'ls around the world in corpuscles of energy hv
and momentum hv c, which never expand, or at all events always
remain small enough to be swallowed up in one gulp by an atom, or
to strike an electron with one single concentrated l)low.

But it is unfair to close the case without |)leading once more the
cause of the undulatory theory — the more so because, in the usual
fashion, I have understated the old and presumptively familiar
arguments in its faNor, and gi\eii all tlic advantages to the arguments
of the opposition, which still Ikim' liic force and charm of novelty.
Furthermore, I ma\- ha\e i^roduced the impression that the conception
of the qiiantimi actualh' unites the corpuscular theory with the wave-
theory, mitigating discord instead of creating it. Why are we not
really \-oicing a perfectly competent wave-theor\- of light, when we
imagine wave-trains limited both in length and in breadth, so narrow
thai they can di\e into an atom, but so long that they contain hv of
energy altogether?.A7a;«CH/an' wave-trains, so to speak, like the tracing
of a sine-wave in chalk upon a blackboard, or the familiar picture of
a sea-serpent.-'

Well, the dilticuity is ihat I hi' pjicnomcna ol iiUcrtcrence and ot
diffraction, which are the basis of the wave-theory, imply that the
wave-trains are broad, that the>' ha\e a consitlerable cross-sectional
area; these phenomena should not occui-. if \\\v wave-trains were
filaments no thicker than an atom, or e\cn so wide that their cross-
sectional area amounted to X-'. Let me cite one or two of these
phenomena, in tardy justice to the imdulatory theory, as a sort of a
makeweight to all the "(|ii.intum " phciminena I have described.
Imagine an opatjue screen witji a slit in it; light flows against the
screen from behind, some passes through the slit. The slit may be
supposed to be half a millimetre wide, or e\en wider. If light consists
of (|uanta only as thick as an atonj. or i-\en as thick as the wave-
length of the light, they will shoot ihn)ui;ii the slit like raindrops or
sand-grains through a wide open sk\lighl. If i1h\' are all mo\ing in
jjarallel directions before the>' reach the sHl, tiie\- will continue so to
mov-e after the>' pass through it— for how shall the\- know that the slit
has any boundaries, since they are so small and the slit is so large/
The beam of light which has passed through the slit will always
retain the same cross-section as the slit. But we know that in truth
the beam widens after it goes through the slit, and it develops a
peculiar distribution of intensity which is accurately the same as we
should expect, if the wavefront is ivider than the slit — so much wider,
that the slit cuts a piece out of it, which piece spreads outwards inde-

soMii coxir.Mi'nK iRv .inr.ixcis ix I'liy^ics rii .us

fHMuU'iilly in its own f-ishion.'*. TluTi-fori' tin- (|uantiin) imisl hv widt-r
than the widest slit which displays rlear ditTraitiDn-phenoniena- and
this makes it at least a millimetre wide! Mut this is not the limit!
("ut another slit in the screen, parallel to the first one, a distance d
away from it. Where the widening; ililTracted li^ht-beams from the
two slits interpenetrate one another, they will produce interferern-e-
pat terns of li^ht and shade, accurately the sanie as we should expect
if the wavefront is wider than the distance d. The quantum must
therefore be wider than the Krt*'>tt-'!^l distance between two slits, the
liv;hi-l)eams passing throuijh which are able to interfere with one
another. The slits may be put cpiite far apart, and the light-beams
brought together by systems of prisms and mirrors. This is the
principle of Michelson's famous method of determining the diameters
of stars. He obtained interference fringes when the two beams of
light were taken from portions of the wavefront twenty feet apart!^^

Therefore the quantum is twenty feet wide! This is the object
from which an atom one ten-millionth of a millimetre wiile can suck
up all its energy! this is what enters as a unit into collision with an
electron ten thousandfold smaller yet!

The evidence is now before the reader: iiol tlu- entire exidenre for
either of the two conceptions of radiation, but, I think, a fair sampling
for both. If either view has been ine(|uitably treated, it is the un-
dulatory theory which has been underrated; for, as I have said already
but cannot say too often, the e\idence that light partakes of the nature
of a wave-motion is tremendously extensi\e and tremendously com-
|ielling; it seems the less powerful only because it is so thoroughly
familiar, and through much repetition has lost the force of no\elty.
.Still, it is not necessary to hold all the rele\ant facts continually in
mind. If one could reconcile a single typical fact of the one sort, such
as the interference between beams of light brought together from par-
allel courses far apart, with a single outstanding fact of the other sort,
sach as the instantaneous emergence of electrons with great energy
from atoms upon which a feeble beam of light has only just been
directed — if one could unify two such phenomena as these, all of the
others would probably fuse spontaneously into a harmonious system.
Hut in thinking about these things, there is one more all-important

''■ ( )nc might, of course, inquire, why should a piece of the uavefronl of a quantum,
rut out of it by the edges of a slit, expaml after passing through the slit when the
quantum itself apparently rushes through spaie without expanding?

" It might be argued that these quanta from stars have come an enormously
long way, and possibly have had a lx;tter chance to expand than the quanta passing
across a laboratory room from an X-ray tube or a mercury arc to a metal plate.
However, since the photoelectric cell is used to measure the brightness of a star, they
evidently prixluce the same sort of photoelectric effect as newborn quanta.

326 BELL SYSTEM TECHNICAL JOURNAL

fact that must never be forgotten: the quantum-theory involxcs the
wave-theory in its root and basis, for the quantum of a given radiation
is defined in terms of the frequency of that radiation, and the frequency
is determined from the wavelength, and the wavelength is determined
by applying the wave-theory to measurements on interference and dif-
fraction patterns. Was there ever an instance in which two such
apparently contradictory theories were wo\en so intiniatcK' the one
with the otiier!

The fusion of the theories is not likely to result from new experi-
mental c\idence. Indeed there are already indications that further
experiments will mereh' accentuate the strangeness, much as happened
with the numerous experiments de\ised and performed three or four
decades ago in the hope of settling whether the earth does or does not
move relatively to the aether. More probably what is required is a
modification, indeed a revolutionary extension in the art of thinking —
such a revolution as look place among a few mathematicians when non-
luididean geometry was established by the side of Euclidean, as is
taking place today among the disciples of Einstein who are striving
to unlearn the habitual distinctions between time and space — such a
revolution, to go centuries back into the past, as occurred in the minds
of men generally when they learned to realize that the earth is round,
and yet at every place upon it the sky is above and the ground is
below. Our descendants may think pityingly of us as we of our
ancestors, who could not comprehend how a man can stand upright
at the Antipodes.

Wave Propagation Over Parallel Tubular

Conductors:

The Alternating Current Resistance

By SALLIE PERO MEAD

Synopsis: On the b.isis of Maxwell's laws and the conditions of con-
tinuity of electric and magnetic forces at the surfaces of the conductor, the
fundamental equations are established for the axial electric force and the
tangential magnetic force in a non-magnetic tubular conductor with parallel
return. The alternating current resistance per unit length is then derived
as the mean dissipation per unit length divided by the mean square current.
The general formula is expresse<l as the product of the alternating current
resistance of the conductor with concentric return and a factor, termed
the "proximity effect correction factor," which formulates the efTert nf
the proximity of the parallel return conductor. The auxiliary functions which
appear in the general formula are each given by the product of the cor-
responding function for the case of a solid wire and a factor involving the
variable inner iKiundary of the conductor.

In general, the resistance may be calculated from this formula, using
tables of P :ssel functions. The most important practical cases, however,
usually in.vjivc only the limiting forms of the Bessel functions. Special
formulae of this kintl are given for the case of relatively large conductors,
with high impressed frequencies, and for thin tubes. .A set of curves illus-
trates the application of the formulae.

I. Introduction

WHI-IRK circular conductors of relatively large diameter are
under consideration, the effect on the alternating current
risistance of the tubular as distinguished from the solid cylindrical
form becomes of practical importance. Mr. Herbert B. Dwight has
worked on a special case of this problem and developed a formula
for the ratio of alternating to direct current resistance in a circuit
a)mposed of two parallel tubes when the tubes are thin.' As infinite
sums of infinite series are involved, however, his result is not well
adapted to computation.

Mr. John R. Carson has gi\en a complete solution for tlie alter-
nating current resistance of two parallel solid wires in his paper
"Wave Propagation Over Parallel Wires: The Proximity Effect,"
Phil. Mag., April, 1921. The analysis of that paper may readily be
extended to the more general case of propagation over two tubular
conductors by a parallel method of development. This is done in
the present paper. As the underKing theory is identical in the two
problems, familiarity with the former pajier will be assumed and the
analysis will merely be sketched after the fundamental equations are
established.

' "Proximity Effect in Wires and Thin Tubes," Trans. .1. /. E. £., Vol. XLll
(.1923), p. 850.

327

328 BELL SYSTEM TECIIKICAL JOURNAL

In this paper formulae for the alternating current resistance have
been worked out in detail with particular reference to the case of
relatively large conductors at high frequencies and to relati\ely
thin tubes. In general the auxiliary functions involved are expressed
as the product of the corresponding functions for solid wires by a
correction factor which formulates the greater generality due to
the variable inner boundary of the conductors. As far as possible
the symbols are the same as in the solid wire case but refer now to
the system of tubular conductors. Primes are added where the
letters denote the corresponding functions for the solid wire case.
This will hardly lead to confusion with the primes used in connection
with the Bessel functions to denote differentiation.

The general solution is developed in section II. The alternating
current resistance of one of the tubular conductors is expressed as the
product of the alternating current resistance of the conductor with
concentric return and a factor which formulates the effect of the
proximity of the parallel return conductor. Section III is a sum-
mary of the general formula, special asymptotic forms and forms
for thin conductors.

II. Ma IIIKMA IH AI. AXAI.VSIS AM) 1 )KKIVATI( >N OK FORMULAE

We require the expression for the axial electric force, £:, in the
conductors. Since the tubular condiuior does not extend to r = 0,
the electric force must be expressed !>> the more general I'ourier-
Bessel expansion,

£z= ^ An{Jn{p) + \„K„(p)\ cos ne,

where

p = />\/47rX/i/u)

= ^ = xi\/i when r = a

= i= yiy/i when r = a,

a and a being the outer and inner radii, respectively, of the con-
ductors. The additional set of constants X„, Xi . . . Xn is to be deter-
mined b>' the conditions of continuity at the inner boundary of the
conductor. It is necessary to satisfy the boundary conditions at the
surface of one conductor only, since the symmetry of the system
insures that they will then be satisfied at the surface of the other also.

/'A'( »/'.»(;. 7 //o.v oj/K i:ii\'.ii.i.ii. ( (».\7'(t /('Ms .w

In the dielectric space inside the lube where r<«, the axial elerlric
force may l>e written

00

E,= y^CnJn(p)cn»ne. (1)

or replacini; tlu- liesscl functions by their \alucs for vaiiihliinnly
small argunuMiis,

£, = V" p^r' cos ti9 (2)

where A.. Di . . . D„ are constants determined !>>• the bounfl.irx- condi-
tions. Applying Maxwell's law relating the normal and tauten li.il
magnetic forces //, and IIq to the axial electric force, gives

nii^-Ilg = '' ^ -1 n [Jn'ip) + X„A."„(p)l cos nO, (3)

pi=()

nioiIlr = -^A„ (y„(p) + X„A'„(p)lsin ne, (4)

for the s()ace inside the conductor, and

iuillg = ^ nPnr"-^ cos }iO. (5)

n=0

foi//, = V" nn„r"-^ sin uO, (6)

«=o

for the inner dielectric (/i = l). Equating the two expressions for
the tangential magnetic force Hf, and for the normal magnetic in-
duction nH, term b>- term at the surface r = a,

Ify,'(M-,i«A(f)l+X,lfAV(f)-|x«A',(nl = 0. (7)

Whence, for the practically important case of non-magnetic con-
ductors in which n = l, we have

and

£' = 2 ^" [•^"(P) - ^;^j ^-(P)] cos >,0. (9)

330 BELL SYSTEM TECHNICAL JOURNAL

In the subsequent analysis /„ (?) of the solution for the solid wire
case is replaced by

M&-{^-lK„{i) = Mn{i), (10)

and Jn (?) is replaced by

A'(^)-^^/^n'(?) =-!/„'(?). (in

Otherwise the formulation of the alternating current resistance of
the conductor proceeds exactly as in the solid wire case. For the
electric force at the surface r=a in the conductor, we write

R..=Ao{Mo{i)+hiMM) cose+/7o.Uo(t) cos 29+ . . .] (12)

and determine the fundamental coefficient Ao in terms of the current
in the conductor. The resistance R of the tubular conductor per
unit length is defined as the mean dissipation per unit length (li\ided
by the mean square current where the mean dissiiiaiion is calculated
by Po)-nting's theorem. Accordingly, we get

' ..=1 '

To determine the harmonic coefficients h\ . . . hn or Ai . . . An,
the total tangential magnetic force and the total normal magnetic
induction at the outer surface of a conductor are expressed in terms
of the coordinates of that conductor alone, and the conditions of
continuity at the surface are applied. This leads to the set of equations

q„ = {-\r2p„k"-^=^ p„k"^J.q) (14)

= 1.2,3 ... «

where

<7, = (?ilV (O-WMMn (?))/{ M'ii),

p, = (^l/»'(f)-WMM,(?))/(.l/„'(f)+M/i.U„(?)),
Qn = trjln.

/•AV )/•./(,". 1 7 /r),V >iriR I'.tK.II.III. COM'I iTOIfS .Ml

Wliiii ihc (HTmeabilily is unity, the solution, to the same order of
approximation as in the solid wire case, is

(ifi)

where

V 2 />[«i(»o+fo)-ri(;<o-t'o)l-(/[«i(/<o-ru) +ri(Ho+t'o)l , , _,

Pn = {-l}"2k's", H = l,2 . . . 00,

■ - (2*)=
Since the resistance R„ of an isolated tubular conductor is given by
/?„_Real^--^^^ (19)

equation (13) becomes equation (I) of the formulae in the next section.
This is the general solution for the case of non-magnetic conductors.
In general R may be calculated from this formula and tables of
Bessel functions. The ber, bei, ker and kei functions - and the recur-
rence fonnulae are sufficient to evaluate the Bessel functions but
the process is long. In the most important practical cases, the
conductors are rather large and the applied frequencies fairly high.
When this is true as well as when the tubes are very thin the formulae
usually involve only the limiting forms of the Bessel functions. These
s[H'cial results are gi\cn in the next section.

III. .AlTERNATIM, ClRRENT RkSIST.WCE FoRMUI..\E FOR
XoN-M.\(..\KTir COVDITTORS

The symlKils used are :

a =outer radius of conductor in centimeters,

a = inner radius of conductor in centimeters, v

(" = interaxial separation between conductors in centimeters,

k=a c

X = conductivity of conductor in electroinagnetic c.g.s. units,

- .\ convenient table of these functions for arguments from 0 to 10 at intervals of
0.1 is incorporated in Mr. Dwight's paper ".\ Precise Mcthorl of Calculation of
Skin Kffect in Isolated Tulies," /. A. I. E. E., Aug., 1923.

3i2 BELL SySTHM TECHNICAL JOURNAL

;i = permeability of conductor in electromagnetic c.g.s. units,
co = 2ir times frequency in cycles per second,
t = \/^
X = ay/ AirKiii

y = a\/4irXa)

i = yiVi
X.,= -y„+.(f)/ii:„+i(f)

/«(?) =Un-\-iVn

= Bessel function of first kind of cirdiT /; .uui ari;uiiiL'nt xiy/i,

ii„'-\-iv„' =

dk

dJni^)

dx

K (^) = Bessel function of second kind of order ;/ and argument xi\/i,
dK„{^)

i? = resistancc per unit length of tubular conductor with parallel
return,

^0 = resistance per unit icngtli of tubular conductor with con-
centric return in electromagnetic c.g.s. units,

C = proximity effect correction factor,

R = CRo. (I)

The auxiliary functions invoKed are:

M Uollo'+Vc

,;?„^j;;,„(l-^"°"»+''t) (20^

\ m UoVo — Uo Vol

wlH-rc

/?-= 1 IJl»ot'o'-"o't'o (21)

a \ ttX Wi^+i'i"
= resistance of solid wire with (■(inccntric return,

'" + '"= i+x„/c„'(«)/yo'(«)" ^^^^

,.l, g[«l(»o-fo)+t'l(t<o+t'o)l^ fcyos

«=«^r"p[«.("o+t,)-t,(«„-t-„)ii' ^2^)

' The ratio R„/ R'. oscillates about unity which it approaches more and more
closely as the frec|Uency increases. It is clue to the fact that the phase of the current
in the inner portion of the solid conductor may be such as to oppose the current
in the outer portion, that the resistance of the solid conductor may be grcilcr than
that of the tube even though the heating effect in the latter is the greater.

I'Kor.ic.inox (Hi:i< r.iR.n.i.ii. iosdiutoks .vu

where

, n/'I Ui{Uo + Vo)-Hi(ll„-Vo) ,»..

where

.. + ,...(,„.^„„i.(l+44{|'). (28)

J-Vl-(2t)- (29)

- (2*)'
The formula for the correction factor (" is tlien

where

5,= N«^u-,F" s2-, (30)

Si=^^mvnk-''s-+K (31)

(32)

Kor large values of the argument
and the correction factor is

c=i+2 ^-^/V ^'^■-^/'+'/(i-4-)>--^0 nil)

w-n(l-l/\/2A.-)^ ^ L*^ 'V V2.v''J ^

When .V and y are both large quantities, the auxiliary functions are
as follows, provided terms of the second order in l/x and \/y are
negligible, n in d and h below being equal to the number of terms
in which Si and 52 converge to a required order of approximation.

With the notation

cos = cos-\/2(x — v) ,
sin=sin\/2(A: — v).
exp = exp [— \/2(x — _v)],
p ^ p,l + [(l+a)sin-(l-a)coslexp-a exp'
" ■^ l-[(l-6)sin + (H-6)cos]e.xp+6exp^ ^ '

M4 mil. I. srsrr.M riicnxic.ii. journ.il

where

0 = 1 —

b = l +

2-\/2.v 2V'2v'
3 3

2-v/2:c 2\/2y'
aRc'ywX ^ x'

(34)

wliere

^ , l + I(l-c)cos— (14-c) sin] exp-c exp' , ,

^ ^ 1-1(1+0 cos+(l-c) sin] exp + fexp'' ^ '

. 1 15

c = l —

2V2.r 2\/2)''
' = - V2/x, (36)

_ , 1 — ((1— rf) cos— (l+«f) sin] exp — rf exp-

whcre

d = l +
h = \ +

1 — [(1 + //) cos+(l— A) sin]exp+/2 exp^'

4>r-l 4(m + 1)-'-1
2\/2x 2\/2y '

4{n-iy-l 4(n + l)'-l

(37)

2V2x 2y/2y

' 1 2w-l ,_,

u<„ =—^ ^ — . (38)

\/2 2.V

At frefiiicnries sultuientK' lii^h to aftord practi(all\' skin coiuliutidii,
the following fornuilae indicate the way in whidi the resistance of

the tnl)nlar conductor approaches its limit, the resistance of the
solid wire.

R„=.Rj\±%I^''^^\ (39)
1 —2 cos exp

C = C„{\-A/x), (IV)

C. = }±|^,. (40)

A-2y/2 ^,-}A^2k^'f^'f\^^^^\. (41)
1— «V( (1— k's)- 1—2 cos exp)

I'h'OI'.ICIIlOX Orih' I'.tR.lt.l! I. (<)XI>C(T(^RS .U5

Whfn thf coiuluotors an- \ery thin IuIh's, i.e.. iliin as compared to
the radius, ((j— u) ii is lU'Cfssarily small and. in ni-nt-ral. .v— v is
small. Of course, wlii-n iht- frc<|ut'ncy is liiuli (.'nouKJi. .v— v becomes
large in any case. When this is true with respect to thin tubes, how-
ever, .V and V will usnaliy be lar^e enoui;li to ni.ike the asymptotic for-
mulae applicai)le: but, if x—y is small, tiie approximations

y»(n=A(j)-(j-nA'({) + --^f-'-^/'a),

reduce the correction factor lo

, .a — a

where p= ,

a

(1+^/2)' ^ cj
^ X+ff+ff-- do'

X*

.■=i+(„+.)>.+'"+'y"+^v.

and the resistance with concentric return to

" 2xXa(a-a) H-/3/2 " ^ ^

I 2)rXn(a — a) is. of course, the direct current resistance of a \ery thin
conductor.

If (a — a) a is very small and negligible compared w'ith 2n 'x-, where
n is the number of terms in which the series of (\') converge to a
re(|uired order of apprf>xiniati(»n.

j (i-— ")j y*-^+2*=.iog(i-*=.)i

2 \ 0 / I a - a I k*s'' )

336 BELL SYSTEM TECHNICAL JOURNAL

As a check on formulae (V) and (VI), the limiting cases may be
arrived at directly as follows. If the conductors are thin tubes,
the harmonic coefficients are given by

/», = (- l)«+'2;t" ^"^

4;-i)

When f is very large

= (-l)"2/fe"5", (44)

and

^-=^' = 1 (45)

Mo Mo'

so that

C=Real[l + igl/.„4;:conj.^,]

1-ifeV

(46)

the same result as for the corresponding liniitiiig case of a solid con-
ductor.

On the other hand, if ^ is not large and J — f is very small,

(47)
(48)
(49)

so that
and

//,.

= (-

-l)"+>

n

£(^

-f),

Mn
Mo

= 1,

Mn'

= -

in

Mo'

x{x —

y)'

C

= 1,

R

= Ro

= Rj.

„

(50)
(51)

I'KOr.lC.tllOM ori:R I'AR.M.I.EI. VOMHK'TOHS

where Rj, is the direct current resistance of the tliin tulmlar con-
ductor. K(is. (4t)) and (")()) a^;rce willi tlie corresponiliiin limits of
formulae V and VI respecti\el\ .

The curves of the acconipain in^ ligiiri- iV^ not prilcnd in re|)risent
the proximity elTecl correction factor with precision. Thex' .ire, how-
ever, accurate for thin tubes, and inchcate the order of inaKnitu<fe
of the factor for \arious vahies of the thickness of the tubular con-
ductor and show the nature of its \ariation with respect to the applied

r

~

'

—

—

Values

of Corr

ecti

in Facto

r C

1,

,

1 —

— ■

— ■

fc

«■ k

-0.2

5

^

,--

^^'

/

,y

'

/

y

/

/

/'

/

/

/

y

/

/

/

/

r

/

/

/

/

y

/

/

/

I

/

/

: !/

—

/

'

1

/

/

/

1

/

/

/

/

/

J

t

/

}

/

f

' /

/

/

/

'

/ '7

/

Y

/

/

/

^

iVay'ai/oo

y, ,

m/

/

0.01/^

^

/'■/

/ ^

/

A i

y

^

c^^

■^

^

1 t
Values of 3

c-a.\

fZn\

u

0 113 4 5 6 7

10 II 12 13 14 15 16 17 18 19 20

frequency. They are computed from formula (\') whicli is \alid
for quite high frequencies when the tubes are thin. When the thick-
ness of the tubes is greater, however, the range of validity with respect
to frequency is smaller, the dotted portions indicating a doubtful
degree of precision. It was previously pointed out in connection
with formula (I\') and is immediately deducible from physical con-
siderations, that all of the curves eventually coincide with the curve
for the solid wire which approaches the value 1.155 asymptotically.
As a simple application, suppose the resistance is required of a
tubular conductor with an outer radius of 0.4125 cm. (that of No. O
gauge A.W.Ci. copper wire) whose resistivity is 1090.5 electromagnetic

338 BELL SYSTEM TECIISICAL JOIRSAL

units i)iT (in., wluTf tluTO is an equal parallel rt-turn sn siui.ited tliat
k=0.2.") and a frequency of 5,000 c\'cles per second is applied to the
circuit. Then m = -\/47rXa) = 15.26 and .v- = /«a = 15.20X0.4125 = 0.30.
When the ratio of the thickness of the conductor to the radius is
greater than about 0.01 the prc)\iinit\- effect correction factor C is
appreciahk'. If the ratio is 0.05, reading C from the curves, gives
C= 1.004. I'roni formula (42), 7?o = 5.24 ohms per mi. wiiich makes
the resistance R = 'y.i>.\ ohms |)er mi.

Abstracts of Bell System Technical Papers

Not Appearing in this Journal

Voice- Frequency Carrier Telegraph System for Cables.^ H. P.
Hamilton, H. Nvgiisx. M. B. I.oxr. ami \V. P. Puki.is. Carrier
telegraph systems usinij frequencies above the voire range have been
in use for a number of years on open-wire lines. These systems,
however, are not suitable for long toll cable operation because cable
circuits greatly attenuate currents of high fretjuencies. The system
described in this paper uses frequencies in the voice range and is
specially adaptetl for operation on long four-wire cable circuits ten
or more telegraph circuits being obtainable from one four-wire circuit.
The siime carrier frecjuencies are used in both directions and are
spaceil 170 cycles apart. The carrier currents are supplied at each
terminal station by means of a single multi-frequency generator.

Metallic Polar-Duplex Telegraph System for Long Small-Gage Cables.-
John H. Bi;ll, R. B. Sh.\N( k, and D. E. Br.wson. In connection
with carrying out the toll-cable program of the Bell System, a metallic-
circuit polar-duplex telegraph system was developed. The metallic-
return type of circuit lends itself readily to the cable conditions, its
freedom from interference allowing the use of low potentials and
currents so that the telegraph may be superposed on tele[)hone cir-
cuits. The new system represents an unusual refinement in direct
current telegraph circuits, the operating current being of the same
order of magnitude as that of the telephone circuits on which the
telegraph is superposed.

The following are some of the outstanding features of the present
system. Sensitive relays with closely balanced windings are employed
in the metallic circuit, and "vibrating circuits" are provided for
minimizing distortion of signals. Repeaters are usually spaced
about 100 miles apart. Thirty-four-volt line batteries are used and
the line current is four or five milli-amperes on representative circuits.
Superposition is accomplished by the compositing method which
depends upon frequency discrimination, the telegraph occup\ing the
frequency range below that of the telephone. New local-circuit
arrangements have l)een designed, employing polar relays for repeti-
tion of the signals; these arrangements are suitable for use in making
up circuits in combination with carrier-current and ground-return
polar-duplex telegraph sections. New forms of mounting are em-

' Journal A. I. E. E.. Vol. 44, p. 213, 1925.

- Presented at the mid-winter convention of the .A. I. E. E., Feb., 1025.

340 BF.l.I. SYSTEM TECHNICAL JOURNAL

ployed in which a repeater is either built as a conipait unit or is
made up of several units which are mounted on I-beams, and sub-
sequently interconnected. In the latter case the usual arrangements
for sending and receiving from the repeater are omitted, and a sep-
arate "monitoring" unit provided for connection to any one of a
group of repeaters.

The metallic system is suitable for providing circuits up to 1,000
miles or more in length, the grade of service being better than that
usually obtained from ground-return circuits on open-wire lines for
such distances. About 55,000 miles of this type of telegraph circuit
are in service at present.

Polarized Telegraph Relays} J. R. Fry and L. A. G.xrdixer.
This paper discusses two forms of polarized telegraph relay which
have been developed by the Bell System for metallic telegraph cir-
cuits and for carrier current telegraph circuits. Both relays are of
the same general construction except that one is more sensitive and
carries an auxiliary accelerating winding. The more sensiti\'e relay
is re(|uired to operate on reversals of line current of one miliiampere,
and at the same time retain its adjustment over long periods and
faithfully and accurately repeat signals. It is interesting to note
that under a\'crage conditions the ratio of power controlled by the
contact circuit to that required by the line windings is about 5,000
to one. The parts entering into the magnetic circuit of this relay
except for a permanent magnet, are made of the new magnetic alloy
(permalloy) recently developed in the Bell Telephone Laboratories.
Permalloy lends itself to use in this relay because of its high perme-
ability and very small residual effects. The design of the rela\-
armature and the support for the moving contacts is such that con-
tact chatter is practically eliminated. Photo-micrograms showing
practically no destructive action are given of the contacts of a relay
which was in continuous service for 8^2 months, during which time
each contact made and broke its circuit approximately 45, 000, 000
times.

Supervisory Systems for Remote Control.* J. C. Fikld. With tiie
great growth in power distributor systems and especially with the
advent of the automatic substations with no attendant there has arisen
need for a suiierxisory system to indicate to the central load dis-
patcher tlie position or operating condition of each important power
unit in the outlying stations and also to give him means to operate
promptly these power units when desired.

'Journal A. 1. E. E., Vol. 43, p. 223, 192S.

' Elfclrical Coiiiiiiuiiicalioiis, Vol. 3, pp.127-133, 1924.

.IBSIK.ICIS ()/• Hr.l.l. SYSTluM Tl-.CIINICAI. i'Al'ERS 341

By the turning of a key the dispatilu-r can (ipon or close any switch
or circuit breaker, start or stop any of tlu- machines and receive back
ahiiost instantly a visual anil continuous sij^nal of a red or green lamp.
The present systems provide in effect a key and two lamps, one red,
one green, for each unit sup»r\iM-d mounted in easy access of thi-
dis|Mtcher.

Two main systems known as the distributor supervisory and the
selector su|)ervisory have been developed to meet the varying con-
ditions of service.

The distributor system is recommended when there is a large num-
ber of units to be su[)ervised in a given station. It consists essen-
tially of two niotor-dri\en distributors, one in each station, running
in synchronism. Brushes on each distributor pass over correspond-
ing segments of two sets of 50 segments at the same instant. Thus
by means of only four connecting wires between the stations the con-
trol and continuous indication of 50 power units is possible.

The selector system is recommended when there is only a few
switches to be supervised in a single station or in several stations
located some distance apart. It consists essentially of hand oper-
ated keys to send predetermined codes of impulses to operate se-
lectively step by step selectors at the distant stations. After the
selector has operated the power unit, an auxiliary contact on this
unit operates a motor-driven key to send coded impulses to operate
a selector at the dispatcher's station to indicate the condition of the
unit by lighting a red or green lamp. Several stations can be super-
vised over the same three-line wires.

The dispatcher, by looking at the lamps on his control boaril, can
thus tell at all times the electrical and mechanical conditions at all
points in the system and has means to change the operating condi-
tions at any substation according to the demand for power.

Note on Dr. Louis Cohen's Paper on Alternating Current Cable
Telegraphy} L. A. M.acColl. This is a criticism of two papers
which were published in the Journal of the Franklin Institute by
Dr. Louis Cohen. It is shown that Cohen's development of the
theorj' of cable telegraphy contains many defects and errors, and in
particular that his criticisms of H. W. Malcolm's book, "The Theory
of the Submarine Telegraph and Telephone Cable," are without
foundation.

Telephone Circuit Unbalances, Determination of Magnitude and
Location.^ L. P. Ferris and R. G. McCurdv. This paper dis-

' Journal of the Franklin Institute, Vol. 199, p. 99, 1925.
• Journal A. I. E. E.. Vol. 43, p. 1 133, 1924.

342 BELL SYSTEM TECHXICAL JOIKXAL

cusses the (.'fleets of uiihalaiiccs ol ukphone eirciiits (in noise and
crosstalk, and describes nietiiods for (ieleeting the presence of these
unbalances and locating them when detected. The maintenance
of telephone circuits in a high state of efticiency with respect to
balance is important since iinlialances contribute to crosstalk between
telephone circuits and to noise when such circuits are inNohed in
inductive exposures. Difterent types of unbalances are included
and their effects under different conditions of energization of the
uni)aianced circuit and neighboring conductors are discussed. Methods
are described for determining:

(1) The general condition of c~ircuil> witli reN|)cTl lo balancr liy
crosstalk measurements from tluir t(iniiiia!>.

(2) The approximate location ol unlialaiue> aloiii; a iiiU' !)>• iiicas-
iireincnls o\'er a rangi' of freciui'urio willi .i liri(li;t- ai one end ol ihe
line.

(3) The final location of unbal.inci^ li\ liclil inc.i>nrenuiiis wiiji
an unbalance deieclor whicii nKi> hi' opcraiiil li\ .i lini-nian .iiul
w iiirh usual I\" does nol re(|uire intiTrnpl ion ol Icicplione service, I'xci-pt
inonu'nlarily.

Toil circuit oltice unbalances are brielK' discussed and a sjieci.d
bridge for detecting and measuring ihe tnibalances ol composite sets
is described. A mathematical treatment ol the bridge method for
locating unbalances and a discussion of the tiecessity of terminating
the circuits invoked in the tests in their characteristic line impetl-
anies are given in an appeiidi.x. The luethods and apparatus
described are wideK- tised in the Bell System and afford operating
telephone companies means for maintaining their circuits in the
condition of minimum practicable unbalance.

The Theory of Prohabilily and Some Applications lo F.ni;_iiiceriiii^
Problems.'' K. C". IMoi.iN.v. The |)urpose of this pajjcr is to sug-
gest a wider recognition b\- engineers of a body of principles which,
in lis mathematical form, is a powerful instrument for the solution
of practical problems. Certain fimdaiuental |irinciples of the theory
of probabilities are stated and ajiplied to three j)rol)lems from the
field of telephone engineering.

Note on the Least Mechanical Ei/nivalent of Lii^lit.'^ Hi;Kiu:Kr K.
Iviis. In this paper the \alue for ilie brightness of tin- bl.ick body
at the melting point of platinum reientK- obtained b\ ilu writer is

' Journal A. I. M. K., Vol. 44, p. 122, 1925.

'Journal of the Optical .Society of .-Xnifrican and Rev. of .Scicnlilic Inslruineiits,
Vol. Id, .N". .?, M.ircli, 1<)2.S, p. 289.

.iHMN.icis Oh HI. 1. 1. srsriM iia iixic.u. I'.iri.Rs m.\

ustnl to Kind a valiH- fur tin- U-ast nu'rhaiiic.il r(nii\'.iU-nl of li^jlil iisinj;
thi- latfst willies for tlu- Itl.ick Ixxly ronstaiils and llu- inciting point
of plaliiniM). Till- s|HTtral luminous I'lTicicncy curxi.' ol>laiii(.-(l by
T\iulall ami (iil)son is cuiployrd. It is found that omt tlii- t-nliri'
range of probable values of the black bod\- constants, the values for
the least mechanical e(|uivalent of IIkIu may be plotted as a straigln

line in liTtns of ' sn that llic prix'nl conipiii.ii ions may be I'x-

pressed in a simple e(iiiation in which any desired \aliies of the black
Ixnly constants may be inserted. I'sinj; the latest \-alues the least
mechanical equiN'alent of light is found to be .OOHil watts per lumen.
This is practicalK' iilentical with the value obtained by using the
author's earlier experimental determination using the monochromatic
green mercury light, when combined with the (iibson and Tyndall
liimuious efticiencN' cur\e.

Pholoelfdric Properties of Thin Films of Alkali Melals.' HisREiicr i
I-".. Ivi-:s. The thin hlms of alkali metals which deposit spontaneously
on clean metal surfaces in highh' exhausted inclosures are studied.
The alkali metals, sodium, potassiimi, rubidiimi. and caesium, in the
thin film form all exhibit, to a striking degree, the selectise plioio-
electric effect first discovered in sodium-potassium alloy. Kxperi-
ments on \arying the thickness of the deposited film show that the
selective effect only occurs at a certain stage of the tilni's (li\(l()[)-
ment; for \-ery thin films the selecti\'e effect is absent, .iiid il dis-
appears again for thick layers of the pure alkali metal. The wa\e-
Icngth maxima of emission previously ascribed to the selecti\e effect
in the pure alkali metals on the basis o{ observations with rough or
colloidal surfaces are absent in these thin films.

The Normal and Selective Photoelectric Effects in the Alkali MrUtIs
and Their Alloys.*" Hkrbkrt E. Ivks and A. L. Johnsri d. The
photoelectric currents from specular surfaces of molten sodiiuu. pol-
assiimi. rubidium, and caesium, and their alloys are studied at
\arious angles of incidence for the two principal planes of polariza-
tion. The selective photoelectric effect is clearly exhibited only in
the case of the lifjuid alloy of sodiimi and potassium. Wave-length
distribution curves show maxima of emission, which are usually, but
not always, most pronounced for light polarized with the electric
vector parallel to the plane of incidence. The wave-length maxima
previously assigned to the several elements are not confirmed; the

' .\strophysiral Journal, Vol. LX, No. 4, November, 1924.
"" .Xstrophysical Journal, Vol. LX, No. 4, November, 1924.

344 BELL SYSTEM TECIIXICAL JOURNAL

maxima vary in position for the same element willi tlie condition
and mode of preparation of the surface.

Theory of the Schroteffekt}^ T. C. Fry. The current from a
vacuum tube is composed of discrete particles of electricity which
emerge according to no regular law but in an accidental, statistical
fashion. The current therefore fluctuates with time. If the fluctua-
tions are amplified sufficiently they may be heard in a telephone
receiver as "noise" — a type of noise which is due to the mechanism
of electron emission itself and nfit to outside interference. This
noise is called the "SchrotefTekt."

The effect is of certain importance from the telephone standpoint,
for it appears that signals, the intensity of which is lower than that
of the accidental current fluctuations, can never be rendered intel-
ligible liy vacuum tube amplification since the noise due to the sta-
tistical fluctuations of space current would be amplified to the same
extent and would mask the signals. Fortunately, however, the
effect is much less pronounced under operating conditions than it is
under the conditions which are most favorable for laboratory study.
This is due to the fact that the presence of space charge under operat-
ing conditions smooths out the electron stream to a very material
extent, and thus reduces the tube noise. The limitation imposed
upon amplification is therefore not serious.

The present paper deals with what we have termed "laboratory
conditions" as distinct from "operating conditions." Its principal
result, arrived at by theoretical consideration, is: That if the elec-
trons are emitted independently of one another the intensity of the
noise in the measuring instrument is

S=VU'\,

where v is tlu' luiiiibiT of t'it'ctroiis I'liiillt'd per unit liiiii' and ?c'i is
the average over all electrons of the energ\' that each would have
caused to be dissipated in the measuring tle\ice if not other had eviT
been emitted.

When this formula is ajjpiicd to llic ty|)i' nf sinipK tuned circuil
that was considered by earlier writers, it leads to substantially the
the same results as they had obtained. It is more general than these
earlier results, however, and rests on less questionable methods of
derivation. It is, in fact, more general than the problem of the
SchrotefTekt itself and applies ecjually well to the absorption of
energ>' from any type of accidental disturbance which satisfies the
condition that the individual electromoti\-e impulses occur inde-

" Journal of Franklin Institute, Vol, 109, p. 203, 1925.

.IFSTRACTS OF PF.l.l. SYSTF.M TECIINICAL PAPERS 345

pciulently of one another. Static in r.iclio tek-phony anil rcrl.iiii
types of crosstalk probably satisf\- these conditions.

The Transmission i'nil." R. \'. L. H.vrti.ky. The Bell System
has recently adopted a new transmission unit, abbreviated TU, for
ex[>ressing those quantities which heretofore have been expressed in
miles of standard cable, or in Fairofie in terms of the fil unit. It *is
shown that units of this t>pe measure the logarithm of a ratio, and
that the present art reijuires that this ratio be tiiat of two amoimts
of [lower. Any of the proposed units may be so defined. Their
essential difference is in the ratio chosen to correspond to one unit.
The ratio chosen for the TU, 10 ' , makes it nearly the same in size
as the 800-cycIe mile, which has advantages. It also facilitates the
use of common logarithms in preference to natural logarithms for
which the ratio e of the /3/ unit is adapted. A distortionless refer-
ence system calibrated in 7"C/ is discussed, and conversion tables for
the various units are given.

The Thermionic Work Function of Oxide Coated Platinum}^ C.
D.wissoN anf! L. H. Germer. Measurements of the thermionic
work function of pure platinum coated with oxides of barium and
strontium have been made simultaneously by two methods for the
same segment of a uniformly heated filament. The theory of the
measurements and the experimental arrangements are the same as
used in an earlier e.xperiment on the thermionic work function of
pure tungsten." Filament temperatures accurate to ±5°, were found
from the resistance of the filament at 0° C. in conjunction with the
temperature coefficients of resistance, (l) In the Calorimclric method
the equivalent voltage of the work function was computed from the
sudden voltage change resulting from switching off the space current,
due to the cooling effect of the emission. The determination was
much more difficult that in the case of the tungsten filament, and
measurements were made at the signle temperature, 1064° K. At
this temperature the work function <i> was found to be equal to
l.70±.03 volts. (2) In the temperature \ariation method ii was
ftiund that, after the temperature had been changed suddenh from
one value to another, the emission changed approximately exponen-
tialh' from an initial value to a final steady value. The half value
pericKl of this change varied from a few seconds at high temperature
to over a quarter of an hour at low temperature. Interpreting this

'• Klectrical Communications, July, 1924. London Klectrician, January 16 and
U. 1025.

" Physical Review, Vol. 24, p. 666, 1924.

" Uavisson and Germer, Phys. Rev., 20, 300 (1922).

346 BEl.L SYSTEM TECTIMC.II. JOVRNAL

phenomenon as due to a progressi\-e and reversible change of the
character of the filament with temperature, the initial emissions after
temperature changes from 10(i4 K, were used to determine the b
constant of Richardson's et|uation corresponding to the c(|uilil)rium
character of the filament at 1004° K, and similar measurements
were made for the b constant corresponding to the character of the
filament at 911° K. The two determinations lead, through the
relationship <t> = bk/e, to 1.79 volts and 1.60 volts for the correspond-
ing values of (t>. For 10(54° K, then, the two methods give values
for <t> in agreement. The measurements are, howe\-er, not sufficiently
accurate to give any indication whether or not an electron within
the metal possesses the thermal energy '3kT/2. The various cor-
rections made and possible errors are thoroughly discussed. It is
pointed out that if the transition from the ecjuilibrium state at one
temperature to that at another had occurred so rapidly as to avoid
observation, a disagreement of 2.5 per cent, between the values of
<t> gi\'en by the Iwf) methods wnuKi lia\c been obtained wliicli miiL;lii
have been misinterpreted.

Contributors to this Issue

Hi;khi-,ki \:. I\i;s, U.S.. rni\rr^it>- ol l'riins\ K.mi^i. IIMI.'); I'li.I).,
Johns Hopkins. 1!)08; assistant and assistant |)h_\sirist, Hiireaii of
Standards. liU)S ()(); [)hysicist, Nila Ri-soarch I-ahoralory, ("kveland,
P.KH.t 12; physicist, rnited Cias IniprovcnR'nt C"onipan\'. F'hiladi-Iphi.x,
liU'2 18; r. S. .-\rniy Air SiT\icf, IDIS M); research iiijiiiuer. W'esteVn
Electric Company (Bell Telephone I,alK)ratories), 191!) to date.
Dr. Ives" work has had to do principally with the production, measure-
ment and utilization of liijlit.

J. \V. HuRToN, B.S., Massachusetts Institute of Technolojiy, 1914;
instructor in physics, 1914-lt); HnjjineerinR Department of the
Western Electric Company, 1911) — . Mr. Horton has been cfosely
connected with the development of apparatus for carrier current
commimication.

R.\i.zi;monu D. P.\kki:r. B.S., I'niversity of Michigan, 190.'); M.S.,
190(5; instructor in Electrical Engineering, l'ni\-ersity of Michigan,
l9(H>-09; assistant professor, 1909 1."?; Engineering Department,
.American Telephone and Telegraph Company, 1913-19; Department
of Development and Research, 1919 — . Mr. Parker's work has
related particularh- to telegraphy, included the development of
printing telegraph apparatus, carrier, and metallic circuit systems
for fine wire cables.

A. B. Cl..\RK, B.E.K., I'niversity of Michigan. 1911; .\nurican
Telephone and Telegraph Company, Engineering Department,
1911-19; Department of Development and Research, 1919 — . Mr.
Clark's work has been connected with toll telephone and telegraph
systems.

H. \V. Nichols, B.S., 1908. E.E.. 1911. Armour Institute of Tech-
nolog>-; M.S.. 1909, Ph.D., 1918. University of Chicago; Assistant
Professor of Electrical Engineering, Armour Institute of Technology,
1909-14; Engineering Department, Western Electric Company (Bell
Telephone Laboratories), 1914 — . Since 1916 Mr. Nichols has been
in charge of the laboratories research in radio communication.

J. C. ScHELLENG, A.B.. 1915; instructor in physics, Cornell I'ni-
versity, 191") 18; Engineering Department, Western Electric Com-
pany (Bell Telephone Laboratories), 191& — . Since 1918, Mr. Schelleng
has been engaged in research in radio communication.

347

348 BELL SYSTEM TECHNICAL JOVRKAL

T. C. Smith, B.S., Purdue l'niversit\-, 1010; Plain Kngineering,
New York Telephone Company, 1010 14; engineering construction
of high tension lines and municipal electric light plants. 1915; Outside
Plant Engineering, \ew York Telephone C"ompan\ . lOli; 19; Aulo-
moti\e Engineering, New York Telephone ("ompaiu, UU'.) L'l; Au-
tomotive and Construction Apparatus Engiiieerin;^, Anuric.in
Telephone and Telegraph Company, 1921 — .

John R. Carson, B.S., Prin.cKui. I'.IOT; E.E., 1909; M.S., 1912;
Re.search Department, Westinghouse Electric and Manufacturing
Company, 1910 12; instructor of ph>sics and electrical engineering,
Princeton, 1912-14; American Telephone and Telegraph Company,
Engineering Department, 1914-15; Patent Department, 1910 17;
Flngineering Department, 1918; Department of Development and
Research, 1919 — . Mr. Carson's work has been along theoretical
lines and he has published sexeral papers on theor\- of electric circuits
and elect ri( \va\c iiroiiagaticin.

Kaki. K. Dakkiiw, S.H., I ni\ersity of Chicago. I'.Ml: I ni\ersii\
of Paris, 1911 12; LiiiversiiN oi Berlin, 1912; Ph.D., in ph\sics anil
mathematics, l^niversity of Chicago, 1917; Engineering Department,
Western Electric Company, 1917-24; Bell Telephone Laboratories,
Inc., 1925 — . Mr. Darrow has been engaged largely in jireparing
studies and anahses of published research in \arious fields of ph\sics.

Sai.i.ik Pkko Mkad, A.B., Barnard College, 1913; M.A., Columbia
University, 1914; American Telei>honc and Telegraph Conipan\-,
Engineering Department, 1915 19; Department of De\eloi)ment
and Research, 1919 — . Mrs. Mead's work has been of a matlu in.ilic.i]
character relating to telephone transmission.

I ,.ur;,-..v ../ ■■/•:(.-./iki,i>i," London

THE LATE OLIVER HEAVISIDE, F.R.S.

The Bell System Technical Journal

July. 1925

Oliver Heaviside

By F. GILL

ALTMOrciH abler pens' liave exjjressed ajjpreciation of the late
()li\er Heaviside, it is perhaps pcrmissil)le for an English tele-
phone engineer to present a note reRardinR him. Of his hfe-history
not very much is known; but he may ha\e been influenced in his
choice of a career by the fact that he was a nephew of the famous
telegraph engineer Sir Charles Wheatstone. Hea\iside was born in
London on May 13, IS.iO; he entered the service of the GreatNorthern
Telegraph Company, operating sui>marine cables, and he remained
in that service, at Newcastle-on-Tyne, until 1874. While he was
with the Telegraph Compan\-, he published in 1873 a paper showing
the possibility of quadruples telegraphy.

.■\t the age of about 24, owing, it is suggested, to increasing deafness,
he left the ser\ice of that Compan>- and look up mathematical research
work. How he acquired his mathematical training does not seem to
be known;- perhaps he was self-taught, — in some of his Papers he
implies it. By whatever means he mastered the principles, it is
evident that he was an ardent student of Maxwell, for constantly
in Heaviside's own writing runs a vein of appreciation of Maxwell.
For some time he lived in London, then he mo\-ed to Paignton in
Devonshire; his KIcctrical Papers are written from there, and he died
at the neighboring town of Tor(|uay on February 4, 1925, in his
7.^th >ear.

That is about all the personal history at present available, and yet
it gives a clue to a dominant note in his character, viz., reluctance to
come into prominence, originating, perhaps, in a kind of shyness,
which ultimately led to the recluse state. It is strange that so remark-
able an investigator should, in his earlier manhood, have convinced
so few, notwithstanding the fact that his voluminous writings made
his name well known. It must, however, be remembered that his
articles were very difficult, even for advanced mathematicians to
follow, for he used a system of mathematics which, at that time

' The FJedrician, \"ol. XCI\', p. 174, by Sir Oliver Lodge. F.R.S., O.M. Nature,
Vol. 115, p. 2J7, by Dr. .•\lex. Russell, F.R.S.

' Was he the youth with the frown in the library? He says he "then died," but
also says "he was eaten up by lions." (E.M.T., V'ol. Ill, pp. 1 and 135.)

349

350 BFJJ. SYSTEM TECHXICAL JOURNAL

was unusual. Whatever the cause, the fact remains that until al)i)ul
the year 1900 few engineers understood him.

Coming to his work, what was it that Heaviside did, and upon
what does his fame rest? That is too large a subject for a telephone
engineer to answer fully, but as regards communication engineering
something may be said. His great achie\emenl was the discovery
of the laws governing the propagation of energy in circuits. He
recognized the relationship between frequency and distortion; he
illustrated it by numerical examples, and he showed what was re-
quired to make a "distortionless circuit." Further, he showed the
effects of "attenuation" and the result of "inductance" (these words
were his own coinage) in improving telephony. He also explained
how the inductance of circuits could be increased; he suggested the
use of continuous loading, of lumped inductance in the form of coils,
and he pointed out the difficulty of obtaining sufficiently low resistance
in such coils. He in\esti8atcd the etTect of sea and land and the
upper atmosphere on the propagation of radio energy and how it was
that this energy could be transmitted o\er the mountain of earth
intervening between two distant places.

His acti\ity in these matters can best be illustrated by extracts
from his writings, as follows:

In his "Electrical Papers," \(ii. II, written in ISS", p. Uil, he
gives numerical e\am[iles of fre(|uenc\' distortion and of its correction,
and says :

"It is tlie \er\- essence of good long distance teli-piion\- that
inductance should not be negligible."

In his "Electromagnetic Theor\-," \'oi. I, j)ui>iishe(l in hSiKi, he
considers in Section 218, p. 441.

"various ways, good and bad, of increasing the inductance of
circuits"

He suggests, page 44."), the use of

". . . inductance in isolated lumps. This means the insertion
of inductance coils at inter\als in the main circuit. That is to say
just as the effect of uniform leakage may be imitated by leakage
concentrated at distinct points, so we should try to imitate the
inertial effects of uniform inductance by concentrating the induct-
ance at distinct points. The more points the better, of course . . .
The Electrical difficulty here is that inductance coils ha\e resistance
as well, and if this is too great the remedy is worse than the disease.

I

OLIll-.R lll-.insiDE 351

. . . To gi't larjjc inductance with small resistance, or, more gen-
iT.ill\ , to make coils havinK large time constants, re(|uires the use
of plenty of copper to get the conductance, and plenty of iron to
get the inductance, employing a properly closed magnetic circuit
profxrly di\ ided to prevent extra resistance and cancellation of th«
increased inductance . . . This plan ... is a straightforward
way of increasing the L largely without too much increasing the
resistance and may be worth working out and de\elopment. But
I should add that there is, so far, no direct evidence of the beneficial
action of inductance brought about in this way."

In "Klectrical Papers," \'oI. II. p. 'M\. he tieals with rctlected
wa\es. and on page 347 he sa\s:

"... but the transmitter and the recei\ ing teleplionc distort
the proper signals themselves. The distortion due to the electrical
part of the receiver may, however, be minimized by a suitable
choice of its impedance.

"Klectromagnetic Theory," \'ol. I, p. 404: —

"We have seen that there are four distinct ciuantities which
fundamentalh' control the propagation of 'signals' or disturbances
along a circuit, symbolized by R, K, L, and 5, the resistance,
external conductance, inductance, and permittance;"

"Klectromagnetic Theory," \'ol. I, p. 411 : —

"It is not merely enough that signals should arri\c without being
distorted too much; but they must also be big enough to be useful
. . . Nor can we fix any limiting distance by consideration of dis-
tortion alone. And even if we could magnify very weak currents,
say a thousandfold, at the receiving end, we should simultaneously
magnify the foreign interferences. In a normal state of things
interferences should be only a small fraction of the principal or
working current. But if the latter be too much attenuated, the
interferences become relatively important, and a source of very
serious distortion. We are, therefore, led to examine the influence
of the different circuit constants on the attenuation, as compared
with their influence on the distortion."

"F^lectrical Papers," \'ol. II, p. 402: —

"I was led to it (the distortionless circuits), by an examination
of the effect of telephones bridged across a common circuit (the
proper place for intermediate apparatus, remo\'ing their impedance)
on waves transmitted along the circuit."

352 HELL SYSTEM TECHNICAL JOCRSAL

With regard tu Radii) COinmuiiicalion, one extract imisl suffice
writing on The Electric Telegraph in June, 1902, for the Knc\clopedia
Britannica, he says, — "Electromagnetic Theory," Vol. Ill, p. 335: —

"There is something similar in 'wireless' telegraphy. Sea water,
though transparent to light, has quite enough conductivity to
make it behave as a conductor for Hertzian waves, and the same
is true in a more imperfect manner of the earth. Hence the waves
accommodate themselves to the surface of the sea in the same way
as waves follow' wires. The irregularities make confusion, no
doubt, but the main waves are pulled round by the curvature of
the earth, and do not jump off. There is another consideration.
There may possibly be a sufficiently conducting la\cr in the upper
air. If so, the waves will, so to speak, catch on to ii more or less.
Then the guidance will be by the sea on one side and the upper
layer on the other. But obstructions, on land espccialK', may
not be conducting enough to make waves go round them fairK'.
The waves will go partly through them."

Probably due to his long seclusion, his approach to certain subjects
was rather critical. At one time I tried to get a portrait of him for
the Institution of Electrical F-ngineers, but failed; — he did not wish
to have his photograph exhibited, he thought that "one of the worst
results (of such exhibition) was that it makes the public characters
think they really are very important people, and that it is therefore a
principle of their lives to stand upon doorsteps to be photographed."

On another occasion when I sent him a copy of an article by a dis-
tinguished telephone engineer on "The Heaviside Operational Cal-
culus," he replied that he had "looked through the paper . . . with
much interest, to see what progress is being made witii the academical
lot, whom I have usually found to be very stublxirn and sometimes
wilfully blind."

Some have held that Heaviside was not reaignized as he ought to
have been. This was probably the case some time ago, but not in
recent years. The same is true of many very great men who were
much in advance of their time, for the English have the national
characteristic that they do not make much fuss about their great
men. So if Heaviside suffered, he shared this experience in common
with other pioneers who deserved higher recognition. See, for ex-
ample, what Heaviside himself said about one of these, in a footnote
in "Electromagnetic Theory," \oi. HI, p. 89:

"George Francis Fitzgerald is dead. Tlic |)ninature loss of a
man of such striking original genius and such wide syni|iathies

oi.ii'f-K iir.irisiiu- 35.5

will hv nmsidtTi'd by those who kiu-w him and his work to l)i' a
national niisfortune. Of roiirso, the 'nation' knows nothing about
it. or why it should i)e so "

DurinR the last 20 years or mori.-, tin- siKnidiMiui.- and luminous
i|ualily of the work of Heaviside has been increasing by acknowledge;!
mathematicians and by practical telephone, telegraph and radio
engineers. To other electrical engineers his treatment of wave-
transmission has not yet apjK'aled (|uite so strongly.

Probably his first recognition came from his contribution to the
problem — "Electromagnetic Induction and its Propagation" in the
Electrician. It appeared as a .scries of articles between January,
1885 and December. 1887. His "Electrical Papers" were written
at various times and were published in two volumes in 18!)2. Then
followed his three volumes on "Electromagnetic Theory" — on the
basis of the Electrician articles— published in 18!>3, 1899 and 1912.
He also wrote, in 1902, the article on the "Theory of the Electric
Telegraph" in the "F^ncyclopedia Britannica."

In 1891. the Royal Society made him a Eellow. In 1899, the
-American Academy of Arts and Sciences elected him an Honorary
Member. In 1908 the Institution of Electrical Engineers did the
same, followed by the American Institute of Electrical Engineers in
1917. The Literary and Philosophical Society of Manchester also
elected him an Honorar\- Member. He was an Hon. Ph.D. of the
University of Gottingen. and in 1921, the Institution of Electrical
Engineers conferred upon him the highest award in their gift — the
Faraday Medal. He was the first recipient of this Medal which was
established to commemorate the ,50th anniversary of the founding of
the original Society of Telegraph Engineers and of Electricians, and
since then the medal has been bestowed upon -Sir Charles Parsons,
Dr. S. Z. de Ferranti, and Sir J. J. Thom.son.

From time to time there were reports of his li\ing in great poverty,
and attempts were made to help him. These reports lacked propor-
tion, but it is true he had not much money and perhaps still le.ss com-
fort; he was a difficult man to help. Towards the end of his life he
received from the British Government a Civil Pension. His inde-
pendent character rendered it necessar>- that offers of assistance should
be tactfully made and apparently this was not always the case, as I
believe help was sometimes refused; but there were those who suc-
ceeded. Another difficulty was his unconventional mode of living
which cause<l him, in his last years, to live as a recluse, cooking and
looking after his house alone.

354 HULL SVSIIiM II.CIIMCAL JOIRXAL

Just what other work Heaviside did, in addition to his published
writings, is not at present known to me. I beheve he left a good
deal of manuscript, but whether it is in such a state that it could
be completed by another, I do not know. Let me conclude this note
by an e.xtract from his last chapter of his last book, "Electromagnetic
Theory," \'ol. HI, page 519: —

".As the universe is i)oundless one way, towards the great, so it
is ecjualK' boundless the .other way, towards the small; and im-
portant events may arise from what is going on in the inside of
atoms, and again, in the inside of electrons. There is no energetic
difficulty. Large amounts of energy may be very condensed by
reason of great forces at small distances. How electrons are made
has not yet been discovered. From the atom to the electron is a
great step, but is not finality.

"Living matter is sometimes, perhaps generally, left out of
consideration when asserting the well-known proposition that the
course of events in the physical world is determined by its present
state, and by the laws followed. But I do not see how living
matter can be fairly left out. For we do not know where life
begins, if it has a beginning. There may be and probably is no
ultimate distinction between the living and the dead."

I

The Loaded Submarine Telegraph Cable'

By OLIVER E. BUCKLEY

Synopsis: With an iiu-rcase of trartir carrying capacity of MW ', over
that of corrcs|X)n<lin){ cahlcs of the previous art, the New York-Azores
()eruialloy-liMile<l calile marks a revohilioii in siiliinarine cal>lc practice.
This cjlile represents the first practical application of iiiihictive loading
to transiK'eanic cables. The copper conductor of the cable is surrounded by
a thin l.iyer of the new magnetic material, (lermalloy, which serves to increase
its inductance and conseipiently its ability to transmit a rapi<l succession
of telegraph signals.

This (xi(H-r explains the part played by loading in the oix-'ration of a cable
of the new ty(H- and disciis.ses some of the problems which were involved in
the develr>i>ment leading up to the first commercial installation. Particular
attention is given to those features of the transmission problent wherein
a practical cable differs from the ideal cable of previous theoretical dis-
cussions.

Brief mention is made of means of operating loaded cables and the |h)S-
sible trenil of future development.

I'KR.M.M.LOV Lo.\I)IN(.

Till-; .iiiiioiiiufnu-iil on Se()loml)er 21, 1921, that an oprr.itiii^;
speed of over l,iOO letters per minute had been oljtained with
the new 2,;i00 mile New \'ork-A/ores permalloy-loaded cable of the
Western I'nion Telegraph Company, brought to the attention of the
public a development which promises to revolutionize the art of sub-
n:arine cable telegraphy. This announcement was based on the
result of the first test of the operation of the new cable. A few weeks
later, with an improved adjustment of the terminal a[)[)aratiis, a
speed of over 1,900 letters per minute was obtained. Since this
speed represents about four times the traffic capacity of an ordinary
cable of the same size and length, it is clear that the permallo\-loaded
cable marks a new era in transoceanic communication.

The \ew York-Azores cable represents the first practical attempi
to secure increased speed of a long submarine telegraph cable by
inductive loading and it is the large distributed inductance of this
cable which is principally responsible for its remarkable performance.
This inductance is secured b>' surrotinding the conductor of the cable
with a thin layer of permalloy. Fig. 1 shows the cf)nstruction of
the deep sea section of the cable. In appearance it differs from the
ordinary ty|K- t>f cable principally in ha\'ing a permalloy tape 0.00 >
inch thick and 0.125 inch wide, wrapped in a close helix around the
stranded cop[H-r conductor.

Permalloy, which has been described by Arnold and Mlmen,' is an
allf)y consisting principally of nickel and iron, characterized b\' very

' Presented iH-fore the A. I. E. E., June 26, 1Q25.

'- Jour. Franklin Inst.. \ol. 195, pp. 621-6.?2, May 192.5; B. S. T. J., \ol. II, N'o. 3,
p. 101.

355

356 BELL SYSTEM TECHXICAL JOLRXAI.

high permeability at low magnetizinR forces. The relative propor-
tion of nickel and iron in permalloy may be varied through a wide
range of additional elements as, for example, chromium may be added
to secure high resistivity or other desirable properties. On account

Fi};. 1 — rtriiialloN -Loaded C'alile. .Al)o\c, section of deep sea ty[>e showing con-
struction. Below, section of core showing permalloy tape partly unwound.

of its extremely high initial permeabilit\- a ihiii la\er of |)ermalloy

wrapped around the copper conductor of a cable great 1\- increases its

inductance even for the smallest currents.

In the case of the New York-Azores cable the permalloy tape is

composed of approximately 78\2% nickel and 21 J o*^ iron and gives

the cable an inductance of about 54 millihenries per nautical mile.

An approximate \alue of the initial permeal)ilit\' of the permallo\'

in that cable ma\- be got by assuming the helical tape replaced b>' a

continuous c\'linder of magnetic material of the same thickness.'

This material would have to ha\e a jxTmeabiiity of about 2,300 to

give the observed inductance. A belter appreciation of the extraor-

dinar\- properties of the new loading material may be obtained b>'

(■om|)aring this [lermeabiiity with tlial w liich has pre\'iously been

obtained with iron as the loading material. The Key West-Ha\ana

telephone cables are loaded with 0.1)0^ inch diameter s<jft iron wire.

The permeability' of this wire, which was tlie ln'sl which coiilii i)e

obtaini'd coinmercialK- wlu-n tli.il lalilr was maili', i> onK alxml II."),

'The true initial pernieaMlity is slightly higher. To loiiipiite it, account nuist
he taken of the fact that, contrary to what has lH.'en sometimes assumed, the mag-
netic lines of in(hiction in the tape do not form doseil loops around the wire but tenil
to follow the tape in a helical path. The pitch of the helical path of the lines of
induction is slightly less than that of the permalloy tape with the result that a line
of induction takes a numher of turns around the conductor, then crosses an airgap
Iwlween two adjacent turns of tape and continues along the tape to a point where
it again slips hack across an airgap. O. K. Buckley, British Patent No. 206,104,
March 27, 1924, also K. U. Wagner, K.N.T., Vol. f, No. S, p. 1.S7, 1924.

ruF. i.oAi^rn sin.M.ih'ixr. rr.rr.CK.ii'if c.ini.r. .157

or api>r<>xiniatt'ly mu'-twi'iilii'lli iImI of ilu- pt-rtn.illoy t.ipc nf tlu'
New York-Azori-s cal>li-.

1'ki)HI.i:ms I'.st ointisKici)

Tlu- |)ri)|)(i>.il Id um' |Hrm.illi)\ liLuliii^ lo iiii rciM- tin- -.pct-d uf
li)HK tflt-nraph cal)li's was <>iu' outronu' of an in\ isti^;ation under-
takt'ii liy the author soon after the war to determine whetlier some of
the new melho<ls and materials deveh)ped primarily for telejjhony
mijjht not find important application to siihmarine lele^jraphy. In
the sul)se(iiient de\eiopment of the permalio>- loaded cable a large
number of new problems, both theoretical and practical, had to be
solved iK'fore the manufacture of a cable for a commercial project
could be uniiertaken with reasonable assurance of success. The
problems encountered were of three principal kinds. First was that
of the transmission of signals over a cable having the characteristics
of the trial conductors made in the laboratory. Although the theory
of transmission o\er a loaded cable had been prexiously treated by
others, the problem considered had been that of an ideal loaded cable
with simple assumptions as to its electrical constants and without
regard to the practical limitations of a real cable. The second class
of problems had to do with the practical aspects of design, manu-
facture and installation. In this connection an extensive series of
exiHTiments was conducted to determine the means required to
secure at the ocean bottom the characteristics of the laboratory
samples on which the transmission studies were based. Among the
numerous problems which arose in this connection were those con-
cerned with protecting the copper conductor from any possible dam-
age in the heat-treating operation which was necessary to secure the
desired magnetic characteristics, and those concerned with protecting
the strain-sensitive permalloy tape from being damaged by sub-
merging the cable to a great depth. The third class of problem had
to do with terminal apparatus and methods of operation. The
prospective speed of the new cable was ciuite bcyonti the capabilities
of standard cable equipment and accordingly new apparatus and
operating methods suited to the loaded cable had to be worked out.
In particular it was necessary to develop and construct instruments
which could l)e used to demonstrate that the speed which had been
predicted could actually be secured. The success of the investiga-
tions along all three lines is attested by the results which were ob-
tained with the New York-Azores cable. lig. 2 shows a section of
cable recorfler slip, the easily legible message of which was sent from

358

KELI. SVSTFM TECHX/C.IL JiHKXAL

Horta, I'a\al, and rc-iei\t_-(l al New ^'llrk• at a speed <il \,'*'2i) letters
per mi mile.

!t is |)riiuipall\- with regard to the first of these classes of problems,
that (»l llie transmission of signals, that llu- following discussion is
concerned. .\n attempt will lie m.ide lure in discuss the details of

SI I

l.s

HIS

:i<

Fig. 2 — Test Message. Western I iiioii .New N'ork-.Azores Permalloy -LoadKl
Cable. Sent from Horta (Azores) and received at New York, November 14, 1924.
Speed — 1920 letters per minute. Recorded with special high speed siphon recorder

design and tie\elopmeiU ot the physical striieliire of the cable, nor
will there be given a detailed description of the operating results or
how they were obtained. These subjects must be reserved for later
publication. It is desired in what follows to explain how^ inductive
loading impro\'es the operation of a submarine cable and to point
out some of the |)rol)lems concerned with the transmission of signals
which had in lie considered in engineering the first long loa<ied cable.

I-"a( TORS LiMiriNc Si'i'.i-;!) nt Xon-Lhadi-.I) (ahii:

In onler to muk'rstand the part played b\- loading in ihe trans-
mission of signals it is desirable first to review brieth llu' status of
the cable art prior to the introduction of loading and io consider the
factors then limiting cable speid and the pnssii)U- means of over-
coming them. A cable of the ordinary l>'pe, without loading, is
essentially, so far as its electrical properties are concerned, a resist-
ance WMth a capacity to earth distributed along its length. .Although
it does ha\e some inductance, this is loo small to affect transmission
at ordinary sjieeds of operation except on cables with extremely heavy

77//. i.o.inr.ii sciiM.ikixi i ni.icK.irn (.inir. .w

oondiiitors. Thi- o|KT;itinn spii-d of a non-loailctl inhlv is approxi-
mately inversi'ly proportional to the product of the total resistance
l)V the total capacitv-: that is,

5= *-^
CRP'

where C is capacity anil R resistance per unit lenRlh, and / is the
length of the cable. The coerticient k is generally referred to as the
speed constant. It is. of course, not a constant since it depends on
such factors as terniinal interference and method of operation, hut
is a convenient basis for comparing the efticiencj' of operation of
cables of different electrical dimensions. .As the techni(|ue of oper-
ating cables has improved the accepted value of k has increased, its
value at any time being dependent on the factor then limiting the
maximum speed obtainable. This factt)r has at times been the
sensiti\eness of the receiving apparatus, at other times the distor-
tion of signals, anti in recent years interference. During a great part
of the history- of submarine cable telegraphy distortion was considered
the factor which limited the speed of operation of long cables and on
this account most of the previous discussif)ns of submarine cable
transmission have been concernefl principally with distortion and
means for correcting it. As terminal apparatus was gradually im-
proved means of correcting distortion were fleveloped which prac-
tically eliminated distortion as an important factor in the operation
of long cables. With ilistortion thus eliminated the speed was found
to be limited principally by the sensitiveness of the receiving ap-
paratus. This limit was, however, eliminated in turn by the develop-
ment of signal magnifiers. During recent years, in which numerous
cable signal magnifiers have been available and methods of correcting
distortion have been understood, the only factor limiting cable speed
has been the mutilation of the feeble received signals by interference.
Most cables are operated duplex, and in these the speed is usually
limited by interference between the outgoing anrl incoming signals.
In cables operated simplex, and also in cables operated duplex where
terminal conditions are unfavorable, speed is limited by extraneous
interference which may be from natural or man-made sources and
which varies greatK' in diU'erent locations. The strength of the
received current must in either case be great enough to make the
signals legible through the sujierposed interference current. Owing
to the rapidit> with which the received signal amplitude is decreased
as the speed of sending is increased, the limiting speed is quite sharply
defined by the interference to which the cable is subject.

Mi) fiiiij. svsrr.M ir.ciixic.ii. jor rx.il

Means of In-(kr.\sin(; Spekd

With the speed of operation thus limited there were two ways in
which the hniiling speed could he increased; the interference could
be reduced, or the strength of signals made greater. No great reduc-
tion in interference due to lack of perfect duplex balance could be
expected, as balancing networks had already been greatly refined.
Extraneous interference in certain cases could be reduced by the use
of long, properly terminated sea-earths. The signal strength could
be increased either by increasing the sending voltage or by decreasing
the attenuation of the cable. However, with duplex operation nothing
at all is gained by increasing the voltage in cases where lack of perfect
duplex balance limits the speed, and wiili sini|)lex operation any gain
from raising the \'oltagc is obtained at tlu- cost of increased risk to
the cable, the sending voltage being usually limited to about 50
volts by considerations of safety. The attenuation of the cable could
be reduced and the strength of the signal increased by use of a larger
copper conductor or by using thicker or better insulating material.
None of these possilile improvements, h()we\"er, seemed to offer pros-
pect of very radical advance in the art.

In telephony, both on land and submarine lines, an advantage
had been obtained b>' adding inductance ' in either of two ways, by
coils inserted in series with the line or by wrapjiing the conductor with
a layer of iron. The insertion of coils in a long deep-sea cable was
practicalh' i)rohibited by difficulties of installation and maintenance.
Accordingly, only the second method of adding inductance, com-
monly known as Krarii]) or continuous loading, could be considered

'The idea of improving the transmission of signals over a line by adding dis-
tril)Uted indiictanie to it originated with Oliver lleaviside in 1887 (Klectrician, Vol
XIX, p. 79, and I-:iectromagneti<- Theory, \ol. I, p. 441, 18W), who was the first
to eall attention to the part pla\ed !)>■ inductance in the transmission of current
impulses over the cable. He suggeste<l as a means for obtaining increase<l induct-
ance the use of iron as a part of the conductor or of iron dust embedded in the gutta
percha insulation. He also proposed inserting inductance coils at intervals in a
long line. Other types of coil loading were propo.sed by -S. V. Thompson (British
I'atent 22,304—1891, and U. .S. Patents 571,706 and 57'l,7()7— 18%), and by C. J.
Keed (U. .S. Patents .Sll),612 and .SlO.f.l,? — ISO.?). M. 1. I'upin (A. I. IC. E. trans..
Vol. XVI, p. W, 18'W, and Vol. XVII, p. 445, 1900) was the first to formulate the
criterion on the basis of which coil loaded telephone cables could be designed. Con-
tinuous loading by means of a longitudinally discontinuous layer of iron covering
the conductor was proposed by J. S. .Stone in 1S97 (I'. S. Patent 578,275). Breisig
(E. T. '/,., Nov. 30, 1899) suggested the use of an o|)en helix of iron wire wound
around the conductor and Krarup (E. T. '/.., April 17, 1902) proposed using a closed
spiral so that the adjacent turns were in contact. J. H. Cuntz (U. -S. Patent 977,713
fded March 29, 1901) projMJsed another form of continuous loading. Recent general
discussions of loacled telegraph cable problems have been given by Malcolm (Theory
of Submarine Telegraph and I'elcphone Cable, London, 1917) and by K. W. Wagner
(Elrktr. .\achtr. Tech., Oct., 1924).

THE i.o.miii) siHM.iKixii Ti-.i.i.c.i<.\t'ii c.im.r. m

for a triinsoi-iMiiif tfli'Krapli c.ihk' and it is pritnariK' with ri'^;ar(l t<i
roiitinunus loading that the following discussion is ronrurni-d.

KiKIXTS OF I.OADINt,

Most of the proposals to load telegraph cables have had the ol)j«^c^
of reducing; or eliminating distortion, and accordingly most of the
mathematical treatments of loading have heen from that point of
view. The reduction of distortion is, however, not the only benefit
to Ik- obtained from loading and, in fact, may not always be secured
in the high speed operation of a loaded cable. The principal benefit
of loading from the practical standpoint is to decrease the attenua-
tion of the signals so that for a given freciuency more current will be
received or so that the minimum permissible current may be received
with a greater speed of signalling. From the mathematical stand-
point there are two ways of treating the problem of the loaded cable,
first with regard to the transmission of a transient impulse, and
secontl with regard to setting up steady alternating currents of definite
frequency. In the ultimate analysts the solution of either problem
can be got from the other. However, for practical purposes they
are two distinct means of attack. Which should be used depends
on the object to be secured. If one is concerned primarily with the
effect of the cable on the wave shape of the signal transmitted over
it, it is fairly obvious that the transient treatment has advantages.
If, however, one is concerned only with the strength of the received
signal, as is the case if there is assurance that the signal shape can in
any event be corrected by terminal networks, then the steady state
treatment is sufficient and much more convenient to apply. In
the case of the real loaded cable the complete transient solution is
extremely comple.x and the steady state treatment relatively simple.
The solution of the transient problem of an ideal loaded cable is,
however, very valuable to give a physical picture of how inductive
loading aids the high speed transmission of signals.

The transient solution of the problem of an i^deal heavily loaded
cable has been worked out by Malcolm * and more rigorously by
Carson ', who have determined the curve showing the change of
current with time at one end of the cable if a steady c.m.f. is applied
at zero time between the cable and earth at the distant end. Such a
curve is called an "arrival curve" and for an ideal loaded cable com-
prising only constant distributed resistance, capacity and inductance
may have a form like that shown in Curve b of Fig. ',i, which is to be

•Theory of the Submarine Telegraph and Telephone Calile, I-onclon, 1917.

•Trans. A. I. E. E., Vol. 38, p. 345, 1919.

362 PEI.I. SYSTEM TECIIMCAI. JOVRXAL

compared with Curve a which is tlic arrival curve of a non-loaded
cable. The straight vertical .part of C'ur\e h represents the "head"
of the signal wa\e which has travelled over the cable at a definite
speed and with diminishing amplitude. The definite head of the arrival
curve is the most striking characteristic difference between the ideal
loaded and the non-loaded cable. In the latter, as is evident from
Fig. 3, the current at the receiving end starts to rise slowly almost
as soon as the key is closed at the transmitting end. When an e.m.f.
is applied to the sending end of the non-loaded cable a charge spreads
out rapidly over the whole length, the receiving end charging up
much more slowly than the sending end on account of the resistance
of the intervening conductor. Hence, if a signal train consisting of
rapidly alternating positive and negative impulses is applied to the
sending end, the effect at the receiving end of charging the cable
positively is wiped out by the succeeding negati\e charge before there
has been time to build up a considerable positive potential and the
successive alternating impulses thus tend to annul each other. In
the loaded cable the effect of inductance is to oppose the setting up
of a current and to maintain it once it has been established, and
thus to maintain a definite wave front as the signal impulse travels
over the cable. Hence, with inductive loafling the strength and
individuality of the signal impulses are retained and a much higher
speed of signalling is possible. It should be noted that by speed of
signalling is meant the rapidity with which successive impulses are
sent and not the rate at which they travel over the cable. This speed
of travel is actually decreased by the addition of inductance, about one-
third of a second being required for an iin|)ulso to traverse the \ew
York-Azores cable from end to end.

It should be noted that Curve b of F"ig. ?> is for an ideal loaded
cable in which the factors of resistance, capacity and inductance are
constant. In a real loaded cable none of these factors are constant
and the arrival curve cannot be simply and accurately computed.
Even the capacity which is usually assumed as constant for real
cables varies appreciably with freciuencies in the telegraph range,
and owing to the fact that gutta pcrcha is not a perfect dielectric
material its conductance, which is also variable with frequency, must
be taken into account. Although the inductance of the cable is sub-
stantially constant for small currents of low frequency, it is greater
for the high currents at the sending end of the cable on account of
the increase of magnetic permeability of the loading material with
field strength and is less at high fre(|uencies than at low on account
of the shielding effect due to eddy currents. The resistance is highly

77//i I.O.inr.D \l HM.IKIXli ir.l.liCN.U'll C.IHI.Ii A,.?

variable sinci- it comprises, in addition to tin- rosislatici- of the copper
conductor, etTecli\e resistance due to eddy currents and hysteresis
in the loadini; material, l>otli of which \ary witli fre(iuenc>' and current
anjplitude. I'lirlhermore, there is \arial)le inductance and resistance
in the return circuit outside tlie insulated conduitor wliicli must !"■

3500

r
!

, 1

■

/

I

J

/

3000

/

—

/

r

/

2500

/

/

/

/

2000

/

y

/

/

/

5 1500

Q.

/

/

-

1

f

/

<

1 1000

/

l\

"h

f

J

500

/

f
/

/

i

c

L^

/

O.I

0.Z 0.3 0.4

SECOND

0.5

0.6

Fig. i — .\rrival Curves, a. .N'on-loatlcd cable, b. Ideal loaded cable, c. Real
loaded cable Capproximate)

taken into account. .Xithougii it is very difficult to compute the
e.xact arrival curve of a cable subject to all of these variable factors,
an approximate calculation in a specific case like that of the New
York-Azores cable shows that the arrival curve has the general shape
f)f Curve c of Fig. H. It will \te noticed that although this arrival
curve lacks the sharp definite head, characteristic of the ideal loaded
cable, it still has a relatively sharp rise and that the lime ref|uired
for the impulse to traverse the cable is nf)l greatly difTcrent from
that of the ideal loaded cable.

3(A BELL SYSTEM TECHXICAL JOURNAL

Although it is ciittitult to take- exact account of \bv \aiial)lc char-
acteristics of the loader! cable in the solution of the transient problem,
it is easy to take account of them in the steady state or iK-riotlic
analysis by means of well-known methods. If a steady sinusoidal
voltage, Vs, is applied at one end of the cable the resulting voltage,
/,, at the distant end will lie gi\-en b\- the e(|uali(in

where / is the leiii;lli, P, the |)r()pagalion coiislaiit of tlie caljle and k,
a constant which depends on the terminal impedance and which is
unity in case the cable is terminated at the receiving end in its so-
called characteristic impedance. Tiie propatjation constant is gi\eii
by the formula,

P=\/{R+ipL){G+ipCJ = a+ifi,

where R is the resistance, L, the inductance, G, the leakance and C,
the capacity per unit length and p is 2w times the frequency. The real
part of the propagation constant, a, is called the attenuation constant
and the imaginary part, /3, the wave length constant. By separating
a and 0 the amplitude and phase displacement of the received voltage
relative to the sent voltage may be computed for any particular
frequency and the behavior of a complex signal train may be worked
out b^■ analyzing it into its Fourier components and treating them
separately. The phase shift is, however, of importance mainly as
regards the shape of the received signals and their amplitude may,
in general, be obtained from the attenuation constant alone. Thus
if it is known that the signal shai>e can in any case be corrected by
terminal networks there is no need to be concerned with more than
the attenuation constant to compute the speed of the cable.

In the case of a cable of the permalloy loaded type, a is gi\en with
an apijroximation " sufficiently close for the purposes of this discus-
siiiii li\' llie (-(iiKilidii.

uu-<-P-y

For the purpose of comi)uting R it is ciiineiiienl to sejiarate it into
its components, giving

a=^yj^^(^R, + R. + R, + R,+ ^^,Ly

' Kor accuriite cuinputation of iittenu.itloii the coiiipUtc furimila for a must be

Till- i.o.inr.n scnM.iKixr. rr.i.v.cK.irii ciiur m6

wh«Tr R. = copper resistance per unit leni;th

K, =e<ldy current resistance per unit liiii;ih
R, =sea return resistance per unit liiiutli
/?*= hysteresis resistance per unit Icngtli

The copper resistance Re is that determined !)>• a direct current
measurement of the loaded conductor since the resistance of the
loading tape is so hi^h and its length is so great that the current
Howing longitudinally through it may be safely neglected.

The eddy current resistance Rt is given approximately by the
fornuiia,

R,=

p(d-iy

where / is the lliickness or diameter of the loatling ta[)e or wire, d,
the outside diameter of the loaded conductor, /, the fref|uenc\-, p,
the resistivity of the loading material, fi, its magnetic permeability
and HI. a constant which depends on the form of the loading material
and is in general greater for tape than for wire loading. Although
it is possible to compute a %alue of in, the \'alue found in practice is
<ilwa>s larger than the theoretical \alue which is necessarily based
on simple assumptions and does not take into account such a factor
as variation of permeability through the cross-section or length of the
loading material. Accordingly it is necessary to determine m ex-
fierimentally for any particular type of loaded contluctor.

The sea-return resistance may be safely neglected in the com-
putation of slow speed non-loaded cables, but it is a factor of great
consequence in the behavior of a loaded cable. By sea-return re-
sistance is meant the resistance of the return circuit including the
eflFect of the armor wire and sea water surrounding the core of the
cable. Although the exact calculation ' of this resistance factor is
too complex to be discussed here, the need for taking it into account
may be quite simply explained. Since the cable has a ground return,
current must flow outside the core in the same amount as in the con-
ductor. The distribution of the return current is, howe\er, dependent
on the structure of the cable as well as on the frequencies in\T)lved
in signalling. If a direct current is sent through a long cable with the
earth as return conductor the return current spreads out through sucl^
a great volume of earth and sea water that the resistance of the
return path is negligible. On the other hand if an alternating current
is sent through the cable the return current tends to concentrate

'See Carson and Gilbert, Jour. Franklin Inst., Vol. 192, p. 705, 1921: FJeclrician,
Vol. 88, p. 499, 1922; B. S. T. J., Vol. I, No. 1, p. 88.

366 HELL SYSTEM TECHNICAL JOURNAL

around it, the degree of concentration increasing with the frequency.
With the return current thus concentrated the resistance of the sea
water is of considerable consequence. It is further augmented by a
resistance factor contributed by the cable sheath. This may be
better understood by considering the cable as a transformer of which
the contluctor is the primary and the armor wire and sea water are
each closed secondary circuits. Ob\iously the resistances of the
secondary circuits of armor wire and sea water enter into the primary
circuit and hence serve to increase the attenuation. Tiie presence
of the armor wires may thus be an actual detriment to the trans-
mission of signals.

To take account of the hysteresis resistance, /?/,, and also of the
increased inductance and eddy current resistance at the sending end
of the cable it is most convenient to compute the attenuation of the
cable for currents so small that Rh may be safely neglected. The
attenuation thus computed is that which would be obtained over
the whole cal)Ie if a \(t\ small sending voltage were used. The
additional attenuation at tiie sending end for the desired sending
voltage ma\- then be appro.ximated by computing successively from
the sending end the attenuation of short lengths of cable over which
the current amplitude may be considered ci>nstant, the attenuations
of separate lengths being added together to gi\e the attenuation of
that part of the cable in which hysteresis cannot be neglected. In
this computation account must, of course, be taken of the increased
inductance and eddy current resistance accom|xui\ing the higher
currents at the sending end.

Having calculated or obtained by measurement the sc\eral resist-
ance factors and knowing the capacity, leakance and inductance, the
whole attenuation of a cable for any desired frequency may be com-
puted and a curve drawn showing the variation of received current
with frequency for a given sending voltage. This relation for a
particular case is shown in Curve c of Fig. 4. Cur\e a shows for
comparison the relation between frequency and received current of a
non-loaded cable of the same size, that is, a cable ha\ing a conductor
diameter the same as that of the loaded conductor and having the
same weight of gutta percha. Curve b shows the behavior of an
ideal loaded cable having tlie same inductance, ca|)acity and d.c.
resistance as the real loaded cable of Curve c, but in which the leakance
and alternating current increments of resistance are assumed to be zero.

Now, if the level of interference through which the current must
be received is known, the maximum speed of signalling for the loaded
cable may be obtained from Curve c It is that speed at which the

77//; /.(>. »/)/;/) S( It.M.IRIXr. Tl.l.lCKAl'll C.IHI.I-

.V.7

hisht'st frtMiiK-nry ru'»i'ssar>' to m.iki- tlu- siv;iials li-nil)le is rccfivccl
with siiHuii'iU amplitudi' to salVly override the siifjerposetl inter-
ferenri-. Just what tin- rchitioii of tliat friciuiiuy is to the speed of
sij^naUiiiv; cannot l)e detinitel>' stated, sinie it depends on the nietliod
of operation and code emplo\ed as well as on the doired perfection

1 1 1 ' 1

'

700

1 1

\

' ' 1

\

\

k

1

\

^

b

400

\

I \

1 ' , '

300

\

1

t

\

1

\,

'

N

\

1

\

i '

'

\

•X

1

VJ

'^

L-ui

L^

20

30 40 50
CYCLES PER SECOND

70

60

Kig. 4 — Received Current vs. l"rcquc-ncy. a. Non-loaded cable
cable, c. Real loaded cable

h. Ideal loaded

of signal shape. J. \V. Milnor '' has suggested that for cable code
operation and siphon recorder reception a fair value is about 1.5
times the fundamental frecpicncy of the signals, that is, the funda-
mental freciuency when a series of alternate dots and dashes is being
sent.

r<iM.\RKs ON riiFi I)i:si(ix ()i- I,i).\i)i;i) (".\ni.i:s

By referring again to the eciuation for a, above, it can now be

explained why high permeability is a necessary characteristic of the

* Journal A. I. E. F.., Vol. 41, p. 118, IPii, Transactions .-\. I. E. K., Vol. 41,
p. 20, 1922.

368 BELL SYSTEM TECHNICAL JOURNAL

loading material if a benefit is to be obtained from continuous loading.
The addition of the loading material has two oppositely directed
effects; on the one hand it tends to improve transmission by increasing
the inductance and consequently decreasing the attenuation, and
on the other hand it tends to increase the attenuation by increasing
the effect of leakance and by the addition of resistance. Not only
are the hysteresis and eddy-current factors of resistance added by
the loading material but it must also be looked upon as increasing
either the copper resistance or the capacity on account of the space it
occupies. Generally it is more convenient to look upon the loading
material as replacing some of the copper conductor in the non-loaded
cable with which comparison is made, since by so doing all of the
factors outside of the loaded conductor are unchanged. Now, if the
loading material is to be of any benefit, the decrease in attenuation
due to added inductance must more than offset the increase due in
added resistance, including the added copper resistance due to the
substitution of loading material for copper. In the limiting case the
lowest jjermeability material which will show a theoretical advantage
from this point of view is that which, as applied in a vanishingly thin
layer, gives more gain than loss. For any particular size and length
of cable there is a limiting value of permeability which will satisfy
this condition, this limiting value being greater the longer the cable
and the smaller the diameter of its conductor.' For transatlantic
cables of sizes laid prior to 1923 the minimum initial permeability
required to show an advantage is higher than that of any material
known prior to the invention of permalloy. Actually a considerably
higher permeability than this theoretical minimum was, of course,
required to make loading an economic advantage since there are
practical limits to the thickness of loading material and since the cost
of applying it has also to be taken into account. Further, there are
limits on methods of operation imposed by loading which necessi-
tate still higher permeability to make loading worth while.

Since the addition of loading has two opposite tendencies in its
effect on attenuation, the practical design of the cable must be based
on a compromise between them. Thus, to secure the maxinuini
gain from loading a cable of a given size, the loading material should
be chosen of such a thickness that the gain due to increased induct-
ance from a slight increase of thickness just offsets the loss due to
increased resistance and dielectric leakance. In practice, of course,
economic considerations of the cost of \arious thicknesses of loading
must also be taken into account.

•See British Patent No. 184,774—1923, to O. E. Buckley.

Tiir. i.()Ain-.n sm.u.iRixr. if.i.v.gr.H'ii cahi.e mm

In closinnin^ the New N'ork-Azort-s cable some a.ssuiii|>(i(iii li.id lo
Ik- inatio as to the extraneous interfercnre whicli would be encountered.
Theoretical considerations led us to believe that the loaded cable
woidd l>c no more subject to external interference than non-loaded
cables. It even appeared that it would be less affected by some
tyf)es of interference, for, owinjj to the shorter wave-lcnRth for a
niven frequency, a disturbance which affects a great many miles of
cable simultaneously is less cumulative in its effect at the terminal
of a loaded than a non-loaded cable. A reasonable assumption seemed
to be that the total o\erall attenuation which could be tolerated
for the loaded cable was at least as jjreat as that which experience
had shown to be permissible ftir simplex operation of non-loaded
cables. This maximum permissible attenuation depends, of course,
on conditions of terminal interference and no fixed value can be
given as applicable to all cables. However, for average conditions
of terminal interference in locations free from pf)wer line disturb-
ances and where the cable lies in relati\-ely deep water near to its
terminal landing, a reasonable value of total attenuation constant
for the fundamental frequency- of cable code is about 10 (8(5.9 T.l f.) for
recorder operation and about 0 (78.2 T.U.) for relay operation. These
were the approximate %alues assumed for the New York-Azores cable
and later experience has demonstrated that they were well justified. ■

DlSTORTIUX I.V Lo.XDED ( AHl.KS

Throughout all of the preceding discussion it has been assumed
that the relation between attenuation and terminal interference
would limit the speed of simplex operation rather than that distortion
of signal shafje would be the limiting factor. Although this is, in
fact,'" the case with non-loaded cables it was not -self-evident as
regards the loaded cable, and to make reasonably certain that the
speed could be determined from the attenuation-frequency relation
required a demonstration that the signal distortion of a real loaded
cable could be corrected by suitable terminal apparatus. One of
the merits long claimed for loading was that it would reduce dis-
tortion and, indeed, an ideal loaded cable with constant inductance
and without magnetic hysteresis, eddy current loss, dielectric leak-
ance and sea return resistance would have very little distortion and
would give a speed limited only by terminal apparatus. However,

>• Recent work of J. R. Carson (U. S. Patent 1,315,539—1919) and R. C. Mathes
(U. S. Patent 1,311,283 — 1919) has shown that with the combined use of vacuum
tube amplifiers and distortion correcting networks, distortion in non-loaded cables
can be compensated to any desired degree.

370 BELL SYSTEM TECIIMCAL JOURNAL

a real loaded cable, the iiKiiiciance of which \aries with both cuirent
and frequency and in which all the above noted resistance factors
are present, may give, and in general will give when operated
at its maximum speed, greater distortion of signals than a non-
loaded cable.

To solve the question of distortion on a purely theoretical basis
required consideration of tiie transmission of a transient over the
loaded cable. This was made extremely difficult by the existence
of numerous possible causes of signal distortion, the effects of which
could only be approximated in the solution of the transient problem.
In addition to the distortion resulting from the rajjid increase of
attenuation with fre(]uency due to the various sources of alternating
current losses, distortion peculiar to the magnetic characteristics of
the loading material had also to bo taken into account. There art
several types of magnetic distortion to be concerne<l about. First,
there is the production of harmonics as a result of the non-linear
magnetization cur\e of the loading material; second, there is a pos-
sible asymmetrical distortion due to hysteresis, and third, there
is a possible modulation resulting from the superposition of signals
on each other, that is, in effect, a modulation of the head of the wa\e
of one impulse by the tail of the wave of a preceding impulse. The
first two of these are effective at the sending end of the cable and
the third near the receiving end.

A compulation of distortion, inchuiing ilie i)eciiliar magnetic
effects, by a steady state a.c. nietliod based on measurements of short
loaded conrluctors indicated thai the cable should operate satis-
factorily with ordinary sending xoUagcs. I'lirtlier evidence that
none of these \arioiis types of distortion would be of serious con-
sequence and tlial llu- di>ioilion of a loadi-d lahli- could be corrected
by terminal apjiaralus, was obtained b\' exiK-riments with an arti-
I'uial lini' constructed to simulate closeK', with regard to electrical
characteristics, the t>lie of loaded conductor witli whicli we were then
experimenting. This artiticial line was loaded wiili iron dust core
coils which served the purpose admirabh'. not oiiU- as regards in-
ductance and alternating current resistance but also as regards
m.ignetic distortion. Iron dust is, of course, very different in its
magnetic characteristics from permalloy. However, owing to i In-
large number of turns on a coil, it is operated u mwU liighcr held
strengths and on a part of the magnetization cur\c corresponding
approximately to thai at which permalloy is operated on the cable.
The ca-ic for magnetic distortion was in fact .i little worse with the

nil: i.o.inin si KM.uaxr. n.i.i.cn.ii'ii c.tni.r.

.171

artilicial lint- ih.m witli the tluii |)r()p()st(l c.ildi-. 1"^. ") sliows a photi)-
graph of the artificial liiu', tlie roils of wliicli arc in tin- larj^c iron
jxits and the resistance and paper condenser capacil>' units of which
are in the steel cases. This line was e(|ui\alent to a l.TtM) nautical
mile calile loaded with M) millihenries per ii.m. .ind o\(,r it leKil>I<'

I'ig. 5 — Luailitl Artificial Lint-

signals were secured at speeds up to more than 2, GOO letters per
minute. Such a sfieed of operation was quite beyond the range of the
then available telegraph instruments, and accordingly special transmit-
ting and receiving instruments were required. The multiplex dis-
tributor of the Western Klectric printing telegraph system proved
an excellent transmitter for experimental purposes and, for receiving,

372 BELL SYSIEM TECHNICAL JOURNAL

use was made of a rdinluru'd xacuiiiii Uibe aiiiplitier and signal shaping
network, the signals being recorded on a string oscillograph. Fig. 6
shows part of a test message received over the loaded artificial cable
at a speed of 2,240 letters per minute.

The results of the tests with the artificial loaded cable were en-
tirely in agreement with our (■.•ilrnlatinn-; anri showed iliat it was

Fig. 6 — Test Message. Signals received April 16, 1920, over coil-loaded artificial
line equivalent to a 1700 n.m. cable with 30 m.h. n.ni. Speed 2240 letters per minute

possible to obtain satisfaclor\' signal sliape with a coil-loaded cable
having alternating current resistance and distortion factors ap-
proximating those of the permalloy-loaded cable. The exact behavior
of the proposed cable, including such factors as sea-return resistance
and a somewhat \ariable distributed inductance, could not, of course,
be duplicated without prohibitive expense. The approximation was
considered, howe\er, to be sufficiently good to justif>' proceeding
with a loaded cable installation so far as questions of signal shaping
were concerned. It is interesting to note that the factor which
limited the operating speed of the artificial loaded cable was one
which is not present in a continuously loaded cable but which would
possiljly be a serious factor in the operation of a coil loaded cable,
nameK^he oscillations " resulting from the finite size and separation
of the inihu'l.iiu't' units.

Oi'KR.MioN oi- Loaded Cables

With the comijlelion of the artificial loaded cable tests there was
still one principal question of transmission which had to remain
unanswered until a cable had been installed. This was the question
of balancing the cable for duplex operation. Ordinary submarine
cables are generally operated duplex, the total speed in the two
directions being usually from about 1.3 to 2 times the maximum
simplex or one-way speed. Except in cases where the external inter-
ference is very bad, the limitijig speed of duplex operation is deter-
mined by the accuracy with which an artificial line can be made the
electrical equivalent of the cable. OrdinariK the aitiliciai line is

" Carson, Trans. .■X. I. E. E., Vol. iS, p. 345, 1919.

THE LOADED SUBMARINE TEl.EGH.II'll C.IHI.I-. 373

tnailf up only of units of resistance and capacity arranged to ap-
proximate the (listributeil resistance anfl capacit>' f)f tlie cable. Some-
times inductance units are added to l>.il,in(c the small inductance
which even a non-loaiietl cal)le has. In ilir actual operation of
cables, artificial lines are adjusted with the greatest care and a remark-
able precision of balance is obtained. This is necessary because of
the great difference in current amplitude of the outgoing and incoming
signals, the former being of the order of 10,000 times the latter. It
is quite obvious that it will be much nKjre dilticult to secure duplex
of)eration with a loaded than with an ordinary cable, since not only
do the copp)er resistance and the dielectric capacity have to be bal-
anced, but the artificial line must also be provided with inductance
and alternating current resistance. Also the sea-return resistance
and inductance which vary with frequency must be balanced.

In view of these dirticullies it will probably be impossible to get
as great a proportionate gain from duplex operation of loaded cables
as is secured with ordinary cables. However, it is quite evident that
it will be possible to secure duplex operation at some speed, since,
with loaded as with non-loaded cables, the ratio of received to sent
current increases rapidly as the speed is reduced and on this account
it is much easier to duplex the cable at low speeds than at high. To
make duplexing worth while on a cable with approximately equal
traffic loads in Ixjth directions it is in general only necessary to get
a one-way duplex speed half as great as the simplex speed. In fact
in some cases the operating advantages of duplex would warrant
even a slower duplex speed. On the other hand, there are cables
on which the tratiRc is largely undirectional through most of the
day and which would accordingly require a one-way duplex speed
somewhat higher than half the simplex speed to justify- duplex oper-
ation. Whether a suflicienth- great speed of duplexing could be secured
to justify designing a cable on the basis of duplex operation could
not be judged in advance of laying the first cable, and accordingly
it was decided to engineer that cable on the basis of simplex operation.
Although it was expected that the new cable might at first have to
be operated simplex it should not be supposed that any great diffi-
culty or loss of operating efficiency was anticipated on this account.
The sfx-ed of the New York-Azores cable is so great that to realize
its full commercial advantage practically requires working it on a
multi-channel basis as, for example, with a Baudot code, multiplex
system, similar to that used on land lines. Such a system may be
conveniently adapted to automatic direction reversal and with this
modification most of the common objections to simplex operation are

374 BELL SYSTEM TECHNICAL JOURNAL

removed. Indeed, simplex operation may in this case possess a
real advantage over duplex from the commercial point of view since
it permits dividing the carrying capacity of the cable most efficiently
to handle the excess of traffic in one direction.

Although means have been made available for making efficient
use of the loaded cable it should be recognized that the method of
operation best suited to satisfy commercial demands must be deter-
mined from future experience with cables of the new type. This is
especially true with regard to relatively short cables. The discussion
of the loaded cable problem in this paper has been confined wholly to
the realm of long ocean cables where the limitations of the cable
rather than terminal equipment or operating rec|uirements determine
the best design. This is the simplest case and the one which at present
seems to show the greatest gain from loading. Where traffic require-
ments are limited and where there is no prospect of ever requiring
higher speed than can be obtained with a non-loaded cable of reason-
able weight, the ad\'antage of loading is less and becomes smaller
as the weight of non-loaded cable which will accomplish the desired
result decreases. It should not be concluded, howe\er, that loading
will not find important application to short cables. Many short
cables are parts of great systems and must be worked in conjunction
with long cables. In such cases it may pay to load short sections
where otherwise loading would not be justified. Permalloy loading
also offers great possibilities for multiple-channel carrier-telegraph
operation on both long and short cables and with this t>pe of opera-
tion in prospect it is too early, now, to suggest limits to the future
applications of permalloy to cables or to predict what will be its
ultimate effect on transoceanic commimication.

Useful Numerical Constants of
Speech and Hearing

By HARVEY FLETCHER

Ndtk: The material given in this p;iper was prrparoil in ,i more con-
ilensol form for piililiratlon in the International t ritical Tables. In order
to make it available in convenient form for the use of telephone engineers
it was ileemeil atlvisable to publish it in this journal. The author is
intlebtc<l to Dr. J. C. Steinlierg for able assistance in collecting and
arranging the material.

I Ullll lOf.RAlMIV

Al}lHI.I()t'il\.\l'll 1)1 (Kipcrs on I'iirli Discrimination, Intensity
niscrimination, Absolute Sensitivit\' of the Ear, I'pper Limit
of Autlibility, Lower Limit of Au<lii)ility, Theories of Hearing and
other miscellaneous works on Speech and Hearing are given in a
pafH>r by H. Fletcher, Bell Tech. Jour., Xol. H, 4, pp. 178-180, Oct.,
1023.

11. .AnsoiA'TE Sexsitimtv of the Ev\r

The sensitivity is the minimum audible rins pressure in dynes
cm~- in ear canal. The values below are the average of the results of
Wien (Arch. f. ges. Physiol. 97, p. 1, 1903), Fletcher and Wegcl
(Phys. Rei:. 19, p. 'yn.i. June, 1922), and Kranz (P/»V5. Rei<., 21. p. .57:?,
May, 1923) weighted 3, 72. and 1 L respectively according to number
of ears tested

T.ABI.t: I

Frequencv (dv)' 64 12S 256 512 1024 204,S 4t)%

Sensitivity (dynes I 12 .021 .OO.V) .(X)l 00052 (K)04I 00042

111. MiNtMiM Audible Power for a Normal Ear

The power in microwatts passing through each square centimeter
in the wave front of a free progressive wave in air under average
conditions is related to the rms pressure in dynes by the formula

P = 20.WJ-

The figures of Table I may be converted by this formula to minimum
audible powers. It is thus seen that the minimuin audible accoustical
power is at freciuencies between 2,000 and 4,000 vibrations per second
and is equal to 4X10"'° microwatts per square centimeter
' The symbol dv is used to denote "double" or complete vibrations.
375

376

BELL SYSTEM TECHNICAL JOURNAL

IV. Range of Audition in Frequency and Intknsity

In Fig. 1 the lower curve is a plot of the average sensitivity
values given in Table I. The upper curve gives the pressures that
produce a sensation of feeling and serves as a practical limit to
the range of auditory sensation. (Wegel, Bell Tech. Jour., 1, p. '^^^,

e 32 64 128 256 512 1024 2048 4096 8192 16354 rREOUtUCY D.V.
300 400 SCO 600 100 BOO 900 lOOO 1100 1200 1300 1400 PITCH UNIfS.

Fig, 1

November, 1922.) In\estigators vary from about S to 10 il\ Inr
the lower pitch limit and from about 12,000 to 35,000 dv for tlic
upper limit. (See I.) The values of 20 and 20,000 dv shown (ni
the chart were taken as being most representative. Half of the
observations lie within the dotted curves. The pitch is equal to
100 logo iV and the sensation units equal to 20 log P where iV is the
frcciuency and P is the pressure. (Fletcher, Joiir. Frank. Inst., 194,

\'

. M

MM I

M 1'i;K( El'TIHI.R I

NTREASE

IN

Intensity and Frequency

(Knudsen, Phys

/?«'

21,

P-

84, Jan., 1923)

Sensat

ion Le

vel in Sensation

Pf

r C

t-nt Increase in Intensity

Units or TU's

tL

be Just lVrccptil)le

10

li

20

14

30

12

40

11

SO

10.6

60 to 101)

10
Per Cent Increase in
Frc(iiiency to be Just

Frequency

Perceptible

64

.93

128

.59

256

.40

512

.32

768 to 4096

.30

NUMERICAL CONSTANTS OF SPTrCII .(A7) HEARING 377

p. 28i>. Sopt.. 1023.) The sonsalimi l,\tt S of a smind is (litincd I)y

p
5 = 20 loK where P„ i.s the tlireshold pressure, or it is llu- miniher

of sensation units al)o\e the tlireshold of audil>iiil>-. Tliese sensation
units are the s.iine as the transmission units used in tele|)lione ea-
Kineerinn-

The per cent increase in fretiucncy to lie just perce()lil)Ic varies with
sensation level in about the same way as does the per cent increase in
intensity to be just perceplil)le. The values arc for monaural re-
ception the tones beinjj heard successively.

\I. TiiK \imhi:r of Doriu.R \ihr.\ti()\s Nfxess.arv to
DetivRmine Pitch

(Bode, Psychol. Stud.. 2. p. -JU:}, l'.l()7)
T.XHI.K II

Weak Tones

Medium Tones

Freq. dv

Time (sec.)

No. of dv

Time (sec.)

No. of dv

128
256
384
512

0.0496

.0672
.0579

12.1

24 08
29 64

0 06908

0.0445

0.04274

17.6
17.1
21.8

\1I. The Masking Effect of One Sound J^pon the .AuniBiLiTY
OF .Another Sound

(Wegel and Lane, Phys. Rrc. 2:i, p. 2fi6. Feb., 1924)

If the ear is stimulated by a pure tone of frequency Ni, it is in
general rendered less sensitive to other pure tones. The tone that
constantly stimulates the ear is called the masking tone. The tone
that is heard in the presence of this stimulating tone is called the
masked tone. The masking is measured in sensation units or TU's.
It is equal to 20 X login of the ratio of the pressures necessary to per-
ceive the masked tone with and without the presence of the masking
tone. In other words it is equal to the number of units that the
threshold has been shifted. Fig. 2 shows the amount of masking
(ordinate) of tones of various frequencies as a function of the sensa-

378

HF.LI. SYSTEM I l-.CIIMC.IL JOCKXAL

"

r 10

H,

■ 200

i''f

5

I 20

■/

ff

■iV'

S

YTi

0

L^

1 J

It

o300

^

g

''^

5?

nx

N "Mo!

"l

^C>00

^

^

20

^

:^

'

^

^

-I

^

0^

/

^

■800

-^

M

w

I*

^,0

,

•«,

^K0<

1

^

?0
0

/

3

^

— ^

t_

"i

'160<

y/

o^

^

%

-

^

te

N.

>Z40(

/■

#

2

/

^,

^

^

^

<

X

1 ^ '^

■„

1-ig. 2 — Maskiiii; for To

A

^

A

A

\

^

/

^

^

^

^

^

\

tS

i

h

K

V

w

1

^

^

y

>

V

44

^

^

^

k.

s.

i

'400 600 800 1000 leOO 1600 eOOO tW two 3200 3600^000

FR[QUENCYOF MASKED TONE

(•"ig. 3 — Masking of Wirioiis I'rcniiciuirs l)V 1,20() Cycles at Sensation Levels of
H(\, fid, .III. I 44 I niiv, Rrspertively

NUMIIRICII. CO\'ST.-IMS OV SI'IECII .txn III.INIM; i'"

tion level (al)scissa) and fretiueniy .Vi of tlie masking; tone. In
Fig. 3 data for a niaskinj; Umc of 1,'2(M) dv is plotted in \v1h( ii liu-
frequencies of the masked tones are plotted on the abscissa. In order
to Ret satisfactory curves of this kind it is necessary to take more

^«

!«.

to 40 60 80 too 120
MASKINO TONE

Ni

.700

-

,^

P-»

f40

Nt

1 130< i~

f

/

y

1 20

N,.

90©

•

|40
0

N,=

zooo

/

^

/

/

/

__

_-

-'-

te*-

y

y

|40

0

N,.

tooo

-

.

.-"

/

,

^

^

y

N2= 300(

AA

t

^40

N.

1100

-

_^^

-.'

^

^

1 40

Nt=

4000

-

/
/

/

/

u*^

^

Kig. 4 — Masking Data. Tones in Opposite Kars. Masking Tone 1,200 Cycles

comprehensive data than that shown in Kig. 2. The solid curves of
Fig. 4 show the masking when the masked and masking tones are
introduced into opposite ears. The dottefl curves were taken from
Fig. 2.

380 BELL SYSTEM TECHNICAL JOURNAL

V'lII. Conduction of Skui.l Between the Two Ears

A comparison of the two curves in Fig. 4 sliows that the attenua-
tion introduced by the skull from one ear to the other when the tone
is introduced by a telephone receiver is between 4[) and 50 sensation
units corresponding to an intensity ratio of from 10^ to 10*. This
becomes 7 TU greater when rubber caps are interposed lietween the
head and the receiver cap.

IX. Localization of Pure Tones as a Function of thk Phase

Difference at the Tv;o Ears

(G. W. -Stewart. Phys. Rn:. 2r,, p. 42r,. May, 1920)
The experimental results can be represented by the foriiuila
^=0.0034A' + .8 (approx.)

<l> is the phase difference in degrees of the tones at the two ears.

0 is the number of degrees to the right or left of the median plane
that an observer locates the source of sound. The direction of
location is toward the ear leading in phase.

A^ is the frequency of the tone in dv. The relation applies only for
frequencies of 100 to 1,000 dv., inrlusi\e.

X. Constants Used in the Computation of thk Loudness of

A Com PI EX Sound

(Fletcher and Steinberg, Phys. Rn\. 24, p. 306, Sept., U)24)
(.Steinberg, Phys. Rci'. To he jniblished soon)

II /. 1h' ilir loudness as judged In' an axerage normal car, then
L = 3.;5H log,,

lof v^(ir„^)'T

where

/>n = rms pressure of the mih component,
W„ = a weight factor for the //''' component (I"ig. 5)
r = a root factor (I'ig. o)

The sensation levels (.See I\') given in tiie chart are for the coniiilex
tone.

NUMERICAL COXST.liWTS Ol- Sl'l-ECIl .1X1) Ilf-.IRIXG 381

XI. DVWMK AI, ("oNslAMS ()!• Till-: UKARINd MK(HAMSM

aiowill, W, II., A IVMhook of Physiolony"
(Wrights<in, Sir Thomas, ".\iial\ liial Mechanism of the Internal Kar" )

(a) Kar (".ma! • "

Length. 2.l-2.t» cm.
X'olume, 1 cm'.
Area at Openini;. .'M to .")() cm-.

LOG.„W

WEIGHT FACTORS FOR DIFFERENT

FREQUENCIES AT VARIOUS

SENSATION LEVELS

1,000 e.ooo 3,000 4,000 5,000

FREQUENCY

-—

/

/

VALUES FOR ROOT AT VARIOUS
SENSATION LEVELS

1

i

1

.

1
I

20

40 GO

SENSATION LEVEL

Fig. 5

100

{h) Drum

Vertical Diameter, .85 cm.
Horizontal Diameter, 1.00 cm.
Area, .65 cm-.

382 BELL SYSTEM TECHNICAL JOURNAL

(f) Hainnier

Length, .8 to .9 cm.
Weight, 23 mg.

id) Anvil

W'l-i.nht, '2.') mg.

(e) Stirrup

Weight, 3 mg.

(/) Mechanical Impedance of the Ear Drimi

(Data by Wcgel and Lane. \M\ Telephone Laboratories)

The order of magnitude is 20 to 30 mechanical ohms (cgs units)
over the frequency range from 200 to 4,000 dv.

XIL Si'i;i:(H Knkkc.y

.1. .Speech i'ower

(Data furnished by C. F. -Sacia and L. J. Si\ian, Bell Telephone
Laboratories)

L The average speech power delivered b\- an average speaker is
about 10 microwatts. In the process of obtaining the average the
silent intervals were included. If they are excluded the average
increases about .50'^;. The peak power frequently rises to 2,000
microwatts.

2. \'ariation of average speech i)ii\\tT (leli\ere(l by dilTerenl persons
during conversation. (Fig. ().)

B. Energy Freciuency Distrii)Uti(m of .\\eragc Speech

(Crandall and MacKcnzie, Phys. Rn\. 19. p. 221, ^Llrch, 1922)

(Fig. 7)

C. Acoustic I'ower in \\)wel Sounds

(Data furnished by (". F. Sacia of the Hell Telephdne l.abciratorics.

This data together with a description of the ai)par,itus .ind

methods usi-d in nbl, lining it will be given in a pajier soon to be

published. )

Table III I'ontains data on the power of indixidual xowels obtained
from analyzing the vowel portions of the syllables shown in the key-
word. The first two columns give the average power in microwatts

NUMERICAL COXSI.lNrS ()/• SrElUII .IXI> in-.AKINC, ja»

of S inalfs ami >< females during the particular cycle of the funda-
mental containing the maximum energy for unaccented vowels. A
rough estimate of the corresponding figures of typical accented

DISTRIBUTION OF SPEECH POWEi?

ANY AUCIUA P OlVtJ TMt PtHCtNT Of ift^^Lr:l «M05t iflllH POvytH
ISLEJSTMANWtQUAlTOTHt COmtSfONOIHO ORSIMATt a TIMES THE
*V(»*X POAEK 'M Atl 5«Ant«S CWIVt B*itO » NOIMAi. TELEPHOfiC
T*.V.1S L-VELi or 87 MW /WO 59 WOMEH. SPEECH PC»iU ritlE MEANS
T»E £:£:t,»iCAI. POnMOUm/TOf ACOMHWCIALTtLEPMOIt 5UBSCI.

PERCENT SPEAKtRS P
Fig. 6

aa

n

~i

.oei

/

1

ran

1

j !_,J i— 1 1 ! 1

/^l 1 i 1 i i 1 1 !

1

E>*ERG> FREQUENCY tUSTPlBiniON ■

—

Of AVtRACt SPttCn

Tut 3PtCC»««W(MO*«omTf5n!tOLOICr

ncaot 9CTWIEN n.iflj i» r*cwdn

.03 j

1

;l/i 1 !

/Mil

1

i

1

X

H

1

j

' ; ^ ''a. :

1

1

1 1 i^^._-

-^-x.

'^

^PX 1.500 2.0OO 2^ 1000 iSflO lOO

FRrooENa"

Fig. 7

384

BHU. SYSTEM TECIINICAI. JOURXAL

vowels ma>' be obtained liy multiplying these \alues by a factor of 3.
The third and fourth columns gi\e peak factors which convert the
power figures of the first two columns into maximum instantaneous
powers. Columns 5 and 6 give the maximum values of these peak
factr)rs found among the male and female \()ices, respect i\ely.

TABLE III
Acoustic Power in Microwalls of the Vowel Sounds

(1)

(2)

(3)

(4)

(5)

(6)

Av. Peak

Av. Peak

Max. Peak

Max. Peak

Vowel

Key

Pm

P^

Factor

Factor

Factor

Factor

8 males

8 fem.

8 males

8 fem.

8 males

8 fem.

u

tool

27

41

2.6

2.8

3.8

3.4

u

took

32

49

4.0

3.1

4.9

3 4

6

tone

33

44

4.1

3.4

6 4

4.9

o'

talk

37

49

4.5

i.3

5.7

3.6

o

ton

29

38

4.6

3.9

6.8

5 7

a

top

50

48

4.2

3.6

4.2

4.7

a'

tap

43

39

5.4

4.7

7.4

5.2

e

ten

25

30

5.6

3.8

6.3

4 6

a

tape

21

30

5 3

4.5

6 0

5.1

1

tip

25

31

4 1

3.8

5.8

5.7

e

team

32

23

4.7

2.6

5.8

3.C

XIII. Frequency of Occurrence of English Speech Sounds

(Table IV contains data from a book by Godfrey Dewey, "The

Relativ'e Frequency of English Speech Sounds," Harvard

University Press)

TABLE IV

Relative Frequency of Occurrence of English Speech Sounds

Speech

Rel.

Speech

Rel.

Sound

Key

Freq.

Sound

Key

Freq.

a

top

3.3

g

0.74

a

tape

1.84

h

1.81

a'

tap

3.95

J

0.44

e

ten

3.44

k

2.71

e

eat

2.12

I

3.74

er

term

0.63

m

2.78

1

tip

8.53

n

7.24

1

.like

1.59

ne

hang

0.96

o

ton

6 n

P

2.04

o

tone

1.63

r

6.88

o'

talk

1 35

s

4.55

u

took

0.71

sh

shell

0.87

0

tool

1 89

th

(thin)

.37

ou

our

0.59

th

then

3 43

b

i.ai

t

7.13

ch

chalk

0.52

V

2.28

d

4.31

w

2.08

f

1.84

y

z

0.60
2.97

NUMERICAL CONSTASliS OF Sl'l-.liCll .IXP lll-.IKIXa M<

XIV. In iiKi'KKT.vriDN of Spkixii
(I'lelcliLT. U., Jour. Frank. Inst., H)3, (i, Juiu-, l',t22)

A nu-asurc of the iiUerprelation of speech was ohtaiiied t)y means
>f artkulation tests. Meaningless syllables were pronounced and
>l)ser\ers were required to record the syllables. The articulation is

,

—

80

/

/'

"~-

/

-

—

|(0

1

r

YLL
Of T

ART
N5AI

lONL

HON
CVEL

AS
OF

HE3

CTIO
PEEC

-

1 40

1

1

ZO

1

J

"

-

n

L

40 CO 80 100 leo t40

SENSAnON LEVEL

Fig. 8

'b 40

-Lu

ETFEa

UPON INTERPRETATION Of EUMINATING

1

VWRWOS FWTIONS OF IHE FREQUENCY RANCE

•k^^

i • 1 1 1 1

.■^

S^ ' '

►IF'

■)

f ;

%,.^

J8£S|

Ul,

i !

' oS'^ ' ' 1

i 1 jj^! ^

}x

1

^:

1 1 M

i

%.

1

>y

N

\ t

,

N

'^

,

y 1 '

_

1

"^

200O 3000

FREQUENCr-
Kig. 9

the per cent of syllables that were correctly recorded. The articula-
tion depends upon the sensation level of the speech (Fig. 8), and
upon the width of the frequency band transmitted (Fig. 9).

The syllables that were recorded in these tests were analyzed to
show the articulation of the fundamental speech sounds. Fig. 10

386

BELL SYSTEM TECIIXICAL JOURNAL

shows these artirulations as functions of the sensation level of the
speech. In Fig. 11 they are shown as functions of the width of the
transmiited frequency band. It should be noted that the term
articulation as here employed denotes only the correct interpretation
of unrelated speech sounds and is not a measure of voice naturalness
which is also an inii)c)rtant factor in the telephnnir trnnsini?sinn
of speech.

"" E::: r:;-^i:_:E ■""

:. T ;„■..:;-:, ::--r-:|

» \

- ±-3 -;-■:: :-^ - 'i

'coQUonoi oiooDKoiooo onor

OBOToiooo oooe'r my onoao

CO , ir-i ^ 'v

N 1 1 1 1 i M T 1 l"KI 1 1 1 1 1 M 1 I 1 I M 1 1 1 M 1

z ^ T >

l\ M M n\M M IN 1 M 1 1 I^M t M l\l 1 1 MM 1

S0§ 1 1 IM 1 1 1 1 1 1 1 1 1 1 M 1 M M 1 1 1 M ni 1 1 M VI

N n N^

S 1

1 1 1 M 1 1 1 1 11 1 Ml M 1 1 1 1 M M t t M tin

^m 1 0 no d 0 BO o owo w o no t

onou oloom onoe onojtioiooti o

lOo".--^- .._,^ ._.,_, .__.

s > 1 ""vi ~\ ■ ^ ^

S 5 ^

I- I- X >, ' "t

5o5 :

^ — 4^ >»

BOh oooa'OBOuoiooaoKio

omz ono n onoctiOiooK ono % o

DO -- ^. -"-^ s ■*"S .-5

r ->^rr

^ _ -5 ' X s;- - -

L- A \ ARTICULATION OF FUNOAMENTAL SOUNDS

1

loo; oioop oiooe oioov oioot onoui o
FiR. 10

1

E^E

44H hH=^

^

^^^^UA

[A _U

J ,/ 1 1 1 i 1 , ; 1 (

1 / 1 1 1 ' ' 1 '

> I 1 1 1 1 1 1 1 '1

^

OI23450l23.d50l23^50l23450IZ3^50IZ3-150l23450IJ3-150l234501J3A5

BUinttJ r 1 o'eVya

CO ' . . ' I ' ' ' . H— ' — ; I ' ' ■ ■ ' >/ ■ I i It'll \-A

pOI23i)}Oi23il30IZ3.i:OI234J0123430i;}4SOI234)OIZ}4 90l23'd50l23ii;

1 dowtamestib

•^i>^.

lii2345Ci23^50i2345Oi23^3OI2343OI234S0l234J0l2345CI23^5OI2345

h a'u aj zncliK s

ARTICULATION AS A FUNCTION OF THE
BAND WIDTH PASSED BY HIGH OR
LOW PASS riLTtRS. ABSCISSA IS

-IE cuT-orr FRtfluENCY in mlo-
cycles.

Fig. U

Graphic Representation of the Impedance of Net-
works Containing Resistances and Two Reactances

By CHARLES W. CARTER. Jr.

AiisTHACT: The driving-jtolnt linpcdanrc of an electrical network com-i
jiosttl of any nunifier of resistances, arrangcil in any way, and two pure
reactances, of any degree of complication within themselves but not related
to each other by mutual reactance, inserted at any two points in the resist-
ance network, is limited to an eccentric annul.ir region in the complex plane
which is <lctermincd by the resistance network alone.

The Iwundaries of this region are non-intersecting circles centered on
the a.xis of reals. The tliameter of the exterior boundary extends from the
value of the impedance when both reactances are short-circuited to its
value when Ixtth are o|>cn-circuited. The diameter of the interior boundary
extends from the value of the impedance when one reactance is short-
circuited and the other o|x.-n-cirouited to its value when the first reactance
is open-circuitc<l and the second short-circuited.

VV'hcn either reactance is fixed and the other varies over its complete
range, the locus of the driving-point impedance is a circle tangent to both
boun<iaries. By means of this grid of intersecting circles the locus of the
driving-point impedance may be shown over any frequency range or over
any variation of elements of the reactances. This is most conveniently
done on a doubly-sheeted surface.

The paper is illustrated by numerical examples.

iNTROnLCTION

SIPPOSK that any numljer of resistances are combined into a
network of any sort and provided with three pairs of terminals,
nimibered (1) to (3) as in Fig. 1. The problem set in this paper is
to in\estigate the driving-point impedance' of such a network at

VariaOie

Any

VariaWe

Reactance

(2)

Resistance

(3)

Reactance

T-2

Net.v«rk

^3

Fig. 1 — The Network to be Discussed

terminals (1) when variable pure reactances, Z; and Z,i, are connected

to terminals (2) and (3), respectively. Zj and Z3 are forined of

capacities, self and mutual inductances. They are not connected

to each other by mutual reactance, but they may be of any degree

of complication within themselves.

The problem is dealt with in terms of the complex plane: that is,

the resistance components of the impedance, 5, measured at terminals

' The driving-point impedance of a network is the ratio of an impressed electro-
motive force at a point in a branch of the network to the resulting current at the
same point.

387

388

BELL SYSTEM TECHNICAL JOURNAL

(1) are plotted as abscissas and the reactance components as ordinates.
To every value of the impedance, then, there is a corresponding
point, and to the values of the impedance over a range of variation
of some element, or over a frequency range, there corresponds a locus,
in the complex plane. This locus may be labelled at suitable points
with the corresponding \alue of the variable. So labelled, it com-
bines into one the curves which are usually plotted to show separately
the variation of the reactance and resistance components or to show
separately the variation of absolute value and angle.

The use of the complex plane is not new: it is the basis of most
of the vector diagrams for electrical machinery. The character-
istics of both smooth and loaded transmission lines have also been
displayed by its means. Its application to electrical networks, how-
ever, is not common, and it is a subsidiary purpose of this paper
to illustrate the fact that the properties of certain networks, which
have complicated characteristics if exhibited in the usual way, may
be shown quite simply in the complex plane. This simplicity, com-
bined with generality, is attained by application of theorems con-
cerning functions of a complex variable which are immediately avail-
able.

THii FuND.\Mii;NrAL Hyu.vrioNs
The impedance measured in branch 1 of any network is

S = R-\-iX = ^

(1)

where A is the discriminant of the network, (.itiier in terms of branches
or w independent meshes. -

Assigning the reactances Zs and Za to meshes 2 and 3

Rn Rn Ri3 ■ Rm

Ri\ JR22 + Z2 R23 R'ln

Rn Rsi Ri3-\-^i Ran

A =

R.n

Rn-2

R„,

Run

(2)

where Rj^ is the resistance in mesh j and R,k{ = Rkj) that common
to meshes j and k.

»Ste: (;. A. Cam[il)ell. Transactions of thu A. I. K. K., M), 1911, pages 873-909,
for a complete discussion of the stilution of networks by means of determinants.

NETII'OR'KS CtiXI.IIXIXd VIIV) Rr.lCT.IXCf'S 3S0

p. f e i4+i4sjZi+/ljjZj+i4jj.3»ZjZj ,„.

1 luriforf i = -J — p-j „ , . y , . ^-^ (>i)

when- .1 is tin.' iliscrimiiiant of the resistance network alone and /I/,.**.//
denotes the cofactor of the product of the elements of A located at
the intersections of rows /, k and / with columns^, k and /, respectively.
I"or con\eiiience this is written as

a + bZ2+cZ3+dZiZ3 ,..

^ ~ a, + biZi + CiZ3+diZiZ{ ^ '

The constants of (3) and (4) are real and positive since they are
cofactors of terms in the leadint; diagonal of the discriminant of a
resistance network. The determinant liciii^ sxinmclrical, there is
the following relation among them :

(adi — a id + bci — bic)- = i{bd I — bid){aci — (liC) . (5)

The function to be studied is, then, a rational function of two
variables, having positive real coefficients determined by the resist-
ances alone. Furthermore, if one reactance is kept constant while
the other is varied, the function is bilinear. The particular property
of the bilinear function, which has been studied in great detail, of
interest here, is that by it circles are transformed into circles.^

When, as in this case, the variable in a bilinear function is a pure
imaginary, the function may be rewritten in a form which gives
directly the analytical data needed. I'"or suppose

u+vz ,„.

w = — -— (6)

Ui + ViZ

where z is a pure imaginary and the coefficients are complex. This is
w=—-\ r— ^— . (7)

Vi Ui+ViZ

Multi[)lying the second term by a factor identically unity,

t' , U — UiV/Vi ^Vi'{Ui + Viz)+Vi{Ui'+Vi'z') ,„,

■w= 1 i X 7-r — r- • (8)

I'l «I+t'l2 UiVi -|-Mifl

where primes indicate conjugates, or

UVi' + tli'v tlVi-UiV /Ui' + ViZ'\ ,^.

UiVi' + Ui'vt tllVi' + Ui'l'l \ Ul+ViZ )'

• G. A. Campbell discusses, in the paper cited, the theorem that if a single element
of any network be made to traverse any circle whatsoever, the driving-point im-
pedance of the network will also describe a circle.

390

BELL SYSTEM TECtlNlCAL JOURX.IL

Now, as s is \'aried, the first term is constant. In the second term
the first factor is constant and the second factor \aries only in angle.
since the numerator is the conjugate of the denominator. The first
term, therefore, is the center, and the absolute value of the first
factor of the second term is the radius, of the circle in which w moves
as z takes all imaginary \alues.

One X'ariaiu.k Rk.u tam k (iIvinc; Circli.ar Locus

The significance of the equations may he made apparent 1)>' a
study of Fig. 2, which shows the imjjedance S when one of the re-
actances, say Z3, is made zero. We have, then,

5 =

A+AiiZt a+bZi

■4 ll+i4 11.22^2 Cl + biZi

(10)

and the trixial case abi — aib = 0 is excluded. This is of the t\pe of
(6). When 7.2 \aries over all pure imaginary values, S traces out a

Ki^. 2--L0CUS of llic lMi|Hil.nm- .V wiili ( )nc \aii.ililc Kf.ictaiue

circle, which ('.)) shows h.is its ( riiu-r on ilie resistance axis. Its inter-
cepts on the resistance axis are

and

.S"= =R,„ sav, when /. = ()
«i

S= T- =Jii; when ^2 = 00.

(11)
(12)

xr.riroRKS coxt.iimxg rii'o reactances .wi

Hut in .1 symmrtric.il (Icti-rniiii.iiit

• J 1.-1.= -. 1 1.- =.1.1,.....; (i:j)

tliiTi'furt'

w llCIII

ab^Kaxh (14)

° < ,'

<i 05)

R., < R,. (1(>)

To tiiul till' \>ilur of .V wlifii Zt lias some \aliK-, say Zi = iXi, it s
only necessary to mark the circular locus with a scale in terms of Z^.
This may be done directly by using (9) to determine the angle, <<>,
which the radius of the circle makes when Z2 = /A'2. It is simpler to
use the fact that a line passing through Rh and the point S has an
intercept on the reactance axis of

X\ = kX2 (17)

where x =6 «..

The factor k is determined by the resistances; therefore the scale,
as well as the locus, is completely fixed by the resistances. .Since k is
always positive, as X; is increased the circle is traversed in a clock-
wise sense; for positive values of Xi the upper semi-circle is covered:
for negative values, the lower. That is, when Zn is an inductance
the impedance of the network varies on the upper semi-circle from
R„ to Rb as the frequenc\- is increased from zero to infinity. When
the magnitutle of Zj is changed the same semi-circle is described but
each point (except the initial and final ones) is reached at a different
frequency. When Zj is a capacity the lower semi-circle, from Ri,
to Ra, is traced out.

We know that, in general, the value of a pure reactance ■* increases
algebraically with frequency, and that its resonant and anti-resonant
frequencies alternate, beginning with one or the other at zero fre-
quency. When Z: is a general reactance, therefore, as the frequency
increases the entire circle is described in a clockwise sense between
each consecutive pair of resonant (or anti-resonant) frequencies.
For example, if Zj is made up of w branches in parallel, one being an
inductance, one a capacity and the others inductance in series with
capacity, as the frequency increases from zero to infinity the circle is
traced out completely «— 1 times commencing with Ra.

'See: A Reactance Theorem, R. M. Foster, Bell System Technical Journal, .April,
1924, pages 250-267; also: Theory and Design of Uniform and Composite Electric
Wave-Filters, (). J. Zobel, Bell System Technical Journal, January, 1923, pages
1-47, especially pages 35-37.

392

liEU. SYSTEM TECHNICAL JOURNAL

Kig. 3— Impeilanie of Resistance Network Containing One Variable Reactance

W

7

,

. .

/

^

,^

o.*o

^en"^

/

^^

/

/-

^

pO<-^

/

/'

^

^C

06''

500

t

/

/

y

y

1

/

/

/

R<

sisU

ince

Cor

ipor

snts

4O0

I
o

/

/

/

/

300

/

/

y

R(

act!

nee

Con

pon«

nts

200

/

A

.^

X

"

0.(

57S

;^

-^

/

/

%

V,

"a?

'~—

''IB/,

>""

'

—

^^

,

0.2

5~h;;

ry

__

V 5C

10

10

DO

FP
15

EQl.
DO

JEN
20

oo

25

DO

30

DO

1 i^. .i.i C'oiiipoiiciUs of liii|K.ilaiuo in I'in. 3 wlun Z; is an liidiiitancc Having llic
Values 0.05, 0.10, ami 0.20 Henry

xi:in\)NKS ioxi.iixixa nro la-.icr.ixci-.s .w

In Fin- '>i is shown the iniiHiLuue lorus for tlie p.irtiiuhir network
niven on the diagram. The lirile is marked in terms of Zj. From
it, certain properties of .V nuiy lie read at onee: the resistance com-
ponent. R. \aries between 2('>() and 7")() ohms, and the reactance

1

7CX3

/'

/

000

j

1

^

500

Re!

ista

yce

Con

ipon

snt

/>

y

/

/

400

/

t

in

/

\

/

300

5

\

/

\

/

\

/

V.

y

200

/

\

,^

"

' ■

/

\

/

Rea

ctar

ce C

ami

one*

I

too

/

\

/

\

/

0

/

F(

!EQl

JENI

:y-

^

5(

10

1)

00

/

00

zc

00

25

00

30

00

/

/

-100

_L

^-L^ 1

/

/

Pfir

20O

\

/

/

V

/

J

L

>

Fig. 3b — Components of Impedance in Fig. 3 when Z% is Doubly-Resonant

component, X, is not greater than 245 ohms nor less than —245 ohms,
attaining these values when Z2 is +510/ and —510/, respectively.

When the variation of the reactance Zz with frequency is known
the variation of R and X with frequency may be found by using the
scale on the circle. For a particular reactance network, the scale may
be marked directly in terms of frequency, or if it is desired to compare
the behavior of R andjA' when different reactance networks are sub-

394 HELL SYSTEM TECHNICAL JOURNAL

stituted, the impedance locus may be marked with the frequency
scale for each reactance network in some distinctive manner.

However, to show in the usual way some of the types of R and A'
curves represented by the locus of Fig. 3, as well as to avoid needless
complication of what is intended as an illustrative rather than a
working drawing, Figs. 3a and 3b have been prepared by direct pro-
jection from Fig. 3. In Fig. 3a are shown the R and A' curves plotted
against frequency when Zj is an inductance. In Fig. 3b are shown
similar cur\es when Z« is a doubly-resonant reactance. The R com-
ponent has a minimum at each resonant frequency and a maximum
at each anti-resonant frequency, while the A' component becomes
zero at resonant and anti-resonant frequencies alike. The number
of examples from this one resistance network might be multiplied
endlessly; it is believed, however, that these are sufficient to show the
great amount of information to be obtained in very compact form
from one simple figure in the complex plane, and the especial superior-
ity of the complex plane in displaying the characteristic common to
all the curves of F-igs. 3a and 3b: namely, that R and A at any fre-
quency, with any reactance network, are such that the impedance
lies on one circle.

Two V.'\RiABLE Reactances Giving Eccentric
Annular Domain

Returning to the more general impedance of (4) it is seen that in
each case short-circuiting and open-circuiting the terminals (2) and
(3) one at a time, and varying the reactance across the other termi-
nals, yields a locus for 5 which is a circle of the type just discussed.
These circles are determined as follows :

Extremities

Circle

of Diameter

Sea

le Factor k

Z2=()

Ra and R^

c/ai

Zj=x

/?(, and R,t

d/b,

z,=o

Ra and Rt.

b/a,

Z,= x

Re and R,,

d/ci

where R, =c/c\ and Rj = d/d\. .\n examination similar to that in

(13)-(15) shows that

R^<.Rk<Ri, (18)

R.<Rc<Rd. (19)

NETH'OKKS CONIAIMNG 7110 Ix'li.lCr.l.VCliS ,w;

It may furilu'rinore be assiimf<l without loss of vti-niTality, since it
is nuToK' .1 matter of l.ihellinn the re.irtaiues Z-i and Z^, that Rk^R,-

Hence, the four critical pniuis of the imped. nice .ire .dw.us in the
folldwim; order ;

R^^Ri<,R,<. Rj.

(20)

These circles are shown in Fig. 4. By means of the appropriate scale
factors K each may be marked in terms of the reactance which is left
in the circuit.

Now suppose Zi is kept constant at some \alue which is a pure
imaginary, and Z: is varied over the range — /» <Z2^+'^. We
may rewrite (4) in the normal form ((5):

5 =

a+cZ3+{b+dZ3)Zi
a 1 + C1Z3+ {hi +diZ3)Zi

(21)

^er Bounda^

Fijj. 4 — The Region to which 5 is Restricted and the Critical Circles

The locus of S is one of a family of circles, each circle corresjionding
to a \alue of Z3 and completely traced out by complete \ariation of Z-.
The properties of each circle may be found by substitution in (9).

396 BELL SYSTEM TECHNICAL JOi'RX.IL

Similarly, if Z; is held constant while Z3 \'aries, the locus of 5 is one
of another family of circles.

By the use of (9), keeping (5) in mind, it ma>' be shown that the
circles of each of these families are tangent to two circles determined
by the resistance network alone. Both families are tangent inter-
nallj- to a circle centered on the resistance axis, extending from Ra to
Rd. Both are tangent to a circle centered on the resistance axis, ex-
tending from Rb to Re, in such a way that the Zj-constant circles are
tangent externally and the Z2-constant circles are tangent enclosing the
circle from Ri to Re- These relationships are illustrated in Fig. 4.

The circles Ra to R,i and Rb to Rt are, therefore, outer and inner
boundaries, respectively, of the region mapped out by the two families
of circles generated when tirst one and then the other reactance is
treated as a parameter while the remaining reactance is treated as
the variable. No matter what reactances ma>- be attached to termi-
nals (2) and (3), the resistance component R, measured at terminals
(1), is not greater than the resistance when terminals (2) and (3) are
open and not less than the resistance when terminals (2) and (3) are
short-circuited, and the reactance component A', measured at termi-
nals (1), is not greater in absolute value than half the difference of
the resistances measured when terminals (2) and (3) are open and
short-circuitcfi. That is,

Ra<R<Rd. (22)

\X\<hiRj-Ra). (23)

The two families of circles (Zj-conslant and Zs-constant) intersect
and may be used as a coordinate system from which the components
of 5 may be read for any pair of values Zj, Z.i. To avoid inter-
sections giving extraneous values of 5 resort is made to a doubly-
sheeted surface, analogous to a Riemann surface, for which the two
boundary circles are junction lines. That is, the impedance plane is
conceived of as two superposed sheets, transition from one to the
other being made at the boundary circles. Thus, in Fig. 5, where
the two sheets are separated, each Z2-constant circle is shown run-
ning from the outer to the inner boundary in Sheet I (using the clock-
wise sense), and from the inner to the outer boundary in Sheet II,
while the Zs-constanl circles run from the inner to the outer boundary
in Sheet I and are completed in Sheet II.''

' It may be mentioned that the inner and outer boundaries are iinpedaiu'e curves

traced out when ZiZj = - — '-^ and -^ = ." ,"", respectively.

A ij.u A ii.:j ^) A 12 A ij.jj

xniH'OKKs coxT.-iixixa /no I<I-..ICT.IXCF.S .W7

Sheet II
Kig. 5 — The Doubly-Sheeted Surface

398

HELL SYSTEM TECHNICAL JOURNAL

100 200 300 4-00 500 600 700 800 900 1000

Kig. 6^Sheet I

Sheets I and II of I-"ig. 6, taken together, show the impedance domain of the network
at the bottom of the opposite page, made up of three fixed resistances and two
varialjle reactances. The dashed curve, appearing in four distinct parts, two on
each sheet, shows the impedance .V when /; is the doubly-resonant circuit of Fig. 3b,
and Z| is an inductance of I.O henry. Points on this curve are labelled in terms of
frequency

XnntONKS COM.IIMXu /no KI.ICT.IXCI S .VX>

Fig. 6— Sheet II

Z2(2)

(3)Z3

400 BELL SySTEM TECHNICAL JOLRXAL

The numbering of the sheets is, of course, arbitrary. If the upper
half of the Zj = 0 circle is put on Sheet I, the arcs of the other critical
circles are determined as follows:"

Circle On Sheet I On Sheet II

Zi = 0 Upper half Lower half

Zi=<x) Lower half I'pper half

Z3 = 0 Lower half Upper half

Zi=oo Upper half Lower half

Each sheet, then, is divided into four sub-regions, indicated on
Fig. 5 by the signs of the reactances for which S is within them. When
Zi and Zz are composed of single elements the sub-regions in which 5
falls at any frequency are as follows :

Zj

Zi

Sub-
Region

( + . + )

At Frequency
Zero Infinity

Inductance

Inductance

S = Ra

S = Ri

Inductance

Capacity

( + .-)

Re

Ri

Capacity

Inductance

(-, + )

Rb

Re

Capacity

Capacity

(-.-)

Ri

Ra

The course of S over the complete frequency range may be shown
by a curve through the appropriate intersections of the Zj-constant
and Za-constant circles, as in the following example.

The impedance region for a particular bridge network is illustrated
in the two sheets of Fig. 6. The arcs of Z;-constant and Zj-constant
circles in each sheet form a curvilinear grid superposed on the R,X
grid of the complex plane. For e.xamplc, if Z2 = '200/' and Z3 = 900j,
the value of 5 is read from Sheet I as 327 + '29L and 5 has this value
irrespective of the structure of Zj and Z3.

An impedance cur\c (dashed) is shown in Fig. li representing the
variation of 5 with frequency when Zj is the doubly-resonant reactance

' When the sheets arc numliered in this way, the point .S falls on Sheet I or Sheet 1 1
according to the following talile, in which kt and k; arc the critical values for the
product and quotient of Z2 and Zj, respectively, given in Footnote 5:

(Z,, Z.)

( + . + ) -

(+.-)

(-.+)

(-,-)

On Sheet I, if

Z,/Z,<k,

Z,Z.>k,

Z,Z,<k,

Z,/Z,>k,

On Sheet II, if

Zi/Z,>k,

Z,Z,<k,

/.:Z:>k,

Z,/Zi<k,

For the network of Fig. 6, *i = 116,875 and *2 = 0.9721 11.

NF.nroKKS cox 1. 11 mm; /jro Hn.icT.-txcF.s mi

ustxl in !•"!>;. .'Ui and Za is ;ui indurtani'i- of I.O lu-nry. This inipt'dancr
curve has four parts, (wo in carii shed. It starts on tlu- resistance
axis at the intersection of the Z3=oc and ^3 = 0 circles. As the fre-
quency increases from zero the first part of tiie cur\e is traced out in
Sheet II. At 2'i cycles the impedance is approximately HlO+iHO
The reactance com[)i)nent has a maximum of aboiil 2')() ohms at about
70 cycles, the resistance component has a maximum of about 720
ohms at alwut U»0 cycles, the reactance component has a minimum
of alxiut —110 ohms at about 300 cycles, and finally at about 480
cycles the curve reaches the inner boundary, whereupon it changes
to Sheet I. It remains in .Sheet I up to a frequency of about 910
cycles, the resistance component having a minimum and the react-
ance component a maximum, which may be read from the diagram.
The im|X'dance between 010 cycles and approximately 1,300 cycles
lies on Sheet II, and from 1,390 cycles to infinite frequency on Sheet I.
The resistance component has a total of three maxima and three
minima, and the reactance component three maxima anfl two minima,
following the cyclical order: /?-minimum, A'-maximum, /^-maximum,
A'-minimum.

An interesting e.xercise is to obser\e the effect on the impedance
curve of changing the value of the inductance Z3. The curve inter-
sects the Zj-constant circles at the same frequencies in each case,
l)Ut the points of intersection are moved in a clockwise or counter-
clockwise sense as Z3 is increased or decreased. With each such
change parts of the impedance curve disap[)ear from one sheet and
reappear on the other. For instance, with a decrease of the inductance
Zj the first loop of the impedance curve on Sheet II shrinks, and with
sufficient decrease in inductance may become too small to plot, al-
though it does not disappear entireK'.

It is evident that if Z; and Z,i are formed of reactance networks of
greater complication the impedance curve may be very involved.
But no matter how tortuous its path, it is restricted to the impedance
region, that is, to the ring-shaped region between the non-intersecting
boundary circles determined by the resistance network alone.

My thanks are due to Dr. George A. Campbell for his stimulating,
continued interest, and to Mr. R. M. Foster for suggestions on every
phase of this work.

The Vibratory Characteristics and Impedance of
Telephone Receivers at Low Power Inputs

By A. S. CURTIS

THK <)r(linar>- telephone recei\er is one of the most sensitive
known detectors of weak alternatinj; currents over a considerable
part of the audible frcquenc\- range. Its high sensitivity, combined
with its simplicity and convenience, have led to its general adoption
as the detecting element in the A(" impedance bridge and other
measuring apparatus employing the nul method. There are also a
number of cases outside of the laboratory- where a knowledge of the
behavior of the recei\er o[)erating near its minimum audible power
input is of importance. In apparatus developed during the World
War, such as that for detecting and locating submarines, in radio
reception, and in the reception of various other sorts of signals, the
receiver is frequently operated near the threshold of audibilit>'.
While it is in general possible to employ a vacuum tube amplifier to
render weak signals more easily audible, considerations of cost or
increased complication often make it impracticable to do so. In
any case, if it is desired to reduce to the limit the minimum audible
signal, it is necessary to know the constants of the receiver working
on these low power inputs, in order to design intelligenth' its circuits
and other associated apparatus.

Current literature dealing with the sensitivity of telephone receivers
indicates that the relation between the impedance and \ibratory
characteristics of the receiver at currents near minimum audibility to
those as ordinarih- determined in the laboratory, is not generally
known. It would, therefore, seem of interest to publish the results
of an experimental determination of receiver characteristics at very
low currents. Such an investigation was carried on in 1918 and
1919, using the Western Klectric Xo. 509 radio receiver (the present
standard Western Electric Receiver for radio use). The work,
however, was done, not merelj' with the idea of determining the
characteristics of this particular instrument, but for the purpose of
ascertaining the behavior of receivers in general, near minimum
audibility.

Inasmuch as the daiiipid impidance of tin- receiver- that is liie
impedance with the dia|>hragm held motionless — is very close to
the impedance obtained with the instrument on the ear, it is com-
monly used as the basis of circuit calculations. A knowledge of its
value for weak currents is therefore of importance. Measurements

402

lELEl'UONE RECFJV'ERf; AT LOW fOllT.R IXPl'TS

40.1

wiri> lirst inadf of the clanipc*! impidatuc r»f six instruinenls at a
fri'<|iK'iuv of 1,()(K) cycles for a widi- ranRi- of input currt-nt, and later
till' work was i-xti'iidod to the measurement of the vibratory charac-
teristics. A l)rid^;e network was used for measuring the current
supplied to the impeilance bridge and from the circuit constants the
current through llie receiver under test could lie calculated. TheVe-

Controlling Nthvtjrk Impedanct B''idfl«

Oscillator

Htod Receivers

Fig.

sistances in the various arn)s of the controlling bridge network were
chosen so as to furnish an essentially constant current through the
receiver under test, although its impedance might vary through a rather
wide range. With the extremely small values of currents involved,
it was necessar>' to amplify the power to the bridge balancing receivers
approximately 100 TU. For this amount of amplification, it was
obviously necessary to take extreme precautions in grounding and
shielding the apparatus, in order to reduce to inaudibility the effect
of stray fields from the source of current supply. This was success-

404

BELL SYSTEM TECHNICAL JOURNAL

fully (lone and the impedance bridge measured impedance accurately
with currents as low as IQ-^ amperes, through the receiver under
test. The correctness of the point of balance of the bridge was estab-
lished by measurements of standard impedances over the range of
currents employed in the receiver tests. A schematic diagram of
the circuit is shown in Fig. 1.

For measurements of damped impedance, the receiver was placed
in a small sound-proof box, with its diaphragm damped by a microm-
eter depth gauge, which was carefully adjusted so as just to impinge
upon the diaphragm. It was necessary to insulate the receiver from
mechanical agitation, since minute voltages generated in it were
sufficiently amplified to cause an excessive noise in the head receivers.

Fig. 2 shows the damped eflfective resistance and reactance of the
six instruments, taken at 1,000 cycles, plotted on semi-logarithmic

Mk. 1

paper. It will be seen lii.n Inluw approximately 10 '' amperes, the
impedance is constant. However, above this value both the efTective
resistance and the reactance show a consistent increase with the
current. The minimum current employed (lO"" amperes), is between
two and three times the minimum audible current for this type of
instrunient, but from the data- taken there is no reason to suppose
that the impedance would vary for smaller currents. This receiver
has a winding of 11,000 turns, and it can, therefore, be assumed that
this type of structure will have constant impedance below a magneto-

rr.i.F.riioNF. receiveks at /.oic roni-n inpcts

405

motive force of .01 ampere turns. I'or laboratory measurements on
this instrument a current of 2X10 '- amperes is ordinarily used, and
it will l)e noted that the inipedaiuc at extremely low currents is not
greatly different.

It is generally known that, in the case of either a steady or an
alternating lield, the jK-rmeability and the shape of the hysteresis

^

^

aeceiN

CB •

2

1

>

•?1

BECt'Vtt

—

2

-\

/

1

1^

J

POO" TsnP J4'c 1

/

'n

Boon Ttno wc 1

1

^ 1

r

1

k

J

/

^

w

/

i

s

n

/

^■

/

/

o.

R^

'St

b. -

r^

y

^

«r

y

w

y^ !

/I

A

//'

//

\y

}. - »07
6 = 101
19- 22'
2. = 11250

R = nooo
Vi- o.»i

2<(«M.1>

T50 .jiOJSO

i. ' 110

A = 15

2» = 22*
Z-= 10*50
ft ' 12*00
'-A- CM
Zj {.».,) -
10U>jl0500

<f

k

Ssooo

a

j

\f\

y

/

^

/a

//ll

/

7

J

1

J

r

1

/

u

J

/

|[

/

5

/

Y

1

L

/

^

--

/

/

/

r--

^-^

r"

/'

»H

-■

a

,

/

A^

1 /I

y.

^^

lA'"^ — i"

i'

\

--f^

XT i 1

1 1

1 1

/^T^^ i 1

Fig. 3 — /, = natural frequency: A = logarithmic decrement per second; 2^ = depression

angle of principal diameter; 2„ = maximum motional im[)edance; /f = free resistance

at resonance; /C„ = damped impedance.

loop for ordinary- magnetic materials reach limiting values as the
magnetomotive force is reduced, that is, further reductions of the
magnetomotive force have no effect on these magnetic characteristics.
The results cited above show that this condition obtains for a weak
alternating field when it is superimposed on a relatively strong steady
field.

In the measurements of free impedance for determining the vibra-
tory characteristics the small sound-proof bo.\ could not be used on
account of the proximity of its walls. Accordingly, the receiver
and the impedance bridge were placed in a large sound-proof booth
with padded walls where the effect of reflection of sound waves was
very small. With the diaphragm of the instrument free to vibrate,
its efficiency as a sound detector was materially increased and the
noise in the head receivers due to the slightest movements of the
observer became so serious that it was not feasible to take data with
currents of less than 2X10"' amperes.

406 BELL SYSTEM TECHNICAL JOURNAL

Fig. 3 shows impedance characteristics, with their associated circles,
of the same receiver with currents of 2X10~' and 2X10"' amperes.
It will be seen that the differences between these curves are insignifi-
cant when one considers the low precision of motional impedance data
in the absence of extreme precautions with regard to constancy of
temperature, etc. Moreover, other impedance analyses at inter-
mediate values of current agree with the abo\e within the precision
of the measurements.

To summarize the results, it may be said that the characteristics
of receivers remain substantially unaltered as the current is reduced to
the point of minimum audibility. In taking impedance measurements,
it is well to use a current which is low enough to be on the flat part
of the curve. This can usually be done without the use of ampli-
fiers between the impedance bridge and balancing receivers. The
fact that the vibratory characteristics of the receiver remain un-
altered as the power input is reduced to the threshold of audibility
throws an interesting light on the behavior of the diapihragm material
iiiulur very small motions. Calculations of the minimum audible
<implitude near resonance, based on the fact that the constants of the
material remain unchanged, show it to be of the order of 10~^ centi-
meters. This motion is less than the mean molecular diameter of
the diaphragm material.

Some Contemporary Advances in Physics VIII
The Atom-Model, First Part

By KARL K. DARROW
A. lMK(ii)r( roKV KiMAkKs Audi r Atom-Mohi-is

MOKK than .iii> otluT word ol ilu- I.iiijjiiagc, tlu- word atom
is iinplir.ited with the histors- of human sporuUitions con-
ivrning the nature of things. It is intnKiuced wlien people cease to
content themselves with obser\ing, and begin to philosophize. There
are man>' of the fundamental and essential writings of the literature of
physics in which it does not appear, or appears without warrant.
These are the descriptions of things observed, the accounts of experi-
ments, the records of measurements, on which the edifice of theoretical
physics is founded. There are many articles of what is commonly
called the "theoretical" sort in which it does not occur. Such are the
pafX'rs on the motions of planets, on the vibrations of elastic solids,
on the currents in electrical networks, on the courses of light-rays
through optical systems — papers which are essentially descriptions,
although they give the impression of being something greater and
deeper because they relate to idealized cases, and are phrased in the
laconic language of mathematics. When the word atom appears
justifiably in a discourse, it means that the author has departed from
the safe routine of describing observed and obser\able events, how-
ever selectively, however skilfulK', however intelligently. It signifies
that he has gone beyond the limits of obser\ation, and has entered
upon the audacious adventure of constructing by the side of the real
universe an ideal one, which shall act as the real one does, and be
intelligible through and through.

Atoms are the building stones of this art-world or image-world,
which is intended to represent the actual world, imperfectly indeed
for the time being, perhaps completely at some distant day. Some
few experiments, it is true, prove (as well as anything can prove any-
thing else) the existence of very minute particles of matter ha\'ing the
minute charges, the minute masses, the minute magnetic moments

' This part, the first of two composing the article, is devoted chiefly to the facts
of observation which the favorite atom-model of the physicists of toda> — the atom-
model known by the names of Rutherford and of Bohr — is designed to interpret.
.■\ brief description of this atom-model is included: but the detailed account of the
peculiar features, of the strange ajid important limitations which are imposed upon
it to adjust it to all the phenomena mentioned, is reserved for the second part.
Owing to the great quantity of information which it is desirable to present, the
article needs all the Ijcnefit it can derive from a careful and obvious organization,
and I have sacrificed fluency to a quite formal arrangement under headings and
sub- headings.

407

408 BELL SYSTEM TECHNICAL JOURNAL

which it is found expedient to ascribe to the atoms. These experi-
ments are enormously important, for they iinest the atom with a
reality which nothing else could give it. To some they have given
the hope that all the properties of the atom may one day be demon-
strated unquestionably by direct evidence. There is little reason
to expect that we shall see that day. The atom is no longer entirely
a product of the scientific imagination; but neither is it entirely an
object of experience. Most of its properties are invented, not dis-
covered. Whether this in\ented and imagined entity is "real" is a
difificult question. Perhaps it is best to evade such a question by
asking the questioner what he means by "reality". As a matter of
fact, it is not pcjssible to discuss atomic theories thoroughly without
raising and settling such formidable questions as, what is a theory?
and, what is an explanation? and e\-en, what is reality? perhaps
eventually, what is truth? I do not aspire to answer these questions.
But there are some common misconceptions about atoms which it is
prudent to clear away at the beginning.

In the first place, one does not utter an atomic theory by saying
that a substance is made up of small pieces, each exactly like a large
piece of the substance in every respect except size. We should
achieve nothing by saying that iron is made of black lustrous con-
ductive magnetic atoms, or that glass is built of colorless transparent
brittle insulating atoms, or that an apple consists of white soft
sweet juicy atoms. The atoms must be endowed with fewer and
simpler properties than the substance they are meant to compose,
else they are futile. One must select some of the properties of the
substance to be attributed to its atoms, and st-t tlu' others aside
to be explained by those.

Again, it is not obvious which properties should be selected for
the atom; these depend largely on the fantasy of the atom-builder.
However, certain qualities such as viscosity and plasticity, con-
ductance for heat and conductance for electricity, opacity and trans-
parency and lustre, warmth and flavor and fragrance, are not usually
assigned to atoms. In general, the more a quality of a substance
varies with its state, the less it is suited to be made an atomic quality.
Ferromagnetism is a quality which one would assign almost in-
stinctively to the iron atom; but it is possiljle to deprive iron alto-
gether of this quality by a simple heat treatment, and hence it is not
generally supposed to be a feature of the atom. But the rule is not
an absolute one. The visible radiations from gaseous iron are sup-
posed to be characteristic above all other things of the atom itself,
yet they cease when the iron is condensed. It is supposed that in the

SOME CONTF.MI'ON.lKy .ll>rAXCi:S IX /7/V.S7CV nil 4(«

condensed phases the atoms are so close together that they distort
one another — a perniissiMe idea if used with discretion, yet an atomic
thcor>' coiiltl easily liecome a meaningless form of words if this device
were employed without limit. Of all the properties of matter, mass
alone appears to be entirely exempt from change. For this reason
all atom-mtxlels involve mass as an essential property of the atom; and
this is the oidy respect in which they all agree.

Few and simple, therefore, must be the properties of the atom; yet
we must not rush to the other extreme, and contri\e atoms simplitied
into usclessness. The chemists know of eighty-eight different ele-
ments, sufHciently unlike to be distinguished; and we all know how
great is the contrast between carbon and gold, hydrogen and lead,
fluorine and helium. It is scarcely likely that such differences as
these can be explained by atoms which are simply hard pellets differing
only in size and shape and weight, like those of Lucretius and Newton,
or by atoms which are abstract centres of force, like those of Boscovich.
We are forced to invent atoms more complicated that these; and from
this it is not far to say that we must imagine a structure for the atom;
and from this scarcely farther to say that we must imagine an atom
built of parts.

At this point we meet with a clamor from a number of excellent
people, many of them otherwise quite innocent of Hellenic culture,
who have it firmly fixed in their minds that atom is the Greek word
for indivisible; whence they conclude that when the ph>'sicist speaks
of subdividing his atoms, he is contradicting his own terms, he is
violating the rules of his own game, and has forfeited his right to be
heard.- The premise may be right, but the conclusion is absurd. If
some of the properties of gold are explained by assuming it made of
atoms with fewer properties, and later the explanation is impro\ed
and extended by assuming these atoms made of still smaller particles
with still fewer properties, the second step is not less legitimate than
the first. It may l)e contended, with some reason, that the name
atom should be transferred at once to the smaller particles. At best
this would be one of the changes which are desirable in principle but
cause more trouble than they are worth. The contention is, however,
weakened by the fact that some at least of the smaller particles of
which we imagine gold atoms to be made are not imagined to be
peculiar t(j gold, but are conceived as particles of a fundamental sub-
stance common to all elements. That the "atoms" of the many

' I should have put this passage even more strongly, but that Schuster tells that
Kelvin himself inveighed on one occasion against the idea of subdividing atoms.
He was answered by a young man who said, "There you see the disadvantages of
knowing Greek." This seems as good an answer as any.

410 lilH.L SYSTEM TECIIMCAL JOVRXAL

elements slmiild be systems of "atoms" of one or a few fundamental
materials is a thoroughly pleasing idea, although at present an un-
realized ideal. It is unknown how far our descendants will find it
expedient to dissect the atom; hut it is certain that the\- will not be
stopped by etymology.

Another fact about atom-models is tliat they are not always dis-
placed by their successors; several may and do persist side by side,
each adapted to a certain set of facts and observations. E\ery atom is
designed in view of a very small fraction of the available knowledge
about properties of matter; and this applies to the latest model as
well as the earliest. The chemists of the nineteenth century were
most impressed by the immutable weight of matter and In- the laws
of chemical combination; hence their atoms were mereK' weighted
particles equipped with hooks to catch the hooks of other atoms. To
the physicists of fifty years ago the physical properties of gases seemed
the easiest phenomena to interpret, and they imagined atoms as
rigid elastic spheres with radii of some 10"' centimetre; by the masses
and motions of such atoms they explained the pressure, elasticity,
viscosity, diffusion and specific heats of gases. The physicists of the
next generation attended chiefly to the emission, the refraction, the
dispersion of vibratory radiations b\' luminous gases, and concci\ed
the atom as a framework hoUling \ibrators, like a belfry with a carillon
of bells. This third model is inferior to the second in explaining the
properties of gases, inferior to the first in explaining the laws of chem-
ical combination; each of the three is superior in its own field to the
atom-model to which this article is chiefly devoted, and which in its
turn is primarily adapted to a field of its own. Still other atom-
models have been de\ised, endowed with other properties, to account
for other phenomena; and it is altogether probable that many more
will be presented Ix'fore the eventual one is attained, if it ever is.
For instance, we ina\' some day behold an atom-model devised to
explain the conduction of electricity in solids, ver>' competent in its
field and quite unlike these others. In the eventual atom-model
the essential (jualities of all of these, and of man\' others, must be
happih' combined; it does not matter about the inessential ones.'

• Now and then an article appears in a physical or chemical journal, in which
an oddly unconventional atom-model is proposed to interpret some such property
of matter as the tlU-'rmoclcctric effects, or supra-conriuctivity, or valence, or some
other with which the Kutherford-Bohr atom-model has not as yet been matched. It is
easy for a physicist to ignore sudi articles, on the ground that any model departing
from that of Rutherford and Hohr must l>e wrong. This is certainly a nnstaken
policy. .\n\ partially competent atom-model deserves to l)e examined with care;
its essential features nuist reai>|)ear in the eventual model. But, of course, the
essential feature is not always tnc conspicuous one.

.vo.u/i coNTEMroN.iRy .■inr.ixci.s ix physics riii 411

In awaiting that eventual atom-model, it is best to regard the
atoms of the present day as mutable anti transitory. Like railway
time-tables, atom-nuxicls should be inscribed "sui)jert to change
without notice." Nothing is irrevocable in plusics, except the
record of past events; and we who have seen the undulatory theory
of light assailed and shaken may well hesitate to put uniiuestionirfg
faith in any atom-m(xlel. K\en if there is no daiij^er of chanjje, it
is a virtue to keep data and theories sharply sejiarated in one's mind.
In no field is this more diflicult and important than in the field of
this article, where the ver>' language used to describe the data is
saturated with the spirit of a particular conception of the atom, and
it is customary to expoimd the theory before the facts. For these
reasons I shall go to the opposite extreme, and treat the contemporary
atomic theory with an exaggerated reserve which in many places will
seem excessive to the reader and in some to the writer himself.

The favorite atom-model of the physicists of toda>- is a structure of
electrons, congregated about a positiveK'-charged nucleus. The
data which this atom is designed primarily to interpret were discovered
before 1913, or else since 1913 by methods developed before that
time. These discoveries are due largely to Rutherford, whose name
the model often bears. The sections of this article which are labelled
B, C and I) are de\oted to these data, and to the inferences from
them. In 1913 a great change in the situation was wrought by a
brilliant idea of Niels Bohr. Bohr did not discover new data; he
taught a new way of interpreting old ones, he showed men how to
read spectra. Through this interpretation of spectra, and through
data which were discovered by men inspired with his idea, a previ-
ously-unknown property of matter was disclosed. This is expressed
by saying that each atom possesses many distinct Stationary States.
The largest section of this First Part of the article, the section E,
is devoted to the knowledge of these Stationary States. Had these
been discovered earlier, an atom-model might have been devised to
explain them and them alone. Rutherford's atom-model was already
in the field, and it was modified so that it might interpret the new
knowledge. To these modifications, of which some are of a remark-
able simplicity and beauty, the .Second Part of this article will be

devoted.

B. TiiK Electron^

The electron is the atom of negative electricity. An individual

electron can be captured upon a droplet of oil or mercury, or a minute

• This section is rlrastirnlly curtailed, for the chief facts about the electron should
by this time be common knowledge. .Millikan's book "The Electron" (now in its
aecond edition) may be consulted.

412 BELL SYSTEM TECIISICAL JOIRXAL

solid particle, and the amount of its charge determined. This amount
is 4.774.10"'° in electrostatic units, according to Millikan. It is
designated by the symbol e. When a magnetic field is applied to a
stream of electrons all moving with the same speed, the electrons are
deflected all to the same degree, which shows that they all have the
same mass. This mass is practically equal to 9.10 "* in grammes,
unless the electron is moving at a very uncommonly high speed, in
which case it is appreciably greater.

These facts of experience are about all that is definitely known
or needs to be known about the electron, in order to appreciate its
role in modern atomic theory. There is no good way of determining
its size, although the length of its mean free path in certain gases
indicates, perhaps definitely pro\es, that it is much smaller than
an atom. If the electron is a spherule of negative electricity uni-
formly dense, then its radius cannot be less than 2.10"" cm, for if
it were, the electromagnetic mass of the spherule would exceed the
observed mass of the electron.' This size is much smaller than the
one which it is expedient to attribute to the atom, happily for us,
since otherwise it would be difficult to conceive of atoms containing
electrons.

Since electrons can be coaxed or forced out of substances of every
kind — elements and compounds, metals and non-metals, liquids and
solids and gases — the atoms are supposed to contain one or more
electrons apiece. This argument was formerly fortified !)>■ the fact
that the light emitted from glowing gases is in many respects such as
oscillating electrons would emit. This second argument is for the
present under a cloud. ^

' This is a short way of saying that, if the electron were a particle of smaller radius
than 2.10~" cm., more energy would have to be supplied to it to increase its speed
than is actually required. For, in order to set an electrified particle into motion,
energy must l)e supplied to build up the magnetic field which surrounds a moving
electric charge; this energy V is additional to the kinetic energy \mv- recjuired to
set the mass m associated with the charge into motion with s|>ecd f, and it may be
regarded as the kinetic energy associated with an extra "electromagnetic" mass
2U/v' which the particle possesses by virtue of its charge. This (piantity 21' v''
can Ik; calculated, for a given size and shaiie of the electron; if we make the electron
too small, 21' v' conies out larger than its observed mass, which is a reduclio ad
ahsurdiim. This illustrates the rather surprising fact that we are not permitted
to imagine the electron as an infinitely small particle, a mere geometrical point
loaded with an infinitely concentrated charge and mass. Speculations about its
size and sha|K- and the distribution of charge within it are not nccessiirily trivial;
some may even lie verifiable. W'c also meet with this dilemma: how dt)es the elec-
tron, a piece of negative electricity of which each part should repel every other,
keep from exphxling.''

* I'erhaps I ought to mention that K. Khrenhaft of Vienna has been ardently
contending for about fifteen years that there is no such thing as an electron. He
maintains that he can demonstrate negative charges much smaller in amount than

SOME CONTEMPORARY ADl'.-tXCFS IX rilVSICS I'lll 41.1
C. Positively-Charged Particles Accepted as Atoms'

Posit ivcly-charRcd particles are found in abundance in gases in
which an electrical discharRe is or has lately been maintained, and
they nuiy Ik- prtxiiiced under weil-controlletl circumstances by pouring
a stream of electrons with properly-adjusted s|ieeds into a gas, and
in other ways. Only the ratio of the ciiarge to the mass can be
iK'termined for these particles, not the charge individually nor the
mass individually. But particles of apparently the same substance
show distinct values of this ratio, which stand to one another as
the numbers 1, 2, 3, . . . and the intermediate values do not occur.
This sup[K)rts the quite natural idea that these particles are atoms
which have lost one or two or three or more of their electrons. If
we make this sup()osition, we thereb\' assume values for the charges,
and can calcidate the masses of the particles from these and the
observed values of the charge-mass ratio. The masses lie between
10 -'and 10~-' (in grammes) for particles occurring in the vapors of
the various chemical elements, and they lie in the same order as the
coinbining-weights of the chemical elements. This is powerful testi-
mony that the particles indeed deser\e the name of "atoms".

There is one sort of positive particle for which the charge can be
measured directly. This is the alpha-particle, which cannot be pro-
duced at will but is supplied by Nature from rtidio-active substances.
Counting the number of these particles emitted from a bit of radio-
active substance in a given time, and measuring the total electrical
charge lost by the substance in the same time, and dividing the latter
figure by the former, Rutherford and Regener obtained the charge
of the alpha-particle, which is twice the electron-charge (with reversed
sign) within the limits of experimental error. This suggests that the
alpha-particle is an atom of something or other, which has lost two
electrons. As an evacuated tube into which alpha-particles are ad-
mitted is presently found to contain helium, the "something or other"
is supposed to be helium. The mass of the alpha-particle can be de-
termined directly from its charge and charge-mass ratio. It amounts
to G.OOlO -', and this agrees with the mass inferred in the foregoing
way for the positive particles found in helium.

4.774-10"'". .Anyone interested in his case may find it presented in the .'\pril, 1925,
numlier of the Philosophical Magazine. The question is for e.xperimental physicists
to discuss; but it is not likely that the edifice of mo<lern physics is liable to Ix; ruined
by a flaw at its very' foundation, such as this would l)C.

' The material of this section may l>c found much more extensively presented in
my fourth article, in which I have also written about isotopes, a subject omitted
here for the sake of brevity.

414 HELL SVSrEAf TF.CHMCAL JOURNAL

The aljiha-particle is siii)[K)seci, like tlie electnm, to be imuii smaller
than an atom; partly because it can go through a thin sheet of metal,
chiefl>' because of evidence to be expounded in the next paragraph.

Collisions between alpha-particles and other jiarticles of similar
mass are occasionally observed; the mass of the struck particle can
be deduced from the directions in which it and the alpha-particle fly
off after the impact, assuming only that conservation of momentum
and conservation of kinetic energv- prevail during the impact. In
this way it is possible to determine the masses of tiny particles (pre-
sumably atoms) of hvdrogen, helium, oxvgen and nitrogen (perhaps
eventually of other elements) in terms of the mass of the alpha-
particle, which is determined from its charge-mass ratio and its
charge, which are determined directly. If all the properties of the
elements could be explained In- atoms possessing no features except
charge and mass, all the fuuncj.iiinns of science nii.ulu be laid dnwii
already.

The alpha-particle is one of liie most \aluabk- and jjowirlul instru-
ments in the physicist's equipment. It is a sort of luper-microscope,
penetrating and revealing the arrangements of sv'stems so minute
that microscopic objects are universes compared with them. Ruther-
ford's development of the technique of using the ali)lia-pariicle is to
be ranked among his greatest works.

Positively-charged particles with masses as low as that of the
electron have never been observed; the least massive of the knnwii
positively-charged particles has 1,840 times the mass of ilu' eitciron.

|). lui. Nil i.i-;ar .\i(im-M()1)I-;i,

Since we ha\e met with positively-charged particles which are
accepted as atoms deprived of one or more of their electrons, and
since these incomplete atoms are much greater in mass than the
electrons, it is natural to suppose that the completed atom consists
of a positively-charged particle or nucleus in which almost its entire
mass is concentrated, and one or more electrons which compensate
the charge of the positive particle but add little to the mass of the
atom. If we further suppose that the dimensions of the electrons
and of the positi\el\-charged particle are small in comparison with
the distance between them, we invent the nuclear atom-model.^

The flirect evidence for the nuclear atom-model consists of a very

' ('(itniiiDiily known as tlif Uiiihirford atoni-niodi'l, after the physicist who in-
vrnteil il and diMovcred most of thri-vidi-nre for il; ixcasionally as Nagaoka's, after
another physicist who suKRcsted it; occasionally as the Satiirnian model, as some
have siipiHisetl that the electrons lie in Mat rings around the nucleus like the rings of
.Siiturn around that planet.

SOME coxruMroR.iRy .mr.ixci-.s i\ I'livsics riii 415

small l)ut a lii-aiitifui and ooiuincinK scries of experiments, of which
the (irst and the most were performed by Sir l-.rnest Rutherford anfl
his pupils." These experiments are designed to show that the orbit
of a minute ehar^ed particle (usually an alpha-particle), flyinn iIuoukIi
a thin film of mel.il, is in certain cases very like the hyperbolic orh't
of a comet around the sun. Such an orbit is the [)ath of a particle
moving near to an immobile particle, for instance a li^ht particle
moving close to a much more massive one, which attracts it or repels
it by a force varying inversely as the square of their distance apart.
If these e.xperiments show what they are designed to show, then thc\'
indicate that the atom includes a particle much more massive than
an electron, hearing an electric charge, and sufticiently isolated from
the other charges in the atom (such as the electrons) so that its field
of force in a measurable space around it is not disturbed by theirs.
We cannot, however, trace the entire path of an individual flying
charged particle as it swings around through an atom, and are forced
to make up for this deficiency by a statistical study of the visible
portions of the paths of a great multitude of charge particles.

Let us consider exactly what these experiments show; for whatever
they do prove is the most securely proved of all the beliefs about
atoms. In the first place, they show that there is a nucleus; and a
vacant space surrounding it, in which an inverse-square force centred
upon the nucleus prevails; and they indicate the dimensions of this
vacant space. This commences within 10~'- cm. of the nucleus,
which is another way of saying that the diameter of the nucleus is
less than 10"'- cm.; and it extends beyond a distance given (to take
instances) as 14.10"'- cm. for platinum and 10*' cm. for argon, which
is another way of saying that nearly all of the negative charge of the
atom lies still farther out from the nucleus. If the negative charge
is indeed subdi\ ided into electrons, then the atom is formed like a
hollow cloud of electrons, with a massive positively-charged nucleus
at the centre of the interior hollow.

The diameter of this cloud of electrons is not furnished li\- tlic
experiments on alpha-particle deflections; but considering that the
distance between adjacent atoms locked into a crystal lattice is
generally a small multiple of 10"' cm., it cannot be much greater than
10 ' cm. unless we are prepared to admit interpenetration or violent
distortion of atoms; nor does it seem likely that the diameter is very
much smaller than this amount. I have already mentioned that
some of the properties of gases are adequately explained by assuming

• For the mathematical theory of these experiments, the second article of this
scries may be consulted.

416 BELL SYSTEM TECHNICAL JOURNAL

that the atoms are elastic rigid spheres with a diameter of about
10"' cm. Unlilce as an elastic rigid sphere and a cloud of electrons
seem, this agreement between so difTerenth' made estimates is proli-
ably no mere coincidence. It will be noticed that all of the figures
about sizes at which we have arrived in such various \va>'s (diameters
for the electron and the nucleus, for the vacant space inside the
electron-cloud, for the entire atom) are quite compatible with one
another. If the value derived for the diameter of the interior hollow
had been ten times the spacing of atoms in a crystal, or a tenth the
diameter of a spherule of electricity with the same electromagnetic
mass as an electron, we should indeed be in trouble.

In the second place, these studies of the deflections of alpha-particles
yield numerical values for the nuclear charge : (77.4 ± I)e for platinum,
(46.3±0.7)e for silver, (2!).3±0.7)«' for copper, 19e for argon, (iJie
for "air" (a sort of statistical average of the \alues for oxygen and
nitrogen).'" To these must be added the \alue +2e for the nuclear
charge of helium; for we have alrcach' seen the evidence that the
alpha-particle is what is left of a helium atom when two electrons are
renio\X'd, and these last-cited experiments show that it is itself a
nucleus, hence a helium nucleus. This nuclear charge must be bal-
anced by negati\e charges within the atom; if this balancing negati\e
charge is subdivided into electrons, then the numerical factors of e
occurring in these numerical values are equal respectively to the
number of electrons belonging to each atom. We thus ha\e f,iirl>-
accurate estimates of the number of constituent electrons witiiiii
each of four or live atoms.

These estimates agree, within their experimental uncertainties,
with the famous and splendid idea of van den liroek and Moseley :
that the number of electrons in each atom, and the nuclear charge
measured as a multiple of the electron-charge, "is the same as the
niMuber of the place occupied by the element in the periodic tai>ie".
'I'his idea is also supporteti by rough measurements of aliiha-particle
dellections by a few other atoms, and by the extent to which (iitTereni
atoms .scatter X-ra\s; but the most important of the adililional
evidence will find its appropriate place in the second section of this
article.

These conclusions are almost .ill tiial c.in be (k< I need from the data.
The arrangement of electrons within the electron-cloud is almost

'" KcfcroiK cs (iir ihcsu ilata an- given in llu' fourth article of this scries. The
"lal.i ot.tained hy K. .S. Uielcr (l'r(x-. Ko\'. Sck., 10S.\, pp. 4.?4-4.S(), 19241 show
ineiilcnlally, if I do not misread his article, that the nuclear charges of Mg and .Al
have the desired values 12e and lie, rcsix-ctively, within a few per cent. Kulher-
ford's studies of encounters between alpha-jiarticlcs and hydrogen atoms prove
a nuclear charge of e for the latter.

SOME CONTEMrOK.INY .-(/)r.-l,VC£.V IN rUVSICS nil Jl"

entirt'ly coiirfak-tl. It is not altogftluT inarci'ssihU'; for llu- di-llec-
tions sufferetl liy alpha-particles ami electrons living throuKli atoms
are iiithienced !>>• the electrons of the atom, not by the nucleus ex-
clusiveK ; anti from the decree in which the observed deflections difTcr
from what the nucleus alone would compel, it is possible to draw-
some conclusions about the way in which the electrons are arranged.
The mathematical ililViculties, as the reader will readily admit, are
tremenilous; the problem of determiniiiK the path of a n\'in>; electron
through a cloud of electrons, probably themselves in motion, is
enough to make the best of mathematicians despair; yet some progress
in this direction has already been achieved, as I narrated in the second
article of this series. Again, the scattering of X-rays by atoms
should depend on the manner in which their electrons are arranged;
and some measurements and some deductions have already been
made, although the researches have been in abeyance for some years,
probably because the newest disco\eries about X-ray scattering make
it extremely doubtful what the mechanism of the effect really is.

The study of deflections of alpha-particles by atoms has thus
brought precious guidance to the atom-builder, and imposed severe
limitations upim him, yet only partial ones. He is constrained to erect
his atom according to certain fundamental rules, and yet has an ex-
tremely free hand in arranging the details. He is practically com-
pelled to build the atom of an element which occupies the iVth place
in the periodic system, out of N electrons and a much more massive
nucleus with a positive charge Ne. The data which I have cited do
not absolutely enforce these numerical values; but there is no other
model which they permit which could possibly rival this one in
respect of convincing simplicity. He may not make the electrons
go more than a few times 10~' cm. from the nucleus; he is constrained
to leave a small vacant space around the nucleus, and within this
space he may not tamper with the inverse-square law of force (a
restriction which has eliminated several favored atom-models of the
decade before 1910)." Having conformed to these restrictions he

" Except that he may and must alter the inverse-square law of force to just the
extent that further and more delicate exjieriments of this type require. Thus
Bieler (I.e. supra) concludes, from a study of tletlections of alpha-particles passing
close to the nuclei of aluminium atoms, that within about 10"'' cm. of the aluminium
nucleus the inverse-square repulsion which it exerts upon an alpha-particle is
supplemented by an attractive force — perhaps an inverse-fourth-powcr attraction,
just balancing the repulsion at a distance of .^.44- lO^'-" cm. from the centre of the
nucleus. Rutherford earlier found anomalies in the encounters between hydrogen
nuclei and alpha-particles, which suggested to Uarwin that the latter might be
considere<l as a disc-shapc<l hard particle, or an oblate spheroid of semi-axes 4.10 "
and 8.10" cm.; this would repel hydrogen nuclei according to the inverse-square
law so long as it did not actually strike them.

418 BELL SYSTEM TECHS ICAI. .lOlRXAL

ma\' do \ery nearly as he pleases with the ekclinns and the rei^ion
they occupy. No tlata can be iinoked in suppori him nor to
confute.

Having expounded the merits of the nuclear atom, I will proceed
to undo my work in part by pointing out its great and grave defect.
No less a defect than this, that it is impossible. It cannot e.xist.
Even if it were brought into existence miraculousK' at an instant, it
could not survive, for it carries the seeds of its own dissolution within
itself. For if at that initial instant all of the electrons were at rest
relatively to the nucleus, tliey would immediately start towards it,
fall into it, and expire. Of course, this con-secjuence is so obvious
that the notion of stationary electrons would not even occur to any-
one ha\ing a bowing acquaintance with mechanics. Such a person
would immediately assume that the electrons were in motion around
the nucleus as the planets are around the sun; he would convert the
nuclear atom-model into what I might call a siin-attd- planets atom-
model, the nucleus pla\ing the role of the sun, the electrons those of
the planets. .Such an idea is alluring in the extreme; it implies that
Nature acts similarly in great things and in small, copying the solar
system within the atom; and this is most acceptable, partly because
of its philosophical beauty and partly because it enables us to use
the intellectual methods and habits accjuired in thestud\- of astrononn-,
relieving us of the labor of acquiring new ones. I'nfortunately it is
as untenable as the idea that the electrons stand still. For owing
to the radiation of energy which continualK' goes on from accelerated
electrified particles, an electron cannot describe a circle or an ellipse
about a nucleus, as a planet may about the sun; it can only describe
a narrowing spiral, ending in a collision lietween electron ,iiui nucleus.
The nuclear atom is not stable nor enduring; and liic liikuiiua is
complete.

The only recourse is to make some cntireK' rii-w and unpreccdenttd
assumption; for instance, that the electrons, in s()itc of c\er> thing,
can stand still in certain positions without falling into liie nucleus; or
that they, in spite of everj'thing, can rc\olve interminably in certain
closed orbits without spiralling into the nucleus. Such a modifica-
tion of the nuclear atom is, of course, essentially a denial of it. .\n
atom composed of masses and electrostatic charges, jilus certain
restrictive rules or arbitrary assertions, is no longer simply an atom
composed of masses and electrostatic charges. Instead of giving
to our ultimate particles a few properties selected from among the
ones which matter en masse displays to our senses or our instruments.

SlKMli COXIliMl'DH.IKy .//»('. I.V(/.\ /.V /'//Js/cV ;/// Alt

\\v li.iM- to invent some new ones for them. Tliis seems regret I, iMe.
liiit only l>ee.iuse our expectations were too liinh-

Another eireiimstance leads us to another dilemma. Su|)pose that
we could circumvent that ditticulty alxxit the revoKinn electron,
which radiates part of its energy at each revolution and slides down
a spiral [lath into the nucleus; supjiose that we could find justifica-
tion for sayinn that no radiation occurs, that the electron like a planet
may revoke forexer in an ellipse. If two atoms colliiled, as in a K^i^
they must ver\' frecpiently do, would not the electrons all he dis-
arranged, ilisorganized, Himj; over from one orbit into another.'' This
we should certainly expect; yet if it happens, no two atoms in a gas
can In.' exactly alike, ni>r can any atom retain its character for more
than a fraction of a second. If this is so, then the various sharpK-
det'metl properties of a gas must, each and every one of them, be
statistical properties- -not themseU'es properties of indi\idual atoms,
but the results of other properties of individual atoms, held in different
amounts by different atoms and all averaged together. In some
cases this is unobjectionable; the pressure and the temperature of a
gas are sharply definite properties, resulting from the mass and the
motion of the atoms, and the latter of these properties is not neces-
sarily the same for any two att)ms at the same moment nor for any
atom at different moments. But one wouki be reluctant to treat the
spectrum of a gas as such a prfiperty; according to all the traditions
of physics this is one of the properties of the individual atoms, liut
the sjjectrum is very constant, sharp, immutably defined; we must
therefore assume either that it de[)ends onh' on the number of elec-
trons in the atom and not upon their motion nor position, an idea
which would be difficult to carry through; or that the electrons are
ineluctably constrained to certain orbits or certain positions, so that
the atom retains its personality and its character.

We have now inade the accjuaintance of two ideas whicli will be
exceedingly prominent in the second di\ision of this article. Tlu'
nuclear atom-nnKlel is of itself unstable; therefore stability mu>i be
enforced ut)on it by outright assumption, it must be made stable b\
fiat. But this stability may nf)t be extended to all concei\ablc
arrangements or configurations of the nuKlel; it must be reserved
for one or a few, that the atom may possess a fixed character and a
personality.

We now arrive at the phenomena by means of which these vagueK-
expressed ideas are t(j be sharpeiieil and hardened into detinite
doctrines.

420 BELL SYSTEM TECHNICAL JOURNAL

E. The Stationary States
E 1. The Direct Evidence for the Stationary Slates

Imagine a tube filled with gaseous helium, and containing a hot
filament from which electrons emerge. By means of an accelerating
potential applied between the filament and a fine-meshed gauze close
in front of it, the electrons are speeded up, and pass through the gas
with an energy which is accurately controlled by the accelerating-
potential. A third electrode is maintained at a potential only slightly
higher than that of the filament. To reach this electrode, the elec-
trons must sacrifice nearly all of the energy which they acquired in
coming up to the gauze. If they lose little or no energy in their
progress through the gas, they can win their way to the third elec-
trode, like water rising again to the level of its source. If, however,
they lose a notable amount of energy to the atoms with which they
collide, they cannot reach the third electrode, as water which has
turned a mill-wheel cannot climb again to the level whence it fell.

By measuring the current into the third electrode in the helium-
filled tube, it is found that if the electrons ha\e an amoimt of energy
lower than 19.75 equivalent \olts, they lose scarcely any of it in
their progress through the gas; but if the energy of an electron is just
equal to 19.75 e(|uivalent volts, it may and frequently does lose its
energy altogether; and if the energy of an electron surpasses 19.75,
it may and frequently does surrender just 19.75 equivalent volts to
the gas, retaining the residuum itself. Imagining that the electron
collides with atoms of helium on its way across the gas, we conclude
that the helium atom can receive exactly 19.75 of these units of
energy, no lesser quantity and (within certain limits) no greater.
From similar e.xperiments it appears that the mercury atom can
receive 4.GG equivalent volts of energy, no smaller amount and (within
certain limits) no larger. It appears that the sodium atom can
receive 2.1 equivalent Nolts, no less and (within certain limits) no
more — and the list can be extended to some thirty elements.

Another way of saying the same thing is this: the helium atom may
exist (at least transiently) in its normal state, or also in a second
state in which its energy is greater by 19.75 equivalent volts than in
its normal state, — but not, so far as we can find evidence, in any stale
with any intermediate value of energy. Let us call this second
state an "excited state." The mercury atom then has, in adtiilion
to its normal state of undefined energy, an excited state of energy-
greater by 4.()() equivalent volts. The sodium atom has, in addition
to its normal stale, an excited state of energy greater by 2.1 equivalent

SOME CONTEMFOR.INV .tl>i:it\CF.S IX I'liysiCS 17// 421

\oIis and so with a niiinliiT of oIIuts. I L;i\i' llii'sc and a fvw
other vahit's in the following lal)le:

TAItl K 1

.

He

Ne

Na

C»

Mg

H»-

Knergy-valuc of the

0
19.75
20. 5S

24.5

0
16.65
18.45

21.5

0
2.1

5.12

0
1.45

3.9

0

2 7
4 4

7.6

0

First excited state

< Uher excited states. . . .

4 66
4.86

5 43
6.7

10.4

It will he noticed that values are given for several excited states in
the same column; these rest upon evidence of the same sort as docs
the first e.xcited state, so that in general the atom must be cf)nsidered
to jxissess not one onl\', but se\eral possible states in addition to its
normal state.

It will be noticed also that values are given for the "ionized atom."
These are the amounts of energy just sufficient (when applied by
means of an impinging electron) to detach an electron froin the atom.
When electrons with so much energy or more are poured into the
gas in question, positively-charged particles, such as I previously
mentioned and characterized as the residues of atoms deprived of an
electron apiece, appear in it. It is not absurd to call this an "excited
state." If it takes just 24.5 equivalent volts of energy to detach an
electron from a helium atom, then the system formed of an ionized
helium atoin and a free electron has a potential energy of 24.") equiva-
lent volts. Any experiment, therefore, in which the energ\' required
to detach an electron from an atom is measured — any experiment
for determining the ionizing- potential, as this energy when expressed
in equivalent volts is called — is essentially an experiment for locating
one of the excited states of the atom.

In this sense the energ>'-values of the last line in Table I are to be
taken. I introduce them here for two reasons. In the first place,
the fact that this energy-value is greater than any of the others in
the same column suggests this interpretation f(jr the excited slates:
that they correspond each to a certain partial lifting-out of an electron,
to a certain stage of incomplete separation, while the energy-value of
the ionized atom corresponds to the total lifting-out or to the complete
separation. This idea is fortified by the fact that a helium atom
may be ionized by two consecutive blows from electrons each with

422

BELL SYSTEM TECHNICAL JOIRSAL

20 equi\alent volts of energy, if the blows fall closely enough together —
as if the energy spent in raising the atom to its first excited state
were paid into account, and could be used toward detaching the
electron when the deficiency is supplied. This fact is exceedingly
important for the theory, and I mention it here as a passing anticipa-
tion. In the second place it is desirable — for a j-eason which will
presently appear — to measure the energy-values of the normal and
of the excited states not from the energy of the normal state, as I
have done in Tabic I, but from the energy <>f the ionized atom as
zero-value. This is done in Table II.

TABLE

11

He

Ne

Na

Cs

Mg

Hg

Energy-value of the

Ionized atom

0

0

0

0

0

0

Non-ionized atom

-3.2

- 3 7

Excited states. . . .

- 3 <)5

- i.»

- 4.97

- 5.54

First excited state.

- 4 75

- 4.S5

-.M)

-2 45

-4 9

- 5.74

Normal state

-24.5

-21.5

-5.1

-3.9

-7.6

-10.4

With this convention, all the energy-values for the non-ionized atom
liecome negative— a source of confusion, but not of nearly so much
confusion as the previous convention would eventually entail. It
is well to remember tenaciously that, in at least nine cases out of
ten in the literature, the energy-values of the normal state and the
excited states are referred to the energy of the ionized atom as zero,
and that the\' all should aKva\s bear the minus sign, though generalK'
it is left olT.

For the excited states and for the normal state, I will employ the
common general name of Stationary States; occasionalh', for the .sake
of variety, the alternati\e name levels. Another conininn word is
term, the origin of which will appear in the next section. '-

As the reader will be forced to make himself familiar with schematic
representations of the Stationary States, he may as well begin at
once with a simple one. Fig. 1 is a diagram showing the stationary
states listed for helium in the foregoing tables. The levels are repre-
sented by horizontal lines, separated by distances proportional to the

"Anyone who reads the physical literature of today soon becomes familiar with
the phrase "the electron is in the . . . orhit" used instead of "the atom is in the
. . . state." This phrase expresses theory rather than facts of observation, and
docs not always express theory adequately; 1 have avoided it in this article.

SOME CO.XTEMPOR.IRy .IPr.lXCF.S IX I'llVSICS llll 42.1

clitTiTt'iirt's iH'IWft'H tlu'ir fiKTK>-valiii's (tisualK', liowi-vi-r, thfso
(listaruTs an- distorU-d for convi-iiience). Tlu- i-iuTny-valuos, cx-
pri'ssftl in t(iiii\alcnt volts, art- aftixi-d to tlu- liius; on tlic left, they
are measured from the normal state of the neutral atom as /.cro of

■feTiOtf »r: I ■■-it
lQ!Nt2.E.O WTOr- r

fcJLCITE-O 3TfiTE.3

or flT,o^fl.

£0.55 •

" 19 7S:

iy^^-\ ■■ i.t- i,'

E-lsteGi

1

-H^

:.[^!

:^i^:^l-^Fl^i.:|:::i:::l:n-|.i.±:i::

l-ig. 1 — Uiagram of the stationary states of helium, dctcrniined liy the method of
electron-impacts

424 BELL SYSTEM TECHNICAL JOURSAL

energy; on the right, they are measureci from the state of ilii- idiii/cd
atom (which is the more common practice;".

R 2. Bohr's Inter pretalion of Spectra

in 1!I12. ilie e\icience to wiiich the foregoing section is de\()ted was
still eniireh' undiscovered, the Stationary States were unknown.
That evidence was sought and found because N'icls Bohr had divined
the Stationary States in de\eloping a new and brilliant interpretation
of spectra. Until then, all physicists had wished to interpret the fre-
quencies forming the spectrum of an atom as the natural resonance-
frequencies of an elastic system. Bohr supplanted this idea with
an idea of his own, one of the most no\el, fecund and potent in all
the long evolution of physics. Several of the ideas incorporated in
the contemporary atom-model are due to Bohr; among them all this
is I In- [jrimary and fimdamental one, and certainly the most secure.

Consider the spectrum of hydrogen. In the visible region, this
spectrum consists of a "line-scries" — that is to say, a procession of
lines converging upon a limit, falling at intervals ever narrower and
narrower, these intervals so smoothly diminishing that they bear
witness lo m common character and a mutual origin of all the lines.

E

I

■

Fig.

. n( liius ill I lie hydnigin s|>( el i urn.
Koote & Mohler, "Origin of Spectra")

rli-s, hdrn

This line-series is shown in I'ig. 2. Not only to the eye is it of a

wonderful regularit\-; the fre(|uencies of its consecutive lines are bound

together in a simple numerical law. They are equal successively to

vii^-R/V; vii„-R/A^, vii„-R/r>\ viir,-R/Q>-, etc. (1)

" This method of l<K-atiiiK stationary states by observing transfers of energy from
electrons at atoms is called I he melhoil of inelastic impacts; for the impacts of electrons
against atoms are elastic (by definition) so long as there is no transfer of energy
into the internal economy of the atom, and are inelastic when such transfers occur.
When an atom returns into its normal state from an e.\cited state, it usually emits
radiation; hence a method for detecting the first commencement of radiation is
usually (|)erhaps not always) equivalent to a method for detecting the first com-
mencement of inelastic impacts. As it is generally easier lo set up apparatus for
iletecting radiation than to seek evidence for elastic impacts, tlirect ol)scrvations
upon Ihesi' last are not so abundant. as they should be. Nobody really knows how
many stationary states mi^;ht be discovered by the method of inelastic impacts,
although Francic and Kinsporn detected over a dozen for mercury (of which those
given in Table II are some). In fact they detected more than could conveniently
be a.scrilH'd to mercury atoms, so that it was necessary to attribute some of them
to molecules.

SOME COXTEMPOR-tRY ADWANCES IN PHYSICS- VlII 425

in which

v/in, = f ri'qui'iir\' of the limit of the scries = i? '4

R s'.iiuliiiK for a cert.iiii conslant. TIuti- is another series of lines
in the iihraviolel part of the same siiectriim, whereof llie fre(|nencics
are etinal conscriiti\ely to

V = VU„-R \, V,im-R''^, l-^m-/?. Iti. etc. (2)

in which

Vlim = R,

R having the same value as before. The utter simplicity of the
terms to l>e subtracted from vum in eacii of these cases, not to speak
of the related form of the expres.sions for k;,™, suggests like simple
laws in other fields of physics that in this formulation of the facts
.something highly important has been partially unveiled. There are
certain other series in the spectrum of hydrogen, and inspecting them
all one is led to the rule that ei'ery frequency emitted by the hydrogen
atom can be calculated by inserting different pairs of integers in the
places of m and n /// the formula

The case of the ionized-helium '■' atom is quite as simple. Kvery fre-
quency emitted by this atom can be calculated by assigning different
pairs of integer values to the constants m and n in the formula

= 4/?

ih-l^- <«

Line-series have been found in the spectra of many other elements.
Some of them are as strikingly outstanding as the line-series in the
sfK-ctrum of hydrogen, and converge upon limits scarcely less easy
to locate; for instance, the "principal" series of the spectrum of
sotlium (Fig. 3). Most are by no means so obvious; often they are
involved in the midst of a luxuriant jungle of unrelated or otherwise-
related lines. Most spectra conceal their structures from the un-
practised eye, as a tone-poem of Strauss its themes or an opera of
the Ring its Leitmotiv from the ine.xperienced ear. Long training
and a skilled judgment are required in the deciphering of spectra,
except in the few untypically simple cases; and usually the arrange-
ment of lines into series which the spectroscopist presents must be

" The reader may take this, for the time being, simply as the name of a particular
element.

426

BELL SYSTEM TECIISICAL JOVRSAL

accepted hy the theorist without Cjuestion and without suggestion,
for he is not competent to analyze the data for himself.

Having grouped a certain number of lines into a series, ha\ing
guessed as well as possible the convergence-frequency vum of this
series, the spectroscopist has still the task of finding the numerical

a

10

I"'ig. 3 — I'riiiripal scrlc-

)f soiliiim (two photonraphsl. ((i. K. Harrison, Physical
Kniiiv I

l.iw to which the consecutive frequencies conform. As a matter of
course, all the fre(|uencies can be e\|)ressed by a formula j^eiurali/cd
from (1) and (2):

vi = viim -f(i) (o)

in which / is the oriler-number distinguishing each line, and /(/) is a
different quantity for each of the lines, which approaches zero as we
pass along the series to the limit. This means nothing by itself; the
(juestion is, does the function /(/) ha\'e a simplicity comparable wiili
the simplicity of the subtrahenda in (1) and (2) which suggested that
the>' are the symbols of something deeply important? In general,
the function /(/) is not so simple as the function which occurs in the
series of the spectra of hydrogen and ionized helium. In many cases,
howe\er, it is almost as sim|)le, in others a little more complicated,
in others a little more complicated yet, and so forth; so that the
eventual result is this, that the formula (8) appears to be the proper
way of de.scribing the lines of series spectra, even in cases where the
'^cric'; i>; so irregular and the form of the function /(») .so intricate

SOME coxTF.MPtm-.ihy .ii>r.ixcF.s ix riiysics riii 427

that if it wiTf the i>nly series in ixislfiue. no (inc would .iit.n h any
particular iniix)rtanre to it."

Ti) the physicists of a Kt^'itTi*''"" i>K'>. wht) reKarded the spertrum
fre(|iien»ies as natural \il)ralion-fre(|ucnries of the atom, and tried
hard to invent a nieehanieal niode! of which the vihration-frequencips
should conform to the formula ('.i) or the more general formula (o),
the character of these formulae was an insurmountable obstacle,
l-^lsewhere '" I have given a brief account of the \ain attempts to con-
trive such a nuxlel. Bohr abandoned this procedure altogether; and
taking equation (3), he multiplied both sides of it by Planck's con-
stant /; I =()..")•;■ 10 -■").

h, = l,R(\-\). (6)

The significance of this act depends on the meaning of //. Planck
hail found it expedient, in tleveloping an adequate theory of radiation,
tt> assume that soliti hot bodies are popul.ited willi multitudes of

I'.tlll

1 1

1

.'ll M )

ill.

«

•

1

1

1

1

! 1 ! 1

•

^

1

Kii;. I I'riiicip.il scries of helium (singlet systini . 1. l.yni.in, A^trnphyiiiat
Journal)

oscillating electrons of all the various frecpiencies, possessing a very
curious and inexplicable property; this being, that an oscillator
vibrating with frequency v can emit radiant energy of that same fre-
quency V only in units or quanta of amount hv. Kinstein had found
it exjiedicnt, in describing the photoelectric effect and other phe-
nomena, to assume that radiant energy of the frequency v goes about
in units or quanta of the amount hv, emitted integrally, absorbed
integrally, travelling integrally. Suppose then that we assume that
the quantity hv, standing on the left-hand side of the equation (6),
represents the amount of radiant energy emitted by the hjdrogen

'• As a matter of fact, the series-limit is not generally so obvious to the eye that
it can be l<x-ate«l at once: it is determined after and by means of a careful choice
of the most suital)lc form for the function /(i). This is one of the difficulties of the
spectroscopist's task.

'• In the seventh article of this series (footnote 9).

428 BELL SYSTEM TECHNICAL JOURNAL

atom in the process of pouring out radiation of the frequency v. The
right-hand side is the difference between two terms. One term is
the energ>' of the hydrogen atom before it emits the radiation of fre-
quency v; the other is the energy of the atom after the emission is
concluded. The radiation of frequency v is emitted by reason of a transi-
tion between two stationary states of the hydrogen atom; the energies of
these states are equal to the terms whereof the frequency v is the difference,
each term multiplied by h. The terms of the spectrum formulae are
the energy-values of the stationary states of the atom, when trans-
lated into the same units by multiplying them by h. When trans-
lated into proper units, the terms are energies, and the energies are
terms. This is Bohr's great and memorable idea.

Once this idea is accepted, the known stationary states of the atom
increase enormously in number. The paltry one, two, or half-dozen,
which are all that Iiave been detected by obser\ing the energy-losses
of rebounding electrons, are multiplied into hundreds and thousands.
The accuracy with which each energy-value is known is augmented
tenfold or a hundredfold, sometimes far more; for spectroscopic
measurements are among the most accurate in ph\sics, although the
necessity of extrapolating the observed frequencies to arri\e at the
series-limit neutralizes some of their precision.

One point must be kept clearly and always in mind, at the peril of
infinite confusion. The energy-values which the spectrum terms supply
are not the energy-values of the stationary states measured from
the normal state, as might seem natural; they are the energy-values
measured from the state of the ionized atom. These being negative,
it is the negati\'e term-value which is significant. Equation (6)
must ihcrcfore be rewritten in this fashion:

'-H-J^-H-m^- (^)

The energies of the successive stationary states of the hydrogen atom
are -RJi. -Rli/4, -Rli/9, -Rh/l(i, and so forth, relatively to the
energy of the ionized atom as zero. They are not Rh, Rh/4, Rh/9,
and so forth, relati\cly to the normal state of the atom as zero. Any-
one who entertains this last idea is doomed to trouble.

The stationary states of the hydrogen atom are shown in Fig. 5,
which is constructed like Fig. 1, with the energy-values of the various
le\cls measured downwards from the state of the ionized atom, and
affixed f)n the right. The distances from the various levels to the
zero-line are (iroportional to these energy-values (this feature will
henceforth be found too inconvenient to maintain).

soMi (d.v// u/v'A'. ;/vi .//I/ .;.\( / V i\ riiysns iiii 4J<>

riif fiuTn\-valui' of .1 st.»tii>iiary stale, wlu-n (il>taiiu-<l l>y aiialy/iiig
.1 .-iH-tiruin, is m-nerally niwii not in e(|uivalrnt \olis, Imt in a unit
lalU'd ilif "\v.i\<.--nuinlHT." This unit is \, he timi-s as urcat as an fr^,
and ;{()()//( e (ahoui .()()012;{7) limes as great as an equivalent volt.
When the eiH'rv;>-s allies of two sialiiinar\' slates are expressed in

IONIZED

i^Ton

16
-E-k

A-

STflTL

Fig. 5 — Diagram of the stationary states of hydrogen, deduced from Its spectrui:

430 BELL SYSTEM TECIIMCAL JOVRSAL

iliis iiiiii. ilii' (litTcrence between them is equal to 1 'c times the fre-
quency' III ilu' line whirh corresponds to the transition from one to
the other.

A speclruni-line corresponding; to a transition between two station-
ary states is symbolized, on a diagram of statit)nary states, by an
arrow connecting the dashes (or whatever marks are used) which
symbolize the two levels. This is illustrated in Fig. 6.

I pause at this point to remark that each of what I ha\e been
calling the "stationary states" is in fact usually a group of two or
more stationary states, often but not always exceedingly close to-
gether; just as many stars in the sk\- are in fact groups of stars too
close together for any but an excellent telescope to discriminate.
This will be discussed at length in a later section; at present it is
expedient to regard each of these groups as one stationar\' state.

The experimental test of Bohr's method for identifying stationary
states consists in comparing the stationary states inferred from the
spectrum, according to Bohr's procedure, with the stationary states
derived directly by the study of electron-impacts. The agreement
is perfect where\'er the experiments by the latter method can be
carried out. By a curious fatality, this is impracticable for hydrogen
and ionized helium, as neither sort of atom occurs in gas quiescent
enough for experiments on energy-transfers from electrons to atoms.

For about fifteen other elements, the comparison has been made
for two or more of the Stationary States. Every energy-value given in
Table II was obtained by the method of electron impacts, and con-
firmed b\- analyzing the spectrum of the element.

E 3. The Classification of Stalioiiary Slates hy Vtiliziiig "Rules of
Selection"

I have said that e\ery line in a spectrum, at least of those arranged
in series, may be represented by an arrow connecting two stationar\-
states. If arrows are drawn from every one of the stationary states
to everj' other, will every arrow correspond to a line actually observed
in the spectrum? Kvery line has an arrow; does everj' arrow have a
line? By no means; the answer is definiteh- and strongly negative.
If the wave lengths deduced from all the possible arrows are sought
in the spectrum, most o( them are found unoccupied by lines. The
great majority of the apparently po.ssible transitions either do not
occur at all, or if they do occur, the energy which is liberated is dis-
posed of in some other way than by radiation. There is reason for
believing that the atom may embrace this last alternative if it col-

. OS56-
•0.6a7-

-O 79e-

S-COLUMN

d-COLUMN f-COLUMN

K =3 K =4

Fig. 6 — Diagram of the stationar>' states of sodium, sorted out into columns by

applying the selection-principle. Arrows represent various lines (blue for principal,

yellow for sharp, red for diffuse and green for Hcrgniann scries)

S!OME CONTEMPOR.IRV .IPl.tXCFS IX PHYSICS-VIll 4.M

lilies with another atom or with an electron. Otherwise, it seems
that if the atom cannot radiate the enern>' liiieratetl in a transition,
the transition itself cannot hap(X'n at all. If, therefore, the line ror-
resjiontlini; to an arrow is niissin^, the transition corresponding to
the arrow must he inhit)ile<l by some agency as yet imknown. M.iiu'
transitions must he inhihiteii, for many lines are missing.

These missing lines are precious to the student of spectra and to
the .irchitect of atom-models. \Vhate\er explanation is devised for
the stationar>- states must include a reason for the occurrence of
some transitions and the non-occurrence of some others. This is
gcMxl rather than had fortune, since if such a reason is demanded, it
may he found in one and not in another of two competing theories
which otherwise wouUl stand on an equal footing; the missing lines
may even suggest a theory. At all events they suggest a system of
classitication; and, while the hardcne<I theorizer may regard a system
of classitication as merely the forerunner of a theory, a theory is itself
often nothing more than a classification stated in the language of an
artificial analogy. It is, in fact, possible to arrange the stationary
states, not in a single column as in Figs. 1 or 5, but in several as in
Fig. G; this arrangement being so contrived, that any transition can be
identified in a moment as belonging among those which occur, or
among those which are missing, whichever its case may be.

The mere fact that such an arrangement can be contrived shows
that the missing lines are not distributed at random, but subject to
some sort of a rule. Such rules are known as principles of selection.
The missing lines are commonly called verboten lines by the German
physicists, [xissihly because that was the most conspicuous word
in the otTicial German language before the war. It is not a happily-
chosen word, neither are the English equivalents "forbidden" and
"prohibited"; since while we know that the lines are missing, we do
not definiteK' know what circumstance is responsible; and, whatever
that circumstance may be, it is highly unconventional for a ph>'sicist
to say that it "forbids" the lines. The same objection applies with
extra force to the phrase "forbidden by the selection-principle".
It is much better to accept the fact that certain lines are missing as
a fact of experience, and the selection-principles as rules of experience
whereby the facts are codified.

£ 4- The Families of Stationary States (for Other Atoms than Hydrogen)

There is a far-reaching contrast between the spectra of all atoms
hut hydrogen and ionized helium, on the one hand, and the spectra
of these two atoms on the other. The selection-principles at first

432 BELL SYSTEM TECHNICAL JOVR\AL

accentuati' this conlrast, and l.Ui-r to a certain extent aid to explain
it away. I commence with the atoms other than hydrogen, and take
sodium as the specific instance.

A few of the stationary' states of the sodium atom are exhibited in a
single column on the left of Fig. 6. The energ>-value of each IcncI,
measured from the energy of the ionized atom as zero, is affixed at
the left ; but the practice of drawing the le\e!s at distances proportional
to their energy-values has had to be discarded for the sake of lucidity.
In this case, the distances are proportioned to the differences Ijetween
the logarithms of the energy-values. Drawing arrows from each of the
levels to every other, and ascertaining which of them correspond to
actual and which to missing lines, we find that the missing lines are
such that the stationary states can be sorted out into several families,
to be arranged in parallel columns as on the right of Fig. 6. There are
at least seven of these, but it is of no advantage to us to consider more
than the first four. The feature of this arrangement is, that transitions
between stationary states in adjacent columns correspond to actual tines;
but the lines corresponding to all other transitions are missing.

This is a principle of selection. It may be phrased in an equixalent
but pregnant way, in this maniuT. Let me attach to the several
columns the numerals 1, 2, 1^, 4 . . . , as they are indicated at the
bases; and let me use k as the general symbol for each and all of these
numerals. Then this particular selection-principle ma\' be i)lirased
thus:

The only transitions which correspond to actual spectrum
lines are those in which k changes by unity; Ak = ±l.

The numeral k bears the ponderous name of azimuthal quantum-
number. This is a name dcri\-ed from theory and not from experience,
as will be made clear in due time. The principle of selection which
has just been stated is the .selection-principle for the azimuthal (juan-
tum-number.

Kxceptions to this rule occur; tiu' verbolcn lint's, like oilier vcrholen
things, occasionalh' c\ade the prohibition. This happens particu-
larly when the atoms are subjected to intense electric fields, or to
violent spasmodic electrical discharges in which strong transient
fields are produced: in these circumstances great numbers of the
missing lines leap suddenK' into sight. In Fig. 11 some of these lines
appear elicited by a strong electric field. Some lines corresjKJnding
to changes of k by two units or by none, which by the foregoing rule
should be absent, do actually occur even when there is no obvious

soMF. coMi.\H'(U<.ih:y .tnr.ixcis- i\ riiysn\- riii 4,u

riMson whaU'viT for thinking llial tlii- atoms arr siiliji-cl to tiiuisii.il
strt'sscs." The fxci'ptions, howi-vt-r, aro iint mmuToiis «-iioii^;h to
jeopardize the rule.

Two other features of tlu- roliimns slioiiKI l)e pointed oiil; first,
that tlie suiTessive levels in each column are not scattered at random,
l)ut form a converging series approaching the lop of the column as
limit (their energy-values form a secpience converging to zero); and
secontl, that there is nothing arbitrary about the order of the coiumrts,
since the cohnnn at the extreme left admits of transitions to only
one other column and therefore is unmistakable, and all the others
follow after it in an immutable order.

E 0. A Digression About Xotation

The symbol for a transition between two stationary states, and for
the spectrum line which corresponds to that transition, consists of
the symlx)ls for the two states separated by an arrow, or a dash, or a
semicolon, or any convenient mark. The final state is commonly
written first. Thus the line due to the transition from a state B to
a state A is designated thus: {A) — {B). Chess-players will be re-
minded of the "Continental" system of describing moves at chess, in
which symbols for the squares from which and to which the piece is
moved are written down one before the other.

The notation for spectrum lines thus flows easily and naturall\'
from the notation for stationary states. This notation is not in
principle ver\' difficult, but it has become confused and confusing,
largely because of the alterations which have been wrought upon it
to make it express not the facts, but divers theoretical interpretations
of the facts. Alterations in names and notations generally produce
an e\il effect in physics even when justified in the highest degree,
for the old systems and the new persist side by side and cause in-
terminable trouble; all the more is this so when the alterations are
based on uncertain grounds and impermanent. The notation for
stationar\- states has already suffered much in this manner, and
probably the worst is yet to come.

The classification of levels which I ha\e just (lescrit)ed enables and
ref|uires us to give a twofold symbol to each le\el; the symbol must
designate the column in which the le%el stands, and its order-number
or serial number in that column. The columns are generalh' desig-

" Footc, Meggers antl Mohler observed a line corresponding to a change of two
units in k (the line i\,s) — {^,d), in the notation to lie explained in section K5) under
circumstances in which it seemed im|X)ssililc to t)elieve in an abnormally large
electric field.

434 BELL SYSTEM TECHNICAL JOURNAL

nated b\- the letters 5, p, d, f (or their capital, or Gothic, or Greek
equivalents).'" A spectroscopist using these symbols generally writes
the serial number of the le%el before the letter, with a comma between,
thus: (1,5) and (2,p) and (3,f/). Or the columns may be designated
by their values of the numeral k. which is then commonly written as a
subscript to the serial number. These s\'mboIs have at least the
ad\antage of being comparativeh' ti,\ed. It is far otherwise with the
serial numbers. One might expect that the level having the greatest
energy-value in a particular column would be called Number 1, and
the successive ones Number 2, Number 3, and so forth towards the
convergence-limit. Unfortunately (though for not a bad reason)
the habit is to designate the first levels of the successive columns by
the order-numbers 1, 2, 3 and 4, successi\ely; so that their respective
symbols are (l,s); {2,p); (Z,d) and (4,/). These are the symbols I
have affixed in Fig. 6; but they are not the only ones, as the order-
numbers have jumped up and down several times to satisfy the ex-
igencies of new atom-models. It would be unprofitable to confuse
the reader with further details, at least at this point. The important
things to remember are three: that the symbol for each stalionar\-
state must contain one index for its column and another for its place
in its column — that the former index is usually one of the specified
letters — that the latter index is a number, usually beginning with
1, 2, 3, 4 for the first le\'el in the 5, p, </,/ columns, respectively, and
ascending along the column in unit steps.

E 6. Names and Features of the Most Noted Line-Series

Every line in every series, according to Bohr's fundamental idea,
corresponds to a transition or "combination" between two stationary
states of the atom — -to a transition from an initial state to a final state.
The atom possesses more energy in the initial state than in the final
state (we are speaking of emission-spectra only). Hence the energy-
value of the initial state, reckoned as it usually is from the energy of
the ionized atom as zero, is algebraically higher and ariihmeticalh'
lower than the energy-value of the final state.

The various lines of any one line-series have this in common : they
correspond to transitions from \arious initial states which however
all lie in one and the same colimui, into one final state which is the
same for all and lies in an adjacent column. Each line-series thus

"The symbol b is sometimes used instcail of/. For the columns following to the
right of the /-column there are various notations, particularly/',/",/'" and g, /i, i.
See also footnote 21.

SOME CONTEMPORARY AIH-ANCES IN PHYSICS-yill 4.13

l>cl<)n^s to one p.irlit'iil.ir llii.il ^t.iit-, .iiul in unt- |).irti< til.ir ciilinnii of
initial stalt-s.

The linc-sories consisting of transitions into the state (\,s), or
Urmimtting upon (1,5) as the phrase sometimes is, hears the name of
principal series. Its consecutive lines are: {\,s) — (2,p)\ (1,5) — (3,^);
(1,5) — (4, p) and so forth. The>' are signified by the blue arrows'of

A7.irmiili Quaiiiuin Number

Fig. 7 — .Vnotht-r way of mapping the staliunarj' states of sodium

Fig. 6. The general symbol for this series is (1,5) — (»/,/>); which will
be quite intelligible. The (1,5) level is the normal state of the att)m;
consequently, the various lines of the principal series correspond to
transitions, by which the atom regains its normal state after a tempo-
rary e.xile from it. It is probably for this reason that the series is
prominent enough to have received the name principal from the
spectroscopists.

Two series terminate upon the {2,p) level. One of these consists of

436

BELL SYSTEM TECHNICAL JOURX.IL

,ransilinn> from various l.xc-ls of Hr- .s-rnlu,nn. This is ihc sharp
(or second) subordimite scries, and us syiiilx.l is (2,/>) - (w.^). 1 he
other series consists of transitions from various levels of the rf-column;
it is the diffuse (or first) subordinate series, and its symbol is {2,p)-
(m4). ^'elUnv and red arrows signify these series, respectively, in
Fig. G. Of the two line-series terminating upon the (3,rf) level, only
one has been endowed with a name; this is the series (3,<f)-(m/),
known alternatively as the Berf-mann or xhi^ fundamental series (the
second name is a bad one) and symbolized by green arrows in Pig. /.
These series seem to be the only ones which impressed themselves
strongly enough up.^n the minds of spectroscopic experts to receive
names '' from them. Howe%er, many other series have been identihed,
and emphasized, especially since Bohr's manner of thinking took root
among the students of spectra; for instance, series terminating upon
(2,x) and (3,s), which are conspicuous in the spectrum d luliuni. an<i
such line-series as (3,./) - (m,/'), and (4,/)-(w,rf).

Several rules about line-series, which are very promnuiu in accounts
spectra, become self-evident when the rules governing the stationary
states are mastered (of c.u.rs., this is only because the latter rules
are based upon the former). For instance, there is a rule that the
sharp and the diffuse series haNe the same limiting-frequency; and
there is a rule that the difference between this limiting-frequency
and the limiling-fre(|uency of the principal series is equal to the
frequency of the first line of the principal series. The reader may
derive these bv inspecting Fig. (i. , r . • i

Such rules do not ai>i)lv to the spectra of hydrogen and of iomze<l-
helium which are profoundly different from the spectra of sodmm
and other elements; and it is perilous to attach such names as principal
or subordinate to the line-series of those fust elements. The stationary
stales of those elements are known by their energy-values, and the
series by the names of their discoverers or iiiieriireters.

E 7. Further A nalysis of the SUiliomiry States of llydroiien a nd Ionized
Helium ; Fine Structure

In our earlier analysis of the spectrum ..f iiydrogcn and the siHctrum
of ionized helium, we inferred from each of these spectra ., tarn, Is ol
stationary states, the energy-values of which follow one upon Uic
oilur in a verv regular [irocession governed hy a snniile luimcncal
law This makes it practically impossible i.. .liv l.lc up ''h'sc station-
ary stales into classes; all of the levels for each .,f ihe at..ms must

"The reader will recognize, in the initials of those names, thr l.iuis x, /', ■/, /',
:in<l I iis<-<l to ilesiRnale the several .oliiMins "I le\cls.

so.\ir. coMF.Mfoh-.iKy .iKi.ixcr.s i\ i:iiysn.s- i iii m

iiif\ ital)l\' In' .irr.iiiKi'd in •> single coluinn. as il was doiu- in Vi^. *>.
Hill in this arraniii-nuMit the si'k'rtion-priiu'ipli' of thi- fori'noinjj p.ira-
Kraph is app.iri-iitly rontravt-ni'd. lM>r, when tlie Ie\els of the scKliiiin
atom were arranjjiHl into <-oliiniiis, the transitions lu-tween levels
l>eloni;iiiK to one and the same column were amonn the inhil>itefl
transitions, the lines corresponding to these were amon^ the missing
lines. But the transitions between the levels in the single column
which contains all of them for the hydroijen atom, correspond to the
actual lines which constitute the entire Indrogen spectrum.

This ili.scord is only ap[)arent. It vanishes when we recall the fact,
already once mentionetl as a forewarning and then neglected for ease
of e.xposition, that the stationary states of the hydrogen atoms are
compound — that what has been called a "stationary state" in the
precetling pages is really an ensemble of adjacent stationars' states.
Kvery line of the Balmer series, the series R(l nr— 12^), is actually a
close doublet; the frec|uency -differences between the components of
all the doublets are approximately the same. Interpreted in the
new fashion, this means that what we have called the stationary state
of energy —Rii/-i is actually a pair of "component" stationary states
very close together — so close together, that if the energy of one were
exactly —R)t 4, the energy- of the other would depart from that
value by less than one part in forty thousand. Further in analyzing
the sf)ectrum of hydrogen we cannot go, probably because the minute
details (if there are any) of the structure of its lines overtax the
resolving-power of our spectroscopes. The spectrum of ionized
helium, however, is spread out in a more generous scale; and some
of its lines were analyzed by Paschen. Among these were the lines
of frequency 4/?(l, 3=- 1/4=); 4/?(l/3=- 1/5=); and 4/?(l/3=- 1/6=).
They were resolved respectively, into six, fi\c, and three components;
and the line 4/?(l '4=— 1 5=) resolved into four.

Interpreted in the new manner, these data mean that what we have
called the stationary states of energy-values —4Rli 9, — 4/?/;,'16,
— ARh 2.5, and — Rh 'i<o, are really ensembles of "component" sta-
tionary states lying very closely together. It would scarcely be
possible to infer from these data, independently and without ex-
traneous guidance, just how many "com[)onents" belong to each of
the four ensembles. Fortunately or unfortunateK', Paschen's measure-
ments were preceded and inspired by a specific prediction of the
number of components in each ensemble — a prediction that what
we have called the «th stationary state should be a group of n "com-
ponent" stationary states. This prediction is graphically set forth
in the second column of Fig. 8, in which the level of energy-value

438 BELL. SYSTEM TECHNICAL JOURNAL

— iRIi is drawn as a single dash, the next le\el as two dashes, the
next as three, and so forth. Paschcn's data were therefore compared
with this prediction.

The data and the prediction were found compatible. If arrows
are drawn from every "component" stationary state to every other
"component" stationary state, it is found that each of the lines which
was observed corresponds to one of the arrows (but it is necessary
to assume that, in some places, two or more adjacent lines are fused
apparently into one by reason of the insufficient resolving-power of
the spectroscope). Some of the arrows, however, correspond to missing
lines. Evidently some sort of inhibiting agency is at work; some
sort of a selection-principle is adumbrated. Furthermore, some and
perhaps all of the missing lines appear when the electric field strength
acting upon the radiating atoms is increased, and this, it will be
remembered, is the beha\ior of the missing lines in the sodium spec-
trum. Whether the selection-principle could ever have been inferred
from these data alone seems doubtful. Naturally one proceeds to
try out the same principle as served for the previous case. Can the
component stationary states of the ionized-helium atom be sorted
out into parallel columns, in such a manner that transitions between
lev'els in adjacent colunms correspond to actual, all the other trans-
itions to missing, lines?

This is attempted in iIk- ni.inni-r siiown in I-"ig. 8. The result is
fairly satisfactory. The lines due to transitions between levels in
adjacent columns should by this principle be visible, and they are.
The lines corresponding to transitions between levels in the same
column, or more than one column apart, should be missing; and
some of them are, but also some of them undeniably can be seen.
To account for these unwelcome guests, it is necessary to assume
that some of the radiating atoms are subject to a strong electric field
which might, but would not be likely to, exist in the discharge. This
is an unconiforlable solution; but there are other numerical agree-
ments between the prediction and the data, which it is not expedient
to describe at this point, but which are good enough to excuse that
deficiency to some extent. Eti somme, the evidence presents no
insuperable objection to our arranging the component stationar\-
states of the ionized-helium atom in parallel columns, and declaring
that the only transitions which occur (except in strong electric fields)
are those between members of adjacent columns; and this is just
what we did with the sodium atom, and can in general do with every
other kind of atom whereof the spectrum has been interpreted. This
being granted, we can assert that the spectra and the stationary

SOME CONTEMPORARY ADVANCES IN PHYSICS- llll AM)

sl.itfs of the ionizi-d-lu'liuin atom (ami |)ri'siimal)ly those of tlic
liy(ln)Ki'n atom) are not so radically ditTi-riMU from lliosi- of the scMliuiu
atom as thoy sicmoti to be; some of the apparent dilTererues heiiin
traceable to the fact that corresponding levels in the/, the </, the />

2

A = a

Hg. 8 — Diagram of the stationary states of ionized helium, resolved to account for
the fine structure of the spectrum lines

440 BELL SYSTEM TECHNICAL JOURNAL

and the 5-c<)liiinns, which in the sodium atom are widely separated,
are in the former atoms so closely crowded together that lines, which
in the sodium spectrum are far apart, are in the former spectra packed
into all-but-irresolublc groups. This is prol)able, but not certain.
Further data about other lines in the ionizcd-helium spectrum would
be gratefully received.-"

The notation for the various "component" stationary states of the
ionized-helium atom is shown in Fig. 8. The successi\e columns
are denoted by the numerals 1, 2, 3, 4 . . . for which the general
symbol is k, as previously. This numeral is written as a subscript
to the serial number of the le\-el in its column, which commences with
1 in the first column, 2 in the second, 3 in the third, and so forth.
By inspecting the figure, the reader will see a reason for using these
ditTcrent values of the serial-number for the first levels of the different
columns. The serial-number is designated b\' n and called the total-
qiiantum-nmnber. The numeral k is called the azimiilhal-qitantum
number, as before. These hea\ily long names are imposed by the
theory and not by the data.

E S. Further Analysis of the Stationary States of Other Elements than
Hydrogen and Ionized Helium; Multiplets

Ha\ing performed a two-stage analysis of the spectra of ionized
helium and of hydrogen, we return to the spectra of the other elements
for a second attack.

Let us consider the reasons for making these anahses in two stages.

When the mid-Victorian physicist trained his spectroscope upon a

tube full of glowing hydrogen, he saw the spectacle of Fig. 2 — the

converging procession of distinct bright lines, of which the frequencies

form that delightfully smooth numerical progression which we have

already met. Later physicists with better instruments discovered

that each of these "lines" was in fact a pair of lines. Now in strict

iniiii, this discovery show'ed that the "lines" of the Balmer series

were no lines at all; for a doublet is not a line. But the phj-sicists

continued to refer to the "lines" of the Balmer series, chiefly no doubt

because to anyone equipped with an ordinary spectroscope the doublets

do appear as single lines. By itself this is little reason; but ilie usage

is not altogether faulty. Few people w'ould hesitate lo admit that

each of these doublets is not a couple of casual neighbors, not two

'" It would be particularly interesting to settle beyond question whether the
niissinc lines demand the select ion-princi|)le already explained in section K4, rather
than tile one to be explained in section K8. This is one of the reasons for wanting
to produce and examine the spectrum of doubly-ionized lithium, in which the evi-
dence would probably be much clearer.

soMi- coxrr..\tr(}K iKv .inr.ixirs ix riivsns- iiii -m

imri'latrd liiu-s forliiitously rlosi- to>;fther, l)Ut a pair of lines shariiiR
sonu- (li'tply limd.imiMital {|uality in common. This is indiralt-H
rhii'tly by the fai'ts tliat tlu- distance (me.isiired in fre(]iiency) between
the components of a doublet is the same for all the doublets, and very
sm.dl comparml with the distance between consecutive doublfls.
For this re.ison the tloublets are treatetl as entities, and they retiilire
.1 n.ime: which is what physicists have preser\ed for them, in con-
tinuing to call them "lines." "Doublet" would be better than "line",
.md "group" would be better yet; but we cannot ever be sure that
even the apparently-single lines are not very close groups, and yet
it would be silly to call every line a group. Sirius appears as a df)uble
star in a few of the most powerful telescopes, but nobody would
insist on calling it a double star when pointing it out in the night sky.

.All this is not so trivial as it sounds. It is easy enough to speak
of doublets when looking at lines which appear single except when
viewed in the most powerful spectroscope, and then are resoKed
into components much closer together than the nearest similar line
is to either. Such lines occur not in the spectra of hydrogen and
ioniKed helium only, but in the spectra of sodium and other elements
generally. But the spectroscopist is constantly applying such names
as "doublet" and "triplet" and "quadruplet", and the inclusive
name "multiplet" to groups of lines which lie far apart in the spec-
trum, with scores of others inter\ening. Here his function is not
to split apparent lines into narrow groups, but to unite widely-scat-
tere<i lines into wide groups. This he does not because of propinquity
of the lines, but because of resemblances or analogies or fixed intensity-
relations between them, or because he finds it possible to construct
a series of such groups with identical frequency-differences between
corresponding lines within them, or because of analogies with other
elements with more perspicuous spectra, or theoretical predictions,
or intuitions or clairvoyance. Ciroups such as these are not generally
termed lines, except in very abstract discussions; it is difficult to
call a group a line, when it is clearly resolved b%- any instrument
worthy the name of spectroscope. But they are like the lines of the
Balmer series, treated as entities because their lines are believed to
share some deeply fundamental quality in common.

What I have said about lines and groups of lines is transferable in
substance to stationary states and groups of stationary states. What
we had originally called the levels of hydrogen and ionized helium,
with their energy-values -Rli'n^ and -ARh/n} (w = l, 2, 3 . . . ),
were resolved into groups of levels in order to interpret the fine
structure of the lines. But owing to the propinquity and to certain

442 BELL SYSTEM TECHNICAL JOURNAL

numerical relations of the levels in a group, and to certain qualities
of the transitions between them, it was felt that the levels of each
group share some deeply fundamental quality in common. For this
reason we used a system of classification in which each level is repre-
sented b\- two symbols, one for its group and one for its place in its
ijroup; and we numbered the le\'els in succession, not 1 and 2 and 3
and 4 and 5 and so forth, but li and 2i and 22 and 3i and Sj and 3a
and so forth. Interpreting the groups of lines in the spectra of
.sodium and other atoms, we infer groups of levels. The levels in
one of these groups are often far apart. They may be eighteen or
more in number, other levels may lie between; but by reason of the
resemblances between the lines whence they were inferred, by reason
of certain numerical relations between the levels themselves, they
are believed to have some deeply fundamental qualit\' in common.
If this is vague, so also at times is the interpretation.

The statements in the foregoing sections about the stationary
states of sodium are now to be understood as relating to groups of
stationary states. It is the groups of slatiotiary slates which are
(irranji^ed in parallel columns, desigJiated by numerals k, such that no
transition takes place unless in it k changes by one unit. It is the group
of stationary states which is marked by a pair of numerals, one to
designate its column and the other its place in its column; or by a
letter to designate its column and a numeral to designate its place in
its column. It is the group of stationary states which is denoted by
(32) or (l,s) or (5,rf).

To denote a particular stationary slate we must add, to the symbols
for its group, a third s>-mbol for its place in its group. This s>mbol
is generall>' a numeral, hung on as a subscript to the letter desig-
nating the column (thus: (2,/'i) and {2,p2) ) or as an additional sub-
script to the two numerals (thus: 32i and Ssj).-' The most common
general symbol for this numeral is j. Geometrically, the stationary
states may be represented by lines or dots arranged, not in one row
of se\cral parallel columns as in Fig. 7, but in .se\eral rows of parallel
cf)himns. Readers with three-dimensional imaginations in good
working order may develop this idea ad libitum. The systems for
assigning the values of j are shifted around every few months to
correspond to new atom-models, and are scarcely worth memorizing.

" The notation suggested by Saunders and Russell, evidently in concord with a
niiniljcr of other experts, is built in this way: Designate the column to which a
group lielongs by the letters suggested in section E5, capitalized (i.e., .S", P, P, F,
G, 11 for ^ = 1, 1, ?i, 4, .S, (>); write the serial-nunil«?r of the proup before the letter,
and ajipcnd the value of jf as a subscript to the letter. If it is desired to state what
sort of a system (cf. section ElO) a level belongs to, one may add an index to the
left of the letter and above it.

SOME COXTEMPOR.IKV .inr.lWr.S /.V rilYSlCS nil 44.?

The host of tlieni, however, are adjusted so as to express a new and
additional selertioii-principle, which is roec|iial with the other selcr-
tion-prinrii>le we met a few pages above.

This principle is derived in the .same way as the first one. Tin-
groups of levels are established by inference from tiie groups of lines;
then arrows are drawn from every level to e\ery other, the corrc-
s|H)nding spectrum-lines are sought, and most of them arc not foimd.
.Some of these missing lines are those which would contravene the
first selection-principle, as they correspond to transitions in which
the numeral k changes by more than one unit, or not at all. Putting
these aside, there are still a number of missing lines, to which the
first selection-principle has offered no objection. Now it is found
possible to chcHKse the numeral j in such a manner that the only
transitions which correspond to actual spectrum lines are those in
which 7 changes by one unit or not at all iSj = 0,±l). Furthermore
it is possible to adjust the values of _; in such a manner that the lines
corres^Kinding to transitions, in which j is initiall\- zero and remains
unchanged, are missing.

This is the selection- principle for the inner quantum number; for
the numeral j. when adjusted in this manner, is known as the inner
quantum number. This again is a name imposed b\- theoni- and not
by the data of experience.

As the two selection-principles arc etTective concurrently, the pair
of them may be fused into this one:

Of the three numerals n, k and j, which specify a stationary stale com-
pletely, two (k and j) may be so chosen that the only transitions which
correspond to actual lines are those in which : first, Ak = ± 1 ; second,
S]=0, ± 1 ; third, j is not zero both before and after the transition.

This complicated rule is evidently the sign of some very important
principle, the full nature of which thus far escapes us. It will prohahh'
seem dithcult to grasp and fix in mind; but difficulty of this sort is
likely to alH)und in the physics of the near future. Not so many
years ago the physicist's path lay among differential equations; the
defter he was in integrating hard specimens of these, the better he
was fitted for his profession. I should not care to say that this is no
longer true; but he will probably have to cultivate a sense for prob-
lerps such as this.

It remains to give some idea aliout the number of stationary states
in the various groups. P'or sodium, as laid out in Fig. 6, the groups
in the j-column are merely single levels (this sounds like a contra-
diction in terms, but may be borne for the sake of the generality):
the groups in the other columns are pairs of levels, or "doublet terms."

444 BELL SYSTEM TECHNICAL JOURNAL

This is the common character of the alkali elements Li, Na, K, Rb
and Cs, which occupy the first column of the periodic table; prob-
ably also for the noble metals which share this column, but the data
are few. For elements of the second column of the periodic table
there are two complete systems of stationary states, each having
its own s-column, its own />-column, its own rf-column, and all the
rest. In one system, all the groups in e\ery column reduce to single
levels; it is a singlet system; in the other, all the groups in the 5-column
are single levels, all the groups in the other column are triads of
levels or "triplet terms;" it is a "triplet system." The complc\it\-
mounts up stage by stage as we cross the periodic table of the ele-
ments from left to right, and soon becomes terrific.

E 9. Effect of Magnetic Field on the Stationary States

When a magnetic field is applied to a radiating gas, most of the
lines of its spectrum are replaced by triplets (Fig. 9), or by even richer
groups of lines (Fig. 10). By a somewhat loose usage the lines are said
to be resolved into three or more components. This is the "Zeeman
effect." There is a multitude of empirical rules about these compo-
nents, their spacings, the way in which their number and their spacings
vary from one line to another, and other features. According to the
new fashion, however, we focus our attention not on the component
lines, but on the stationary states which are inferred from them.

The effect of a magnetic field may be described by saying that it
replaces each stationary state (with a few e.xceptions) by two or
more new ones. Each of these new states requires four symbols to
designate it; the symbols n, k and j for the original stationary state,
and a new symbol tn to denote its place in the resulting group. As
heretofore, when every stationary state is connected with e\ery other
by an arrow and the corresponding lines are sought, it is found that
some of the lines are missing. Still another selection principle is
therefore to be sought, and the values of the new numeral ni are to
be so adjusted — if possit)Ie — that the selection-principle can be read
easily from them. When so adjusted m is called the magnetic quantum-
number.

In certain cases the empirical rules for the components whereby
the magnetic field replaces the indi\idual lines are simple; and the
derived rules for the new stationary states which arise out of the
original ones when the magnetic field is applied are correspondingh'
simple. These are the cases of "normal" Zeeman effect (the ad-
jective "normal" may be an entirely misleading choice). Let A Um

SOME CONTEMPOR.fRV .{m.lXCr.S IX rilVSICS rill 445

represent the enery;y-(litTerence between the new stationary state
(Icnotetl by the index m, and the original slalionar\' state. The rules
are compriseil in the formula,

and ill the selection-principle. In the fornuila // stands for the
magnetic t'leld; w is a factor equal within experimental error to e/4rnr
(/i = mass of the electron) and commonly identified with it. in has two
or more \aliies spacetl one unit .ijiarl (for instance, I and •>. (ir ." and
-i. or 1 and 0 and -1).

The selection principle is as follows: The only transitions 'iuliich cor-
rrspiniil !o ih fthtl !iiir\ art' llio'ic in whiih m rlunii^cs hy unity or not

I 1

^ 1

\ 1

I __ ^ i, tU-l.l oTi spi'ctrum lliu-^. I', /rem, 111, Jri,',

t'ranktin Institute)

at all: Am=0,±l. This is the selection-primiple for tlic magnetic
qnatititm number.

If we allow m to assume onh- two \alues, this i)rinciple Incomes
nugatory. If on the other hand, we aflopt the principle, m can assume
an>' number of values whatever, provided onh' lhc\' are spaced at unit

Fig. 10 — More complicated effects of magnetic fields on spectriiin lini>.
(P. Zeeman, I.e.)

intervals; it makes no difference with the observed lines wheltier there
are two or two hundred new stationary states for every original one.
This is convenient for theorizing. In dealing with the Zeeman effect
in general, and not merely with these special "normal" ca.ses, it is
neces.sary to assume that oi is not restricted to the particular value

446

BELL SYSTEM TECHXIC.IL JOURXAL

just j;i\c-n. Imi depends on the stationary state in question: and that
m depends on the value of 7 for the stationary state in question.

Very strong magnetic fields treat a group of stationary states as if
they were one single state — as if they were first all fused together into
one, and this one then resolved according to equation (8). This is
the Paschen-Back effect. It e\idenlly means a great deal.

The light emitted from a gas exposed to a magnetic field is polarized.
Some of the new lines are circularly polarized about the direction of
the magnetic field as axis; others are plane-polarized, with the electric
vector parallel to the direction of the magnetic field. The lines cor-
res[)onding to transitions in wliicli /;; changes by one unit are all
polarized in the former way: the liius corresponding to transitions
in which in does not change are all jjolari/.id in ihe lailer wa\.-'-

E III. Iiilcrrclalions of Midliplels and Zeenian Effect

I insert this section chiefiy for the benefit of such readers as may
be preparing for a thoroughgoing study of atomic theory. Others
may do well to pass it o\-er, as the statements it contains can scarcely
be apprehended with any \ividness, except by the aid of pencil and
paper and hours of reiteration. For those who omit this section I
will merely say, that the material described in it goes far to show that
the numerical \alues which we have been assigning to k and j are
not quite arbitrary, but are determined by something fundamental;
although the ones heretofore assigned are not necessarih' the most
exjiressive.

I begin with a descri|jtion of the \ arious known systems of stationary
states, condensed into Table III. To make this table clear I will
exjjlain the fourth line; this line contains the statement that a "quartet
SNstem" of stationary states consists of an s-coliuitn of single le\els, a
/>-column of groups of three levels each, and a ^/-column, an /-colinnn.
and additional columns of groups of four le\ els each.
TABLE ill

Name of System

p

d

/

1

2

.^

4

5

6

7

5

7

/'

/"

Siiiulet. .

Doublet.

Triplet.

yuartet .

Quintet

.St-xtft

Septet

Octet

" The effect of a macnetir field on resonance-radiation, discovered by Wood ami
Elicit, will be dcscrilird in the Second Part.

S(hMH ahwuMriU.'.iKy .ini-.txcrs ix /'insics riii' 447

Mk-nients of tlu- first roluiiin of tlu* pt-rioclir tal)l«' possi-ss a (loiil)li'l
syslt'in of s(.ilion.ir\' slali-s; i-IimiumUs of llu- tliird (-oliiiun, a (loiil)l(.-t
systfin .111(1 ill addition a (|viarli.'l systi'in. It is infiTn-d tlial flrnu-nts
of tlu' fifth column possess tlu-sf and a sextt-t system in addition;
i-k'UK-nts of tlu- svvi-nlli. tlu-si- tlirt-f and an octi-t systi-m in addition.
Kli-ntents of tlu- soi-ond roliimn of tlu- periodic tahle |M)ssess a singk-l
system and in atklilion a tripk-t system. Il is inferreil that eknnents
of tlie fourth column possess the.se two and ,i i|iiintet system in arldi-
tion; ek'inents of the sixth cokimn, these three and a septet system;
ek-ments of the einhth. the.se four and a nonet system. These infer-
ences h.ue been partialK' \erilie<i. I'or titanium, in the fourth rokimn
of the (leriodic table, the triplet and (juintet systcn^s have been dis-
coNereti; for vanadiimi (fifth cohmin) the (|uartcl and sextet; for
chromium (sixth) the quintet and sejitet ; for manganese (seventh) the
quartet, sextet, and octet; for iron (eiglith) the triplii. (|iiinlet. and
septet. Apparently it is by no means certain tli.it tlu- unicuniinncd
systems are really missing, as the dilVu iiliies of anal\/.in^ these com-
plex spectra are terrific.

There are certain rules governing the number of le\els in a grouj),
and the effect of a magnetic tiekl upon these le\els. These rules
were tliscovered chiefly by I.ande; I give them in his iKil.iiioii. I
recall, to begin, that we ha\e designated each group <it lc\tN li\ ,i
numeral it, which is 1 for all the groups in the s-column, 2 for all
groups in the /)-column, 3 for all groups in the rf-column, and so forth.
We have further distinguished the different le\els in a group by
assigning them ditTercnt values of another numeral _/; the manner in
which these values of j arc cho.sen was described in section KX. Lande
introduces a numeral K which is smaller than ^ by I; K thus is \ for
all groups in the 5-column, 1.'. for all groups in the />-column, and so
forth. He also introduces a numeral J which is greater than 7 by 5;
and a numeral R which is ^ for every level belonging to a singlet
system, 2 2 for every level belonging to a doublet system, 3 2 for
every level belonging to a triplet system, anfl so fr)rth.

These are Land^''s rules:

(1) The total number of le\'els in a grf)up characterized by the
numeral K, belonging to a system characterized by the numeral R,
is twice the smaller of the two numerals R and K (that is, it is '2R if
R<K, 2K if R>K: 2R = 2K if R = K).

(2) In the formula (8) for the Zecman effect, the factor a? is equal
to e -iiriic multiplied by a factor g, which depends on the numerals
R. K. and J for the level in question in the following manner:

g = 3/2+(/?=-A:')/2(y^-i) (9)

448 BELL SYSTEM TECHNICAL JOLRSAL

(3) In the same formula, the magnetic quantum-number m depends
on the numeral J for the level in question; it assumes 27 ^•alues
altogetlicr, commencing at the maximum \alue {J—\) and going
downwards across zero to { — J+\).

These rules form a beautiful little problem for the designer of
atom-models. They have often been tested and \erified (it is not easy
to find out just how far), and at present are widely used in the decipher-
ing of spectra. It appears, however, that some spectra — particular!}'
those of the inert gases — are too complicated even for these rules, and
possess a structure even more elaborate. Considering how difficult
it is to grasp the structures already described, one ma>' be excused
for feeling some dismay at the prospect.

E 11. Effect of Eleclric Field on the Stationary Slates

W'JU'ii an ck-rtric ticld is applied to a radialiiig gas, the lines of its
spectrum arc rcplarcil hy j^roups of lines, dticn rich and ciimijliratcd.

X4388:S

>VS

X4026:S

l-ijC. 11 -Kcsohition of spcclnim-liiies into groups, displacement of lines, and rinit-
Reiice of missing lines, prodiued liy a strong electric field (increasing from the lop
downwards to nearly the bottom of the picture). (J. S. Foster, Pliysical Rn'inc}

(Fig. 11.) F'rom these we infer, as heretofore, that the stationary states
are replaced by grou[)s of stationary states. The atom-model jiro-
posed for lu'drogen and ionized heliinn has been i\t r.inrdinariJN
successful in di'scribing the elTect of electric field iipnn llieir spectra.

soMii coNTEMi'tu^.iKy .//>r./.V( 7; v /.v riiysus iiii a\»

and ihtTi-forc I sli.ill Niolati' llu' ruli- I li.i\r luTfiufnrf followed, .ind
|M)stjH)nc the (U'scripiion of tlu- plifiionu'iia until tin- tlifory is st.iti-il.
Atoms of otluT kinds are atTerted in at least two ways; the stationarN-
states are displ.ired, .md tlie "missing lines" are csoked, as I have
siiid ulread\ .

li I J. lulensily-Ralios

The relative intensities of the various lines of a doublet, or triplet,
or multiplet are often equal within the (fairly large) uncertainties of
measurement to simple ratios, such as 1 : 2, 2: 3, !i : 4. This ha[)pens
tiK) often to be easily put down as a mere coincidence, and indicates
that the occurrence of transitions is governed by simple laws. Our
selection-principles are themselves indications of the same t>pe, since
they may be taken as signifying that the intensity-ratio of certain
lines to certain others is zero. This problem may be more difficult
than the ones I have stressed hitherto, since each line involves two
stationary states and is not a quality of one only. This applies to
other properties of lines, such as their sharpness or diffuseness.

E IS. Excitation of Individual Frequencies

So long as an atom is concei%-ed as a belfry full of bells of various
pitches, it would probably be argued that a shock to the atom would
set all the bells to jangling, and a gas bombarded by electrons would
emit all of its natural frequencies if any. The interpretation of
spectra to which these pages are devoted leads to a very different
idea. A spectrum-line of frequency t> is emitted when the atom
passes from a stationary state 5 to a stationary state A. The energy-
\alue of state B by itself does not determine v; this is controlled b%-
the difference between the energ>'-values of B and A, which is hv.
But the energ>-value of B has everything to do with whether or not
the frequency v is emitted under given conditions; for it will not be
emitted at all unless the atom is first put into state B. If the gas is
bombarded with electrons of energy insufficient to raise an atom from
its normal state to state B, then the line in question, and all of the
other lines which result from transitions from B to other levels of
lower energy-value, will fail to appear. If the energy' of the electrons
is raised past the critical value (the difference between the energy-
value of B and the energy-value of the normal state) all of these lines
suddenly appear.

This is illustrated by Fig. 12, relating to magnesium. An electron
striking a magensium atom and having an energy equal to 3.2 eriuiva-

450 nr.l.I. SYSTEM TECHMCAl. JOIRXAL

k'lii volts is alili- to f)iii tlif atom into a p.iriicuiar excited state; the
atom emits radiation of wavelength 4o71 in returning to its normal
state. To get the atom to emit another sort of radiation, tlie electron
must possess 6.5 e<|iii\ ilciil \olis lo piii i( into another excited state.
Any excited state can Ik- reaclu-d if the ilecunn has 10 e(nii\alent
volts to pass over to tlie atom.

In a gas sustaining an electrical discharge, the atoms ari' snhji-ct
to stimuli of such variegated force and type that the distinctions
between ilifTerent lines are not so clearly marked; but it can be seen

J/MJU

LMf specTin/M

3? t«73

6S

/O

yr :^^cr,..»

...

'i 5

inwu^inii ii^H

Fig. 12 — Successive excitation of lines requiring electron-impacts of successively
greater violence to liring atoms into the neccssarv initial states. (Foote, Meggers,

.\nil Mnlilcr, Pliili>xi>t>liinil'\Jiixi'zi>ie)

that mild discharges faxnr lines for wliicii ihc iniii.il le\el is adjacent
or close to the normal levil, wliiie otiur lines ri(|uire .i more \iolent
stimulus. Furthermore, when a gas is steadiK' heated to higher and
higher temperatures, various lines of its spectrum apjiear in more or
less the order of the stationary states which are the initial states of
the transitions responsible for these lines. Accordingh' a "tempera-
ture classification" of spectrum lines has been dexeloped at Mount
Wilson Obserxatory and elsewhere, and is \aluable in deciphering
intricate s|)ectra.

E IJf. Absorplion-Sprrlni

An atom which will emit a fniiuency r when it is originall\ in a
state B and passi's over into a >late .1, will absorb light of the same
freciuenc\' if it is inili.illy in the state .1. This has the important
conse(|ueiice that the lines which a gas absorbs, when King at rest
and imexcited, are those which it emits in passing from an\' and e\er\'
other state itilo Ike normal slalc. The line^ einiiicil when .in .iloni
passes from one of its stationary slates into .mother which l,ill(.'r is
not the normal state, are not absorbed b\- thi' gas King quiesci'nl ,ind
undislurbi'd. l-"or this reason heliimi and neon and argon are (|uile
tr.insp.irent lo .ill visible lii;lii, .illlioiii;h llicy li,i\e many i-mission-

SOStR CONrEMPOh'.IKV .IDr.lXCIS l\ l-UYSICS rill 451

liiu's in this rt-jjioii of llu- siHTtrum; for racli of tiu'st- liiu-s ntrrv-
s|xii)(ls to a transition into sonu- oIIut tlian tlit- normal slati- and tin-
linos which correspond to transitions into the norma! slate lie far
off in the nllrax iolet. Hut if such a gas is made the theatri' of a self-
snstainiiiK l-lectrii-al (lischar^;e, the other lines likewise are absorbed ■
for the disch.irije pnts the atoms of the >;as tempor.iriK' hnt fre(|nenlly
into various almormal st.ites. This inci<lentally is one of the hits
of evidence that an atfun may sojourn for a finitely lon>{ lime in
another stationar>' state than the normal one. If the gas is heated,
the s;une effect occurs; for the violent collisions between atoms in a
hot gas occasionally bring atoms into excited states.

By observing the absorption-spectrum of a quiescent gas one learns
which lines in the emission-spiectrum correspond to transitions into
the normal state — a valuable piece of information in the cases of
elements of whiili the spectr.i are complicali'd and obscure.

F. /•). Spectra of Ionized Atoms

In a \iolent electrical discharge, such as a spark, the gas emits
many lines which cannot be fitted into the system of series of the
usual spectrum of the gas. These may also be produced by bom-
barding the gas with electrons possessing more than enough energy
to ionize its atoms. They are belie\'cd to emanate from ioni/i-d
atoms, or from atoms deprived of one electron. The sped nun nl
ionizcfl-helium has been ver\- imjjortant in these pages. In very
violent sparks many more lines emerge, and these are associated with
atoms deprived of two, three, or even more electrons.

The spectrum of the ionized atom of an element resembles, in its
system of series, and in more minute details, the spectrum of the
neutral atom of the element preceding it in the periodic system.
The spectrum of an atom deprived of n electrons resembles the spec-
trum of the neutral atom preceding it by n places in the periodic
system. This confirms the belief that the spectrum and the other
properties of an element are determined chiefly by the number of
electrons which its atom contains.

E 111. X-ray Spectra

The difference between the X-ray spectra to which we now come,
and the "optical" spectra which we have been discussing seemed
profound and vital in the era of very defective knowledge, but it
has faded steadily away with the dee[)ening of understanding. TweUe
or fifteen years ago the contrast was multiform and very sharp; for

452 BELL SYSTEM TECHNICAL JOURNAL

the oiitical spectra were produced chiefly by maintaining an electrical
discharge in a gas, the X-ray spectra invariably by bombarding a
solid body with exceedingly fasl-mo\ing electrons or with other
X-ra\s: the optical frequencies could be diffracted and refracted,
the X-rays not at all or almost imperceptibly little; the optical fre-
quencies were all inferior to 3.10'^, the X-ray frequencies all clearK-
more than a thousand limes as great. Since then, rays of almost
all the intermediate frequencies and with intermediate properties
have been generated in a variety of ways, and the distinction is no
longer trenchant, except between the extremes. To make it so, one
must seek a theoretical reason — and perhaps there is none to be found.

There is, however, apparently good ground for introducing a
theoretical distinction. I have pointed out heretofore that the energy
which an atom loses, when it radiates one of the lines of its "optical"
spectrum, is less than the ionizing-energy. Or, turning this state-
ment around and amplifying it a little: the energy which an atom
absorbs, when it absorbs one of the rays of its optical spectrum, is
less than what is required to detach the loosest electron from it.
Therefore it is possible to assume, at least as a trial hypothesis, that
the energy is spent in lifting the loosest electron partway out — a
hypothesis fortified 1)\ ilu' t.ui ih.it, w hen the atom has just absorbed
some energy in this niaiiner, the eleitron can be detached by sup])lying
the atom with enough extra encrg>- to bring the total amount up to
the ionizing-energ\-. But if we take one of the typical X-ray fre-
quencies, and multiply it by It to ascertain how much energy the atom
gains in the process of absorbing that frequency, we find that the
cjiiantity lii> exceeds the ionizing-energy tremendously. This circum-
stance makes it quite out of the question to imagine that the X-ra\s
are due to changes in the position or the motion of the loosest electron
alone. We may therefore define the X-ray frequencies as those which
cannot be explained as due to transitions of the loosest electron,
from one motion or position to another, unaccompanied by other
changes. By this definition, every frequency v for which the quantum-
energy liv is greater than the ionizing-energy, goes into the X-ra\
spectrum. For the remaining frequencies the question is more
dubious, perhaps never quite to be settled unless and until com-
plete theoretical classification of all the lines is attained. In this
section, howe\'er, I shall speak only of frerjuencies hundreds or thou-
sands of limes greater than the ionizing-frequency.

Clazing upon typical X-ray emission spectra one sees that the\'
consist of groups of lines with wide inter\-als between. Going from
higher frequencies towards lower, the groups are known successively

SOME CONTF.MI'OR.IRV .IPr.lXCF.S IX rilYSlCS -llll 453

as the K Kr<>»p. llu- L uroiip, the .\/ jjroiip and tin- .V nn>ii|). Tlu-
wuril series is mort- nunmoiily used tlian g,roiip: Ixii this is a inis-
fortuiic. for it suggests a daiiKerously misleading .m.ilony witli the
series in the optical spectra wliich we have studied with so much
care." The process of measiirinu these Hues and cl.issifyinj; them

f!t,*^?i

IM

m

L Muii-W 'i-xMM^Hi.iSt

/»:^^
*, ^

1^

/ViVfl, /( y

EE

4im.

■/. d

■ z, b

3,

a

3:.

a

J.

b

Jj

b

f,

b

y,

o

c,-

a

».

6

c,

fi

y,

a

^'k

a

/.

b

>»

o

/'

1^

Kig. 13— Diagram of stationan,- states designed to account for the X-ra\- si)cctriir
of uranium. (From Sicgbahn, after Coster)

was carried out after the dissemination of Bohr's great idea that
each line-frequency should be multiplied by // and the product in-
terpreter! as the difference between the energy-values of two stationar>
states of the atom. The complete analysis of an X-ray spectrum

"In fact the usage is inverted. A series, in the optical spectrum, is a set of lines
havmg the same jinal state in common; but the " k-series" is a group of lines having
the same initial state in common, the L-series a set of 3 groups corresponding to 3
initial states.

454 BELL SYSTEM TECllXICAL JOURNAL

lluis culminates in a (iiagrain of stationary states, as for llu- ojilical
spectra.

Such a diagram is shown in l"i^'. IH, wliich is for an t-k'nu-ni far up
in the periodic system, therefore with a rich s>'stcm of X-ray hnes
and stati<jnary states. In comparing it with one of the diagrams
made for optical spectra, it must be remembered that its scale is
enormously more compressed — the distance from top to bottom cor-
responds to about one hundred thousand equivalent volts. Each line
in the X-ray spectrum corresponds to an arrow between two of the
le\'els, but not every arrow- corresponds to a line. Again there is a
selection-principle, and this selection-principle is partly expressed by
attaching a double index to each of the levels. When the indices
are assigned as in Fig. 13, transitions between levels for which the
second numeral differs by one unit include the onh' ones which actualK'
occur. But this is not the complete selection-principle; it is neces-
sar>' to add that in any actually occurring transition, the first numeral
must change b\' one or more units; and further, that transitions may
occur only between levels to which ditTiTt-ni k'tiers are attached.
The first numeral is designated li\ n. tin- sicdnd !>> k; they are called
the total and the azimuthal quantiini-nunilicr.

The levels are also frecjuently known li\' kilcrs with suliscript
numerals, as the diagram shows. The letters by now are i>retty
definitely fixed, but the subscripts are still being shuttled around.
The notation for the X-ray lines is in a terrible state.

A curious and evidently important feature of the.se levels is, that
when an atom is put into any one of them — say into the K level,
or the Li level, or the L« le\el — it extrudes an electron. < )r. in other
words, each of these stationary states is a state in wliich the atom
lacks one of its electrons — like the "ionized-atom" state from which
we previously measured the energy-values in dealing with the optical
spectra. All of them, at least the highest ones, are in fact "ioni/ed-
atom states." Since, how'c\er, they are all different, it is natural to
suppose that a different electron is missing, or that an electron is
missing from a different place, in each of the different cases. .\|)-
|)arentl\' an atom cannot enter into a sl.iii(>nar\ si.ite with so liigh
an energy, and remain neutral.

We must pause to consider from wji.u si.mdaiil slate the energy-
values of these stationary states are measuretl. In the prexious case
of the optical spectra, the energy-values of the stationary states were
measured, so to speak, downwards from the state of the ionized atom
to the normal state of the neutral atom; the energy of the ionized
atom was set equal to zero, that f)f the neutral atom in its normal state

SOMf: CiWTF.MfOR.tRy .ll^.tMhS IX rilYSlCS nil 455

ilu'ii h.ul a (iTt.iin iu-ii.iti\i' \.iliii'. .ill ilu- nilu-r ener^jy-valiirs wvn-
iu'xaii\t' .iiul sc.ittfri'<l JK-lwi-fii {Uv>v iwd. In this case of lIu- X-ray
siHTtra, the eruTKy-valiR's of tlir siatioiian- states are nu-asured
tifnvards from the normal state of the neutral atom, to which the
enerj;y-value zero is assijjned. while all the other energies are |>ositivc.
In Fii;. 13 this zero-line must he imaijined just luuler the level marked

The exact (Position of this zero-line for the hi^h enerj;\- stationary
states is not \-cry accurateK' known; although the distance between
any two levels is determinetl with all the usually \ery great exactitude
of X-ray wavelength-measurements, the distance from any level to
the zero-line is uncertain within a few tens of volts. This uncer-
tainty is not great enough lo be ini|)()rtaiit wlu-ii dealing with the
high-frequency X-rays.

This point being attended to, we are now in position to consider
the striking difference between X-ray emission-spectra and X-ray
absorption sjiectra — striking indeed when one looks at typical photo-
graphs, apparently altogether a different matter from the contrast
between optical emi.ssion-spectra and optical absorption-spectra, yet
in principle very much the same thing. In dealing with optical
spectra, I remarked that while an atom may absorb any frequency
which it can emit — while the complete absorption-spectrum of a gas
is identical with its complete emission-spectrum, yet the absorption-
spectra one ordinarily sees contain only a small selection of the emis-
sion-lines. This occurs because when a gas is being examined for its
absorption-sfiectrum in the laboratory, by sending light through it,
it is generall>- in an untroubled and quiescent ccjndition, each of its
atoms being in the normal state; therefore it absorbs only such fre-
(juencies as provoke transitions from the normal state to the various
excited states, and not such frequencies as would induce transitions
from one excited state to another, for few or none of the atoms are in
any one of the excited states to start with. Such also is the case
with the X-ray spectra. Quiescent atoms absorb only such X-ray
frequencies as produce transitions from the normal state into one
of the stationarv- states flesignated by K, or L\, or Li, and so forth —
they do not absorb such frequencies as would produce the transitions
from L\ or Lj to K, for instance, for the atoms are not initialK- in the
states Li or Lj. This is quite the same behavior as is observed in the
resp<^)nse of atoms to radiations in their optical spectra. It is much
more pronounced, however; for, while it is possible to make a gas
absorb frequencies which produce transitions from one excited state
to another, by maintaining the gas in a state of intense electrical

456 BELL SYSTEM TECHNICAL JOURNAL

excitation, this has ne\er been tloiie with metals or gases exposed to
X-ray freciiiencies.

Atoms therefore do not absorb such X-ray frequencies as are
represented by the downward-pointing arrows in Fig. 13. They do
absorb such frequencies as would be represented by arrows drawn
from the very bottom of the diagram — a little below the le\'el marked
P — up to the various le\"els; and (it may seem, unexpectedly) they also
absorb frec)uencies somewhat higher than these. This however does
not mean that the atom may be put into an excited state of higher
energy than the K state, for instance; it means simply, as direct evi-
dence proves, that the extruded electron receives the extra energy and
goes away with it. Owing to this fact, the X-ray absorption-spectrum
consists not of sharp absorption-lines at the several fretjuencies cor-
responding to a transfer of the atom into the K-state, the Li-state,
and so forth, but of continuous bands commencing with sharp edges
at these frequencies, and Irailini; out gradually towards higher fre-
quencies.

Another curious feature of the X-ray spectra is that transitions
from the various excited states of high energy-values, such as the
A'-stale and the L-states, direct K' into the normal state, ajiparentK-
do not occur.

E 17. Bands pedra

Band-spectra are the s[)eclra of molecules, — that is to say, of
clusters of two or more atoms, such as appear in certain gases. This
is proved by the fact that they are displayed by gases which are
known in other ways (gramme-molecular volume, specific heat) to
consist of molecules; by the fact that the band-spectrum of such a
gas disappears when the gas is heated to the point where its molecules
are dissociated into atoms; and by the general successfulness of the
quantitative theory based on the assumption that they are due to
molecules. Occasionalh' band-s])ectra are displayed by gases which
are not otherwise known to contain molecules, such as helium and
potassium; it is supposed that they are due to molecules too few
to be detected by the other acce|)ted methods. I'sually they arc
easy to distinguish at first glance from the optical spectra of atoms,
although there are exceptions, such as the band-spectrum of the
Indrogen molecule, l.ike the spectra we have di.scussed, they consist
(jf lines; the term "band-spectrum" describes the manner in which
these lines are grouped. Again like the spectra we have discussed,
they are analyzed according to Bohr's funtlamental principle, by

SOME coxTEMPOR.-iRy .iDf.ixcr.s i\ pnysics rni 457

interpreting the lines ns the results of tr.insiiiDiis hetween sialionarN-
states.

!'. M\(.\i III Mii\ii;nts f)F Atoms

Of the enormous and chaotic variety of facts about the nianneli-
pro[x"rties of materials, only a few of the least conspicuous have been
serviceable to atom-builders; the notorious ones have helped very
little or not at all. The famous and characteristic magnetic prop-
erties of iron, nickel, cobalt, depend on the arranRement of the atoms
and on the temperature of the metal, and cannot safely be attributed
to the atoms themsehes. Diamagnetism, an inconspicuous and
rarely-mentioned (juality of certain elements, is in some instances
(|uite independent of temperature, and may well be a properly of
the atoms. Paramagnetism, an almost ctjualh' incons(iicuous quality
of certain other elements, depends on temperature, but in such a way
that it may sometimes be explained b\- assuming that each atom has
a characteristic magnetic moment, the same for all the atoms of a
substance. The value of this magnetic moment of the atom may be
calculated from measurements on the paramagnetism of the sub-
stance; the process of calculation invokes certain assumptions, at
least one of which is at the present open to question.

Direct measurements upon the magnetic moments of certain atoms
are now being made by C.erlach; and they are among the most im-
portant achievements of these years. In a small electric oven, a
metal such as silver is vaporized; a beam of the outflowing atoms,
passing through a small orifice in the wall of the oven and through
others beyond this one, eventually tra\cls across a strong magnetic
field with a strong field-gradient and falls upon a plate. Suppose
that each atom is a bar-magnet, oriented with its length parallel to
the magnetic field. If the field were uniform, the bar-magnet would
not be deflected, it would travel across the field in a straight line;
for although its north pole would be drawn sidewise by a force, its
south pole would be pushed by an exactly equal force in the exactly
oppf)site direction. That the atom may be drawn aside, the field
must be perceptibly different at two points as close together as the
two poles of the magnet. When one considers how small an object
the atom is, it is clear that the field must change very rapidly from
one fx)int of space to another, its gradient must be enormous. Gerlach
succeeded in contriving so great a magnetic field with so great a
gradient that the beam of flying atoms was perceptibly drawn aside.
The most-deflected atoms are those of which the magnetic axes are
most nearly parallel to the magnetic field. From their deflections,

458 BELL SYSTEM TECHNICAL JOURNAL

the field, and the field-gradient, the ni;i^;iHiii' munu'iu of tlu' atom
can be computed very simpK . Tlu- \.iliu> tlui> (ilnaiiK-d are of the
order of 10 ""in CGS units.

I shall comment in the second part of this article uyum other infer-
ences frf)m these experiments, which are as valuable as the experiments
upon the transfer of energy from electrons to atoms. At this point it is
sufficient lo realize that these experiments pro\e that atoms, or at least
the atoms of some elements, possess magnetic moment. If magnetic
moment is due to electric current flowing in closed orbits, as Ampere
and Weber guessed a century ago, the atom must be suppf)sed to
contain such currents; if the atom consists of a nucleus and electrons,
some at least among the electrons must be supposed to circulate.
And if the electrons are assumed to circulate in a particular manner
the magnetic moment of the atom so designed can be computed,
and thereupon tested by experiment.

Tiiis complete^ tile list of the phentjniena, tlie jjioiierties of matter,
which are used in designing the contemporary atom-model. Nobody
will require to be con\inced that it is not a list of all properties of
matter, nor of all i)henomena. These are not among the obvious
and familiar tiualities of matter; and no one meets any of them in
everyday life, nor perceives an>- ol tlu'iii with his unaided senses.
They are phenomena of the laboralor\', discoxered after a long and
painstaking de\eloi)nuiit of laboratory technique. Lucretius did
not know tliem, and tlie.N were inaccessible even to Newton and
to Dal I on. Tliey are a very limited selection from among the phe-
nomen.i ol n.itiire, but not for that the less important. The atom-
model which is de\ised to explain them is at best a partial atom-model ;
thus far it ser\es for no other phenomena than these, but these it does
interpret with an elegance and a competence Cjuite without precedent
among atom-models. I have said that .some of these phenomena are
explained b>' conceiving an atom made of a positively-charged nucleus
and a family of electrons around it; but this conception is not tenable
if immodihe<l. It can be modified so as to interpret the rest of these
phenomena; but this means little by itself. The important fact
is this, that the modifications which are demanded appear in some
cases tf) be endf)wed with a beauty and a sim])licity, which indicate
that they are the expressions of an underhing principle of N.iture.
To these the following article will be devoted.

Transatlantic Radio Telephone Transmission '

By I,LOYD ESPENSCHIED, C. N. ANDERSON
i.iul AUSTIN BAILEY

.S\Mii'sis: i 111, juiHT j;ivi> .in.iKx's o( i>l>s(Tv.iii(ins iil Iohk-w.ivc trans-
mission across the Atlantii' over a |HTio<l of aliotit two years. The principiil
conchisions which the data seem to justify are as follows:

1. S<jlar radiation is shown to Ik- the conlrolling factor in flelermininR
the iliiirnal and season.d variations in signal field. Transmission from
east to west and west to east e.\hil>it similar characteristics.

2. Transmissiim in the region l>or<leringon thedlvisioii between the illumi-
nated and the <larkeni'j| hemispheres is characterizetl by increaseil attenu-
ation. This manifests itself in the sunset and sunrise dips, the decrease
in the persistence of high night-time values in sununer anil the decrease
in daylight values during the winter.

^. Definite correlation has been found between abnormal radio trans-
mission and disturluinces in the earth's magnetic fiekl. The effect is to
decrease greatly the night-time field strength and to increase slightly the
daylight values.

4. The limit of the high-night-time value of signal field strength for
transatlantic distance is essentially that given by the Inverse Distance
Law. The normal daylight field strengths obtained in these tests can Iw
ajiroxiniated by a formula of the same form as those earlier proposed but
with somewhat different constants.

5. The major source of long wave static, as rcceivefl in both England and
the I'nited Slates, is indicated to be of tropical origin.

6. In general, the static noise is lower at the higher frequencies. M
night the decrease with increase in frequencv is exiwncntial. In day-time
the decrease with increase in frequency is bnear in the range of 15 to 40
kilcx-ycles. The difference between day antl night static is, therefore,
apparently due largely to daylight attenuation.

7. The effect of the static noise in interfering with signal transmission,
as shown by the diurnal variations in the signal-to-noise ratio, is found
to be generally similar on lx)th sides of the Atlantic.

8. Experiments in both the I'nited States and England with directional
receiving antennas of the wave antenna ty|)e show an average improve-
ment in the signal-to-static ratio of about 5 as compared with loop reception.

IT will Ix^ recalled th.it something over two years ago, experiments
in one-way radio telephone transmission were conducted from
the I'nited States to England.- In respect to the clarity and uni-
formity of the reception obtained in Flurope, the results represented a
distinct advance in the art over the transatlantic tests of 1915.
However, they were carried out during the winter, which is most
favorable to radio transmission, and it was realized that an extensive
favorable to radio transmission, and it was realized that extensive
study of the transmission obtainable during less favorable times
would Ik; ret|uired before the development of a transatlantic radio
telephf)ne service could Ix; undertaken upon a sound engineering basis.

' Presented before the Institute of Radio Engineers, May 6, 1925.

' "Transatlantic Radio Telephony," .Arnold and Espens»hicd, Journal of A. I.E. E.,
.August, 1923. .See also, "Power .Amplifiers in Transatlantic Telephony," Oswald
and Schelleng, presented before the Institute of Radio Engineers, May 7, 1924.

459

460 BELL SYSTEM TECHNICAL JOURNAL

ConsequentK-, an extended program of measurements was initiated
to disclose the transmission conditions obtaining throughout the
twenty-four hours of the day and the various seasons of the year.
The methods used in conducting these measurements and the results
obtained during the first few months of them have already been
described in the paper previously mentioned. The results there
reported upon were limited to one-way transmission from the I'nited
Stales t(i luigland upon the telcplioiie channel. .Since then the

Fig. 1

measurements have been extended to include transmission on several
frequencies in each direction from radio telegraph stations in addition
to the 57 kilocycles employed by the telephone chaiiiiel.

Tlie present paper is, therefore, in tlic iiaiiirc of a rtporl upon the
results thus far obtained in work currenll\- uiiilcr w.»\-. It seems
desirable to make public these results because of tin- large amount
of \aluable data which they have already yielded, and because of the
timely interest which attaches to information bearing u|>on the
fimdamentals of radio transmission. The carr>-ing on of this ex-
tensive measurement program has been made possible through the
co()i)eration of engineers of the following organizations: in the I'nited
Slates— The American Telephone and Telegraph Company and the
Bell Teleiihonc Laboratories, Inc., with the Radio Corporation of
America and its Associated Companies; in England — The Inter-
national Western Electric Compaiu', Inc., and the British Post Office.

TK.ixs.ii i..i\in K.tnio Tr.i.nriiDM-: iu.ixsmissiox 401

MlCASl'RKMKM I'RIXIKAM

The siCfiH- of tlu'st- Ir.msallaiitic i-x|H>riiiu'iits is shown in Via. 1
The British ti-rminal stations will i)0 seen to lii' in tlic vicinily f)f
London and thi- Anurican stations in the northeastern part of the
Inited States. The United States transmiltinj; stations are the
radio tele|)lioiie transmitter at Ro(k\- I'oint. ami tlie iiorin.d radio

Fig. 2 — Exterior of Ki\crlica'l Kadio Reccivinj; Station

telejjraph transmitters at Rocky Point and Marion, Mass. The
measurements of these stations were made at New Soiithgatc and
at Chedzoy, England. The British transmitting stations utilized
in measuring the east to west transmission were the British Post
OlVire telegraph stations at Lcafield and at Xortholt. The receiving
measurements in the I'nited States were initiated at (ireen Harbor,
Mass.. and continued at Belfast, Maine and Rivcrhead, L. I.

The Ri\erhead receiving station, shown in Figs. 2 and 3, is t\|)ical
of the receiving stations involved in the measurement program. The
interior view of Fig. 3 shows the group of recei\ing measurement
apparatus at the right and the loop at the left. The three bays of
apparatus shown are as follows: That at the left is the receiving
set proper which is, in reality, two receiving sets in one, arranged so
that one may be set for measurements on one frequency band and

462

BELL SYSTEM TECHNICAL JOVRKAL

the other set upon another band. The set is provided with variable
filters which accounts for the considerable number of condenser dials.
The second bay from the left contains \oice-frcquency output appar-
atus, cathode ray osrilIoy:ra|)h and frequency meter. The third bay

I'ig. 3 — Interior l<i\<rluMii M.nicm

carries the source of local signal and means for attenuating it, and
the fourth bay contains means for monitoring the transmission from
the nearby Rocky Point radio telephone transmitter.

The measurements are of two quantities: (1), the strength of re-
ceived field, and (2) the strength of received noise caused by static.
The particular frequencies upon which the measurements were taken

TR.I.\S.II I^IMIC K.iniO ll-lJil'llOXi: IK.IWMISSIOX 4<0

(given in tht- chart of Fin. \) lit- in a ranKf in-lwrrn lo and <)() kr.
The arrows indicate the single fre(iiiency tr.insniissions whicii were
emplo>ed for signal field strength measurements, those at the left
indicating the fret|Uencies received in the United Stales from I'.ngiand,
and those at the right, the frecjuencies received in fuigl.ind from the
I'nited States. The l)lack scjuares in the chart denote ttie hands in
which the noise me.isurements were l.ikcii. In i;iiici-,d llic measure-

♦-

L[.(iei.r tssi)

«;a) crais

►•

*"

i<a:«» "OiNi |«,L
17110 ciacs

,

*

Fig. 4 — Frequency di.stribution of measurements. Black squares tleridte t>and in
whiih noise measurement was taken

nients of both fickl strength and noise have been carried out on both
sides of the Atlantic at hourly intervals for one day of each week.
The data presented herewith are assembled from some 40,000 in-
dividual measurements taken during the past two years in tlic fre-
(|uency range noted above. The transmitting antenna current has
l)een obtained for each individual field strength measurement and all
values corrected to a definite reference antenna current for each
station measured. The data have been subject to careful analysis
in order to disclose what physical factors, such as sunlight and the
earth's magnetic field, affect radio transmission.

Measurement Methods
Although it will not be necessary to describe in atu detail tlie t\pc of
apparatus employed in making these measurements, as this informa-
tion has already been published,' a brief review of the methods involved
will facilitate an unflerstanding of the data.

' RaHio Transmission Measurements, Bown, Engiund, and Friis. Proceedings
I R K., April, 1923.

BF.IJ. SYSTEM TliCIIXIC.U. JOVRXAL

In general the method cm|)lo\f(l in nif.isuriiig the signal t'leUl
strength is a compiarison one. A reference radio-frequency \ollage
of known \alue is introduced in the loop antenna and adjusted to
give the same receiver output as that from the distant signal. This
is determined either by aural or visual means. Under such condi-
tions equal voltages are introduced in the antenna from local and
distant sources, and by calculating the effective height of the loop
I he (ield strength of the received signal is determined.

Ill the noise measurements, static noise is admiited ihr(iiii;h a
delinite frequency band appro.ximately 2,700 cycles wide. -A ioral
ra(lio-frec]uency signal of known and adjustable voltage is tlun in-

5iGN»L TiELD rooM Rockv PointLI. 2XS
Received at New Southgate Cng ScptK-15 I92<
°b«D.R»«fe20|Kw| STtoOOhvcikr

Signal Field foom Nom
Received at Belfast Ma

HOL
NE

T Eng GKR
Sept ISM 1924

B*^

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US «80Km|

t

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^

^

- "^ \ ,

/-

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1 1

—

Kig. 5 — Diurnal variation in signal field

lrii<iuci-(l. riic ra(lio-frc(|iii'nc\' sounx' of this siijnal is subji'cti'd to a
continual frec|iienc\- fluctuation so that the detected note has a
warliling sound. This is done in order that the effect of static upon
speech can be more closely simulated than by using a steady tone.
The intensity of the signal is then adjusted to such a value tliat
further decrease results in a rapid extinction. The comparison
signal is then ex[)ressed in terms of an e(iui\alent radio field strength.
Thus the static noise is measured in terms of a definite reference
signal with which it interferes and is expressed in microvolts per
meter.

Ih'.IXS.m.tMIC A'. //>/<) TEl.l-.niOM. IK.IXSMISSIOS M6

SiiiNAi. FiKi.i) Sthi;ni;tu

riu- riirvts tif Fij;. o arc given as examplos of the field strength
measurements nivcring a single day's run. The curves iiavc been
eonslructed by ronnecling with straight lines the datum points of
measurenients taken at hourly intervals. Ii will be evident lli.it

SC'TCMCR 192}

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C.S.t

100

»«.

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ova

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•SO .J5700 CY;i.ts\ / r" i

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u

Fig. 6 — Monthly average of diurnal variation In signal field transmission from

.American stations on various frequencies received at New Southgate, England,

September, 1923

they portray the major fluctuations occurring throughout the tlay, but
that they are not sufficiently continuous to disclose, in detail, the
intermediate rtuctuations to which the transmission is subject.

Diurnal Variation. The left-hand curve is for transmission from
Kngland to America on .52 kilocycles, and the right-hand one for
transmission from .America to Fngland on .")7 kilocycles. These curves
illustrate the fact, which further data substantiate, that both trans-
missions are subject to substantially the same diurnal variation. The

466 /*/!/-/- SYSTEM TECHNICAL JOrRXAL

condition of iIil' iransatlaiuic transmission paili with ros|)fct to liay-
light and darkness is indicated 1)>' the bands beneath the curves.
The black portion indicates the time (hiring which the transathintic
path is entirely in darkness, the shaded portions the time during
which it is only partially in darkness, and the unshaded portions
the time during which da\light pervades the entire path.
The diurnal variation may lie traced through as follows:

1. Relatively constant ('ulil >lrcni;i!) |)rt-\ails during the daylight
period.

2. A decided drop in transmission accompanies the occurrence of
sunset in the transmission path between the two terminals.

3. The advent of night-time con(liti<jns causes a rapid rise in field
strength to high values which are mainlained until dajlight approaches.

4. The encroachment of daylight upon the eastern terminal causes
a rapid drop in signal strength. This drop sometimes extends into a
morning dip similar to, but smaller than, the evening dip. After
this, relatively- steady daylight field strengths again obtain.

Three or four cur\'es similar to l-'ig. o are obtained each month.
B>' taking the a\erage of such curves for the month of September, 1923,
the lower cur\e on Fig. (> is obtained. The upper curves are for
similar averages of measurements made on the lower frequencies.
These curves show clearly that the range of the diurnal fluctuation
is less for the lower frequencies. This is because of the lesser day-
light absorption.

The mechanism by wliiih llu- trans.iilaniir transmission path is
subjected to these daily and seasonal controls on the part of the sun,
would be more evident were we enabled to obser\-e the earth from a
fixed point in space. We should then be able to see the North Atlantic
area plunged alternately into daylight and darkness as the earth
rotates upon its axis, and to visualize the seasonal variation of this
exposure to sunlight as the earth revolves about the sun. Photographs
of a model of the earth showing these conditions have been made, and
are shown in Fig. 7. 'I'lie first cc)ndilion is that for January, in which
the entire path is in da\light. The curve of diurnal variation is
shown in the picture and that part which corresponds to the daylight
condition is indicated b\- the arrow. In the next position the earth
has rotated so that the London terminal is in darkness while the United
States terminal is still in da%light. This corresponds to the evening
dip, the period of poorest transmission. With the further rotation of
the earth into full nighl-time conditions for the entire |)alh, the re-
ceived signal rist's to the high niglu-timi' \alues. These high \alues
contiiuic until llu- p.iih appro.n Ins the d.i\liglil hemisphere as indi-

I K.iXS.tTl..l\TlC K.tniO TEI.EPIIOSE TKASSMISSION Abl

cati'il in the fmirth iiositioii. As ilic |),ilh t-iitiTs into stinli^lii, ilic
sign.il sfrciiKlh drops with a small dip orciirriti^j whon sunrisr iiiur-
\fiK"s iR-twi-fii tin- twi) ttTininals.

Seasonal Vuriation. By assfnil)liiij; the ino[itlil>' a\fra^c- iiir\i's
for all months of ilu- Nrar, thr i-lTi-cl of the seasonal variation on .he-

Fig- " — Signal Field January — Variation with exposure of transmis^sion path to
sunlight

468

HEI.L SYSTEM TECflXIC.IL JOURNAL

(iimiial characteristic becomes e\i(Kiil. Tliis i> shown in I-'ig. 8, the
data lor which actually co\'er two \ears.

Tile outstancling points to be observed in this figure are:

1. The continuance of the high night-lime \aliies throughout the
\ear.

2. The [lersislence of the high nigltt-time \alues for a longer period
in the winter than in the summer months.

Fig. 8 — Monthly averages of fliurnal variation in signal field, Rwky F'oint, L. I.

(2XS) to New Southgatc, Kngland, 57,(M)0 cycles— Ant. Current, 300 Amps—

5480 Km. 1923-1924

3. The da\ light \;dues show a coniparati\el\- small range of \aria-
tion.

■I. The extreme range of \ariation shown between the minimum
of the sunset dip and the maximum of the high night-time values is
of the order of 1 to 100 in held strength. This is e(iui\alent to 1 to
lO.OOO in power ratio.

It will be recalled tiial the cause of the seasonal changes upon the
earth's surface resides in the fact that the earth's axis is inclined .iiul
not perpendicular to the plane of its orbit about the sun. As I he
earth revolves about the sun, the sunlit hemisphere gradually extends
farther and farther northward in the si>ring months and by the summer
solstice reaches well l)eyond the north pole, as indicated in Fig. !).
As the earth continues to revolve about the sun, the sunlit hemisj^here
recedes southward until at the winter .solstice it fails considerably
short of the north pole and extends correspondingly beyond the
south pole. Since the transatlantic path lies fairly high in the north-
ern latitude, it is not surprising that the transmission conditions dis-

ih:i\s.iTi..i.\ric N.inio ir.i.i-riioxr. i h-.ixsMissiox 4<.q

tlost- a (U-ritlfd st'asoii.il iiitliifnce. The etTt'ct i>f lliis seasonal iii-
thifiue ill shiflinjj the diurnal transmissiim rharailerislic is ln-tter
shown in l"\^. 10. This tij^ure consists of the same monthly average
diurnal ciirNes ,is an- .issemhled in Fig. 8, arranged one aliove the
citlur instead of side h\ side.

Kig. 9 — Signal l"ii-lil Jiiiic — .Night conditions showiiii; proximity of transmission
path to sunlit heniisphcrc

In particular, there should be noted:

1. The time at which the sunset dip occurs changes with the change
in time of sunset.

2. Similarly, the time at which liie morning drop in field streiigtli
occurs changes with the time "of sunrise.

3. The period of high night-time values, boinided between the
time of sunset in the I'nited States anil the time of sunrise in ICiiglaiid,
is much longer in the winter than in the summer months.

It is also to be observed that, as a rule, full night-time values of
signal field strength are not attained until some time after sunset at
the western terminal and that they begin to decrease before sunrise
at the eastern terminal. In other words, the daylight effects appear
to extend into the period in which the transmission path along the
earth's surface is unexposed to direct rays of the sun. The effect
of this is that with the advance of the season from winter to summer
the time at which the high night-time value is fully attained occurs
later and later whereas the time at w'hich it begins to fall off occurs
earlier and earlier, until the latter part of April when these two times
coincide. .At this time, then, the transmission path no sooner comes
into the full night-time conditions than it again emerges. As the
season further advances into summer, the day conditions begin to
set in while the night-time field strength is still rising. The proximity
to the daylight hemisphere, which the transatlantic path reaches at
night during this season of the year is illustrated in Fig. 9.

BELL SYSTEM TECIISICAL JOfRSAL

Fig. 10 — Monthly averages of diurnal variation of signal field, Rocl<\ I'oim, I.. I.

(2 X S) to New Southgate, England; 20.8 K.W. radiated power, 57,000 cycles,

1923-1924

iH.i\s.iii..L\nc RADIO ir.i.ri'iioM: i k.ixsmissiox a7\

As the sunlit hcinispluTc ri-cfdos soutlnvard aftir the siimiiu'r solstice
a tinu- is rtMclu'd. about the niiildli- of August, at vvhirh thf full uinlit-
tiiui- valufs arc again ri-alizrd. liiyond this time they are sustained
for increasing iH'riiHJs of lime. It is of interest to note that at tiiese
two limes of the year, ihe last of April and the middle of August,
direct simlighl exists over the darkened hemis(ilure sonie aOO kiU)-
melers above the great circle path.

Kor all of ihe conditions noted above, n.inu-K', sunset, sunrise, .ind
summer approach of the transmission path to the northern boundary
of the night hemisphere, the path lies in a region wherein the radiation

Jtn rtb Uv >er Iby .Juw .July tu^ S«l Oct Nm Ok

F«b >br A(r May Am JiJy <tJ9 Scpl Oct Nov Dk.

Fig. II — Monthly averages of daylight field strength

from the sun grazes the earth's surface at the edge of the sun-lit
hemisphere. The transmission path also approaches this region
during daylight in the winter months, as will be seen by reference
to the first position of Kig. 7 for the month of January. The results
of measurements for the months of November, December and Janu-
ary- for all of the frequencies measured show definite reductions in the
daylight field strengths. This reduction is evident in Fig. 8 for the
.57-kiloc>cle transmission, but shows up more strikingly in the curves
of Fig. 11. The effect of each of these conditions, in which the trans-
mission pa^h approaches the region in which the solar emanation is
tangential to the earth's surface, will be observed to be that of an
increase in the transmission loss. The fact that in one instance this

472 BELL SYSTEM TECIIMCAL JOURXAL

occurs in daylight would seem to suggest for its explanation the pres-
ence of some factor in atldition to sunlight, such as electron emission.

Field Strength Formulae. The two major phases of the diurnal
variation of signal field strength which lend themseK'es to possible
predetermination are the daylight values and the established night-
time \alues. As to the night-time values our data show, within the
limits of experimental error, that the maximum values do not exceed
that defined b>' the inverse distance law. This fact seems to support
the viewpoint * that the high night-time values are merely the result
of a reduction of the absorption experienced during the day. Fig. 11
presents the monthly a\erages of the daylight field strengths for the
various frequencies on which measurements were taken. The chart
at the left is for reception in England and that at the right for recep-
tion in the United States.

The difficulty in predicting b\- transmission formuliK', \alucs to be
expected at any one time will be evident and the best that can be
expected is to approximate the average. The formulae of Sommer-
field, Austin-Cohen and Fuller take the form

„ ,,, 377/// _«o

where the coefficient -^7) — represents the simple Ikrizian radiation

field and the expoiuniial '' X' the attenuation factor. From theo-
retical considerations, Stjmmerfeld (U)OV)) gave a=.0019 and x = }/i.
In the Austin-Cohen formula a is given as .0015 and x = l^. Fuller
gives a = .004.^ and .v = 1.4. The Austin-Cohen formula was tested
out experimentally chiefly with data obtained from the Brant Rock
station (1911) and from the Arlington station by the U.S.S. Salem
in Fel)ruar>' and March, 1913. Fuller derived his .0045 value of a
from 25 selected observations from tests between San I'rancisco and
Honolulu in 1914.

An attempt has been made to determine the constants of a formula
of the above form which would approximate axerages of some 5,000
observed values of field strength over this particular New York to
London |)alh and over the freciuency range of 17 kc. to tiO kc. For
each transmitting station a series of comparatively local measure-
ments were taken to determine the power radiated. By combining
these local measurements with the values obtained on the other side

' Sec also " Kailio Kxtcnsiun of Telephone System to Ships at Sea," Nichols and
Espcnschied, I'roc. I. R. E., June, 1923, pages 226-227.

rK.i.\s.iri..t.\iic R.inio TEi.nriiosii ikassmissios 47.»

(if ilu- Atl.uilir wi- fiiuiid tli.it ,ipi>r<>\iin.itcl\ it .()().") .uul .v=I.'J."i.
rill- tr.insmissinii fnrimil.i tlu-ii biTomcs

,, Mini .^n

or ill terms t)f powi-r radiated

298X10' MM)
E = \/p j-^ e- jrs

wluTC

/{ = Field strength in microvolts per meter
P = Radiated power in kw.
/? = Distance in km.
X = Wave length in km.

The table sh;)\vn on next page summarizes the data relative to
da\light transmission.

C"(iRKi:i.ATi()N Iii:r\vi;i;N Radio Tkansmission and I-.akhi's
Magnetic Kikld

In anaKzing the measurements we were impressctl h> the occa-
sional occurrence of marked deviations from the apparent normal
diurnal characteristic. A series of measurements which includes an
example of this condition is represented in the upper curves of Fig. 12.
The curves of the first four days exhibit the normal diurnal char-
acteristic as did the curves of the preceding measurements. The
next test of February 25-26 exhibits a marked contrast with that
of two days pre\ious. Such abnormality continues in greater or less
degree until partial recovery in the test of April 29-30.

C"omj)arison of these data with that of the earth's magnetic field
for corresponding days shows a rather consistent correlation. This
will Im? evident from inspection of the magnetic data plotted below
in the .siime figure. Both the horizontal and vertical components
of the earth's field are shown. The first decided abnormality- occurs
February 25-2(5. The three succeeding periods shf)w a tendency to
recover followed by a second abnormality on March 25 26 and again
one on .April 22-23. It is of interest to note that within limitations
of the intervals at which measurements were taken, these periods
correspond roughly to the 27-da>' period of the sun. Coincidences
similar to those described above ha\e been found for other periods.
Kxcept for this coincidence of abnormal variations in earth's magnetic
field and radio transmission, exact correlation of the fluctuations
has not been found possible.

474

BELL SYSTEM TECIISICAL JOVRSAL

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TR.I.yS.tTl^iNTlC RADIO TELEPHONE TRANSMISSION 475

riu- luaniutic ilata have iK-rii sii|)pli«(l through (he courtesy of
the Iniled States ("leodetie Siirves . Siinil.ir data taken in lainlaiul
were ohtaiiieil from the Kew ol)servator> and sliow similar results.

The contrast in the diurnal variations of radio transmission liefore
• lid after the time a magnetic storm is known to have started, is

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Fitj. 12 — Correlation of radio transmission and earth's magnetic field — Transmission

from Rocky Point, U. S. A. (57,000 cycles) to London, Eng. — Earth's magnetic

field measured at Cheltenham, Md., I'. S. A.

further brought out in Fig. 13. The lower left-hand curve in this
figure superimposes curves of February 22-23 and February 25-26
of the previous figure, .\dflitional cases where such marked changes
occur are also shown. It will be seen that similar effects exist on the
lower frequency of 17 kc. All of these examples are for days of other
than maximum magnetic disturbance. In general the effect is to
reduce greatly the night-time values and slightly increase the day-
light values. The higher peaks in the daylight field strength of
Fig. 11 are due to the high daylight values which prevailefl at the
time of tiiese disturbances.

476

lUil.L SYSTEM TECHNICAL JOURNAL
NoisK Stkkncth

Next to field strength the most important factor in determining
the communication possibilities of a radio channel is that of the
interfering noise. The extent to which noise is subject to (liuni.il
and seasonal xariations is therefore of first order of importance.

Transmission from Ffacky PpintLI.(WQL) to New Southqate Eno

GMT IE PU 12 AM 12 12 PM 12 AM e 12 PM 12 AM B. K. PM 12

F«b. S2-25 S«pU 23-24 Jan. 27-28 Oct. ft-

25-26 JO-Oct. I F»b. 1-

12 12 PM 12 AM IZ

1924

1 livlurc
riul afte

lagnctic storm had !>cgiin.

I'iR. 1.? — Correlation I>ctwccn radio transmission and variations in earth's
niadndir field

Diiiniul Vdrialion. An ex.imi)le of llie diurnal characteristic of
the noise for both ends of the transatlantic path is given in Fig. 14.
One curve is shown for each of the several frecjuencics measured.
The outstanding points to be observed are:

1. The rise of the static noise about the time of sunset at the receiv-
ing station, the high \alue.s. prevailing at night, and the rather sharp
decrease accompan_\ing sunrise. The curve for 15 kc. shows the ex-
istence of high \alues also in the afternoon. During the summer
months higii afternoon values are usual for all fretiuencies in this

TH.tXS.tlL.IMH K.tlHO I i:i.l:ril<)\l. I K.IXSMISSIOS 477

,

-

JD

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C--

Y

5

SI

yn. *»^

■Nr

>«,

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;^»

\ \

'"^■c Die

.«..^_

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^--^

-.

a

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w^JU-It.JULY

AUS."^

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t. J<N<

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.OCTO-ES

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^

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: M

Fig. 15 — Fre(|ucncy distribution of noise, New Southgatc, EiiKlaiid
Night time Day time 1923-1924

478 BELL SYSTEM TECHNICAL JOURNAL

range. Thiy rxtcnd later into the fall for the lower fretiiiencies, and
hence arc in e\idence on the date mi which these measurements
were taken, October-November.

2. In genera! the noise is greater the lower the frequency.

Noise as a Function of Frequency and of Receiving Location. The
distribution of static noise in the frequency range under consider-
ation is depicted in Fig. 15 for the case of reception at New Southgate,
England. The set of full-line curves is for daylight reception and the
set of dash-line curves for night-time reception. The values obtaining
during the transition period between day and night have been ex-
cluded. For both conditions three curves are shown, one the average
of the summer months, another the average of winter months and the
third, the heavj' line, the average for the entire year. The curves
represent averages for all of the measurements taken during both
1923 and 1924. In considering curves of this type it should be re-
membered that they represent an average of a wide range of condi-
tions and at any one time the distribution of static may differ widely
irom that indicated by the curves. Also it should be realized that
the extreme difference between winter and summer static is much
greater than the difference between the averages.

A similar study of frequency distribution was made at two locations
in the United States, Belfast and Riverhead. The results obtained
at these two locations together with those for New Southgate, England,
are presented in Fig. 16 for a period during w'hich data were obtained
for all three places. The similarity of the three sets of curves shows
that there is an underlying cause common to both sides of the Atlantic
which may account for the ditference between the daytime and night-
time static on the longer waves. It will bee\ident from the curves that
for frequencies around 20 kc. there is not \ery much difference between
the day and night static noise but that at the higher freciuencies
in the range studied, the dajlight values become considerably less
than the night-time values. Actually the divergence betw-een the
night-time and the daytime noise curves up to about 40 kc. is an
exponential one. This suggests that the lowering of the daylight
values may be largely due to the higher absorjition which occurs in
the transmission medium during the day. There is a further inter-
esting point to be noted concerning both figures, namel>-, ihai the
night-time values decrease exponentially with increase in freiiiiency.
Since these night-time values are but little affected by absorption
in the transmitting medium, the ilistribution of the static energy as
received, alsfi roughly represents the distribution of the static power
generated.

rK.IXS.lTLMXTlC R.iniO IT.I.F.rilOXn TR.IXS.UISSIOX 479

riu- nirvi's of Fi^. 1() show also the substantial (litToroiirr in tlu'
noise li'Vfi whirli exists at the three receiving points. As has been
exix-riencx'il in practice, the New Southgate curve indicates that
Kngl.ind is less subject to interference tli.iti ikh llu-.i^icrii I'tiited

i-y

. .

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hig. 16 — Frcquenry ilistrihution of noise, New Southgutc, Eng., Belfast, Maine
Riverhead, L. I. — Night time Day time Aug.-Dec, 1924

States. In the I'nited States the superiority of Belfast over River-
head is also consistent with the better receiving results which in
general have Ijeen experienced in Maine. There should be noted also
the fact that the cur\es for these three locations lie one above the
other in the inverse order of the latitudes. This is in keeping with
other evidence which pf>ints towards the tropical belt as being a
general center of static disturbance on the longer wave lengths.
Further evidence on this point is presented below in connection with
the seasonal variations of noise.

Seasonal Variation. Cur\es showing the diurnal \ariation in
noise level for each month of the year together with the \ariati(>n

480

BELL SYSTEM TECHNICAL JOURXAL

in time of sunset and of sunrise, are shown in I'"ig. 17. Eacli curve is
the average of all the measurements taken during that particular
month in 1023 and 1924. The diurnal variations are generally similar
for the different months in respect to the high night-time values
which are limited to the period between the times of sunset and sun-

ri({. 17 -Monthly avuraRcs of diurnal variation of noise, New .Soiithj;ate, England-
57,000 cycles— 1923-1924

7/v'./.V.V.///„/iV//l" A'.//>/() TF.l.lil'IIOXi: I K.IXS.UISSlOX 481

rise in Kn^land. TIuto is a certain deviation, however, wliirh it is
well to {M>int out. Durinj; the sutnnier months the rise in niRht-time
static starts several hours iK'fore and reaches hi^;h values at about
hUnset in En^iand, whereas in the winter-time, the niKht-timcstatic
Ijcgins to rise at ai)out sunset and reaches high values several houf.v
Liter. .\ similar elTect is ol)ser\ed for the sunrise <-oiiditioii wherein

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«rru

. \

^

1

1

I

101

OArr

WIS

IE«E

■

1

NOI

SE LE

EL

1

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1

/

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\

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n

\

\

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\

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r

I

\

\

■ooi usMioai nooi

Fig. 18— Seasonal variation in dislrihution of {laytimc and night time noise with
respect to sunset and sunrise. New Southgate, England — 1923-1924

the reduction of static sets in during the summer months about the
time of sunrise, reaches low daylight values several hours later, and
in the winter the reduction commences se\eral hours before sumise
and reaches low daylight values at sunrise. In other words, the rise
to high night-time values occurs earlier with respect to sunset in the
summer than in the winter, and conversely the fall from high night-
time static to the lower daylight values occurs later with respect to
sunrise, in the summer than in the winter.

This is more definitely brought out in Fig. 18 which combines
the data for all frequencies measured. The dash-lines associated
with the sunset curves, delineate the beginning and the attainment
of the night-time increases and those associated with the sunrise
curve delineate the Ix-ginning and the attainment of the low daylight
values. This discloses the fact that sunset and sunrise at the receiving

AS2

BELL SYSTEM TECHNICAL JOURNAL

Fig. 19 — Noise at New Soutligatc, Eiiglaiul, in January — Wiriation with exposure
of equatorial belt to sunlight

point docs not roniiilftely control the rise and fall of liie iiigii night-
time static. It has been foniul that the discrepancy can be accounted
for if sunrise and sunset are .taken with respect to a static transmission
path as distinKuished from the receiving point alone, and if the as-
sumption is made that the effect of sunliglit upon the static trans-
mission path is similar to that on usual radio transmission.

TK.IXS.II L.tXriC RADIO IT.I.lil'llOXIi IK.IXSAflSSION AM

Major Rkgional Source of Static Noise

A l)r().ultr conception as to the causes imclerlyinR the (hiiriial and
seasonal variation is obtained by considerini; tlie time of sunset and
sunrise over a considerable area of the earth's surface. Fig. 19 shows
a series of day and night conditions for three representative parts. 3f
tlie diurnal noise characteristic at Kngland for January. It will l)c
seen that the rise to high night values does not l)egin until practically
the time of sunset in ICngl.\nd with over half of .Africa still in daylight.
My the time the high night-time values are reached, as indicated in
the .second phase, darkness has pervaded all of the e(|ualorial belt to
the south of Kngland. Incidentally at this time sunset occurs between
the I'nited States anil Kngland, resulting in very poor signal trans-
mission. The third phase of this series shows the noise luuing just
reached the low daytime value and, although the sun is just rising
in Knglanil, the African equatorial belt is in sunlight, subjecting the
static transmission path to high daylight attenuation.

The sunset conditions which existed for the afternoon and evening
of the day upon which the diurnal measurements of Fig. 14 were
taken are shown in Fig. 20. The hourly positions of the sunset line
,irc shown in relation to the evening rise of st.ilic in London. The
coincidence between the arrival of sunset in l.niiilon and the sUirl
of the high night-time noise on the higher freciuencies is evident.
By the time the high night-time values are reached, about 7 o'clock
G.M.T., the equatorial belt to the south of London is in darkness.
Fig. 21 shows the sunrise conditions in relation to the decrease in
static froin the high night-time values to the lower daylight values.
The decline starts about 5 or 6 o'clock an hour or two before sunrise,
and is not completetl until several hours later, at which time daylight
has extended over practically the entire tropical belt to the south of
England which corresponds in general to equatorial Africa.

Another fact presented in the previous figures which appears to be
significant in shedding light upon the source of static, is that noise
on the lower frecjuencies rises earlier in the afternoon and persists
later into the morning than does the noise on the higher frequencies.
This could be accounted for on the basis that the limits of the area
from which the received longer wave static originates, extend farther
along the eciuatorial zone than they do for the higher frequencies.

The inclination of the shadow line on the earth's surface, which is
indicated in the previous figure for October 28, shifts to a maximum
at the winter solstice, recedes to a vertical position at the equinox
and then inclines in the opjx)site direction. These several positions

484

Hr.l.L SYSTEM TECHXICAI. JOVRNAL

are illuslratcii in Fig. 22. Tlu- sot of tlin-r full liiu's to ihi- right
shows the position which the sunset shaciow line assumes upon the
earth's surface for each of three seasons — winter solstice, equinox,
and summer solstice. Likewise, the dash-line curves show the position
assumed by the sunrise line for the corresponding seasons. The

I-Ik. 2(1 — Kelat ion of sunset shadow wall tn noise at New SoutliKate, Knglaiu
Oct. 28 iO, 1<).'.<

IR.IXS.II I.IXI IC A'.//'/() ll.l.lirilOSr IKAXSMISSIOS 4}<5

|i,irticular tiim- of day for wliirli i-acli of \\w sunsi-t curves is taken, is
that at which tin- static in I.oiulon bi'Kins to increase to lar^e ni^ht
values. In winter, this occurs about sunset, at the eciuinox al)out
one hour earlier, anil in siuniner about two hours earlier, as illustrated
in I'ig. 18. C'orrespondingK-, the time for which each of the sunrise
curves is taken, is that at which ihc iiii;Ii iiiijlit-iinie values have
reached the lower d.i\lii;hi \.iliir-. I'loin lit;. 1^ ii will be e\i<lent

Fig. 21 — Relation of sunrise shuduw wall tonoiseat New Southgate, England-
(Jct. 28-29, 1923

4S6

BELL SYSTEM TECHNICAL JOURNAL

that this orciirs during the winter at aliout sunrise, at the ecjuinox
about an hour later, and during the summer some two hours later.

It will be observed that the two sets of curves, one for sunset and
the other for sunrise, intersect at approximately the same latitude,
the sunset curves southeast and the sunrise curves southwest of

Kig. 21 — I'osition of sunset lines at sunset dip and sunrise lines at sunrise dip in
noise level in England for various seasons

Kngland. If it is assumed that the effect of the shadow wall upon the
transmission of static is similar to that upon signal transmission across
the Atlantic, namely, the high night-lime values commence when
the shadow wall is approximately half-wa\- between the terminals,
the crossing of the lines upon the chart may be taken as having sig-
nificance in roughh' determining the limits of the tropical area from
which the major static originates. The crossing of the sunset lines
indicates that the eastern limit of the area which contributes most
of the static to Kngland is equatorial East Africa. Tlie crossing
of the sunrise lines indicates that the corresponding western limit
is somewhere in the South Atlantic, between Africa and South America.
In other words, from these data the indications are that there is a
more or less distinct center of gravity of static, which extend along the
tropical belt, and that most of the long-wave static which affects
reception in Kngland comes from the equatorial region to the south
of England, namely, ctiuatorial Africa. This is exclusive of the high
afternf)on static prevailing during the summer months.

77<r. /.v.v. ///„/. V//C' N.inio iiu.r.riioxn ikaxsmissiom ax?

Tlu- tlata ohtaiiicil in the rniled Status iiidirate that generally
similar conditions i-xist thrrc as to the relation heivveen sunset and
sunrise path and the major rise and fall of static. This relationship
is shown in l-ij;. 2:5, which allows in llic upper h ilf tiie course of tiie

Kig. 23 — Relation of sunset shadow wall to noise at Belfast, Maine, U. S. — Oct. 30 —
Nov. 1, 1924

night-time belt as it proceeds from Europe to America and the corre-
sponding rise in the static noise. The noise level curves are the
same as those shown in Fig. 14 for reception at Belfast, Maine. The
rise commences about one hour before and continues for one hour
or so after sundown. This is for the fall season of the year. A
similar chart for the sunrise conditions is given in Fig. 24. Although

ASS

BEI.I. SYSTEM rECIIXIC.II. JOl'liX.-IL

hiyli iiiglit-tiniL- \aliies started to lall <ilT soint- five hours before sun-
down in Belfast, the more rapid drop was within some two hours
in advance. While these curves are f(^r hut a single clay, they are
fairly representative of the average of a greater amount of data.
The change in the inclination of the sunset-sunrise curves w'ith the

KiK. 24 -Krialioii of siinrisc- nIi.kIow wall to noise at Belfast, Maim- I' S —Oct .?0-
Nov. 1, 1924

season of the year effects changes for .American rec» piioii soniewiiat
similar to those shown for reception in ICngland, excei)t that for the
summer months (he coincidem-c is less delinite. It may he that this
is Ix-cause of the somewhat lower latitude of llic InitedStates terminal
and (»f the reception of a greater propoiiimi of iho static from the
Xorlli .Amcric.in conlincnl.

/AM.vs.(//../.v//(" R.inn) ir.i.f:rii(K\ii /am.v.v.u/w/o.v •«,'«)

In K^-iuTal, lIuTi'fort', tlu- AiiUTtran ri-snlts arrortl with thosr
cil)t.iiiH'(l in l-jinland in indiratin^ (|uiti' di-fuiitfly that a larjii" pro-
portion of ihf st.itic ri.'ii'i\f<l on ilir lon^i-r \va\r-. i-- of tropical origin.

Si(iN.\i. TO NoisK R.\rii)

It is. of roiirsi", the ratio of the signal to noisi- str(.n^;th which
(icti'rmines the commiiniration merit of a radio transmission channel.

Variation with Frequency. A comparison for representative summer
and winter months is given in Fig. 25 of the signal-to-noisc ratio

rd

—

3

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— '

ITS

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0 «

Fig. 25 — \'ariation of signal to noise ratio with frequency. Corrected to same
antenna input power (68.5 K\V) in Rocky Point antenna — Reception at New South-
gate, England

for the two extreme frequencies measured. Both of these trans-
missions were efTected from the same station, Rocky Point, and sim-
ilar antennae were employed. Comparison is made of the overall
transmission by correcting the values of the two curves to the same
antenna power input, the pow'er of both channels being scaled down
to t)8 kilowatts, the |)ower used in the telephone channel during the
early parts of the e.xperiment. This chart shows clearly the greater
stability in signal to noise ratio obtainable on the lower frequency
channel. While for certain perituls of the day the higher frequency
gives a much better ratio, it is subject to a much more severe sunset

490

BELL SYSTEM TECHNICAL JOURNAL

CUT SI234S87B 90nSI t 3ije7 t JOt S

WON V'O NOON

EST ;9iii}(r9iii3j;

Fi([. 26 — Monthly avcraRvs of (liu'riial variation of sijjnal to noise ratio; Rocky

Point, L. I. (2 X S) reccivi-il at New SoiitliKati-, Knuland; 20.8 KW radiated Power

—57,000 t vcles— 5480 Km— 1')23-24

TK.ixs.tri.iMic R.inio TEi.r.riioxn ir.insihission 491

3 S 7 9 It I 3 3

Fig. 27 — Monthly averages of diurnal variation of signal to noise ratio, Northolt,
Eng. (GKB) received at Belfast, Maine— 20.8 K\V radiated power — 4980 Km—
52,000 cycles— 1924

492 BELL SYSTEM TECH SIC AL JOl'RX.IL

decline than is the lower frequency. During the summer time,
afternoon reception in England is belter on the higher frequency
channel. This is Ijecause of the considerably greater static exper-
ienced at this time on the lower frequency. The higher signal-to-
noise ratio prevailing during the winter month of January as com-
pared with the summer month of July is evident. This is due primar-
ily to higher summer static.

Seasonal Variation in Eni^land and United States. 1-Or the 57-
kilocycle channel there is shown in Fig. 20, for each month of the
year, signal-to-noise ratios of two years' data. These show a distinct
dip corresponding to the sunset dip of the signal field strength. The
night-time values arc generally high in accordance with the high
night-time signal strength but the maximum values are shifted toward
the lime of sunrise. This is due to the fact that the noise rises earlier
in the afternoon and declines earlier in the indiniiig than do the cor-
responding variations in signal slrengiii.

Fig. 27 presents the signal-to-noise ratios for such data as have
thus far been obtained upon transmission from England to the I'nited
States on a frequency of .52 kilocycles. The low values obtained
about sunset are, of course, due to the evening dip in field strength.
In general, the night-time ratios do not reach high values as do those
for England because the early morning signal field strength begins
to fall off while the noise level is still high. Comparisons of the
signal-to-noise ratios obtained at New Southgate and at Belfast
show that the Belfast values are somewhat higher for that part of
the day, corresponding to forenoon in the United States and after-
noon in England. This is because the forenoon static in the United
States is lower than the afternoon static in England.

DlRIiCTIVK RliCKIVI\(, AnthnnaI';

The |)icture whicli has been gi\en of the transmission of static
northward from the tropical lielt suggests that the signal-to-noise
ratio might be materially' improved by the use of directional receiving
systems. This is, of course, what has actually been found to be
the case in commercial transatlantic radio telegraphy wherein the
Radio Corporation has made such effective use of the wave antemia
devised by Be\erage. The expectations are confirmed by measure-
ments which have been made in the |)resent experiments using sucii
wave antennae.

A year and a half ago the British Post Office established a wave
antenna with which to recei\e from the Rocky Point radio telephone

I h'.tw.ii I .i.Mic K.inio n.i.i.i'iiosr. i u.ixsmissiox -vks

iransiniittT. Morr rt'cently a proKrain of consisti-nt (>l)st'rvalii)ns
in iliriTtional n-ci-ption of east-to-wi-st traiisiiiission was also undcr-
taktn in whiili were oniployi'd, wave anti-nnai- hiiilt by the F<a(lio
Corporation of America for radio tt-Ii-graph o[HTatinn upon lower
freqiUMicii-s.

An indication of llu- inipni\cnu'ni which ilu- w.i\c antenna >{i\'es
in signal-to-noise ratio is had 1>\ reference lo l-'ii;. 2S. Thi- set of

\» («S>U I n>c»r>

2KS (S7K^ aacovaa «t

-A.i>ftV^

Fig. 28 — Improvement in sij;nal noise ratio of wave antenna over loop reception

curves to the right is for reception at Chedzcn', England, and those
at the left for reception at Belfast and Riverhead in the linited
States. The improvement is measured in terms of the signal-to-
noise ratio obtained on the wave antenna, divided h\' the signal-to-
noise ratio measured on the loop. For the particular days and fre-
C4uency indicated, the improvement in England will he seen to vary
over a considerable range, averaging about 5. Data for reception
in England is for 1024 while that for the Ignited States is for the
corresponding period of 1925. The Tniled States results will be seen
to be generally similar to those obtained in England. .Although
these experiments are still in an early stage, the results do give a
measure of the order of imprf)vement which can be expected.

Tesl of Words I'nderslood. Perhaps the most convincing measure
of the efficiency of directional recei\ing systems for transatlantic

494 BliU. SVSIhM TECHSICAl. JOLRX.IL

iraiisinission is the improvement effected in the reception of in-
lelligible words. Fig. 29 shows the impro\ement which the wave
antenna in England has made in the ability to receive certain test
words spoken from Rocky Point. For this purpose there was trans-

niittiMl from I^ock\- Point a list of disconnortcd words. .A record

Fig. 29- — Comparison of reception on wave antenna and loop. Per cent of words
understood — Reception of Rocky Point (2 X S) at Chedzoy, England, March, 1924

was made at Chedzoy of the pfrrciilage oi llie words understood for
reception on the loop and on the wave anteima. This constitutes a
con\enient method of rough telephone testing. It will be appre-
ciated, howev-er, that it would be possible to understand a greater
proportion of a conversation than is represented by these results.
The curves show that it was possible to receive, for example, 80%
of the words f(»r but 9 of the 24 hours on the loop, whereas with the
wave antenna recepiion ((Hitinuid fur IS hours.

TH.ixs.ii i.iMic A'. //>/() ii:i.i:rii<>\i-: /a-./.v.vu/.v.s/o.v 495

Al'I'KN'DIX

rr,ins.ill.iMtu- K.iilio IVlcphdiu- MtMsiirriiuiits
19^,?, l<)->4, 1925

Month liy Month Record of Noise and I'ield Strength

wp*«

1 itwp, ■ 1

^■''^i\\fr>.

tfW^Mjy

tfr^

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l_,

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.»sA^,n7v

: 1

. . 1

: II ^11 11

.r.JI

.,-.||...-

11^ 11 1

1 1 1 II

1

iiiiii

mill

Monthly AveraRes of Diurnal Variation of Signal Field Strength

Kotky Point, L. I., U. S. A. (WQL) Measured at New Southgate, England

Corrected to 600 Amperes Antenna Current

5.480 Km. 17,130 Cycles

April, 1923— Feb., 1925

Monthly Averages of Diurnal Variation of Signal Field Strength

Marion, Mass., U. S. A. (WSO) Measured at New Southgate, England

Corrected to 600 .Amperes Antenna Current

5,280 Km. 25,700 Cycles

Aug., 1923— Feb., 1925

496

BELL SYSTEM TECHNICAL JOURNAL

Monthly Averages of Diurnal Variation of Signal Field Strength

Rocky Point, L. 1., U. S. A. (2XS) Measured at New Southgate, England

Corrected to 300 Amperes Antenna Current

5.480 Km. 57,000 Cycles

Jan., 1923— Dec, 1924

.Mdiitlily Averages Diurnal Variation of Signal Field Strength

l.eafield, England (<".RL) Measured at Belfast, Maine

Corrected to 300 Amperes Antenna Current

1924

24,050 Cycles

TR.I.\S.III..I.\IIC RADIO TELEPHONE TRANSMISSION 497

ry||fr!^i||fniHHiTu||iT!i||r||ij|ifT!Ti|pTm

Monthly Averages Oiiirn.il Wirialion of Signal Field Strength

Northolt, England (CKU) Measured at Belfast, Maine

Corrected to 100 Amperes Antenna Current

4,885 Km. 52,000 Cycles

1924

5,360 Km.

Monthly Averages Diurnal V'ariation of Signal Field Strength

Leafield, England (GBL) Measured at Riverhead, L. I.

Corrected to .100 .-Xmperes Antenna Current

1924

24,050 Cycles

498

BEU. sySTEM rr.CIIXlCAL JoriiXAL

Monthly Averages Diurnal Variation of Signal Field Strength

Xortholt, England (GKB) Measured at Riverhead, L. 1.

5,460 Km. 52,000 Cycles

1924

I.

^!

1 1 1 1 i.i

LilU

Uii

Monthly Average of Diurnal Variation of Signal Field Strength

I.eafield, Fngland (CiBL) Measured at dreen Harbor, Mass.

C'orrci-ted to 300 Am|)cres Antenna Current

5,1.50 Km. 24,050 Cycles

July, 1023 -I;in,. ]')24

TK.IXS.ll l..l\l/C A'.//)/() t El.l.l'lli>SI- I R.IXSMISSIOX 4W

Monthly Averanc of Diurnal X'ariation of Signal Field StrenRth

Northolt, EnRland U-KHi Muasured at Green Harbor, Mass.

Corrected to KK) Ani|)crcs Antenna Current

Km. 54,500 Cycles

Aug., 1923— Jan., 1924

Monthly Averages of Diurnal Variation of Noise

New Southgate, England 17,000 Cycles

April, 1923— Feb., 1925

500

PELL SYSTEM TECIISICAI. JOl'RSAL

i\

v'VV

ilh^

Monthly Averages of Diurnal Variation of Noise

New Southgate, England 25,000 Cycles

Aug., 1923— Feb., 1925

Monthly .Averages of Diurnal Variation of Noise

New Southgate, Kngland 37,000 Cycles

Oct., 1923— Feb., 1925

rK.I.\S.ll/..l\llC N.IIUO I F.I. Ill' IK) ST. Ili.lXSMISSIOS 501

Monthly Averagt-s of Diurnal Variation of Noine

New Southgate, Englaml 57,00() Cycles

1923—1924

Monlhiy Average of Diurnal Variation of Noise
Belfast, Maine 15,000 Cycles

1924

502 BELL SYSTf.M TF.CIIXIC.IL JOL'KXAL

«I^Y WlMW MiOl «P».L ■»« JU.! JULY .^«^ST ^ ^S^'-'W'f' ^ pWf ° ^ J'^^T? , 1^''^'*''° [

MdiithK- A\crage of Diurnal X'ariation of Noise
Bi-lfast. Main.- 24,(UII) Cvrli-s

1924

iiifflMimntiii

MoiiiIiIn Avir.iKf of Diiirn.il Wiriation of Noise
Belfast, Maine 36.000 Cycles

1924

TK.ixs.ii I..IMIC A'.//)/() ii:i.i:i'ii(>.\i: i r.ixsmissiox .w

-{ITmi I fW\ 1 1 'T!"; ! 1 1 '^^ 1 1 ! !Th 1 1 !?f ' j 1 1 tlTi ! 1 1 rf^^'' I p'''^| [^'^ • I jT'H'f I fl^i t'°

Mimllilv .\vir.i>;r of Diurnal X'ariation of Noise
Belfast, Maim- 52,000 Cycles

1924

secruoen ocnxtR Novc««efl acnen

Monlhlv Average of Diurnal Variation of Noise
Riverhead, L. I. 15,000 Cycles

1924

504

BELL SYSTEM TECtlMCAL JOURX.IL

ocTOBcn wvtiacB «cn«CT

Moiithh A\tr.ini- I if Diurnal \ari.ilioii of Ncisc
Kivtrhea<l, I.. I. SO.OOO Cyclts

V)24

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MdiilliK Avfnuji' "f Diiini.il Variation of N'oist-
kivcrlu-a.l, I.. I. 24,000 Cycles

1924

rA".).Vs

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c.i/'/o 1 iii.i:rii(>.\r.

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'ii

Monthly Average of Diurnal X'arialion of Xoisc
Rivcrht-ad, I.. I. 52,000 Cycles

Jtiv tuwjT scPTtwetR ocTceen wntiwr cxuftcm

jvi«f

tl

n ;

; r ;i ii

Il 1 1 : ; : . 1 1 !

\

i

Monthly Average of Diurnal Variation of Noise

Green Harbor, Mass. 15,000 Cycles

Oct., 1923— Jan., 1924

506

BELL SYSTEM TECHNICAL JOURNAL

m

rciAiurr

wAw:-

•l^-i

UIIj'IM

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tl ri:;| ' !•:!;

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Montlilv Average of Diurnal Variation of Noise

Green I larhor, Mass. 24,000 Cycles

Sept., 1923— Jan., 1924

TTtTT

I

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M

inlt
I'j!

IIJH

Monthly Average of Diurnal Variation of Noise
Crt-vn Harbor, Mass. 34,000 Cycles

1923

//^./.v.v.,/,..,.v,,c u.inio n-u<ruox,: /a-./vvu/vv/o.v 5..7

Sept., 1923— Jan., 1924 ^^■'^"" ^^"^^^

Abstracts of Bell System Technical Papers
Not Appearing in this Journal

Radioactivity.' A. F. Kovarik and L. W. McKeehan. This
review of progress in radioactivity forms one of a series of mono-
graphs prepared by committees of the National Research Council.
It outlines the experimental and theoretical advances in the subject
since 191(5, the date of the last compendium. The section headings
are: I. Introduction, II. Radioactive Transformations, III. Alpha-
Rays, IV. Beta-Rays, V. Gamma-Rays, \'I. Nuclear Structure and
Radioactive Processes, \TI. Radioactivity in Geology and Cos-
UKjlogy, VIII. The Effects of Radioactive Radiations upon Matter.
The references to periodical literature are particularly detailed.

Echo Suppressors for Long Distance Telephone Circuits.- A. B.
Clark and R. C. M.-\thes. This paper gives a brief description of a
device which has been developed by the Bell System for suppressing
"echo" effects which may be encountered under certain conditions
in telephone circuits which are electrically very long. The device
has been given the name "echo suppressor" and consists of relays in
combination with vacuum tubes which are operated by the voice
currents so as to block the echoes without disturbing the main trans-
mission.

A number of echo suppressors have been operated on commercial
telephone circuits for a considerable period, so that their practicability
has been demonstrated.

The Telephone Transmission Unit} Dr. F. B. Jewett. The
adoption by the Bell System of the TU as a telephone transmission
unit aroused considerable active discussion in foreign circles, namely,
by Colonel Purves, Engineering Chief of the British Post Office
Department, and Dr. Breisig of the German Telephone Administra-
tion. In this short paper, Dr. Jewett explains certain words and
expressions which, when accurately defined, he believes will eliminate
misinterpretations such as seem to ha\e Kd to the (■oiitro\ersies over
the Bell System TU.

Dr. Jewett also points out that the numerical size for a transmission
unit is controlled by two factors, first, the magnitude should be such
that computation is convenient, and second, the magnitude should
be such as to permit telephone engineers and operating people to most

' Bulletin National Research Council, Vol. 10, p.irl 1, March, 192.S, 203 pages.
' Journal A. 1. K. E., Vol. 44. page 618, 1925.
• London I-;icrlri<i.in, \'nl. 94, page 562, 1925

508

.mSTR.-tCTS OF BULL SiSTLM ll.CIIMC.IL r.ll'LKS 511

sample itself is l>.il.iiu'e(l l)>' passing a measured current tliroii^;li a
third roil. The apjilied field and the induced ni.igneti/atiun are then
proportional to the electric currents passeil through the magnetizing
coil and the balancing coil, respectively. A hysteres s loop is shown,
ohiained from an iron wire weighing '.i mg.

An Ex f>Ui nation of Peculiar Reflections Obsenrd on X-Ruy Powder
Photoi^raphs* Richard M. Bozorth. There has been pre\iously
reportcti (J. O. S. A. and R. S. I. 0,989-97; 1922) the existence of
"anotnalous" retleclions of X-rays, observed when analyzing sub-
stances by the melh(xi of Dcbye-Scherrer and Hull. These reflec-
tions are now explained in accordance with the well-known laws
governing X-ray rellections. It is shown that the molybdenum X-ray
spectrum as ordinariK- used, although it is filtered by zirconium
screens, contains in addition to the characteristic Ka radiation a
considerable amount of general radiation. Although usually not
effective, this general radiation becomes important when the sample
iR-ing analyzed is composed of crystal grains of certain sizes. The
etTect under di.scussion is caused by reflection of this general radiation
trom the principal atom planes of these crystals. Several experiments,
and a geometrical analysis of the positions and orientations of the
difTraction effects, confirm this conclusion.
•J. O. S. A. and R. S. I. 9, 123-7 (August, 1924).

Contributors to this Issue

Fr.\NK ("ili.l., Huropean Chicl' lliiginccr dI ihc liiltrnalional Wcstcrii
Electric Company. Mr. Clin has had long experience as a tek-plionc
engineer, first, with the United Telephone Compan\' in London,
then with the National Telephone Company and later as a consulting
engineer. At the outbreak of the war, he was called upon to untler-
takc important work in the Ministr\' of Munition for which he was
later awarded the Order of the British Empire. As European Chief
Engineer of the International Western Electric Compan\-, he is taking
a leading part in the discussion and study of conditions necessary'
for the establishment of an adecjuate l(Mig distance telephone ser\ice
through Europe.

OLiviiK E. Bii Ki.iiV, B..Sc., C.rinneil Colkgc i!H)9: Ph.D., Cornell
University, 1914; Engineering Department, \\\>iem Electric Com-
pany, 1914-1917; U. S. Army Signal Corps. 1!I17 lUlS; Engineering
Department, Western Electric Company (Bell Telephone Labora-
tories), 1918 — •. During the war Major Buckley had charge of the
research section of the Dixision of Research and InspiTtion of the
Signal Corps, .■\. \:. 1'. His early work in the Laboratories was
concerned principally with the iiroduction and measurement of high
vacua and with the development of vacuimi lubes. More recently
he has been connected with the development and aiii)Iications of
magnetic materials and particularly with the de\elopnient of the
perniallo>-loaded likgraph ial)k\

H.\RVi:v FiJiTtiiiiR, B.S., Brigham Young, 1907; Ph.D., Chicago,
1911; instructor of physics, Brigham Young, 1907-08; Chicago,
1909-10; Professor, Brigham Young, 1911-1(1; Engineering Depart-
ment, Western Electric Company, 1916-24; Bell Tele|)hone Labora-
tories, Inc., 1925 — . During recent years, L^r. Fletcher has conducted
extensive in\estigations in the fields of speech and audition.

CiiARi.Ks W. (ARrKK, Jr., A.B., Harx.mi, l'.»'_>(); B..Sc.. Oxford,
1923; .Xmeric.in Telei)h()ne ,ind Telegrajih C(ini|)any, 1 )e|i,irlm(nt
of De\elopment and Research, 1923 — .

.•Xrtihr .S. ClRTis, I'h.H.. 1913; E.E., 1919; .Slul'luld .Sciintilic
.Srhof)l; Instructor in llkrtrical ICngineering, \'ale L'ni\ ersii\-, 1913 17;
Engineering Department, Western Electric Companx . 1917 24;
Bell Telephone Laboratories, Inc., 192.^ — . Mr. Curtis' work has
been comiecifd with the de\eloptnent of lek phone iiistriunents.

512

coMRiinroKs lo mis issue 5ij

Kari. K. I>.\rro\v. S.B., liiiviTsily of Chicino, lHU; liiivcrsity
of P.iris. I'.Ul 12; Iniversity of Mirliii, 1012: I'll. I)., in physics ami
m>itlu"ni>itit-s. I'liiviTsity of I'liir.i^jo. 1!>I7; luiniiuvrini; Di'partnuMit
WVsliTii KIiTlric Company, 1!U7 21; Rill l\liplioiK- Laboratories,
liif.. li)2.>— ^. Mr. Harrow has Ihimi i-n^.i^id lar^;i'ly in prrparinj;
siuilies and analyses of pulilislu-d ri'siMrrh in \arioiis fu-lds of physilrs.

l.i.oVK K-ri:\s( iiiicn. Prali Insiitnti-. I'.KM): riiiii<l Wireless Tele-
i;rapli Conipanv" as radio oper.itor, summers, 1!)()7 08; Teiefiinkeii
W'irekss Telegraph C'ompan\- of America, assistant engineer, 1!H)0 10;
American Telephone and Telejjraiih Company, Hnjiineering Depart-
ment and nep.irtment of I)e\elopment ,iiul Research, 1910 — . Took
p.irt in long ilistance radio telephone experiments from Washington
to Haw.iii and Paris, 191.t; since then his work has been connected
with the de\eli)()menl of raflio and carrier systems.

AisTiN B.\11,i;y, A.B., University of Kansas. 101.5; Ph.D., Cornell
University. 1920; assistant anil instructor in physics, Cornell, 191.5-18;
Signal Corps, U. S. A., 1918 19; fellow in physics. Cornell,
1919-20; Corning Glass Works, 1920 21: assi. prof, of pliysics,
Uni\ersit\- of Kans;»s. 1921 22; Dept. of De\elopment and Research.
1922 Dr. Baile\'s work while with the .American Telei)iione and

Telegrapii Company has been largely along tiie line of meilidds for
making radio transmission measurements.

C. \. .\m)I-kson. Ph.B.. M..S.. Iniversiiy of Wisconsin, 1919:
Technical Asst. I'. S. Xaval forces in l-Vance. 1917 19; instructor
Engineering Physics. University of Wisconsin, 1919-20; General
I'.lectric Co.. 1920 21; F"ellow to Norwa\', -American-Scandinavian
I'oundation. 1921-22; .American Telephone and Telegraph Co., Dept.
of De\elopment and Research, 1922 — . Mr. Amlerson's work has
been chieHv on radio transmission.

.tusTN.icis ()/• iiiii.i. sysriiM ri-ciixicii. i:irr.i<s ?m

ri-.iilily compri'lu-iul tlu' ratios corrcsiioiuliiij; to ,m\- i^ivfii ihiiiiIxt of
imils. Sinri' it is di-siral)!*.- that every imil he hasid on a tiorinia!
system of notation, unless there is some \er\' important reason why
it should not, the 'IT hasiil on the decimal s\stem was chosen. Satis-
factory experience during the past year and a half is pointed to as ■
showing the wisdom of having chosen the Tl'.

.1 Siispfiisionfor SiipportiHi^ Delicate Instruments.^ A. I.. )( iiin^ki n.
Bell Telephone Laboratories, Incorporated, New N'nrk. A (Kscrip-
tion, with diagraiu, is given of a modified Julius suspension designed
especially to eliminate disturbances due to \ertical xibrations from
the building structure. The frame holding the instrument is sup[)orted
!)>• a system of tape-wound coil springs, which, because of the tightly
wound friction tape, damp out mechanical \il)rations. The frame
with its balancing weights, is heav>- (about 120 pounds), and so
proportionetl in mass that a twisting or tilting impulse, necessary- at
times in adjusting the instrument, disturbs its mo\ing system onh' in
a secondary degree. This is a second feature of this suspension.
Surprisingly efFecti\e kinetic insulation is achieved. Quaclrant
electrometers and a moving magnet gal\"anometer have remained
umlisturbed even when heavy trucks were passing on the street seven
fl(K>rs below. This type of suspension, developed some years ago
through the efforts of Mr. H. C. Harrison and Mr. J. P. Ma.xfield,
has been adapted for use throughout the Bel! TeleiilioTie Laboratories
in a variety of ways.

Po'icer Amplifiers in Transatlantic Radio Telephony.'' A. A. Osw.m.d
and J. C. SntELLKNC. The paper describes the dc\eIopment of a
l.")0-kilowatt (output) radio frequenc\' amplifier installation built for
transatlantic telephone tests. The characteristics of the single-
sideband eliminated-carrier method of transmission are discussed
with particular reference to its bearing upon the design of the power
apparatus. A classification of amplifiers is proposed in which there
are three types distinguished from each other by the particular por-
tion of the tube characteristic used. The water-cooled tubes em-
ployed in these tests are briefly described, special consideration being
given to their use in a large installation. The system is then shown
in outline by means of a block diagram, the elements of which are sub-
sequently discussed in greater detail. The theory, electrical design.
and mechanical construction of the last two stages of the amplifier
are outlined, including the output and antenna circuits. Means em-
ployed to prevent spurious oscillations are described. The method

•Journal Opt. Soc. of .^m.. Vol. X, No. 5, pp. 609-611, May, 102$.
* Proc. of I. R. E.. \ol. 1.5. page 313, June, 1925.

510 BELL SYSTEM TECHNICAL JOURNAL

used in increasing the transmission band width to a value much
greater than that of the antenna is explained. The power require-
ments of a single sideband installation are outlined and a description
of the six-phase rectifier, used as a source of high potential direct
current is given, together with a brief theoretical treatment of its
operation. Circuit diagrams, photographs, and a number of char-
acteristic curves are discussed.

Production of Single Sideband for Transatlantic Radio Telephony.^
R. A. Heising. This paper describes in detail the equipment and
circuit used in the production of the single sideband for transatlantic
radio telephony in the experiments at Rocky Point. The set con-
sists of two oscillators, two sets of modulators, two filters, and a
three-stage amplifier. The oscillators and modulators operate at
power levels similar to those in high-frequency communication on
land wires. The three-stage amplifier amplifies the sideband pro-
duced by these mo<lulators to about a 500-watt level for delivery to
the water-cooled tube amplifiers.

The first oscillator operates at about 33, TOO cycles. Tin- iiioclul.aor
is balanced to eliminate the carrier; and the first filter selects the
lower sideband. In these transatlantic experiments the second oscil-
lator operated at 89,200 c\-cles, but might operate an>'where between
74,000 and 102,000 c\cles. The second modulator, which is also
balanced, is supplied with a carrier by the second oscillator and with
modulating currents by the first modulator and first filter. Tlu'
second filter is built to transmit between 41,000 and 71,000 cycles, so
that by varying the second oscillator, the resulting sideband, which
is the lower sideband produced in the second modulating process,
may be placed anywhere between these two figures. Transmission
curves for the filters are given as well as some aniplitude-frcciuency
performance curves of the set.

A Null-Reading Astatic Magnetometer of Novel Design.' Rich.\rd
M. BozoRTH. This instrument is designed for measuring the mag-
netic properties of very small amounts of material in the form of
fine wires, thin tapes, or as thin deposits (electrolytic, evaporateil,
sputtered) supported on non-magnetic forms. The specimen, 4 cm.
long, is mounted parallel to the line joining the two needles, so that
its poles produce the maximum torque on the suspended needle sys-
tem, the position of which is read by mirror and scale. The effect
of the magnetizing cf)il on the needles is annulled once for all b\' the
suitably placing of an ,iu\ili,ir\ coil, and the magnetic efTecl of the

• Proc. of I. R. E.. Vol. 13. page 201, 1925.
' J. O. S. .\. and R. S. 1. 10, 591-8 (May, 1925).

The Bell System Technical Journal

October. 1925

General Engineering Problems of the Bell System

By H. p. CHARLESWORTH

Note: This paprr, rr.ul U-lori' tlii' BiOl S\stcm Kdtiratiiinal C'oiifiTiMnc,
C'hicaKo, Jiini- 22-27, l'J25, disiiissi-s the iharailer and scope of the im-
portant problems involved in earing for the growth and operation of the
Hell System. The plant extensions necessary to meet service re(|iiire-
nients and the neiessity of advanced planning are first taken up. The uses
of the "Commercial ,Surve\-." the " Kiindanienlal i'lan" and engineering
cost studies arc analyzed to illustrate how an engineer attacks the problem
of furnishing Siitisfactory telephone ser\ ice to the public. .A discussion of
the New N'ork-Chicago loll cable and the telephone problem in .New N'ork
("ity, as illustrative of specific engineering problems, concludes the paper.

THK problem of giving telephone senice is quite different from
ttiat of most business enterprises. The merchant, for example,
may take more Imsiness in his store without necessarily always in-
creasing his facilities. The minute we take another subscriber, how-
ever, we afld to our plant and plant investment. Similarly, in con-
nection with the manufacturing industry, the manufacturer, for
instance, is in a position to e.xercise very direct control o\-er his activ-
ities. In the telephone industry, howe\"er, our obligation is to take
the service as requested and be prepared to deliver it when and as it is
re(]uired. Furthermore, the activities of the telephone business are
of such a nature as to make it essential, regardless of the remoteness
of the territory- or of the physical and climatic conditions involved,
that a way be found, as far as practicable, to construct and maintain
the pl.int and safeguard the service to the public.

To meet these e.xacting requirements calls for the greatest ingenuity
and foresight in the design of the tele[)hone plant and involves careful
study of various plans for plant extension and rearrangement with a
view to the selection of the most economical and desirable plan.
Having determined the fundamentals of tiesign, there must, of course
be devi.sed ways ami means of safely constructing and efficiently
maintaining the plant. Furthermore, as the plant is necessarih
scatterefl over a ver\' large territory ami as the different parts must
work together satisfactorily and with the most economical results, a
high degree of standardization is rec|uired, still leaving, however,
freedom to adapt the plant to different local conditions. W'c find
evidence on every hand of the value of this standardization, not only

515

516 BEI.L SYSTEM TECHNICAL JOURNAL

during normal coiiditions, but also during emergencies, when it has
been possible to tiuickly assemble equipment or materials from any
part of the sNstem and promptly restore or expand the service as
required.

Important engineering problems of great variety, therefore, present
themselves on every hand calling for consideration by the engineers
in the General Engineering Departments, as well as the Traffic, Plant
and Commercial engineers associated with the operating divisions
of tlic companies.

I'l .\NT Extensions to Meet Service Requirements

A very large part of the engineering work of the Bell System is
concerned with the design of plant extensions to meet expected future
service requirements with the maximum economy consistent with
maintaining the service standards of the s>stem. I shall not discuss
the magnitude of the various activities and requirements of the
system, but will recall to your mind a few of the outstanding items
to better illustrate the magnitude of this part of the engineering work.

Telephone stations are being connected at the rate of over two and
one-quarter million annuall>-.

The resulting net additions or gain in stations i)er year is approxi-
mateh' 800.000.

To meet this station gain and to replarc (■(iiiipnient remoxed from
plant, switchboards are being adtied at the rate of approximately
l,2(J0,000 station capacity annually.

The Bell System installs in one year approximateK 30 billion feet
of insulated conductor in lead covered cable ranging in unit sizes from
1 pair to 1,212 pairs. Of this amount, more than 27 billion conductor
feet constitute the net annual increase in conductor mileage.

The above plant additions, together with other important items,
such as poles, wire, etc., involve a net increase in the telephone plant
of nearly three hundred million dollars annually.

It is of interest to note, in this connection, that the annual additions
to the telephone ]ilant to(la\' are e(iui\alent to the entire plant in
service in ilu' Bill System as ol aiiout 20 to 2.") \ears ago.

Necessiiv ii>k .\i)\ANn-; I'i.anninc

Obviously with a program of this magnitude and of such diversity'
in the character of its related units, careful advance planning is neces-
sary to insure economical and satisfactory performance.

IIXGINEERIXG I'ROHI.liMS Ol- THE PEI.I. SYSTEM 317

In iln' earliest clays of the telcphiine serxice, the problem of l.iyiiisj
out a telephone plant was a simple one. A \er\' small switchhoard,
simple in rharaeter ami casih' moxetl, if necessary, was plaritl in
some convenient location, usualK' in rented ((iiarters, and from that
switchboard wires were run one by one as nee<le<l, to the premises^ af
those desiring sH.'rvicc, either on poles or over house-tops. I'nder such
simple and ruilimentar\' conditions, no serious question of the future
nei-iled to be answered. Tfxlay, how^ different is the telephone situa-
tion in many large cities, such as Chicago, or throughout the system.
L.irjje and specially designetl buildings must be constructed for the
accommodation of the necessary interconnecting or .switching mecha-
nisms; expensive switchboards must be placed in these buildings;
conduits must be extendetl from each f>f these buildings along appro-
pri.ite routes to reach the thousands of telephones which receive ser\'ice
fro 11 these switchboards; other conduits must be placed between these
switchboards and the other buildings and switchboards throughout
the city so as to provide the means of intercommunication between
the subscribers connected with the switchboards located in different
In.ildings; still other conduits and cables must be placetl between these
switchboards and the central switchboard or toll board from which
radiate cables and conduits and lines extending to the suburban area,
to adjacent cities, to all the other principal cities in the United States,
and to Canada.

Each of the buildings must be placed in some definite location and
it is necessary to plan this well in ad\ance and to direct the growth
of the plant toward that location, even though the building may not
be built for some years hence. Otherwise, very serious and costly
rearrangements of plant would be necessary at the time the office is
opened. Furthermore, each building must be planned for some defi-
nite ultimate size, although, of course, the whole building need not be
built at one time. Ducts cannot be placed under the streets one by
one as needed. Public sentiment would not, of course, tolerate the
opening of imp>ortant street routes several times, or even once, each
year for the purpose of placing an additional duct. Neither would it
he economical, if practicable, to construct conduits in this piecemeal
way. The manholes in these conduits must be planned with reference
to the number of ducts extending into them, not only the ducts initially
placed, but if side runs are to be made from these manholes or if other
ducts are to be placed later, this fact must be foreseen and provided
for, or extensive and expensive alterations are ine\itable at a later date.

I might go on and multiply the conditions which must be met in
constructing telephone pl.int in a conntr\' such as onrs in which not

518 BELL SYSTEM TECIIKICAL JOURNAL

only the population is growing and moving, but where the demand fcjr
telephone service is growing more rapidly than the population. We
are in effect planning a growing organism and we must recognize that
we are dealing with ultimate tendencies largely beyond control, the
effects of which are not capable of exact \aluatioii. However, enough
has been said, I believe, to indicate clearK U) ytm that the telephone
compaiu' on ever>- item of its buildings, conduits and cable construc-
tion must constantly answer for itself \ital cjuestions as to the future
reciuirements of the system.

This was early recognized, and one of the most important unginecr-
ing problems of the Bell System has been the formulation of estimates
of expected future telephone liusiness both as to quantity and expected
location, and the development, from these estimates, of basic plans
of procedure, which plans must, of course, be flexible, capable of
nuKlification from time to time, and such modifications must be madr
as changing conditions show them to be advisable.

Our first step in (lett-rniiuiug the estimated future lileplinne recjuiri-
ments is to prepare a so-called "Commercial Siir\e\" of liie cil\-,
covering the requirements fifteen or twenty years ahead. These
studies include a critical analysis of the existing market for telephone
service, pertinent facts as to the present sale of telephone service, of
classes of service and users and forecasts of the market for telephone
service at the future date or dates. Consideration is also gi\en to the
growth and distribution of population, expected changes in gener;il
wage levels, etc., and assumptions of the amount of business that must
be sold in each area on the future dates selected under assumed rate
conditions.

Having thus determined from the "Commercial ,Sur\ey" the re-
(|uirements for teleplione ser\ice for \ari(}us parts ol the city at the
future dale assumed, it is ni'xt essential to de\elop a comi)reliensi\ i'
plan to serve as a basi> for the la\out of the i)lant to meet these require-
ments. Accord ingl\', a so-called "Fundamental Plan" is made for
the community cowring these conditions as estimated fifteen or twent\'
\ears hence. The importance of such a iilan is ob\ious, but a brief
reference to ><inic dl its fcituro will. 1 liclic\c. be of interi'st.

In laying out a plan for a city, the engineer might, as an extreme
case, center all the subscribers' lines at one building. Obxioush , we
would ha\e a maximum efficiency in operation in .some respects, in
that we had grouiied all of our switchboards together, but our outside
|)Iant costs would be at a maximum and other disadvantages would
be experienced. As the other extreme, the engineer might place many

E\ci\r.F.RiM: I'ROHi.r.MS or iiir. ui.i.i. svsn.si 5I'j

siu.ill Imildiiij-s .iround llu- iil\ , lliiis pl.iriiin the outside (ilaiil costs at
.1 iniiiiimini, Ixit iiuTi'.isin^; tlit.' ditVunilt\' and expense of operating so
many centers. ()l)\iousIy, therefore, there is some arrangement be-
tween the two extremes I ha\e cited wliicli would [)rovide the most
economic.d and satisfactory hiyout of tlie plant. .Several test caj.fs,
which in the judgment of the engineer seem promising, are, therefore,
studied and the most economical and satisfactory |>Ian determined
upon. In completed form, these "Fundamental Plans" furnish us the
following essential information ujion which lo proceid with the more
detailed studies c<nering plant extensions.

.1. The luunher of centred othce districts which will !)(.■ re(|uitc(l lo
provide the telephone service most eioiujmicalh' and tlie hound. ii ics
of these central otVice districts.

1). The number of subscribers" lines to l)e ser\ed b\' i.icli ceiiiral
otTice district.

c. The proper hjcation for the central office in e.ich district lo enable
the service to be gi\-en most economically with regard to cost of cable
plant, land, buildings and other factors.

d. The proper streets and alleys in which to build underground
conduit in order to result in a comprehensive, consistent and econom-
ical distributing system reaching every city block to be ser\'cd by
underground cable.

e. The most economical number of ducts to provide in each con"
duit run as it is built.

Our experience has shown that these fundamental plans reduce
guesswork to a minimum by utilizing the experience of years in stufK-
ing questions of telephone growth in order to make careful forecasts
on the best possible engineering basis. These fundamental plans,
together with related studies, thus provide a general program of plant
extension to be followed throughout the period for each of our cities
and somewhat similar plans are, of course, undertaken for (kti-rniiiiing
the future requirements of our intercity or toll facilities.

ft is evident that both the ultimate arrangement and the program
whereby it is to be obtained must have the utmost flexibilit\' in order
to meet unforeseen requirements, must work in satisfactoriK' with the
existing plant, which represents an investment of over 62. oOl), 1)1)0. ()(),)
must meet immediate service reciuirements, and also permit full
advantage being taken of new developments in the telephone art.

The specific or detailed plan for each project of plant extension,
whether within the cities as discussed or between cities in the toll line

520 BELL SYSTEM TECHS'ICAL JOURNAL

plant must, of course, be started early enough so that adequate time
is allowed for completion of the construction work before the new
facilities are required. The complete interval between starting work
on such a project and getting it into service can seldom be less than
one year and in the case of building and central office e(|uipnicnts
must, of course, be longer.

Enginkerinc; Cost Studies

Owing to the complexil\- of the problem of suitable advance plan-
ning for the growth in the telephone plant as already discussed, it is
evident that in the study of plans for specific projects, selection must
gencralh' be made between a choice of arrangements, more than one
of which might satisfactorily meet the requirements of the service.
It is usually necessar\', therefore, that two or more practical plans or
programs for construction must be compared so that the most ad-
vantageous plan may be selected. An important factor in the selec-
tion of all of these ca-ses is a study of the relative economies of the
different plans; that is to say, a comparative cost study and as these
studies form such an important part of our engineering work, I be-
lieve it will be of interest to de\ote a few moments to a description of
the important considerations generally in\oIvcd.

These engineering cost studies require analysis and consideration
of the cost and resulting annual charges for different amounts and
types of plant included luider each plan. The annual charges com-
prise items of expense incident to ownership of plant and those that
are incurred each year after its installation to keep it in operation and
in serviceable condition. As a general thing, in these cost compari-
sons, another interesting factor is aKso present; namely, most of the
plans which are compared call for expenditures to be made at difTerent
periods. For example, one plan might call for erecting a new building
at a new location immediately; whereas under the other plan being
considered, the necessary additional space required could be secured
liy adding to an existing building and deferring the complete new
project for possibly five or ten years. The relative economy of the
plans, therefore, cannot be determined directly by a detailed com-
parison of the expenditures involved or resulting annual charges, but
it is necessary in order to give a fair comparison to express the relati\e
costs of the different plans in terms of present worths, or equivalent
annuities which give figures for the total expense in which accurate
allowance is made for the variation of expenditures with respect to
time.

ENClM-fiRIXG I'ROIU.F.MS ()/• 77//-; /(/:/./. SYSITM S2\

These engineering cost comparisons may be considered as composed
of four parts or operations; namely, the promises or known factors and
assumptions; the formulation or set-up of the problem ; the solution
or mathematical calculations and tinalK- the interpretation of the
results. The determination of the premises and formulation ai a
i;iven problem is, of course, a matter specific to that problem, and here
the engineer nmst exercise sound judgment, for unless the assumptions
upon which the work is based are reliable the study itself is of little
value. The mathematical calculations arc, of course, a definite thing.
However, the interpretation of the results must always be a matter
of engineering judgment anil full weight must be given to those factors
which by their nature cannot be evaluated in the cost comparison.

A cost study is a fundamentally important tool in assisting the
engineer to reach a decision as to the most desirable plan or program,
but as indicated it cannot be used to replace the exercise of judgment
on his part. The solution of an engineering problem is, in general,
not a matter that can be demonstrated mathematically as can, for
example, the proposition, that the square of the hypotenuse of a right
triangle is equal to the sum of the square of the two sides. An en-
gineering study rather requires in addition to all of the definite facts
that can be brought to bear on the question the exercise of sound
judgment on the part of the engineer in weighing the results of the
cost study with all related business or other factors bearing on the
problem.

Some factors involved in these engineering studies are often of a
character which do not permit of expression as a direct charge against
a given plan, but must be considered on a broader basis such as the
difference in quality or dependability of the service, etc. Also it is
important to keep in mind, for example, that, other things being
equal, a plan requiring large investments has disadvantages as com-
pared with one requiring a smaller investment so that even though the
plan involving a larger investment may prove in from the cost study
by a small margin, it may be desirable to adopt the alternative plan
so as to avoid tying up considerable amounts of fixed capital. Another
question to be kept in mind in interpreting cost studies is whether the
more expensive type of plant, usually a higher type of plant, can be
adopted satisfactorily at a later date or whether the decision to be
made at the present time precludes its adoption later. In the former
case it is often wise to go further in deferring fixed capital expenditures
than in the latter case. F"inall>', throughout all of his work the en-
gineer must have foremost in his mind the fact that the telephone .sys-
tem exists for the purpose of furnishing service to the public and the

522 liF.I.I. SYSTEM TECIIMCAL JOVRSAL

results of his engineering effort should insure a service which is satis-
factory from the subscriber's viewpoint.

It is evident from what has been said, I believe, that these engineer-
ing cost studies are of great benefit in working out the proper pro-
cedure in our engineering work, and I assume the\' arc equally helpful
in the engineering of any kind of growing plant. .Anything that can
reasonably be done, therefore, to gi\e the student an appreciation
of the nature, scope, and application of the economic considerations
of these engineering problems and to develop his faculties of judgment,
imagination, team pla\-, and other related qualities, will doubtless
pro\e of great value to the student in iiis later engineering work.

()TIIi;k I'H.\SES OF ENGINliKKINc; WoKK

I ha\e thus far described to you some of the \ery important engineer-
ing problems involved in the planning and carrv'ing out of plant exten-
sions to meet expected future ser\-ice requirements. I would like
next to consider with you a few of the engineering problems that present
themselves in the actual design or oper.itioii of these large extensions
to plant as introduced.

'{"he rapid (k'v cldpnuiil nf ilu' lelepliime sysliMU, inrhuling llie tre-
mendous growth in the luuiiber of lelei)liones in service and the rapid
increase in the extent of territory which can be reached from any
telephone, has led to a great increase in the imjiortance and difficulty
of the technical jjroblems involved in tiie design and ni.iintenance
of the plant.

These technical probli-ms cover a vi'ry wide rangt.'. The electrical
and acoustic problems involved in the transmission of speech have
led telephone men to much pioneering work dealing with the flow of
sustained and transient alternating currents in electric circuits of all
types and in the fundamental nature of speech and hearing itself.
.Again, the economical design of outside plant with suitable strength
and economy involves investigations of characteristics of construction
and materials and the preservation of limber, and there are, of course,
special mathematical ancl other problems involved in the design of long
cable or wire spans. Buildings and associated central office equip-
ments involve very interesting mechanical and electrical jiroblems
in the matter of the layout ofthe buildings and the arrangement of
a|)paratus to meet exacting re(|uirements. These include many
problems in the design of means for automatically supervising the
|)rogress of telephone connections anil in the design of thousands

n.wci\r.i:ia\r, i'roiu.ims or iiii-. ni:i.i. sysium ?2.\

of typi'S of .ipp.ir.iliis to lucrl s|H'(ilic infcli.mic.il .md clcclricil
ri'(|iiirriiii'iit>.

What I li.iM- .ilr(.-.ul\ s.iiil iiupli.isl/is llii- iiuportaiur of inniiuirini;
work involved in tlu- design of ik-w pi.ml. Wry inli-ri-stinj; iMiniiuvr-
ing studifs arc. howcvi-r, also invoKol in roniu-clioii with tlir niaiii;
tenanrc of the plant as wt-Il. Tiiis inrUidts tlu- di\ilopinc-nl oi im-
proved niaintonanie nu-thods and routines and a eritical analysis ol
the results obtaiiutl, judged from the points of view of excellency of the
service and econonty of operation. To use a homely illustration: one
miRVit have his automobile completeK' gone over by a garage every
UK) or 200 miles of running with the result that he woukl probably be
reasonably sure of perfect maintenance of the automobile (assuming a
perfect garage), but the maintenance costs would be excessively high
and out of proportion to the benefit received. On the other hand,
however, if no attention is gi\en to the maintenance of the automobile,
maintenance costs woukl be at a minimum l)Ut the depreciation would
be high, the operation would soon become unsatisfactory and soonei
or later the results would be a total interruption to service use. The
problem, therefore, evitlently is to find the proper balance litlwtcii
o\erall costs and service results, and this is true, of course, ot tlic
various engineering problems to be soKed in connection witli tin-
maintenance of the telephone plant.

The engineering work of the Bell System also insolves, to a large
extent, relations with other organizations. These relations are very
close with other wire-using companies, including small telephone com-
panies whose lines connect with those of the Bell System. Important re-
lations must be maintained by the engineer with electric power antl
electric railway companies, as particularK' important problems of
safety and of service arise due to the proximity between their electric
circuits and the telephone circuits. These problems involve provision
not only for the protection of the plant and employees against the
flanger of contact with the wires of other companies but also include
coordination of the two systems to prevent excessive inductive effects
which often become important where electric power lines or electric rail-
ways and telephone lines run parallel to each other. The electric com-
panies and the telephone companies often find it advantageous to enter
into arrangements for the joint use of pole lines and this presents
many problems requiring consideration by the engineer. It is evident,
therefore, that the problems of the telephone engineer cover a very
wide and interesting field in mechanical, electrical and other arts.
both within the business itself and in relation with other uiihtics .iiui
municipal, state or national bodies or associ.itions.

524 BEl.L SYSTEM TECHNICAL JOURNAL

SpixiFic Projects Illustrating Telephone Encineering
Problems

Enough has been said, I bche\e, in the foregoing to indicate the
general nature of the engineering problems handled in the Bell System.
It is, of course, impracticable and doubtless would be tiresome in a
talk of this character to deal specifically with many detailed engineei-
ing problems in\ol\-ed in the work which I have just described in
general terms. I believe that you will gather a better appreciation
of what some of these problems are from the inspection trips which
form an important part of this week's program, than you could by a full
discussion of them here. It will probably be of interest, however,
before closing to outline briefly one or two typical telephone engineer-
ing problems of considerable magnitude.

.\i;\\ \'()RK-C"iiicA(i() Toll Carle

The first large engineering problem I will consider is that relating
to the New York-Chicago toll cable as shown in Fig. 1. This cable
follows a route from New York through Harrisburg, Pittsburg, New-
castle, Cle\'eland, antl thence to Toledo, and when completed' will
extend to South Bend and then on to Chicago. For parts of the
distance through the congested sections it is underground, and through
the open country it is aerial.

I'litil a comparati\-ely few years ago practically ail long toll circuits
were in open wire construction; that is, individual wires mounted on
separate insulators attached to cross-arms on poles. This was a
natural development at first, due to the small number of circuits
usually involved, but was also necessary because of the relatively high
transmission losses of cable circuits where, as you know, the wires are
insulated b\' wrappings of paper, closely twisted together in pairs and
quads, and large numbers of the.se compressed together within a lead
sheath. The rapidly increasing use of toll service, however, pointed
to difficulties in pro\iding for future growth with open wire lines. In
different parts of the route between Chicago and New York, for
example, there were three and four heavily loaded open wire toll lines
and the rate of growth was so rapid it was evident that before long
dilTiculty would be experienced in obtaining suitable routes for llu-
addilitjnal [jole lines required.

Early efforts were accordingly made to de\ise means which would
permit of satisfactory talks through cable and as a result of very
intensive research there were developed satisfactor>- forms of telephone
' This cable has recently been completed.

F.NCINF.fiRliWC I'ROIU.r.MS OF I III-. lU.l.l. SySII-M 525

526

BELI. SYSTEM TECIISICAI. JOCRNAL

repeaters; that is, devices for aniplif\ing feeble teleiihone eurrents,
passini; in either direction o\er a telephone cirniit. \viiht)iit apprecialile
distortion. Tlie most successful repeaters of tin's l\pe. as \()ii nia\
know, u^e as the ainplif\injj element the \acmun iu!)e, alihouiih
the tube itself is but a \ery small part of the apparatus required for the
successful operation of the telephone repeater, antl man\- interesting

Fig. 2 — Open wire toll liiu'

engineering pr()i>k'ni> had tii i)c s(>l\ i-<l in piov idin;.; a i(inipi(.'lc rc|)ealei".
A full discussion of this \ery imi^ortanl and interesting de\elopment
is gi\en in a paper by Mr. Gherardi and Dr. Jewett, jiublished in the
Transactions of the A. I. K. E. for 191!).

The loll cable de\elopnient, based on the use of repeaters as outlined
above and many other technical impro\ements, now makes it possible
to gi\'e satisfactors' service between Chicago and New York and inter-
mediate jioints o\er toll cable circuits of such small gauge that dose
to liOO circuits can be included in a single sheath of 25 s" in diaTneter.
The same number of circuits would reciuire four or the \'cr>' hea\il\-
built pole lines of open wire construction such as is shown in Fig. 2.

The construction of the Chicago-New ^'o^k cable was started in
I'.IIS and will be completed this year. As shown in Fig. 1, the cable

i;xGi\i:r.i<ixc, fRoni.r.Ms o/ ////•: iir.i.i. sYsruM

527

is now ill service l)elween Cliicagn and Soulli Hend, Indiana, and
l)el\veen New York and points as far west as Toledo. This cable is
one elcnu-nt of a ver\- extensive network of toll c.iliK-s, |)arti<iil.irl\- in

li<.

Fig. 4— T..1I r.il.lr lii

Allii;lun\ Mountains

the northeastern part of the country. Important cables in service or
Iieing installed out of Chicago, in atkiition to the New York-Chicago
cable, include cables from Chicago to St. Louis, Chicago to Terre
Haute, Chicago to Milwaukee. Chicago to l)a\enport, Iowa. During
this year the Bell System is installing over 1,000 miles of toll cable
containing more than 2 billion 500 million feet of insulated conductor.

528

BELL SYSTEM TECIISICAL JOURXAL

The successful operation of long circuits of this cable network has
been brought about only by the solution of very difificult technical
problems, some of which have alread\- been mentioned. It may be
of interest to state that the long through circuits in this cable will be
in the nature of four-wire circuits; in other words, one pair of small
gauge wires with repeaters will be used for talking in one direction and

• Tfvsmr

l'"ig. 5 — T\|iii.il Irlcphonc r('()<'atfr station

a similar pair so equip|)ed will be used for talking in the other direction.
As an illustration of another type of problem involved, it may be of
interest to mention that it is necessar>' to employ automatic regu-
lators which vary with changes in the temperature of the cable con-
ductors, the amplification introduced into the circuit by some of the
repeaters. Without regulation, the change in temperature occurring
within 21 hours often makes as much as a thousand-fold difference
in the amount of electrical energy received over New York-Chicago
circuit from the same input, a variation which would, of course, utterly
prevent giving service o\er the circuits.

Aside from the electrical difficulties there were also interesting
problems of a mechanic.il engineering nature to overcome in the desing
•ind placing of the cable, particularly where it passes through the
wilderness <if the .\lkghen\- Mountains as shown in Figs. Sand 4.

F.NGmEERlNG PROPl.EMS OF THE PF.I.l. SVSTFM

'-29

Thi- cable is for most of its clistanro siriing on pole lini-s and these lines
were (li-si^ned especially to wilhslanil the stresses cause<l during sleet
slornis. The decision as to wlicllui llie caMe should be iindcri^rninid

^5B^

^■^■pc' n

■

9

I

yj

1

^^^^■^^

1

31

hig. (> — Hank of 2-wire teU'phnnc rcpt-aters

or aerial in the \-arious sections in itself in\ol\e<] iiian\- engineering
considerations.

In addition to the engineering matters in connection with the cable
itself, other interesting problems present themselves, of course, with
regard to the design and construction of the telephone repeater stations
and their associated equipment, the telephone repeaters being inserted
in circuits of this character at intervals of about 50 miles. A typical
re()eatcr station is shown in Fig. .5, a bank of two-wire repeaters in
Fig. 6, and a bank of four-wire repeaters in Fig. 7.

P'ig. 8 shows a view of the completed cable. In this case a loading
coil case is also shown, and the picture indicates again the physical
problem of erecting a cable through the less accessible sections of the
territory'. Fig. 9 shows another section of the completed cable through
open country, and shows loading coil construction and facilities for

530

nEI.L SYSTEM TECHNICAL JOURNAL

l-'ii;. 7--l{ank of 4-«ii. i,l,|.h^

I'ig. S Toll ial>lc line showing loading coil case

r.xGixur.mxG i-rohi.f.ms or hie nii.i. sYsriiM s.m

rut ling in additional loading: roils as rf(|iiirfd. V'm. 10 gives an
intiTi'sting \ii'\v of tlu- i\d)!r n\vr ihv Alk-glu'nii's, showing us again
tlu- ini'cit.inical prolilcins invoKi'd in design and conslruction. In
this ease the fai>le follows c!ose!>' tiie open wire line, which in time will
he disnianlled.

It may be of interest in this connection to state th.it the |)lans to he
compariil in the study of toll cahle projects generally differ primarily
in the dates at which they contemplate supplementing or replacing
open wire service by cable. Conditions under which cable becomes
economical depends, of course, on many factors. Perhaps the most
iinport.uU single factor is the rate of growth of the circuit requirements.
The tletailed design of the cable also involves very interesting studies
of the economical number of circuits to provide in the cable sheath,
.Also the economical gauge of each circuit must be considered, com-
paring in many cases the economies of a larger gauge with those of a
smaller gauge provided with a greater number of telephone repeaters.

The design of the toll cable as discussed is but one illustration of the
design of the toll plant extension as a whole, a problem which, in
general, involves the consideration of the relative desirability of
additions to existing open wire toll lines, building new open wire toll
lines, applying carrier telephone s\'stems to existing lines or installing
toll cable.

Ti:i,i£PHONK Probli:m in Xi w York City

As another specific illustration of the tek'i)h()ne engineering problem,
I will describe briefly the matter of adetiuateh- meeting ref|uirements
in a large city, using for purposes of illustration the situation in New-
York City and the metropolitan area. This [larticular situation doubt-
less presents one of the most difficult engineering problems and in
some respects is unusual, yet, on the other hand, it fairly represents
the kind of engineering problem with which the Hell -System engineers
nuist deal at all times.

Fig. 11 indicates clearly the magnitude of the [)resenl du^\ future
problem in the .\ew York metropolitan area, as viewed from the
number of telephones. In 1(I0."> there were 220,000 stations in New
York Cit\- and 300, ()()() stations in the metropolitan area. By 192.")
the figures had increased to 1,400,000 for New York City and 1,000,000
for the entire area. By 1945 it is estimated there will be over 3,000,000
stations in New York City and over 4,000,000 in the metropolitan area.
Part of this growth can be ascribed to the normal increase in the
popiil.itiot) and p.irt. of course, to the tendency to make more use of

532

BEI.I. SYSTEM TliCHMCAL JOURNAL

k^mc'

F-'ig. 9 — Toll cable liiii- through open toiiiurx-

Kig. 1(1 — C'alilf and oixn \\\rv loll line in Alkgluny Mountains

HNaiMilih'l.w: fKOIU.I.MS ()/• I III-. HI I.I. .SV.SII.M 5.U

the ti.-k'|>luiiK-. In .ulilitioii, p.irt of (lu- urowlli is due 1<> llic cofi-
(litions followiiik; ihc World W.ir ,iiul llu- ^riUTiil rcoiioiiiic Ircnd.

Comparing l!>2l wilh l!)l 4. wliolisali- coinmotlily priix-s, as you
know, ha\t' risen oxer 50 per nut ; tin- cost of li\ injj o\er (>() per cent :
wagt's in mamifarlurinj; industries o\er 100 per cent, while in the same
fX'riod telephone rates generalK- ha\e increased less than 3U per cent.

1

• 4 lOO dill'
NT MIROPOLMSH

ESTIMATED NUMBER Of TELEPHONES

NEW YORK CITY AND

METROPOLITAN AREA

1.300 000

V.r

N r iktnoroLiiM

MCA

i'fjs;-^^

300.000

MTKIWPOUIM

uu--.

1905

1925

945

Imk. 11

and e\en less than this in some of the larger cities. Tele[)hone service,
therefore, represents a hirge value for its price and in a situation like
(ireater New York City, where there are between seven and eight
million people, it is but natural that the new situation in the economic
balance of things, together with the low price of service shown, would
make for a \ery substantial increase in the demand for telephone
service. This has. of course, also been true elsewhere.

As I have shown there are at present a total of over one inillioii
telephone stations within New York City proper served fnjni about
130 central offices, 26 offices ha\ing been added last year. The pre-
dictions are that within the ne.st t\vent\- years the stations and central
offices will have more than doubled. Kach subscriber in this great
network must be able to reach promptly every other subscriber.

534 BEI.l. SYSTEM TECIIMCAL JOURNAL

Due to the large area in\-ol\'C(l. a great number of rails within the city
necessitates extra charges, which means that they must he specially
supervised and recorded. There arc man\- different classes of service
furnished the public, such as measured rate, flat rate, coinbox, etc.,
and, of course, such other special services as Information service.
Not only individual lines but party lines and pri\ate exchanges must
be cared for. Furthermore, the demands for ser\ice to the extensive
area surrounding this great city, as well as the large number of cities,
towns and rural communities throughout the entire country. ri-(|uirt'
that provision be made ft)r thousands of toll mes.sagcs daiK'. Tlu-
problem of gi\ing satisfactory service under these conditions and uiuler
the com])lications that come with the tremendous growth referred
to is a very important one and requires careful and constant stud\-.

In order to properly care for this complex prolilem of furnishing
telephone service in large cities, telephone engineers in line with the
efforts which ha\'e been made from the time of the early switchboards
have endea\ored to perform the \arious operations automaticalh' so
far as consistent with serxice requirements. While the switchboards
which you saw yesterday are called "manual" switchboards, you
doubtless noted from the demonstration and your visit through the
central office that many of the operating features are automatic in
character. The latest step in this general trend of development has
been to develop a switchboarti which would pro\ide for completing
many classes of calls entirely without the aid of an operator, and these
new machine switching equipments which you will see today are
gradually being introduced into .\ew V'ork, Chicago, and other large
cities. This is a large problem in itself and involves not only the
completion of calls from machine switching subscribers to other
machine switching subscribers, but the completion of calls incoming to
machine switching offices from manual offices and outgoing to manual
offices. This must be done without reaction on the service or in-
con\enience to the subscribers and so that the machine equipment
and the manually operated switchboards will work together as a co-
ordinated whole.

I do not know of any mechanical device that reminds one so much
of the functioning of the human brain as does this mechanism for
completing calls following the dialing operation. The completion
of a simple call, while quite in\olved in itself, is by no means the
complete [iroblem. There must be a great many other features pro-
vidtnl, such, ft)r one example, as where a register is provided on the
subscriber's line to register the number of calls under measured rate
service. In these cases it is necessary to insure that there shall be

r.xuiM I ki.m; /'A'( •/(/./ .u.v or iiii. ini.i. svsir.M 5.»5

pri>|H'r rt'nistr.ilion !>>■ llu- in.i«liiiu' .iiid tin- nu'ch.iiiisiii is so .irr.iiim'd.
tlu'rff«)rf, that on tlu' nimpUlion of tlir call it will ti-sl tlif iiiu' to makt-
sure that i-viTsthiiiK was normal iK-fori- rinislration is actually ptr-
fornu'd. Similarly, all the way thronnh the completion of the regular
anil special classes of calls it is necessary for the mechanism lo perform
just such intric.ite functions as that descrihed.

The eiigiiieerinn of the interotTice trunk la\<>ul in a ciiy like New
\'ork is also an im|)ortant and interesting; problem, not only hec.iiisi'
of its m.ignitude l)ul because of the almost unlimited \arialions which

EXCHANGE TRUNKING PLANS

TRUNK GROUPS RCQWREO BETWCEN TEN CENTRAL OFflCES

OlRCCt TRUNK PLAM TANOCU TRUNK PLAN

90 CROUPS JO goouPS

AMDCM AND DIRCCT
TRUNK PLAN
50 GROUPS

NEW YORK METROPOLITAN ATCA

TRUNK 6R0UP3 REQUIRED

OlflCCT TRUNK PLAN TAND£M TRUNK PLAN TANDCM AND DIRCCT

TRUNK PLAN
'aOOO 6R0UPS 850 GROUPS aSOO GROUPS

FiR. 12

might he empl(>\ed, a large number ol which must be carefuih' con-
siderc<l in connection with ailditions to the plant. In opening new
central oftices, trunk circuits must be pro\ided between each new office
and the existing offices and also between the new offices themselves.

Fig. 12 illustrates the range of trunking layouts which might be
used. With the 10 offices assumed and direct trunks between each
office and every other ofitice, 00 groups of trunks would be required.
With the so-called full tandem operation; that is, under an arrange-
ment whereby each office reaches every other office through a central
point, 20 groups of trunks would be required. Between these two
extremes with some offices reaching certain other offices through the
tandem center and certain others by direct trunks, a great many
combinations would be possible. In the case assumed 50 groups
app>eared to be the best combination. The data given at the bottom
of Fig. 12 are of particular interest in this connection. As will be

536

nr.U. SYSTEM Tr.CIIX/C.U. JOfRXAL

noted, if only direct trunks were employed in the metropolitan area,
some 43,000 groups would be required. On the other hand, if we
followed only the strictly tandem plan, 8.50 groups would be rcciuired
but as previously indicated, unwarranted switching costs would be

RELATIVE GROWTH
IN TRUNKIN6 SYSTEM

NEW YORK METROPOLITAN ARE/
INCREASE 1924 OVER

SELECTION OF CENTRAL OFFICE NAMES
NEW YORK CITY

CONSIDCRATIOKS GOVCRNMG SaCCTION

1 DULIHG CODC CONrilCISriRSI IHBtC LCIIfBS

2 PHONETIC COHrilCTS- WITH MORC THAN 500 EXISTING NAMES

3 PRONUNCIATION ■ MUST BE EASILY UNDERSTOOD

CXAUPLC or DIALING
CODE CONfLICT

(IDTiNC NAUC Jw.1,
CnirilCTIIte NAME

J 1 K n SAW PIAl IS)

■M&,

®©d*

SEARCH rOR NAMES
i: 50UICES or KtUES COHSULIEO

1(0.000 HJHES COKSIOEREO
Of •HICK HOT MODE THAN
ISO cm BE USED

0PtRAIl)16 TESTS tlU PROSJBII
ruKTHEB REDUCE THIS NIIUStR

1-in. 14

in\'olved. B>' establishinj.; a pi, in, iiowexcr, in\()l\ini; lidtii t.nuk'ni
and direct trunks, the mosl economical |)lan can be determined upon
and in this case about 0,000 groups of trunks are rcc|uired. Fig. 13
shows how rapidly the trunk groups increase with ilu- .uidiiicni of
stations and central otliccs. You can well imagine the engineering

F.NGiM'.i:His\: /'/?()/v/./;.u.s ()/• ////; Hi.i.i. sy.sir.M

'x\7

prohk'iu iinoUi'cl in workiiin out tlir most ill'iiifiil Irunkiii); pi. in for a
ciiy sui-h as Ni-w York or (."liicMkjo.

Aside from tlu- layout of llu- trunk plant itsolf, tin- unnini-i-rinj; work
involves the design and construction of tlu' underground subway
sNstem and the desikjn of the physical cable i)lani. In one >'ear in

Kig. 1

liii^ <',rei'n ti'lfphoiic hiiililini;. New \'()rk C'it\-

New York City alone, enough cable has been installed and |)laced in
service to make a cable containing 1,2()U wires reaching trom New
N'ork to Chicago.

The expansion of the metropolitan plant to care for the increase in
the number of subscribers also in\olves, of course, opening many new
offices and the provision of new switchboards and additions to the
existing switchboards. The matter of selecting the name for a new
central office would at first apjx-ar to be a simple one, but as indicated
by Fig. 14 it is a very involved problem in itself. As will be noted,
there are many ciuestions to be considered. One feature relates to
the matter of dialing. It is interesting to note from Fig. 14, however,
that while the name "John" does not seem in any way to contlict
with the name " KiiickiTbdcker." \et these two names could not be

538

HI. 1. 1. S)SII.\t I IXllML.M. JOLRSAL

used logcllur in llii: same city because of conflict in the dialing process.
Phonetic conflicts are also exceedingly important in telephone opera-
tion. In fact, they form one of the most important factors that must
be considered in the selection of an office name. Pronunciation of the
name must also be easily understood. Thus we find that in the case
of the metropolitan area something like 72 sources of names were
consulli'd: for instance, historical works, geographical works, postal

Kli;. I() \\'i»l .ililh Strcti liiiilding, Ni-w \"ork titv

guides, telephone directories, and other sources, and out of 100,000
names considered not more than I'lO could be used and possibly .some
of these fni further stuch' will ha\e to be eliminated. 1 lia\e mentioned
this detail of o|)erati()n sim|)l\' to illustrate the \arirl\ of the problems
for the telephone engineer and the extent to which he must consider
them in order to insure the grade of service \\i' are all striving for.

The erection nl mw buildings and .iddilidiis to existing buildings is
also a large problem, there being 12 new i)uildings and 21 additions
erecletl in New \'ork during l'.)23 and 11)24. It might be interesting
to note that for these buildings and eciuipments it is necessary to
consider not onK- the proper association of the various elements of the

/:".V(;/.v/:/;/,v.Y(; rKoni.iMs oi iiii: ni.i.i. sysii.m 3.w

iviitr.il olVicf unit I'riim llu- \ ii'wpoint of si-curiiin s.itisfactorN' (>|RT.tli<in
.iiul in.iiiUiMi.iii(-i' roiiditidiis. Ixii also to proxidi- for an orderly growth
of thi- (lirtVriMil p.irls of riiuipiiU'iit and ImildiiiK. l'"nrtluT, iIk- ci'iilral
otVuf la\i>iil nui>t Iif consldficd from llii- point of \ itw of co-.tv which

:^. Xlu \ork City

may vary ovi-r a widi- ranj^r iindi-r the difTcrent arrangements which
might be used. This you will better ajipreciate from your \isits
through the offtces.

I will next show you a few cases which will illustrate some ol the
problems in the way of providing building sjjace to house switchl)()anl
e(|uipmenls in ihes*.- large metropolitan areas.

Fig. lo is a photograph of the Bowling (ireeii building, located in
the extreme lower end of Manhattan Island and which will i)rovide
space for switchboard recpiirements for that part of Xew York City.

Fig. IG gives a rather interesting example of another of the large
New York telephone buildings, this case being the one located in West
:i»)th Street in the neighborho<xl of the Pennsylvania Station. This

540

BlUJ. SYSTRAf TF.CHSICAL JOURNAL

building and equipment involve an expenditure of 815,000,000 and is
equipped to serve over 100,000 stations. In other words, we find
in this one building and the associated switchboards on subscriber's
premises, provision for handling more stations, for example, than are
in service in a cilv the size of Balliinore, with a ijopiilation ot nearly

l-iv. IS -;i., 1. 1.1

1 y l.l.pl

onslrticliiiM, Ww \'cirk ('\\\

800,000, gi\ing you a further idea of the pr()l)lini of pnixidiiig service
in these large metropolitan centers.

Fig. 17 illustrates the building in New York dexoted to tiie centering
of all long distance lines, i-'acilities are also ])ro\ided for coiuiecting
together the \arious otTices of the city for switching to suburban points
through one of those tandem boards of which I sjioke, as well as for
switching to the great network of toll liiio running out to .ill im-
portant points throughout the coimtrx'. While there arc some locil
switchlK)ard facilities in this liuilding, practicalK' all the space is
devoted to hanilling toll traffic.

ILXCIXF.EKIXG I'ROIil.F.MS Ol- I III-. Hl.l.l. SVSI l-.M ?A\

V'm. IS illiislnilt'^ ilu- tu-w liuildinn licini; Imili lor the New Ndi k
TflfphoiU' ("oiiipaiu- oil West Strrrl in llu- lowrr i).irt ol M.iiili.il l.tii.
'V\u> litiildin^ is designed to liousc a larni- lUimliiT of units of machine
switching i'(|iiipnu'nt, and the u|>pur pari will be iitiii/ud fi)r the
.idnunistrati\e offices of the ("oin|iany. This further illustrates Jhe
type of huilding required in these iarije cenlers, and the many en-
nineerinj; problems inxoKed.

I might go on at length, gi\ing one proljjeni alter another, by vva\'
of iliubtration, but I think enough has been said to give you a general
idea of the nature and great variety of the telephone engineering
problem in\ol\ ing, as it does, almost e\'ery phase of the mechanical,
electrical, and other arts. It is obviously necessary for the engineer
not only to consider the technical problems involved in each of these
matters, but to a greater extent it seems to me than almost any other
situation I have encountered, it is necessary for him to take into
account all of the related broad operating and business factors which
are naturally to be found in an industry of the magnitude of the Bell
System.

Engineering Planning for Manufacture '

By G. A. PENNOCK

SvNpPsis: This artiilu distusscs the complete analysis, from a mami-
facturing point of view, to which every item of telephone apparatus is
submitted at the Hawthorne Plant of the Western Electric Company.
These works employing, at present, about 25,000, produce over 110,000
different kinds of parts which enter into some 13,000 separate forms of
apparatus. The advantages of careful engineering analysis of each new
job coming to the factory, as well as those which have been in production,
are brought out. The various steps which are worked out in connection
with each analysis are as follows: manufacturing drawings: the proper
manufacturing operations and their sequence; the machines best adapted
to carrying out these operations: determination of the kind of tools, gauges,
weighing and other equipment; the determination of the probable hourly
output for each operation; the grade and rate of pay for the operators; the
kind and amount of raw material required; manufacturing layouts which tell
the entire shop organization; each step in the production of the parts, and
finally the best rate to be paid for each operation. In conclusion, the
author discusses the personnel of the I'lanning Organization.

InTKoDI (HON

TlllC (.•>M.'iU(.' of the successful oiRTutioii of an\ industrial eslablisii-
mcnt is contained in the maxim "Plan your work — then work
your plan." The first part of this maxim is In- far the most import-
ant since the al)ilit\- to work aiu' i>l.in diinnds fundaiiuntalK upi n
the excellence of the plan itsell.

Farsighled planning, as applied to elenRnlar\- lactor\- operations,
is a relati\'ely sim|>le problem. For example, the iinii)lem iindlxcd
in ])lanning the work of a foimdry is to a great exttiii nurcK the
the duplication of plans already standardized, but in a plant manu-
facturing widely di\crsilied pro<lucts, such as we have at Hawthorne,
planning becomes at once more difficult and essential.

The Cencral Manufacturing Deparimenl i>[ tiie Weslcrn Kiectric
Company pnnides the Bell System with telephone eciuipment which
iiUdKes the i)r<>diiction of over 13,000 separate ami distinct forms of
ai)i>aratiis, in the construction of which there are used over 110,000
dilTerent kinds of parts made from IS, 000 different kinds, sizes, and
shaiws of raw material. A ntimlur of lluse p;irls .ire produced in
very small qiiaiitilies.

The |)roduction of the varied product mentioned al)o\e inxoKes
not only all the usual wood and metal working operations, but also
such lines of manufacture as:- glass making, textile dyeing, manti-
faclure of porcelain, electrolytic iron, \idcanized and i)henolized fibre,

' l'a|)cr read before llic Mell S\slcm l-'..|ii. .il ioTi.jl ( 'oiifcrence, ('hicat;(i. June
22-27, 1925.

542

F.sci\F.r.fii.\(; ri.i.wixc iok M.ixrr.icrrRR 543

soft and hard riil)lH'r in tlu' form of shod, nnl, lulu-, and molded
shafH's, thi- insulation of wire with ti'Xiiifs, fii.inu-ls, and papiT, and
ihf ronvt-rsion of copptT hiili-ts into win-.

Thcst' materials arc used for iu.ikin>; parts wiiicli, generally speak-
ing, are (|iiite small in size when compared witii parts usetl in stea.'n
ioeomotives, gas engines, dynamos, and otiicr kindred i-(niipinenl
nimmon to the eleetriral and mechanical fields.

The fart that the parts are small in dimension. howe\er. does not
mean that the manufactiiring ditTiciiliies are in proportion. On the
contrary the problems involved in tlnir ni.mufacture are often times
in .m inverse ratio to the size of the p.irt.

Fig. I shows a crank shaft al)oiit three feet long and the shaft used
in the calling dial for machine switching about an inch and a half
long. The layout of the operations retjuircd for machining the crank
shaft is shown in the upper left hand corner. There are a total of
eight.

Below at the left is shown the UiNout of operations fur making the
shaft for the dial. There arc a total of eighteen.

As you will note from the data at the right, the number of machines
involved is, roughly, the same in each case. These data illustrate
the fact, however, that the small part may be more complicated and
invoKe more engineering [iroblems that the larger [lart.

Pl.xnning i-()R Tin-: Fitirf.

.\s the manufacturing unit of the Bell S\stem, the Western Klectric
(\)mpany in planning its production has had to bear in mind, first,
that the facilities shall be adequate to turn out the tremendous
\olume of apparatus and equipment required from year to year:
second, that the System's supply of equipment must be planned to
eliminate, so far as is humanly possible, any interruptions: and third,
that the .System must get its equipment at the lowest po.ssible cost.

BrietK', our program for providing buildings and equipment for
the future is based on a five-year forecast of business made by each
-Associate Company and summarized by the .American Telephone and
Telegraph Conipan>'.

It takes approximately two years to erect and e(|uip new iiuildings;
con.sequently, capacity studies on fioor space are made two years or
more in advanie and tool and machine equipment studies are made
one year or more in advance, as this equipment can usualK be pro-
vided in one year.

544

BULL SVSriiM TECHXICAL JOIRSAL

XOTK COMPARISON OF SIZF. OF SHAFTS

Shaft fok No. 2 I vi'E Cali.in(. Dial
Opcr's. Req'd. (18)

Rough form thread portion, and (). I).
counterlx)rc'. finish turn, thread and cut off

Limits ±.0015" for diam.
=t.002" for I'gth.
Rough and fin. form i diams, shear 1
diam., thd. and polish.

Limits +.00;)",-.()(>5" I'gth.
Shear S. V. face to I'ght. burr and polish
long end. +.0(K)"

Limits — .001" for diam.
Straddle mill Mats— mill four (4) slots.
(2)oper's. +.000"

Limits —.002".

Miifhine and Tools
Davenport .^uto Screw .Machine, .S
chucks, .S pl.iin and form tools, 1 thread

<lie and three gauges.

\o. 1 H. & S. II. S. M.

1 chuck, 2 form tools, thread die, emery

stick and 4 gauges

Xo. 1 B. & S. II. S. M.

1 ( huck, 2 form tex>ls, emery stick ,ind

.S gauges

//./«</ Mill

.Miilinn fixture, vise and jaws and spii .

cutters

C'kankshait fok No. 21 Bli.ss
Pinch Press

Opcr's. Req'd. (8)

Rough and finish, center, turn face com-
plete and polish limits diam. +.008",-
.000" length ±.008". Mill concave key-
wavs, '.I " slot and 4 flats — i oper's.
Limits ±.005". Drill '4" x ^s" hole.

Mochhifs niul Tools

lleiiiK 12" X 5' lathe, center drill, turn-
ing and polishing tools. No. 3 B. <S: S.
mill machine milling fixtures, arbors and
(Utters. Cincinnati 1 sp. D:l'. drill jig
an<l drill

Fig. 1— Dial .Sh.ifl vs. Cr.ink Sh.ill

hxcimj.him; ri..i.\\i.\\; /oa- m.imi .iciiia-. m.^

I'm .\l>\ AN 1 \(.l> OI I'l.WMNC

In onk-r ti) iiu-rl tlu- rf(|uiri-niriils of llir l»-U-|)h()iH- l)usiiU'ss, ihi-
l-".ni;iiut'rinK 1 Vp.irtUKMits of tlu- Sysirm .in- coiisl.iMtly (li'Vi-lopiiiK
lu-w (k-signs ami i'lianj{itiv; pri-si-til (Ifsiijns with tlu- oliji-ct of improv-
ing; the quality of. or ri'tluc-ini; tlu- ro.sl of tfk-phono sorviri-. This*
nu-ans that the pnxlurts that \vi- an- inaiuifactiirin^ an- constantly
utuk-ruoinj; (k'\i'lopnR'ni. with tlu- n-siilt that wi- art' conliinially
lonfroiitwl with rhanijin^ inaniifactiirinji; prohk-nis.

The decisions reached liy the various orijani/ations of tlu Hell
System to proceinl with the intrcHluction of the new and chanj;e(l
designs just referred to arc based entirely on ini|)ro\e(l service, lower
lists, or iMith: conse(iuently, before any work on new developments
An Ik' done the Manufacturing IVpartmenl must furnish firm esti-
mates of the cost of one or any numbei of ])ieiesof apparatus that
may Ix* required.

This is made possible by our al)ilit\' to plan a job in detail on jiapei
Mul to make an accurate appraisal of the manufacturing costs before
pr(xluction is starteti. The cost established, selling prices can be
determinetl. and a final decision made b\- the Systern as to the merits
of any new devlopment.

Furthermore, by scrutinizing the design antl concentrating on the
\arious manufacturing operations to be used before the tools are
built, numerous changes can be introduced to facilitate manufacture
Hid in this way avoid getting into the factory what have been termed
' iiospital jobs " which result in retarded production antl infiated costs.

The two designs illustrated in Fig. 2 bring out what is possible in
.1 manufacturing analysis of an engineering design. The part shown
is the mounting plate used in the calling dial. The design originally
showed ears, which were blanked out and turned over toward the
inside of the blank and perforated, as shown in the upper \ievv.

The lower view shows the design as it was developed due to the
Manufacturing Department's suggestions to blank the ears from the
inside of the bl.ink and turn them outward, thus locating the mounting
holes in exactly the same piosition as the engineering design, but
saving material. It also simplified the bending of the ears. Instead
of a double bend, there is an S bend. The holes were made larger
also to permit perforating instead of drilling. The lugs and holes
were also unevenly spaced so as to make it impossible to perforate
or assemble the part in the wrong position. In shop language, the
part was made "f<K)l proof" in this respect, whereas the model was
not.

546

BELL SYSTEM TECIIXIC.IL JOURNAL

It was formerly common iirartice among many manufacturers If.
leave the actual planning of tlif job to the shop foreman and to sonic
extent this practice still exists. Obviously, under this plan, only the
more commonly known methods will be employed as the shop man
is not in a position to a\ail himself of the mass of engineering knowl-
edge that has accumulated in connection with such work. We are
convinced that the returns from engineering the actual manufacturing;
operations are as great as those realized from engineering the design
of the ])r()(iLicl.

C\1.I.I\(. DIAL NlMlii:K
IM.AI'i; >* I'lMKI'

Original I'i<()1>ii>i;i) Dksicx

(Jl)jecli<)iial)lf features — lugs fornieil inward, ref|uires larjif blank and a cani action

loul or two operations in forming. Small holes do not permit perforating

Design Finally Adopted

KfsuUs of romments^ugs formed outward decreases thi' size ol liLiiik p^■lnlil^•

cond)incd embossing and forming in simple tool. Holes increased in >i/e

l"ig. 2— .A Modified Part

l:\GlXl■:l:Rl.\^; ri.iwi.w; ii>u M.ixri-.u iih'i-. 547

l".\( loKv .\Ki<\\(.i:Mi;Nr

Before (li'srril)iii^ our |)l. inning work mori' in (k'tail, a fi-w wonlN
should Ik- said al)oul our arrani;rnu-nl of tnachiiu' (-(iiiipnu'iit. Our
iiu'tal working maoliiiu- (U-parliiu-nts are laid out in siieh rnanuer
that the niaiuif.u'lurin^i; oiK-ratioiis arc grouped into departments by
class of work or operation and not by class of prcnluct. Kach dejiart-
mcnt jx'rfornis some definite kind of operation, and each handii's all
the parts that re(|uire that particular operation. Thus we ha\c
punch press departments, screw machine departments, a milling
department, a drilling department, etc.

The parts prcnluced in these specializetl departments pass in proper
sequence through all the departments that have work to do on them
and finally reach the assemlily departments, where they are made
up into finished units of apparatus.

The ad\antages of this metho<l of di\-i(ling ni.mulacturing work
are that it minimizes investment by avoiiling duplication, increases
machine acti\ity, provides greater flexibility of equipment, and
permits the training of unskilled labor to the |ioint of full productivity
in the shortest time.

The conclusion may have been reached that departmental groupings
by classes of machines such as ha\'e been described is all right for a
business of little \-ariety. but that in such a large endeavor haTidling
so diversified a product, it would seem nearly impossilile to maintain
a proper balance of equipment in all the departments.

As a matter of fact, adjustments are frequently made due to in-
creased or decreased demands, and we frequently have to step up or
down both our rate of production and our capacity for certain lines
of products or certain definite articles.

To meet this situation, we have capacity data giving the number
of hours required by machine operations, assembly operations, etc.,
for one thousand pieces of each kind of apparatus. With this informa-
tion, we can readily compute the increase or decrease in shop ecjuip-
ment due to changes in schedules.

There are, of course, some departures from this general practice of
functionalizing our machine departments in the case of certain products
that require a large amount of special machinery. In these cases,
the few "general use" type machines required are grouped with the
special machinery into a department for the complete manufacture of
the article.

This special practice is also carried out in connection with the
manufacture of certain piece parts. These cases are confined to a

5-f.S REI.I. SYSTEM TECIISICAL JOURNAL

few parts manufactured in large quantities where it is found ex-
pedient to group a variety of machines in order to reduce the amount
of handhng to a minimum. An example of this is the manufacture
of the top part of the desk stand which supports the transmitter,
which we know as the "lug holder." This part is made from brass
tubing. The operations involved in making the part are. cut to
length, burr, several swaging operations, and a number of punch jiress
operations, such as perforating, embossing, and trimming. We have
in this case grouped together in the proper sequence the rcriuired
number and sizes of milling, burring, swaging and h.minuriiig ma-
chines and jniiich jiresses.

I()liHlN(. Sllol'

We also lia\'e a group of dc])artnKnls kiKiwii coliectix cl\- as the
"jobbing Shop" which is equipiX'd to i)erform all the usual machining
oj)erations. These departments handle the manufacture of sjiecial
apparatus, which is made in such small quantities that it does not
pay to make the elaborate manufacturing preparations which are
justifiable in the case of hi'a\\' running apparatus lor whicii tiure is
an established demand.

To give you some picture of just what we set out to dn wlun we
plan a job, the following flifferent steps or problems wliicli must be
worked out are enunu-raled brietly:

1st. Manufacturing Drawings.

These drawings tell tlu' shop in lUlail wh.il is lo hv rn.idc
and what the requirements are.

2ntl. Manufacturing Ojierations.

The actual operations recjuired to produce the jKirts and
their proper secjuence are decided upon.

.'ird. I'iie machines on whicli liu' ()|)ir,ilions ari' to \iv perloinK-d .ue
determined.

4tli. The kind of tools, fixtures, gauges, con\e\ing. .md oiIht
i(|ui|)nKnt t(i be nsi'd is determined.

.")ili. .\n i'\p(.-cii(l luiuiiy iiuiput for each oi)i'ration is set up.

• ith. The grade and r.itc of p.i\- nf liie (i|)er,ilors to be cinpldNcd
.ue determined.

Till. The kind .md .inidunl ot r,i\\ m.iteri.ii nquiri'd per tiiousand
|)arts .md ihc lonn in whicii il >h,ill in- |)urcli.isrd .ire
determined.

1

i:x(;i\i I HIM. /•/..( v.v/.V(, /(»a' M.txri-.K iria-: 549

Sih. Maniif.u'turinj; Layouts.

Thi'sc layouts loll the niliru shop i>r).;.iiii/.itioii I'.ich sli-p
in making llii' parts siiowii on liic inaiHilactnriiii.; draw-
iii^s.

iUh. Vhv piiTf rate to he paid for i-acli operation is (k-lfrniiiu-<I
al'ti-r arliial manufartun- is slartiKl.

Mam 1 A(HKiN(i Dk wviniis

Thi- nianutarturinj; <lra\vinj;s prepared for an\- |)iei-e of Western
Klectrie apparatus comprise complete detail drawings for each part,
an assembly drawing showing how the \'arious parts are associated,
a stock list of the parts required and the quantities of each, and a
test sheet which shows the mechanical and electrical requirements
which the apparatus must meet in order to insure satisfaclor\- per-
formance in the System.

In the preparation of these drawings, stan<lards are followed which
insure that the designs as far as possible will permit of rugged tool
construction which will insure long tool life; that the holes are of such
dimensions as will permit them to be perforated wherever possible;
that thread sizes for the tapped holes selected are such as to insure
minimum tap breakage; and other similar details.

Manlf.xcturinc. Opkrations

Before deciding upon the manufacturing operations for any part,
a careful detailed analysis is made by the Planning Engineers to deter-
mine just what operations are required and how the operations shall
be performed in order to obtain a satisfactory production in the most
economical way.

In the case of simple parts, it is not a difficult task to determine
the manufacturing o[x-rations reejuired and their proper seciuencc. A
large proportion of the parts, however, is in the fairh' difficult class,
and the ingenuity of the Planning Engineer is called upon, together
with the advice and guidance of his superiors, in determining the
manufacturing operations to be used in these cases.

A fair prf)portion of our product makes up what might be called
the "difficult class" of parts to manufacture, and in setting up the
proper procedure in these cases, we frequently hold conferences where
the best talent along the particular lines under consideration is called
into consultation in determining the Ix'st procedure. In many of
these cases actual experimentation is carried on before the final tool
line-up is decided upon.

550 JUil.L SySlli.M TECIISICAL JOURNAL

MaCIIINF. KyUIPMENT

TIk- niacliiiu' (•(|uii)nu-ni on which the operations are t(5 Ije per-
formed is the next thing gi\en consideration, and the most iniportanl
features arc:

1st. To select a machine that is cai)al)ic of producing the parts to
the desired accuracy.

2nfj. To select a machine that will result in the maximum produc-
tion, keeping in mind, of course, the accuracy required.

3rd. To give proper consideration to the investment, maintenance
and overhead charges incurred by the machine selected
so that these charges do not offset production economies
expected.

4th. To insure that tlie machine selected is u\) to dale with regard
to the latest machine practice developments worked out
by Hawthorne and by commercial machine manu-
facturers.

There are, of course, many other features which must be taken
into account in selecting the machines for the manufacture of various
kinds of parts.

Ill tile case of bl.uiking ojicr.ition on a punch i)rcss, the object is to
secure the smallest and therefore the fastest press which has sufficient
tonnage capacity to perform the operation required.

Where the part is to be manufactured on an automatic screw
machine, the problem is to select the fastest machine that will pro-
duce the work to the accuracy required, and at the same time select
a machine that has a sufficient number of spindles and tool positions
to permit all the operations retiuired being ])irfornu(] l)ilorc the
parts are finalh' cut from the rod.

A part having a large number of holes to be drilled will necessitate
the selection of a nuilti[ile spinille machine that can be set up to
prtxluce the maximum number of holes in one or se\eral parts at
each operation of the drill press.

We have worked out numerous improvements in romnurciai
machinery that ha\c now been incorporated in the prcxluct of many
machine tool manufacturers. .Some of the most important of these
arc motor driven pumh i)re>i-ic<, screw machines, milling machines,
lathes, etc.

/ \^:l.\^l■l:Rl.\^; ri..i\.\i.\(; vor M.ixri-.u hrh 531

I'in- ■{ >liii\\s llu' oltl lult-di i\(ii milliiiv; m.H liinc. 1 1 ileus mil
nivi' \<)n .1 Inii- pictiirr ol llu' wlmlf juli. siiur llu- omtIumiI drisc
which i> thi' mosi ()l)jfcti<)nal)k- fralurr doi-s iiol >\h<\\ in llic |>i( tine.

liy. J- licit Drixin Milling Marhiiie

Fig. 4 shows the nKxIern motor-driven iniMing machine with the
motor mounted in the base and a chain drive enclosed in the housing
at the l)ack driving the spintlle.

At our suggestion, several of the largest manufacturers of screw
machines ha\e incorporated screw slotting devices as standard equip-
ment for multiple spindle machines.

We have just recently worked out a ilesign whereby a high speed
screw machine, formerly adaptefl to bras.s part.s only, can now have
its spindle s[H>ed reduced through change gears so as to make it adapt-
able for iron and nickel silver parts, thus providing greater flexibility.

552

nr.l.I. SYSTEM TECIISICAL JOURNAL

Punch presses were formerly liable to serious damage if two blanks
were accidentally placed in a forming die. We have worked out a
design of ram which contains a "shear ring." This consists of a soft
metal ring so incorporated in the connecting rod of the press as to

Tin. 4 Motor Drivi-n Milllnu Maehinu

shear at any predetermined pressure, thus allowing the connecting
rod to telescoiK' instead of breaking the die or frame of the press.
This impnnement permits operating punch presses .safely at greater
speeds than are usual on this t\'pe of equipment.

Numerous other similar impro\ements have been woiked out,
many of which ha\e bt'cn jjatented.

Tools
The animal demand for the product is the most important factor
in determining tlu' kind of tool, tixluri', and gaugi' t(|uipnunt to he
prcnided.

E.\Gi\r.i:Kixc /7..i.v.\7.\t; /"oa- M.ixir.icirRr. 55.1

Our most intricate cnnineoriiiK pnihk-ms arisi- in connirtion with
punch prt-ss t(H)ls as tht-rc is almost no hmit to the \arii-t\- of opera-
tions that can ho performed on this t\iK' of niariiine.

If the demand for a part tnade on a punch press is small, it is often
found more economical to l)uild simple tools which will hl.mk out,
perforate and form in separate operations, rather than to build more
elahorate tcxils at a higher cost wliicli will comliint' two or more
operations into one.

The effect of ciuantit\- on the desijjii of tools ma\' best be shown b\-
a concrete case.

The EFrecT of An

NUAi. Demand on Choice

OF Man

UFACTURINC Method

Yearly
Req.

Material

Type of
Machine

Tvpe of
Tool

Tool
Cost

Cost
per M

Tool
Cost
per M
Parts

Saving
per
Year

5.000
30,IHX)

500,000
,?,0(K),(XK)

5 'S" Brass
Rod

I 15" Sheet

Hand Screw-
Machine

Punch I'ress

deneral use
Tools

1 at a time
Tandem
Perforating
and Blanking

3 at a time
Tandem
Perforating
Perforating
and Blanking

7 at a time
Tandem
Perforating
and Blanking

$150.00
400.00

600.00

$10 00

2.30
1.72

1.52

S5.00
.80

.20

$231.00
290.00

600.00

Fig. 5

Take, for illustraticin, the case of a simple brass washer 5/8" in
diameter, l/lG" thick and having a l/4" hole. As shown in Fig. 5,
with a requirement of 5,000 a year, the washer would be made from
rod stock in a hand screw machine using general use tools at a cost
of SlO.OO a thousand; for 30,000 a \ear it would be made from sheet
stock in a punch press using a one-at-a-time tool, at a cost of S2.30 a
thousand; for .500,000 a year a three-at-a-time tool would be used
at a cost of SI. 72 a thousand; for 3,000,000 a year a seven-at-a-time
tool would l)e used at a cost of SI. 52 a thousand.

In each one of these steps, as shown in the columns at the right,
the additional tool investment, necessitated by the more advanced

554 PEI.I. SYSTEM TRCIISICAL .'OURSAL

nicth<Kl, would 111' li(|iii(latal in oiu- yi'ar h\ the decreased niaiui-
fartiirinj; tosl.

W'luTf a liii;li (k'jiivc of arcurar\- is required on a piece of apparatus,
the overall effect on the tool equipment is to require a greater number
of individual tools, as well as to require tools of a higher grade of
wi>rknianship. For instance, it may be necessary in the case of a
puncii press part to hold certain dimensions of the blank to extremely
close limits, and this quite often requires an additional operation of
shaving the blank to size. This adds an additional tool to the equip
ment, as well as requiring a tool of greater accuracy.

You will appreciate that the matter of interchangeabilily is one of
great importance — first, because the parts must go together in the
assembly departments without any further fitting — and second,
the parts and pieces of apparatus shipped over the entire country
for repairs and maintenance must be exact duplicates of the old.

It costs more to make interchangeable parts than to make inaccu-
rate ones that are not always interchangeable, and the Planning
Kngineer can coniml liie lool and manufacturing costs very largeK'
by his judgment in liie selection of limits.

HolRI.V OlTPLT

rile I'l.innini; Engineer, in anahzing the wt)rk on a ,i;i\en \raT\ for
the ()i)erati(in^, machines and tools to be provided, from his experience
and training in the particular kind of work he is handling, is able
to establish .in expected hourly production for each operation he
handles. He is, of course, guided in this by his experience on similar
parts and h\ the speed of the machines selected for the operation.

The setting up of the expected output for assembling operations
is more difficult, but here also the special training and experience of
the engineer along that line of assembly work enable him to set up
an expected output which is approximately accurate. In some cases,
we go so far as to tear down and reassemble models of the apparatus
in order to ol)tain the necessary data.

The output per hour on each operation enables the engineer lo
com|)ule the nmnber of each kind of tool, including spares wliicii
must be built, lo [iroduce the retiuired rjuantity of each part. The
number of tools required is obviously dependent on the speed <>f the
operation, and here again you sec the efTect on tool costs if the engineer
fails to select the fastest machine suitable. When it is considered
that we have nearly Sli,()()(), ()()() invested in tools for the manufacture
of panel machine switching apparatus alone, it can be appreciated
wh.it pi, inning means lo us.

F.XGlXiiF.RIXu ril.WlXC, lOR M.IXCr.UIIKI- 555

I.Mlok CkAIUv

I'lif I'l.iiiniiiv; l-'.ni;iiii'rr. in addition lo fslahlisliiiij; tlu- \.diK's
.drt'iuK' iiu-ntioiH'd. l).i> also tlic rt-spoiisiliility of sclirlinR ihv grade of
lalior which is to In.- iisitl in iH-rforininj; tlio \arious opi-ratioiis. I)if-
ft-ri-nt nr.ides ha\i' lii't-n i-stalilislu-d for ini-ii and women, and eath
Kr.idi- rovers a sufficiently broad ranjje of rates to enalile us to hire
the einph>yees at the startinR rate of the grade and to advance them
in the v;ra<Ie as tliey l>econu- more proficient .\\u\ exjierienced.

I\ \\\ Maiikiai,

Ihe I'lanning Kngineer specifies the kind and amount of raw
material recjuired for each part including the scrap allowance. Me
also s[H'cities the form in which it shall be purchased — that is to say,
whether in nnl. tubing, and in the case of sheet stock w-hether in the
sli.ipe of sheets, strips, or rolls.

M AM 1- \( Tt RiN'd Layouts

The next step in preparing a piece of apparatus for manufacture
is the working up of detailed manufacturing layouts. These layouts
constitute the "sailing orders" for the shop, covering each operation
to be performed, how the work is to be done, the sequence of the
o[X'rations, the tools and machinery to be used, raw material and
quantity required, and the stock room to which the parts shall be
delivered upon completion.

These layouts are got out in the form of fluplicated sheets and a
complete layout for each part is sent to e\er\' department ha\'ing
work to perform.

Pir;( K Ratios

When all the preparation steps have been completed and after the
\arious ojK-rations have been tried out and are running in the operat-
ing departments on a satisfactory commercial basis, the Planning
Organization proceeds to establish piece rates on each ofieration.

The piece rates are established by the same organization of engineers
who plan the work, and the responsibility of seeing that the estimated
outputs are realized devolves upon this organization. Before pro-
ceeding with the studies invoked in establishing the piece rate, the
FManning Engineer checks back against the original planning data
and the manufacturing layout, and, in this way, ascertains the met]i(xl

556 nELL SYSTEM TECHSICAI. JOURXAL

as orifjinally laid out, together with the expected outputs. His task
then heconus one of seeing thai the expected output or better is
attained.

Tliis, in nian\- casi'S. iinolxes a very detailed lime and motion
stud\- of the elementar\- oi)erations necessary to complete the job in
order that it be brought to a high stale of efficiency. In cases where
the expected output cannot be realized by the original method, other
methods are worked out wherever possible to bring about the desired
result.

Just a word rigiil lure on our piece rate pf)lic>': when jiiece work
was introduced many years ago, the policy was established that
after a rale had been once issued it should not be cut unless a change
had been maile in the method of manufacture. In other words, we
take the stand that an issued rate is a contract which cannot be
revoked so long as the operation is done in the same manner as covered
by the piece rate card.

To satisfactorily carry out a policy of this kind, it is obvious that
our piece rate setting must be something more than mere stop watch
ob.servation. In order that piece rales are established which are
accurate and fair to both the employee and the Company, it is neces-
sary thai the engineers selling the rates be well versed in the class
of work being rated, and have a thorough knowledge of the amount
of wf)rk which can be consistently produced by the operators.

( )ur experience with the straight piece work form of incentive has
bet'ii \ery gratifying, and in our opinion this is very largely due to
the following three reasons:

isi. Our policy of not culling rates.

2nd. (Jur practice of making careful time studies in setting our
our rales.

Urd. Our guaranteeing the employee's day rale regardless of his
earnings on the piece rate.

The work of tin- I'laniiing Engineer is not coni|iietrd, lu)we\ir,
upon the establishment of the piece rale, since it still rrsts with him
to clear any difficulties the shop may experience due to any short-
comings of an\' of the |)lanning work.

if the raw material providetl will not satisfactorily produce the
parts, he is called upon either to add operations or to specify other
material; if the tools will not produce the parts to the required accu-
racy, or al the recjuired rate, he is called upon to have satisfacloiy
changes marie to the tools or to pro\ide new eciuipmenl

liNGINIiliKINC I'l.lXMXa /OA' M.IMI.K I IKL 5.v

In rasi' llu- oiKT.itors .irc iin.ihlf lo piiMliuc ^iilliciitil p. iris to
make satislaclorN' piivi- work t'arninns alter a roas()iial)U' Irial, the
Planning Kn>;iiH'i'r is called upon It) either demonstrate that satisfac-
tory earnings can lie made, or to increase the rate.

The I'lanniiij; ICngineer is also calle<l upon to assist in nvercnininv;
manufacturing ditliculties for which he is not directly responsible,
and a spx'cial unit has been set up to assist the shop in cases of this
kinil when difficulties are encountered.

From this, it can be seen that the Planning; iMiuiiuer has imi only
the responsibility of planning the work, but lie is also charKiil wiili
seeing to it that the plan works out.

t'osr Ri,i)i( HON W'liHK

There is still one more highi\' iniport.uii tumlion ptrlDinud li>
our Planning Organization, viz., Cost Retiuclion Work.

It might appear that after the careful thought already gisen to
the methcKls to be employed in producing a piece of apparatus, the
necessity for further study has been eliminated. This, howe\er, is
not the case, since in the original planning we must adhere closely to
methods and proce.sses that have been proved in, in order that the
prtxlucts may be prinluced on a specified date and at a prcdetenniiud
cost.

In other words, we cannot take any short cuts at this stage of the
work that we are not sure will work out successfully. However,
after the piece of apparatus is in production, we are in a position to
review the case and try out new ideas, improved methods, tools and
machinery, without jeopardizing pnxluction. Naturally, any im-
provements worked out successfulU- b\- the Cost Reduction Engineers
are later used by the regul.ir Planning Organization when applicable
on future work.

This cost reduction work is ha in lied on a strictly business basis,
i.e., the cost of the case is charged up against the savings effected
and our records show that the returns on this work are very high.

There is a typical illustration of a cost reduction case shown in
F"ig. 6. This is the base for the sub set housing on which the apparatus
is mounted. The old design is shown at the left. There were three
separate pieces which had to be assembled together. Part B was
riveted to the base A- at c, c to form the ears which stand at right
angles to the base. Part D was assembled to the base A with two
machine screws, E, E. The design was changed at the suggestion of

558 BELL SYSTEM TECHNICAL JOURNAL

the manufacturing ilepartnicnl to make the part in one piece. It liad
previously been thought too conipHcated to combine ail these opera-
tions in one part, hut the tools were successfully developed, and the
sa\ing on this particular job amounted to something like one hundred
thousand dollars a \ear, or about ten cents a piece.

I fKii.iN.M. l)i>ii,N .Xdoi'TED Design

(."onsists of three individual parts, re- One piece construction. Same .\o. of

quires assenil)ly with rivets and 0|)cralions retiuired to make as lx)dy

wreus of old design. No brackets required.

Kig. 6 — Sub Set Base

Tilt; 1'i:rs()nni-:i,

.So l.ir llie job we have to do and how we do it has only been dealt
with, and the (lualiticalions and tr.iining of the personnel required
ha\'e ntit been mentioned.

Our I'l.inning ( )rg.inizali()n is l.iid oiii in .i manner similar in our
shop d(p.irlmeni>; tii.ii i>. ilu- pi.inniiii; nf tlic x.irious manufacturing

i.xGiNciiRi.w; /•/.. /.v.\7.V(; iiu< M.ixrr.icrrhT. 559

opt-rations is divided into class of work or opi-rations and not l>y
class of product, each class hciiig haiidlcti !)>• a ^roiip of ]>lai)iiinK
fnniiicers in ch.irj^c of an cx(htI thoroiiRlily familiar with the line of
nianiifaclurc he handles. In this ni. inner each group performs some
different line of planning and handles .ill the wirious parts tha<
re(|uire that particular operation.

The personnel of our I'lanninj; Organization, exclusi\e of depart-
ment supervisors and clerks, consists of 86 college graduates, lf)8
trained men who ha\e come to this organization from our shop de])art-
ments, or who have had experience in other shops, and 38 men who
are neither college graduates nor shop men. The last group of men
are mostly those of high school etlucation who have been trained in
our line of work.

The requirements ot the I'laniiing lliigineer on whom tiie responsi-
bility rests for the successful manufacture of our apparatus are
quite extensive. He must first have the ability to plan the manu-
facture of the apparatus in the most economical manner consistent
with the quantity and quality desired and this, of course, cannot
successfully be done without a thorough knowledge of the methods
and practices necessary in carrying on manufacturing activities
along one or more definite lines. He must have a large measure of
foresight, thereby reducing to a minimum the difficulties that are
bound to occur when the manufacture of a new or changed [)iece of
apparatus is started.

Furthermore, he must make a study of the design of the apparatus
under consideration to determine if there are features of it which
present manufacturing difficulties either from a tool, assembly, or
adjustment standpoint. This part of our work in\olves a discu.ssion
of the manufacturing problems on a new design with the Engineering
Organization and the men who handle this work must be able to express
themselves in a clear and concise manner to insure that proper con-
sideration is given to the manufacturing suggestions.

It goes without saying that the men who fit best into this organi-
zation are those who ha\e had the benefit of an engineering education,
preferably specializing on manufacturing methods.

We have, as you will ha\'e noted, a large number of i)lanning
engineers who have had actual shop experience either with us or in
other manufacturing plants, and little or no technical education
before working in the shops.

It is noticeable that these men, almost without exception, ha\e
realized their handicap due to the lack of a technical education and
have either taken advantage of our schools or school work outside.

360 lU-.I.I. SYSir.M Tl'.CllMCAI. JOrRXAL

As stiitt'd prc\ iousK', wc ha\e tliri-o main sources of supjiK' for
the men making up out Planning Organization: first, the Engineering
Institutions; second, shop men who ha\c the experience anci have to
some degree educated themseKes in engineering; and third, high
school graduates whom we have trained.

Such a combination of trained men makes a strong organization in
which the man of superior education and the practical man are mu-
tualK' helpful to each other in the successtul working out of our
manufacturing problems.

Irregularities in Loaded Telephone Circuits

By GEORGE CRISSON

Synopsis: The development of lonp distance telephone transmission
has made the (|iiestion of line irregularities a matter of great im|«)rtanre
lieeaiise of their harmful effect in prodiicinR echo currents anil causing ^
the re(H"aters to sing.

The structure of coil-loaded circuits |H'rmils the calcul.ilion of the
prolialiility of obtaining an assigned accuracy of balance between line and
network when certain <lata are known or assumed regarding the accuracy
of liKtding coil inductance and si-ction capacity.

Formulae are given and the results of calculations compared with nuasure-
ments made on circuits of known accuracy of loading.

Introdiction

Tld'i application of ri-|H"atC'rs lo telephone' cimiils in which the
speech currents in the two directions of transmission pass through
the siinic electrical path, has caused considerable emphasis to he
placed on the matter of making the telephone circuits as free as
possible from irregularities. This paper aims to present the theory
of the relation between the irregularities in coil loaded lines and the
effects resulting therefrom, which have an important bearing upon
the operation of two-way telephone repeaters.

The idea of applying the theory of probability to the problem of
sutnming up the effects of many small line irregularities was first
suggested in 1912 by Mr. John Mills. The effect upon repeater
operation of impedance unbalance had been mathematically analyzed
by Dr. G. A. Campbell; and the effect upon itnpedance of a single
irregularity of any type had been in\estigated by Mr. R. .S. Hoyt.
Using a probability relationship which was pointed out In- Mr. \'.. C
Molina, Mr. Mills developed a formula which gives the average or
probable impedance departure in terms of average or probable irregu-
larities in inductance or capacity, which served at the time of the
engineering of the transcontinental line (1913-14) and for some
years after.

With the rapid growth of repeatered circuits in cable it became
necessary to calculate what fractif)n of a large number of essentially
similar lines would give a definite impedance unbalance at a given
frequency. The necessiiry mathematical work to indicate the con-
ditions for a large group of similar lines was recently carried out
independently by Messrs. H. Nyquist and R. .S. Hoyt.

The theory which has thus been evolved over a period of \cars is
now presented in a manner which it is hf)ped will be found relali\ely
simple and useful. \'arious charts are given which should be of

561

562 lUll.L SYSTEM TIICIIXICAL JOURNAL

material aid in the application of the theory. There are also given
the results of some experiments made on cable circuits in which
comparison is made between the impedance departures of the circuits
as obtained by direct measurement with the departures as computed
from data coxering the indi\ifhiai irreiiiilaritics. These inipt'danre

G. E

Kit;. 1

departures are expressed as "return losses," the meaning of which
is explained below. The agreement is shown to be dose enough to
constitute a gootl check as to the correrlness of the iinderKing tiu'ory.

M.\GNITUDE OF RKKI.KCTIiU CURRKNT

In Fig. 1, are shown three regular ' telephone lines of the .same
type i)eginning at a certain point A. The first line Li pa.sses througli
anotiier point B and continues on to infinit\\ The second line L-j
terminates at B where it is connected t<i an impedance Zt whicii
differs from the characteristic impedance Z„ of the three lines, thus
constituting an irregular termination. The third line L3 also termi-
nates at B where it is connected to an impedance Z/ and a generator
G of zero impedance whose ])in-pose will l)e described later. At the
sending end A each line is pro\ided with one of three identical genera-
tors, G\, G>, Ci, ha\ing an impedance e(|ual to Zg the characteristic
impedance of the line. The internal voltages of these generators
are all e()ual and represented b\- li. The generator Gi impresses a

' In this paper the term "reRiilar" iinpliis tliat a telephone line is free from elei-
triral irregularities.

//>/v7 i,( / ./A7/// ^ i\ III. Win 1 1 i.i.riioxE ciRcnrs 5w

voltaic Ro=\ E iijK)n the seiuliiij; end of tlu- line L\ and causes a
current /,, to flow into it. Tlie voltage and current waves are propa-
gated rejiularly o\er the hne to the point B wliere lliey set up a poten-
tial dirt'erence R\ between the conductors and cause a current I\ to
How. fii anil I\ are smaller in magnitude and later in phase than
Ro and h l>ecause of the losses and finite velocity of transniissiiiir
of the line Li. Thcst' f|uantities ha\e the rcl.ition

En Ex , .

/„ /, ^'' ^^'

since the line is regular.

In the second line L; a different set of conditions exists. In this
case, the voltajje E- and the current h produced at B by the generator
have the relation

f-=Z,. (2)

When the e.m.f. of the generator G is zero, the conditions in the
third line Lj are the same as in La but by adjusting the phase and
magnitude of the e.m.f. of this generator the current in the terminal
impedance Zt can be made ecjual to I\ and the drop across this im-
pedance l)ecf)mes

£3 = /.Z,. (3)

Tnder these conditions the current /i flows at the end of the line
Li and the potential difference £i exists between the conductors at
this point. The line Lj is then in the same condition as the line L\
between the points A and B. When the waves arrive at B over the
line Z-3 the generator boosts or depresses the voltage at the terminus
of the line by just the amount necessary to cause the terminal ap-
paratus to take the desired current. Then the e.m.f. of the generator
G is

Ec = Ei-E,. (4)

Removing the e.m.f. of the generator G makes the conditions in
line Lj identical with the conditions in Lj, but removing this e.m.f.
is the same thing as introducing another e.m.f. —Ec in series with the
generator which annuls its e.m.f. Ec.. This e.m.f. —Eg causes a
current /j to flow back into the line

En

^'^-z;+zr (^^

.Substituting from equations (1), (.3) and (4) abo%-e

5&4

BELL SYSTEM TECHNICAL JOURNAL

That is, the effect of connecting an impedance Z, to the end of a
line of characteristic impedance Z© is to return toward the source a

7 7

current whose value is ° ' times the current that would exist at
Zo+Z/

the terminus if the line were regularly terminated. The ratio between

— TTOT' i-^ror^

3=

— nm^-' — 'im^-
oouoooooooooo^n

Fig. 2

the rc'tk'Ctcd and ihf incident current is known as ihc "rcllcclicjn
coefficient," the value of which is expressed as follows:

/. Zo+z:

(7)

This ratio can also be expressed in transmission units (TU). When
expressed in TIT this relation will be referred to in this paper as the
"transmission loss of the returned current," or, briefly, as the "return
loss."

If a condition occurs in a line which causes the impedance at any
point to differ from the characteristic impedance it has the same effect
as an irres^ular termination.

Return Loss .\t .\ Repis.mkr Duk td .\ .Singlk Irki;gularity

Fig. 2 shows a No. 21-type repeater connected between a line and
a network whose impedance is exactly equal to the characteristic
impedance Zo of the line. If the line is perfectly regular the repeater
will be perfectly balanced and the gain can be increased indefinitely
witht)ut causing the repeater to sing.

Assume now that the line is terminateil by some apparatus having
an impedance Z» at a distance from the repeater such that the trans-
mission loss of the intervening line is 7" TU. If a wave of current
having a certain magnitude leaves the repealer, it is reduced in
strength by T TU when it reaches the terminus. Of this current, a
certain amount is transmitted back toward the re|)eater, suffering a

INRF.CLLIRITIES !N LOADED TELEPHONE CIRCUITS 565

further loss of 7'TU on the way; consequently, the relation expressed
in Tl' between the strength of the currents leaving and returning
to the re^HMter, that is, the return loss at the repealer, is given by
the eciuation

If the gain of the repeater, expressed in Tl', is ecjual to or greater
than 5 the repeater will sing provided the returning current has the
correct phase relation to reinforce the original wave. For this reason
the term "singing point" has frequently been applied to the quantity
5, which is called returned loss in this paper.

If the line is shortened until the impedance Zi is connected directly
to the repeater terminals, the transmission loss 7' between the repeater
and the irregularit\- is reduced to zero and the return loss becomes

5 = 20 1og,„f^'. (9)

Return Loss of Irregular Lines

In practice, lines are never perfectly regular. Not only is it im-
practicable to build apparatus which would form a perfectly regular
termination for a line, but there are numerous causes of irregularity
in the lines themselves, each one of which is capable of reflecting a
portion of the waves which traverse the line. These irregularities
can be kept smaller than any specified amount if sufficient care is
used in building and maintaining the line but they cannot be entirely
eliminated; consequently, if a length of actual line is terminated
regularly by a network of impedance Zo, the return loss will be high
if the line is carefully built and low if it contains large irregularities.
The return loss of such a line, when terminated regularly by a network
is a measure of the quality of the line from the standpoint of repeater
performance. In measuring the return loss of a line it is necessary
that a rather long section of the line be available so as to include
all irregularities near enough to have an appreciable effect upon the
result. If the section measured is too short, the result will be too
high because only a few irregularities will be included.

Calculation of the Return Loss of Coil Lo.^ded Lines

Owing to the facts that the inductance of coil loaded lines is con-
centrated principally in the loading coils and the capacity is divided
into elements of finite size by the loading coils and, further, that the

565 BELL SYSTEM TECHSICAL JOURNAL

electrical irregularities are due principally to the deviations of the
inductance of the coils and the capacity of the sections from their
a\erage values for the line, it is possible to calculate by a fairly simple
method the \alue of the return loss of a coil loaded line if the repre-
sentati\e \alues of these deviations and the electrical properties of
the line are known or assumed.

Since the return loss depends upon the accidental combination of
a large number of unbalance currents there will not be one definite
value applying to all circuits, but an application of the theory of
prot)abilities makes it possible to compute what return loss will
probably be surpassed by any assigned fraction of a large group of
lines having the given de\'iations.

The method of calculating the return loss of coil loaded lines will
now be described. The symbols used in this description and their
meanings are given in the following table:

TABLE I

A = Attenuation Factor per Loading Section = Ratio of the Current Leaving a

Loading Section to the Current Entering it.
C = Normal Capacity per Loading Section in Farads.
F = Fraction of a Large Group of Lines.
/ =Any Frequency for which a Return Loss is to be Found.

/, = -^^-^ = Critical or Cutoff Frequency of the Line.
■K\LC

He = r<epresentative' Deviation of the Capacity of Loading Sections.

he = Deviation of the Capacity of a Particular Loading Section.
Hi, =Representative= Deviation of the Inductance of Loading Coils.

hi, = Deviation of the Inductance of a Particular Loading Coil.

// = V//c+-''Z = Representative' Combined Deviation.

/. = Current Entering the Line.

/' = Representative- Total In-Phase Returned Current at the Sending End.

/" = Representative' Total Quadrature Returned Current at the Sending End.

/,■ = Value of Returned Current which will be Exceeded in a -Specified Fraction F
of a Large Group of Lines.

i' = Total In-Phase Current at the Sending End of the Line.

i" = Total Quadrature Current at the Sending End of the Line.

«i. U, it, - - - '■ = Currents Returned from the 1, 2, 3, and Hth Irregularities.

«i'. »V. «i'i '»' = In-Phase Components of ii, i-, I'j, - - - i„

ii", it", ii", '," = Quadrature Com|X)nents of ii, Vg, I3, - - - J,

k ='\ 7; = Nominal Characteristic Impedance of the Line.

L = Normal Inductance of a Loading Coil.

n = Number of Irregularities.

P = Probability Function for the Absolute \alue of the Total Returned Current

at the Sending End.
p' = Probabilitv Function of the Total In-Phasc Returned Current.

/A'A7;(;r/../A'////i.v i\ i.o.ini.n i ii.iriioM-: iiNiiirs .^.7

Kc = Kcpri'sont.itivi" Ketlcrtion Cocrticicnt at C'.ipaiity Irri-nularitifs.
/ft - Rrpri'sentative- KflliTtion rofftiiiont at IiKliictance Irrt-giilarilirs.

r,- "• Ki-llt'ition C'lH-tliilcnl .>t a C'apaiity Irrouularily.

fj. = Ri-lliHtion l"(K.'lVuit'nt at an Indiut.iiKf Irri-i;iil,irit\ .
'i. r:. '1. ■ - - r, = RfUcction CiH-nii'ioiit at the 1, 1, .<,--- Mill Irritjularilics

.V ""Return Loss. Infinite Line.

,V, -Return Loss, Finite Line.

Sf - .Attenuation Function.

Sy = Distriliution Function.

Sh = Irregularity Function.

.V, =F"re<|uency Function.

7" = Transmission Loss in a Finite Line.
Hi. O;. Gj, - - - - O, = I'hasc .Angles of the Currents at the .Sending Knd Returned by
the 1, 2, 3, - - - nth Irregularities.

=/./.■

Rkflixtio.n .\r .\ Con, lKRi;(iLi..\RiTv

If a loading coil has too much or too little inductance, the effect
is the same as if a small inductance IilL had been added to or taken
away from the coil. The reactance of this increment is 2irfLhi..
The additional reactance has the same effect wherever it may occur
in the load but it is somewhat simpler to assume that the increment
is introduced at mid-coil. Within the useful range of telephonic
frequencies, the mid-coil impedance of a loaded line is gi\en closely
by the expression k\/l—U'-.

In equation (7) Zg — Zt corresponds to 2irfLliL while Zo+Zi is
approximateK' equal to 2k-\/\—u'- when the irregularity is small,
conseciuenth' :

^^^'^ (10)

and, substituting for /and k their cciuivalents obtained from relations
given in Table 1,

n^K'-"^.,- (11)

•V l—w-

ReFLECTION at .V Si'.U IN(i iKRKdfLARirV

If a loading section has too much or too little capacity, the effect,
neglecting conductor resistance, is the same as if a small bridged
capacity hcC were added to or removed from the line. The effect

- The "representative" deviation or current is an index of the magnitude of the
deviation or current that may l)e e.xpected in accordance with the laws of the
distribution of errors. It cotresfonds to the root-mean-square error. It must
not be confused with the "effective" or r.m.s. value of a particular alternating cur-
rent. The meaning of the term as used here is more completely explained in
the paragraph following equation (24 1.

568 BELL SYSTEM TECHNICAL JOURNAL

is the same for any point in the section, but it is somewhat simpler
to assume that the additional capacity is applied at mid-section.

The reactance of the added capacity is - and the luid-stTiioii

2jr//icC

k
impedance is, closely, /

When the bridged reactance is large compared with the line im-
pedance, the reflection coefficient r^ is given closely by the equation

k

1

''c = 5 ^ (12)

2TTfhcC
from which, substituting the values of/ and k as before

which is identical in form with equation (11) above.

Approximations Made in Deriving rz, and Rc

The expressions for the mid-coil and mid-section impedances used
above in deriving equations (10) and (12) are simple approximations
which take no account of the effects of the resistance of the line
conductors and loading coils, leakage between conductors or dis-
tributed inductance. The errors due to these effects are negligible
in the important parts of the frequency range involved in telephone
transmission when the types of loading and sizes of conductors now
commonly used are considered. The errors due to these causes tend
to increase for frequencies which are very low or which approach the
cutoff frequency. For accurate calculations relating to very light
loading applied to high resistance conductors it would be desirable
to take into account the effects of resistance. Because the use of
the precise expressions would greatly com[)licate this discussion
and would probably serve no very useful pur|)ose at this time, the
approxiinations given above are used.

Current Retirnkd to the .Sknuini; Knd of the I.ine

Consider first a line having only one kind of irregularity' as, for
example, one in which only the loading coils are assumed to vary
from their normal values. If a current h enters such a line, a current

iRh'r.ari..iRmi.s /.v i.o.inr.n rp.i.r.riio.xr. cinccits 5r.o

ii is rt'tiiriU'<l to llii- sending t-iul from llii' first irrc^iil.irit\- (assumc<l
1(1 Ik- \iT\- iK-ar ilu- si'iidinjj i-iul)

«i = rjo (14)

a sfcoiul ciirreiU

i, = /lVi/a (15)

is returned from the IrreKuIarity located al a distance of one loading
section away from the sending end, since the current is reduced by
the factor .4 in going to the irregularity and again in returning.
SimilarK', a current

i„ = .42(— 'V„/„ (16)

i-> returned from the wth irregularity.

The tirst current will return to the sending end with a certain
phase angle Oi with respect to the initial current, the second with a
phase angle H., etc. Kach returned current ma%- be resolved into
two components, one in phase with tiie initial current and one in
quadrature.

The in-phase components of the currents are then:

i\' =/o''i cos 9i from the first irregularity. (17)

ii =IurtA- cos 82 from the second irregularity. (18)

/V = /or 3-4* cos 03 from the third irregularity. (19)

iV = /oN/l^'"~" cos e„ from the «th irregularity. (20)

and the quadrature components are:

ii"=/ori sin 61 from the first irregularity. (21)

i«" =IoriA' sin 83 from the second irregularity. (22)

«3"=/orj-4* sin 83 from the third irregularity. (23)

in" = lornA^'-"'^^ sin 8„ frotii the nth irregularity. (24)

Now the deviations of the inductance (and capacity) resemble the
errors of measurement discussed in nvdny text books dealing with the
precision of measurement, consequently, they can be studied and
their effects combined by the same mathematical law.

Kxamination of measurements of the inductance of large numbers
of loading coils and the capacities of the pairs and phantoms in many
reels of cable ha\e shown that the most reasonable assumption is
that the deviations of inductance and capacity follow the "normal"
law of the distribution of errors.

The deviation at each irregularity is not known but it is possible
to derive from the measurements of the inductance of large numbers
of loading coils (and the capacity of man>- lengths of cable) representa-

570 nr.I.L SYSTEM TECHXIC.IL JOURh'AL

tive values for these deviations similar to liie "mean error." Because
of the wa\- in which the eflfects of irregularities combine, this repre-
sentative deviation is taken as the square root of the mean of the square^.
of the deviations (r.m.s. deviation) of the indix'idual coils. If the
average deviation of a large group of coils is known, but the individual
deviations are not, it may be multiplied by 1.253.'? to obtain the
representative deviation on the assumpiioii that the dexiations
follow the normal law of errors.

If then the representative deviation IIi, is substituted for the par-
licuiar deviatinn /;/, in equation (11), we obtain the representative
retk'ctioii coeHuieiit

RL = nL ,^^. (25)

Now in the usual case where no effort is made to select the loading
coils and so obtain a special distribution of the deviations the repre-
sentative deviation and the representative reflection coefficient are
the same for each coil. Substituting Rl for r\. r<>, etc., in equations
(17) to (24) each equation gives the representative value, at the
sending end of the line, for the current reflectetl from the correspond-
ing irregularity.

According to liie laws for tiie coiiil)iiiali(>u of (k-viaiinns wiiirii are
demonstrated in treatises dealing with precision of measurements
the representative \alue of the current due to all the irregularities
would be the square root of the sum of the squares of the representa-
tive values of the different currents taken separately, consequently
I he representative in-phase current is

/' = /„/?/. ^(cos'e^+^'cos-es+^'cos'eaH /l^<"-'>cos2e„) (26)

and the representative quadrature current is

/" = /,J?;,\/(sin=or-H74\sin-eo + A''sm=e'3+ ^'("-I'sin^e,,)'. (27)

ii\- assuming liiat the re|)resentali\e in-pliase and quadrature
currents are etiual the following steps can be greatl>' simplified. In
view of the varying effects of frequency, distance from the sending
end and nature of the irregularity upon the phase relations iliis
appears to l)e a justifiable assumption, so combining 7' and 1" in
(Uiafiralure,

1=1 =\\ 2-=.

y/2 Vl+A*+A*-\- yl*(«-') (28)

i/^Hi.ci i..ih!iiii:s i.\ iAKii>i:i) lEi.i.riiosr. cum its 57i

I'Or a tiniif iuiiiiIht of irri'niil.iiities, tli.ii is .1 Imilf line tciiuin.ilcd
In a ihtIciI nciwork jiisl Ik'xoiuI llu' «ll\ coil;

which is obtained h\ siiiuniin^ up llu- sirics of trrms iiiidfr tlir radical
in i't|uation VIS).

I'or an inliniii-l\ loiiv; lino .1" becomes zero since -4 <1 and

/' =/"=^i'^\l A.^. (30)

V2^1-^

/' corri'spnnds to the r.ni.s. ernir in tiic ordinary thct)r>' of iTrors,
consf(|iK'ntly the prob.ibilily function for the disiriliution of tiie in-
phase currents is :

fhanijini; the accents, this ecjuation .dso applii's to the quadrature
components.

The probability that the in-phase current lies between two near
b\- values i' and i'+di' is then equal to p' di' and the probability
that the quadrature component also lies between two values i" and
i"+di" at the same time is p'di'Xp"di". Transferring to polar
coordinates,' the probability that the total returni-d current will be
between a value «'= vi'^-1-/"- and a slightly different \alue I'+rf/ and
also have a phase angle between () and 0+dQ is

P = .y-r,ie'^''dide. (32)

Integrating with respect to the phase angle O between 0 and 27r
to find the probability of obtaining a current between ( and i + di
of any pf)ssible phase displacement

/• = ,„ / te 2/1

di. (33)

integrating between /,-. and intuiit\- gi\es llie prolialiilit\- that tiie
total returneil current will exceed the value //..

F^e'^VK (34)

' Kor a more complete description of this 0|)eration, see "Advanced Calculus,"
liy K. \\. Wilson, page .?')() et se(|.

572 nill.I. SYSTEM TP.CIIXIC.U. JOrRXAL

In a large number of lines, F is the fraction of ilic whole group
which will ha\e a return current in excess of Ir-

From the definition of the transmission unit liu- riiurn loss of the
line expressed in TU, is given by the expression

5 = 20 log.o p = -20 log.o'p (35)

from which

7^=72,10-10. (36)

Substituting in (34)

7=- = e-2r3'"
Taking logarithms lo the base e and uansjMtsing

(37)

'I'aking logarillims to the liase 10

5 27'=

10-io = --^log,F. (38)

5= 10 log. 1^27'= log.)]- (=^9)

Sul)siituiing the \alue of 1'-^, from ctiualion (30) for I'

5=10 1og..pi?rX,JJ (40)

and tile wihic of Ri, from cfiuation (2o)

5=101og,o ^Z^"«'^^^^~"'^'^^,^g^l . (41)

By a similar process of reasoning it is e\ident that if the line contains
capacity de\iations only, the return loss is gi\'en by this same ex-
pression with lie sulistilulcd for ///. and if both types of irregularity
occur the rcprcscnlal i\c dc\iali(in is

H=VHi+iri

when He includes the effect of spacing irregularities as well as capacity
deviations in the cable. The foregoing exjiression can, for con-
\cnic-ii(f, be put in lln> form

S = Sn + Su, + SF-SA (42)

ih:h:iu:ri..ii<iiifis in loadi-.d ir.i.r.riioxii circi'its 57.?

ill which iMch irrin ilcpriids upon only oiii' iiKh'pcnilrnl \.iri.il)k-
.mil in whicli I hi' syinliols \\ii\v llu- following mt-anings:

^u = Irregularit\- fiinriion =20 logio^^ (4'S)

7/
51,. = Frequcn( > limrti(>n=2() logio^

(44)

5f = Distribution funrtion = 10 logio, 1 (45)

log.^

Sa = Attenuation function = 10 logui, t^ (46)

Meaning ok EguATioN (42)

To inulerstand more clearly the meaning of equation (42) imagint-
that a large number of circuits of the same type and gauge are to be
built in accordance with the same specifications so that the repre-
sentative (r.m.s.) deviation including all causes has the same value
// for each circuit. Further, imagine that the value of S has been
calculated by formula (42) using a particular frequency / and a con-
venient fraction F. It is to be e.\pected that when the circuits have
been built and their return losses measured at the given frequency /
the fraction F of the whole group will have return losses lower than
5 and the rest will have higher return losses.

In discussing expected results it is sometimes preferable to state
the fraction 1 — F of the circuits whose return losses will be greater
than the assigned value rather than the fraction F whose return
losses will be lower. This is done in Figs. 9 to 14 described below.

Location of rnii First Ikkkgli-akitv

In equations (14), (15) and (16) and all the equations which depend
upon them it was assumed that the first irregularity occurs at the
sending end of the line. Two other assumptions are equally plausi-
ble and might under some circumstances be preferable. These are
that the first irregularity occurs (a) at one-half section from the
end or (b) at a full section. In the first case (a) the current returned
to the sending end from each irregularity will be reduced by the
factor A and in the second (b) by the factor A-, that is the return
loss given by equation (42) should be increased by (a) the amount
of the transmission loss in one loading section or (b) twice the amount
of the transmission loss in one loading section respectively.

574 BEI.L SVSTF.M TECIISICAI. JOURNAL

RkTLKN I.OSSl.S ()!■ SllOKT l.iNi;s

When a line is short and reijularly terminated the returned current
will be somewhat less than if it extends to infinity with irregularities
and consequently the return loss will be higher. I'rom equations (29)

and (80), the returned current is lowered in the ratio , = s/X—A*"
by limiting the line to n sections; consequently

Sn = 5+ {S„ - 5) = .S+ 10 \ogyoY-A^" ^'*'^^

in which

5„-5= 10 login, \.„ (48)

is the increase in return loss.

Since the transmission loss in n sections of the line is

y=20 1og,„J„ (49)

it is easily seen th.it the increase of return loss can be expressed as a
function nf this loss, 'transposing (49) and substituting in (48)

.S-„-.S=10 1og,„^^|_ ^^ _j,. ^^^^

|_log ,02,J

("lI.\KTS

The process of computing return losses can be greatly shortened
Ijy using the graphs of equations (43), (44), (45), (46), and (50) to
obtain the values of the various functions. The accompanying
I-igs. '.i to 8, inclusive, have been prepared to illustrate these graphs
and for use in rough calculations.

Sii may be obtained from any (able or ch.ut giving the relation
between TU and current ratio by using // like a current ratio. Fig. 3
is a chart drawn es[iecialK' for this jjurpose. For values of // lying
between 0.1 and (1.(11 look up a point on the curve corresponding to
10// and add 20 11 in ihc corresponding value of Su, for values of
// lying between 0.01 and 0.001 look up a point corresponding to
100// and add 40 TT to the value of 5//, and so forth.

Figs. 4, 5, G, and 7 are curves giving the relations between the
functions Sv, Sp and Sa, respectively, and the quantities upon which

Irpegularitv Function -Tu
SH-20LoqoX

Ml

^\

' ' ' 1 '

S,

"s

\

s

- XXI Hi

\

\

\,

^

-^ 4-IU-"

NXi , :

_ ii. -....-

' .-v .

n

\

H
Kig. 3

- 2

\! 1 1 1 1 M

\

\; Frequency Function -TU
—X — s„'20ijog« ^'^^•^

—

\ ' '

A 1

i \ j

i \l

i \

1

V

\ 1 ! 1

\ i

|\

i : 6 r\ 8 .9 ^X)

W '

''■.,

1 \

' ' ' 1

\

1 1 i <

\

Fig. 4

ISTRIBUTtON FUNCTION-Tl

SF=-iOLog„Loge^

D

J

30
28
26
24
2 22
. 20

16
U
12
10

6
^
2
0
2-
4
6

d
in

i^

~7-

<

-'

X)l 1

pi

T

F

' —

-"

T

-=J

=:

^ "

1

dd

-

:i

1

-1-^ 1

= = =f

Fig. 5

Attenuation Function — TU
In terms of loss per loading section

5^ = 10 1ogio YZTJi'

A = Attenuation factor per loading section,

L = 20 logio -2-= loss per loading section in TU

26

\,

N

\

'N

N

\

N

\

!0t

\,

^^

\

s

\

■n

^

-i~

.6 .6
TU

Fig. 6

iRKr.a('[..tRiiir.s ix i.o.idi-d rr.i.r.ftioxr. c/za r/r.v 577

r.uh <le|x»n(ls plotted from equations (41). (1')) ;mi<I (Hi). Ilu-se
are all positive except as indicated !)%■ the winil "Subir.ui" oti ilic
diagrams.

A simple method for cxlcndiiii; ilie cnrNe of i'ii;. "> is as follows:
(a) ch(H>se a point on the curve within 3 TV of the lower end, (I))
subtract alxtut '.i TU (accurately, 10 logio 2) from the value of .S'/.- .
for this |H)int, and (c) square the value of F for this point. Tlic
results obtained for (b) and (c) are the coorflinates of another |)oiiii
on the extension of the cur\'c.

Fig. 6 gives the relation between .S',i .iiul the transmission loss jier
loading section. On account of the wide use of (),000 ft. spacing the
curves of Fig. 7 are plotted to give the relation between Sa and the
transmission loss per mile for (l.OOO fi. spacing which is usualK- a
more conxenient arrangemeni.

P"ig. 8 gives the amount, S„ — .S, 1)\- which the return loss of a
regularly terminated line of finite length (w sections) is greater than
that of an infinite line as a function of the transmission loss of the
finite line. This was calculated by formula (oO).

C.\Lcui..\TioN <)!•• Return Loss

The process of finding the return loss by means of the curves is as
follows:

(1) Determine the value of IIl. the representative deviation of the
loading coils, and lie, the representative deviation of the capacity
of the loading sections. These depend upon the variations allowed
in the specifications for loading coils and cable and upon the care
with which the line is built. Calculate n=\/Hi+IIi:, the repre-
sentative combined deviation of the section. Look up the number
i>f TV corresponding to // in any suitable table or chart, such as
l"ig. 3, to find Sh.

(2) Assume the frequency, /, to be considered. Calculate w= ^
and look up the corresponding value of Sw on Fig. 4.

(3) Assume a \-alue of F and look up the corresponding value of
Sp on Fig. 5.

(4) Look up the \alue of Sa on Fig. 7, corresponding to the trans-
mission loss per mile of the circuit at the frequency / if the coils are
spaced (5,000 feet (L13G miles) apart, or calculate the loss per section
and look up Sa on Fig. 6, if some other spacing is used.

(5) Calculate .S = 5//-f5„+5F-54.

Atte.vuation Fun'ction — TU

In terms of loss per mile of the circuit
length of loading section 6000 ft.

>

s.

\

\

\

X

•^

\

""^^v

lili

io___

\

s

\

\

\

\

kss

■^eciiiia.

^ 12

■A '0

8
6

2

0

.1 .2 .3 .4 .5 .6 .7 .8 9 i.u
Loss per Mile TU

FiK- 7
Increase of the return loss when thi' line is limited to ti sections

I '2

'd 1.0

.8
.6

I

4

I'ig. tt

ii<i':F.Gii..iHiTir:s ix loaded tei.i-.puone circuits 579

(ti) If tlu' rt'tiirn loss of a tiiiitc U-iikIIi of line i^ dcsiri'd (Ictcrmiiic
tlic transmission loss of this lentil anil look up tlu- rorn-spoiulinjj
value of S^ — S on l"ig. S. Add this amount to the \alue of >S found
in paragraph (.M.

KXAMI'I.IC

As an example to illustrate the application of these methods let
us calculate a return loss at 1,000 cycles for No. l!)-H-174-()3 * side
circuits such that 90 per cent, of the circuits may be expected to
have a higher value and only 10 per cent, to fail liclow it. The neces-
sary data are given in Table II, below.

(1) //=V0.0O62=+0.01292+0.0O452 = 0.0150.

Fig. 3 gives 36.5 TV as the corresponding value of Sh-

(2) At 1,000 cycles 74'= ^^^=0.356.

^olO

Fig. 4 gives 8.4 TU as the corresponding value of 5a,.

(3) Since 90 per cent, of the finished lines are to ha\e return losses
greater than S and 10 per cent, less F = 0. 1 and f'ig. o gives —3.7
TU as the corresponding value of Sf-

(4) The transmission loss per mile is 0.274. Since the coils are
spaced 0,000 feet apart. Fig. 7 gives 8.7 TU as the value of Sa- This
same value would be obtained less directly by calculating the loss

per loading section, 0.274 X vxs?. =0.311 and using Fig. 6. The latter
o2o0

method is used when the spacing is different from 6,000 feet.

(5) Using equation (42)

S = Su + S^-\-Sf-Sa =36.5+8.4-3.7-8.7 = 32.5 TU.

This will l)e found to agree with the 90 per cent, point on the smooth
curve plotted in Fig. 10 which is described below.

(6) In case it is desired find the return loss of a length of this line
having a transmission loss of. for example, 6 TU instead of the return
loss of the infinite line. Fig. 8 gives S» — 5 = 0.3 from which

5„ =32.5+0.3 = 32.8 TU.

Determin.vtion of Toler-vhle Deviations

To determine the deviations which correspond to an assigned value
of the return loss find values of S^, Sf and Sa as in paragraphs (2),

•In accordance with the practices of the Bell System, this notation indicates a
phantom group of .\o. 19 B. & S. conductors in a cable with loading coils spaced
6,000 feet apart, the side circuit coils having 174 millihenrys inductance and the
phantom coils 63 millihenrys.

580 BELL SYSTEM TECHNICAL JOURNAL

(3) and (4) above and substitute in formula (42) to find the value of 5//.
This with a table or chart of TU and current ratio gives the value of
H. Limits can then be imposed on the loading coil inductances and
section capacities that will insure that the representative deviation
will i^dt exceed the \alue // so found.

Comparison of Different Types of Circuits

These formulae are useful in comparing the return losses to be
expected in various types of circuits which are built with the same
accuracy in the matters of coil inductance and section capacity. In
such cases it is merely necessary to calculate the quantity Sy, — SA
for each circuit and take the difference.

E.X AMPLE

As an example compare the No. 19-H- 174-63 side circuits worked
out above with No. 16-H-44-S * circuits at 1,000 cycles. Since the
deviations and the fraction F are the same only Sw and Sa need be
considered. For the No. l(5-gauge circuit /c = 5560 and the loss in
TU per mile is 0.236. From these figures:

Gauge of Line No. 19 No. 16

1000

5„ TU

0.356

0.18

8.4

14.8

5.4 TU

8.7

9.4

5:.-5.4TU

-0.3

5.4

These figures show that the return loss of the No. 16-H-44-S circuits
should be higher than that of the No. 19-H-174-63 side circuits and the
difference to be expected is 5.4 — ( — 0.3) =5.7 TU.

When the circuits to be compared have the same cutoff frequenc>'
the process of comparison is even simpler since the quantity 5a, is
then the same in each case. Sa is determined for each circuit as in
paragraj)!) (4) above. The difference betwtiii (lie two \ahics of Sa
is the difference between the return losses.

E.XAMPLE

As an example compare the No. 19-H-174-63 side circuits with
No. 16-H-174-63 side circuits. In this case the cutoff frequencies
arc the same so w and Sw are the same. It is then only necessary to
compare Sa- The loss per mile of the No. 16-gauge circuit is 0.161

' This notation indicates a side circuit of No. 16 B. & S. conductors in a ciljlc
loaded with 44 millihenry coils spaced 6,000 feet apart.

ll<Ki:GUL.IKITlES IN LOADED TEl.r.l'HOXE CIHCIITS SKI

Tl' at 1.000 cycles from which 5^ = 11 TU. In equation (42) .S',i is

negative hence the No. 19-gauge will have a higher return loss than

the No. l()-gauge circuits and the expected difference is 11—8.7 =
2.3 TU.

Comparison of Calculated and Mka.-iLuld
Return Losses

In order to test the methods of calculation described above a series
of measurements of return loss at 500, 1000 and 2000 cycles were
made on a group of loaded side and phantom circuits in a cable using
a No. 2-A unbalance measuring set.

The representative inductance deviations were found by analyzing
the inductance measurements on a large group of loading coils similar
to those used in the cable. The representative capacity deviations,
not including the spacing irregularity were found by analyzing the
shop measurements on a number of reels of the cable. This gave
representative figures for reel lengths which were divided by \/l2 (in
accordance with the laws of probability since this cable had 12 reel
lengths in a loading section) to obtain the representative capacity
deviations due to the cable for the loading sections. The spacing
deviations were separately determined from the measured distances
between the loading points.

The data used in the calculation were as follows:

T.ABLE II

Sides Phantoms

Representative inductance deviation 0.0062* 0.0061*

Representative capacity deviation 0.0129* 0.0138*

Representative spacing deviation 0.0045* 0.0045*

Combined representative deviation, H 0.0150* 0.0158*

Cutoff frequency /c (cycles sec.) 2810 3727

( 500 cycles 0.265 0.271

Transmission loss ) ^^^ ^y^,^^ 0.274 0.279

TUpermile ( ,^00 cycles 0.317 0.296

The smooth curves of Figs. 9 to 14, inclusive, were calculated from
the data in Table II using the methods described above. The abscissas
are the percentages of a large group of circuits which may be expected
to have return losses greater than the values given by the ordinates.
This percentage is equal to 100 (1 — F). The points plotted on the

• The figures are "fractional" deviations. Percentage deviations which are
sometmes used are 100 times as large. Care should be taken to avoid errors caused
by failure to divide percentage deviations by 100 before finding the value of Y h-

Retuin less of No. 19-H-1/-1-63 sides exceeded by various percentages
of circuits at 500 c>cles
Smooth curve — theoretical
046-H-174-63 sides Pittsburgh to Ligcnier
H 12-H-174-63 sides Ligonier to Pittsburgh
^ 52-H-174-106 sides Pittsburgh to Ligonier

60

55

35

<})' 30

20

\

-'s;

^

A

•

•

•

■

.

.*^.

" 10 20 30 40 50 60 70 80 90 100
Percent of Circuits
Fig. 9

Return loss of No. 19-H-174-63 sides exceeded by various percentages

of circuits at 1000 Cycles

Smooth curve — theoretical

© 46-11-174-63 sides Pittsburgh to Ligonier

El 12-11-174-63 sides Ligonier to Pittsburgh

^ S2-H- 174-106 sides Pittsburgh to Ligonier

60
55

30

20

"^^_ •

10 20 30 40 50 60 70 80 90 100
Percent of Circuits
Fig. 10

_l — i

V • I. * •

rr.irTi !...< o( No. l<> II 174 63 sides cxirciltd l>y v.iriniii |mti nitaKC*
of circuits ut 20(X) cyclta

Sniuoth curve — theoretical
O 46-11- 174-6,? sides I'ittsburKh to l.iKciiier
H li-ll-l 74-63 sides l.igonier to Pittsburgh
^ S2-H-1 74-106 sides Pittsburgh to Ligonier

60
55

50
45

D 40

t-

J, 35
in
3 30

z
a 25

15

to

5

° (0 20 30 40 50 60 TO 80 90 100
Percent of Circuits
Fig. II

Kcturn loss of No. 19-H-I74-63 phantoms exceeded by various
percentages of circuits at 500 cycles
Smooth cur\'e — theoretical
© 25-H-174-63 phantoms Pittsburgh to Ligonier
r*1 21-H-174-63 phantoms Ligonier to Pittsburgh

60

55
50
45

40
T 35
S 30

I- 20
kJ

■^ .5
10
5

° 10 20 30 40 50 60 70 80 90 100
Percent of Circuits
Fig. 12

1

\j

•>,

•1

■^

^

" a

"■

•

■

a

• 1

Return loss of No. 19-H-174-63 phantoms exceeded by various
percentages of circuits at 1000 cycles

Smooth curve — theoretical
0 25-H-l 74-63 phantoms Pittsburgh to IJgonier
H 21-11-174-63 phantoms Ligonicr to Pittsburgh

60

55

50

45

if)
8 30

25

B

V

a

•

.^

B

8

ae

j^

■>t

^N

10 20 30 40 50 60 70 80 90 (00
Percent of Circuits
Fig. 13

kiturn loss of No. 19-H-l 74-63 phantoms exceeded by various
percentages of circuits at 2000 cycles

Smooth curve — theoretical
0 25-H-174-63 phantoms Pittsburgh to Ligonier
r»1 21-H-174-63 phantoms Ligonier to Pittsburgh

60

55

50

D 40

g 30

g 25

>S»

"^-^ ^' a^

10 20 30 40 50 60 70 80 90 100
Percent of Circuits
Fig. 14

ih:Ki:G{i..iRmis i.\ loaded rr.i.r.riioxr. circl-its ?«

lurvo shwts v;ivi' llu- iiUMMiivd \,iliRs of rrtiirn loss fmiinl in tlic
groups of liaiiils lisUtl in the i-xplanatory notes on the drawings.

In general, it will Ik- observed that there is a fair agreement between
the theoretical curves and the measured rcliirn losses especialK- at
1000 and 21HH) cycles.

Hue to the limited range of the measuring apparatus, readings of
return losses greater than 40.7 TU were not made except in the ca^e
of the Ligonier to Pittsburgh phantoms shown on Figs. 12, 13 and 14,
when a special arrangement was available to extend the range to
47.3 TU. For this reason points representing observed return losses
above these limits are not available which causes the observed values
for .")00 cycles in Figs. 9 and 12 to appear somewhat low at first sight.

Where the highest point in a given set of data represents many
circuits as in the cases represented by the small triangles and circles
in Fig. 9 this point probably gives closely the return loss corresponding
to the percentage of circuits it indicates but the points for higher
return losses are not available. When the highest point represents
only one or two circuits as in the case represented by the square in
Fig. 9, it is likely that the actual return loss is higher than the point
inilicates.

It should also be noted that above 40 TU the actual inipetlaiice
of the line and its characteristic impedance differ by less than 2 per
cent, so that very small departures of the network from the true
characteristic impedance of the line would tend to make the observed
return loss low.

Conclusion

It is believed that the procedure described in this paper offers a
reliable method for determining the probability of attaining a particu-
lar \'aluc of return loss at any assigned frequency when a circuit is
built with definite limitations on inductance and capacity deviations
so that the representative deviations are known.

The Sounds of Speech

By IRVING B. CRANDALL

XOTE: As professor of \iical plusiology, Alexander (jraliaiii Bell did
pioneer research in "devising methods of exhibiting the vibrations of sounds
optically." In 1873, he became familiar with the phonautograph, de-
veloped by Scott and Koenig in 1859, and with the manometric capsule,
developed by Koenig in 1862. (ireatly impressed by the success of these
instruments "to reproduce to the eye those details of sound vibration that
produce in our ears the sensation we term timbre, or quality of sound"
Bell used an improved form of the phonautograph haxing a stylus of wood
al)out a foot long. He obtained "large and very beautiful tracings of the
vibrations of the air of vowel sounds " upon a smoked glass.

In describing his early attempts to improve the methods and apparatus
for making speech waves visible and to interpret wave form. Bell wrote:

"I then s;ing the same vowels, in the same way, into the mouth-i)iece
of the manometric capsule, and compared the tracings of the phonauto-
graph with the flame-undulations visible in the mirror. The shapes of
the vibrations obtained in the two ways were not exactly identical, and I
came to the conclusion that the phonautograph would require considerable
modification to be adapted to my purpose. The membrane was loaded by
being attached to a long lever, and the bristle, too, at the end of the lever,
seeme<l to have a definite rate of vibration of its own. These facts led
me to imagine that the true form of vibration characteristic of the sounds
of speech had been distorted in the phonautograph by the instrumentalities
employed. I therefore made many experiments to improve the con.struc-
tion of the instrument. I constructed, at home, quite a number of different
forms of phonautographs, using membranes of dilTerent diameters and
thicknesses, and of different niaterials, and changing the shape of the
attached lever and bristle."

Struck by the likeness of the phonautograph and the mechanism of the
human ear, Bell conceived the idea of making an instrument modeled after
the pattern of the ear, thinking it would probably produce more accurate
tracings of speech vibrations. In 1874, he consulted a distinguished
aurist. Dr. Clarence Blake of Bostim, who suggested that instead of trving
to make an instrument modeled after the human ear, the human ear itself
be used. Dr. Blake prepared a specimen containing the membrane of
tympanum with two bones attached, the malleus and incus. The other
bone, the stapes, was removed and a stylus of wheat straw about one inch
long was substituted. A sort of speaking tube was arranged to take the
place of the outer ear. "When a person sang or spoke to this ear, I was
delighted to observe the vibrations of all the parts and the style of hay
vibrated with such amplitude as to enable me to obtain tracings of the
vibrations on smoked glass."

In the accompanying paper. Dr. I. B. Crandall describes modern methods
whereby with the most refined apparatus, highly accurate speech wave forms
have been produced. The analysis and interpretation of both vowel and
consonant sounds made possible by these records, are the realization of an
objective sought by Bell a half century ago.

This article is the result of an extended study of 160 gra|)hical records
of vowel and consonant sounds, of which a few are reproduced in the present
publication. One htmdred and four of these records are of vowel sounds
an<l formed the basis of the " Dynamical Study of the Vowel Sounds," by
I. U. Crandall and C. K. Sacia which was published in this Journal in .April,
1924. The purpose of the present article is to describe all of the records
in sufficient detail, including in'one discussion the outstanding character-
istics of vowel, semi-vowel and consonant sounds; it is hoped shortly to
Hupplement lhi.s with a reproduction of a larger group of records from the
coni()lete colled ion. — Editor.

586

587

THE SOUNDS OF Sl'LECIl

CONTKNTS

liilriMliK-tion
1 N'liti- 1)11 the I'harartcristic Kre<iiicnrics of Spcoi h
II Thr Roioriiiiis .\|>|xiratiis
III C'l.issific.ilion iil the Kivortis

l\' St.itisliial StiiiK aiul llartnoiiir Analysis of llu- N'owcl Sdiinds
\' I'mir Si'iiiiA'owcl Sounds
\ I Sixtrrn ("onsiinant SUuukIs

Introihition'

TU the layman speech is a matter of course, but to the student
of science, or of language "the amazing phenomenon of articulate
speech comes home ... as a kind of commonplace miracle." '
Hence we have inquiries into the nature of speech from many points of
view, beginning with fundamentals based on physiology and acoustic

■ -.^A^V W •/• ^ V .^V ~ A/VVVV'. y V W ^/'•W^'rf'»*.>V»-^^y

Speech record made by Hell in 1»75

science and leading to important applications in communication
engineering, phonetics and vocal music.

The scientific study of speech sounds began with Hclmholtz, who
also made a fundamental study of hearing. Hclmholtz had the
advantage, in approaching the.se problems, of a knowledge of physiology
as well as a mastery of theoretical physics. With this equipment
and such simple laboratory apparatus as he created, he did his great
work on speech and hearing of which we have the record (in English
translation) under the title of "Sensations of Tone." ' Today, with

' (irecnough & Kittrcdge, "Words and Their Ways," \. V., 1901.

'"The Sensations of Tone as a I'hysiological Basis for the Study of Music."
Translated from the Fourth derman Edition by .\. J. Ellis: Fourth English Edition,
London, 1912.

588 BELL SYSTEM TECHNICAL JOURNAL

imnicasiirahly sui)erior physical apparatus, and with more specialized
theoretical equipment, the individual investigator usually approaches
one problem at a time, the problem and the method being selected
according to the technique with which he is familiar. The work of
D. C. Miller on sound and sound analysis' represents the beginning
of modern physical research on speech sounds. In medical science
some attention has V)een given to the mechanism of speech ■* and the
psychologists are responsible for an enormous literature on voice
control and the perception of speech and tones. ^ The work of Scrip-
ture * represents the beginning of a science of experimental phonetics,
and in the closely related field of philology there is a rapidh" growing
interest in the physical characteristics of speech sounds.'

In this large field of investigation the physicist finds a real oppor-
tunity in providing means for the stud\' and measurement of speech
sounds, and a real responsibility in broadening the extent and im-
proving the accuracy of such quantitative data as are obtained.

The results obtained from such physical investigations have prac-
tical as well as scientific \alue, and we observe that in a large labora-
tory concerned entirely with the development of electrical com-
munication considerable effort has been devoted to research on speech
and acoustic apparatus.' It has recently been felt that the wave

' "The Science of Musical Sounds," New York, 1916. This contains a bibliography
of 90 special references, some 12 of which relate specifically to speech.

' " \ Contribution to the Mechanism of .Articulate .Speech," by S. W. Carruthers-
i;<lin. .Med. Jour. \111 (New Series) (190()i pp. 236, HI, 426.

'"The I'sycholojry of .Sound," by Henry J. Watt (Cambridge, England, 1917),
contains a bibliography of 159 references. The work of C. E. Seashore is note-
worthy in this field.

•"Researches in Experimental Phonetics." Publication No. 44, Carnegie In-
stitution, Washington, 1906.

'"The Physical Characteristics of Speech Sound," by Marie H. I.iddell. Bulletin
.No. 16, Purdue I'niversity Engineering Experiment Station.

• Sec follov\ing papers, from the Research Laboratories of the .American Telephone
and Telegraph Co. and Western Electric Co., Inc.:

(a) H. D. Arnold and I. B. Crandall; The Thermophone as a Precision Source
of Sound: Phys. Rev. 10, (1917), p. 22.

(b) E. C. Wenle: Condenser Transmitter for Measurement of Sound Intensity:
Phys. Rev. 10 (1917), p. 39.

(c) I. B. Crandall: The Air Damped \ibrating System: Phvs. Rev. 11 (1918),
p. 449.

(d) I. B. Crandall: The Composition of Speech: Phvs. Rev. 10 (1917), p. 74.
(e^ R. L. Wegel: Theory of Telephone Receivers: J. .\. I. E. E. 40 (1921).

(f) E. C. Wente: .Sensitivity and Precision of the Electrostatic Transmitter:
Phys. Rev. 19(1922), p. 498.

(g) I. B. Crandall and D. Mackenzie: Analysis of the Energy Distribution in
S|)eech: Phys. Rev. 19 (1922), p. 221.

(h) II. Eletcher: The .Nature of Speech and its Interpretation: J. Franklin Inst.

193 (1922), p. 729.
(i) J. y. .Stewart: .An Electrical Analogue of the Vocal Organs: Nature, Sept. 2,

1922.

////■; soixns (»/• sriiuii 589

forms ol ilu- >|utrli soiiiuls rctiuiriil inorr pririsc determination, aiici
iiuieiil ri'siarrli in llie art of ti-itplioiiy has emphasizc<l this need.
Thinraphiial reeortls of speech sounds, whicli form ,i siippltincnt to
I he present paper, are contributions to tiiis stu(i> .

I

N(ii|.. i)N nil-; (.'ii.\K.V( TKRisTic Frequencies ok Speech

Spctch is, in itself, a sound wave — a succession of condensations
and rarefactions in the air. For the purposes of this study we are
not |)rimarily concerned with the mechanism of production, nor with
the processes of perception of speech, though it may be necessary
to digress to inquiries of this kind, in their bearing on certain charac-
teristics of speech. We are interested primarily in what can be
learnetl from the records of the speech vibrations themselves.

Speech stiiuids are complex, that is, they are composites of simple
sounds, each component having a particular frequency, amplitude,
phase and duration. Considering speech in the mass, we find its
energy- distributed among frequencies from 75 to above 5,000 cycles
with the larger part of this energy contained in the region below 1,000
cycles. This distribution is shown approximately in Fig. 1 taken
from reference (8g); the limitation on these data being that the measur-
ing apparatus was not sufliciently sensitive to measure the speech
energy as.sociattxl with frequencies higher than 5,000 cycles. Inas-
much as the energy of speech resides largely in the vowel sounds, the
curve in Fig. 1 can also be taken as applying to the average distribu-
tion in the vowel sounds. The energy distribution diagram is of
fundamental importance in the physical study of speech sounds; it
reveals at once the frequencies of large energy content which are
characteristic. For each vowel sound, there is a distinctive energj'
fretiuency diagram.

The consonant soun<ls present a difficult problem because of the
small amount of energy associated with them. Most of our knowledge
of the consonant sounds is qualitative: for example Fletcher (refer-
ence 8h) who studied the nature of speech by the method of testing
articulation when different frequency ranges are eliminated shows
that for t^vo fricative or sibilant consonants 5 and s, there are essential
frequency components which lie above 5,000 cycles. The character-
istic frequencies of the consonant sounds are usually only part of the
whole story; these sounds are richer in transients, and clearly less
periodic in their nature than the vowel sounds. And in between
the two broad classes of consonant and vowel sounds there is a group

590

BELL SYSTEM TECHNICAL JOURNAL

of senii-vowol sounds (r, /, w;, n, ng) closely reUited to the \()\vel
group, and \ielding readih' a determination of tiicir "rharacteristir
frequciicies."

There are two physical theories of vowel production; and these
two theories suggest different methods of analyzing the vowel sounds
into components of simpler nature. These two points of view we

1

^

1

V

\

\

1000 2000 J<-00 4000

Frequency

Fig. I — Energy eiislribution; composite riir\c for male and female voices

shall briefly consider along historical lines. We are indebted to
Helmholtz for the greatest single contribution to the study of the
vowels, in that he gave a complete diagram of the characteristic fre-
quencies of the vowels (ref. 2, pp. 103-109), which w-as based on his
celebrated experiments in analysis and synthesis by means of the
Helmholtz resonators. But in connection with his scheme of char-
acteristic frequencies he took up the theory of Wheatstone (1837) that
these fre(iuencies are true harmonic components of the cord tones,
which were rcenforced by resonance in the oral cavities. Some later
jihysicists have followed this so-called harmonic or steady state theory
of the \()wel sounds, notably Miller (reference 3, pp. 239-243) who

THE SOUNDS OF SPEECH 591

made a very careful study of the whole matter. According to this
theory the obvious procedure is to apply the classical Fourier analysis
to determine the characteristic components of the vowel sounds.

Turninj; now to the other (and earlier) view, the so-called "Inhar-
monic Theory" of Willis (182*.)) later developed by Hermann and
rather recently by Scripture (ref. (6)) we are invited to believe that
the "characteristic frequencies" of the vowel sounds are the natural
vibrations or transients in the oral cavities, when excited impulsively
by the (more or less) periodic puffs of air from the glottis. According
to this theory no harmonic relations need obtain between the charac-
teristic frequencies of the vowels and the fundamental or cord tone
accompanying them; and the classical Fourier analysis is not con-
sidered applicable in resolving the vowel sound into simpler compo-
nents. According to this "inharmonic" or "transient" theory we
must treat the natural \ibrations of the oral cavities as damped
vibrations and find the frequencies and damping constants of their
components, as best we can from the record of the complete sound
vibration.

In favor of the Heimhoitz or "Harmonic" theory we have the careful
studies by Heimhoitz and his successors of the relations between the
cord or fundamental tone, its harmonics as reenforced by the oral
cavities or other resonators, and the observed characteristic frequen-
cies of the vowel sounds. The oral cavities constitute a vibrating
system of two or three degrees of freedom, the theory of which has
been fully developed by Raylcigh and others, and it is to be expected
that, with the speaking mechanism in normal adjustment the vowel
qualities can be well accounted for by postulating harmonic forced
vibrations in these cavities. This expectation has been realized in
the numerous successful attempts which have been made to produce
vowels artificially by using a harmonic series of tones, and reenforcing
certain harmonics by suitable resonators. Miller's experiments with
organ pipes (ref. 3, pp. 246-250), in which he successfully reproduced
certain vowel sounds, are well known.

The Willis-Hermann theory has also suggested much notable experi-
mental work. Scripture (ref. 6, p. 114) constructed a "vowel-organ"
in which a reed pipe was used to excite the natural vibrations in
resonators designed to imitate the conditions in the oral cavities, and
attained some success in reproducing vowels. More recently J. Q.
Stewart (ref. 8i) has produced an "Electrical Analogue" of the vocal
organs with which remarkable results in reproducing vowel sounds
and even some of the consonant sounds have been obtained. In this
electrical arrangement transients excited by an interrupter in oscilla-

592 BELL SYSTEM TECHNICAL JOURNAL

tory circuits take the place of the transient vibrations of the oral
cavities. Finally Paget (reference (9a) below) has constructed a
whole series of double resonators which may be excited by l)lowing
air into them through an "artificial larynx," and from which he has
obtained all of the vowel sounds. As the result of this work he has
given a very complete chart of the characteristic frecjuencies of the
vowels and he has been led to the conclusion that there are two char-
acteristic frequencies or regions of resonance for each vowel sound.

From the standpoint of practical acoustics both theories have con-
tributed to progress, and it seems that the experimental physicist
would not be justified in partiality to either view. Speech is a \ariable
phenomenon; the cord tones are not always stable; in speaking and in
singing there are allowable variations in duration, intensity and fre-
quency of the component tones without essential change in the char-
acteristics of the vowel sounds. Given accurate records of the speech
sounds as normally pronounced by a number of speakers, we should
expect to arrive at nearly the same characteristic frequencies which-
ever mode of analysis we adopt. As pointed out by J. Q. Stewart
(Ref. 8i) Rayleigh has stated (.Sound, \'oi. II, p. 473) that the dis-
agreement between the Helmholtz-Millcr, or steady state theory of
vowels, and the Willis-Hcrmann-Scripturc, or transient theory is onl\-
apparent; to quote Stewart, "The disagreement concerns methods
rather than facts. Which \iewpoint should be adopted is thus a
matter of convenience in a given case. When the transmission of
speech over telephone circuits is in question, for example, the steady
state theory often possesses obvious mathematical achanlages. On
the other hand, the quantitati\e data relating to the physical nature of
\owels which are gi\en in D. C. Miller's well-known book "The Science
of Musical Sounds" expressed as ihey are in terms of the steady slate
theory are less compact and definite than the data of Table I (Stewart's
paper) which are expressed in terms of the transient theory. The
general agreement between the two sets of data is, of course, obvious."

In stud\ing the behavior of \ibrating systems from the theoretical
standpoint, there is a tendenc\' to emphasize the intimate relations
that exist between transient and steady state phenomena. Both
depend only on the dri\ing forces and the constants of the system,

'(a) Sir K. .-\. S. Pagcl: "The I'roduclion of .^rlifitial \owcl Sound,';." I'roc. Ko\-.
Soc. .A 102, Mar. 1, V)li, p. 752.

'(!>) .A second memoir: "Tlic Nature and .Artificial Production of Consonant
Sounds." I'roc. Roy. S<jc. .\ 106, .Aug. 1, l')2-l, p. 150, to which reference will Ic
made in more detail later.

Other papers liy Paget include: .Nature, Jan. 6, V)li, "Nature and Reproduction
of Speech Sounils." Klectrician, .Apr. 11, 1924. The Same Title. Proc. Land.
Phys. Sot. .<0 pt. i, .\pr. 15, 1924, p. 213: Discussion on Loud Speakers.

THE SOi'XnS OF SPEECH 593

tu'iut- "the solution for transient oscillations of the system is reduced
to forinul.ie which are functionally the same as those for steatly state
oscillations" (reference 10; see also reference 11). But before leaving
this tliscussion of speech characteristics it should he noted that the
essence of the matter lies not so much in reconciling the two theories,
of the vowel sounds as in ascertaining what motions really take place
in the oral cavities, anti in the air near the vocal cords. Though the
process of harnjonic analysis is to be applied to the records of the
vowel sounds, we must recognize its limitations, and not necessarily
infer steady state conditions. Indeed the most casual inspection
of the records shows a certain lack of periodicity in the phenomena
recorded; and it is hardly to be expected that all the phenomena can
be satisfactorily summed up on the basis of the harmnnic theory.

II

Till-: RixoRDiNT. App,\ratus'=

In providing means for accurately recording .sound waves, use has
been made of three devices recently developed in this Laboratory and
we believe that by properly connecting these together we have obtained
a recording instrument which is superior in accurac>- and power to any
heretofore used. These three devices were each nearly free from dis-
tortion, and such residual distortions as could not be eliminated were
so controlled that they practically offset one anoltuT n\cr a wide range
of frequencies.

The first element in the recording set is the condenser transmitter,
which has been thoroughly investigated by Wente (refs. 8b, 8c, 8f);
its frequency characteristics, in both amplitude and phase are shown
in Fig. 2. The particular transmitter u.sed was of recent design and
had been carefully standardized and calibrated especially for this
work.

The condenser transmitter was connected to the input terminals
of a seven-stage amplifier as shown in the large diagram of Fig. 5
which gives the details of the electrical circuit, including tlio third

"J. R. Carson: Phys. Rev. X, 1917, p. 217, "On a (jencral Expansion ThcarL-m
for the Transient Oscillations of a Connected .System."

" T. C. Fry, Phys. Rev. XI\', V)V), p. 1 17. "The Solution of Circuit Problems."
'= Thanks are due to Messrs. C. F. Sacia and C. J. Beck for the skill and care
with which they assembled and calibrated the recording apparatus, and made the
complete set of records. The writer is also under obligation to Mr. Sacia for aid in
choosing the sounds to he recorded, an<l systematizing the collection; Mr. Sacia
also developed and applied the photomechanical method of analyzing records, the
results of which arc given in Figs. 13 and 14 of this paper.

594

BELL SYSTEM TECHNICAL JOURNAL

element, a special oscillograph, which was connected to the output
terminals of the amplifier. The first six tubes, in cascade, provided a
voltage amplification of about 40,000; the last eight tubes, in parallel,
constituted a "current transformer" working into the low impedance
of the oscillograph vibrator, with a small resistance in series. The coup-
ling between the stages, and between amplifier and terminal apparatus,

JX/O"'

1000 ZOOO JOOO 4000 ^000 6000 jooo 600 gooo

Fig. 2 — Curve A : Output of transmitter in volts per dyne per sq. cm. Curve B:
Phase lag of voltage behind pressure in condenser transmitter

was entirely of resistance and capacity, with the capacity reactance
minimized. In all tests of the circuit the conden.ser transmitter and
the oscillograph vibrator remained in their fixed positions, as shown in
the diagram, so as not to disturb the electrical characteristics of the
circuit. The frequency characteristics of the amplifier in amplitude
and phase are shown in Fig. 3. In measuring the amplitude character-
istic a small electromoti\-e force was introduced in series with the
transmitter, in the input mesh; and in measuring the phase lead of
the output as a function of frequency use was made of the Alternating
Current Potentiometer of Wente (Jour. A. I. E. E. Dec. 1921) the
other details of procedure being as usual.

The characteristics of the oscillograph \ibrator are shown in Fig. 4.
This vibrator was specially constructed, with small mass, high tension
and damping; when the requisite dynamical characteristics were once
obtained, its calibration presented no great difficulty.

THE souxns or srnncn

595

In coinl)initisj thi" transmit tor, tin- ainplifuT and the osrilloKraiili to
form till' (•oin()li"tc rirortlitig .ipparatus thi-ro were two primary ri'fiuire-
nu'iits; first, tlu- set as a whole should bo free from frreiiu'tiiy distortion

/"

\yB

V

•^

Fii;. 3 — Curve .'1; Atnplitucic frequency characteristic of amplifier. Curve B:
Phase lead of output, vs. frefiuency of voltage iii[)ut to amplifier

/

^

/^

/

/

^B

/

/

/

toot) 3000 _}OiJO 4000

Frrtfuency

Fig. 4 — Curve .l; .Amplitude frequency characteristic of oscillograph. Curve B:
Phase lag of amplitude behind current in oscillograph

in both amplitude and phase, and second, the output of the set as
a whole should be a linear function of the input within the working
energ>- range at each frequency. The first of these conditions is in

5%

lUU.I. SYSTEM TF.CIIXIC.il .IOURX.IL

general the harder to fulfil. Frequency-amplitude distortion has been
practically eliminated as we have seen from each of the three essential
parts of this apparatus; and although it was found impracticable to
make each part of the apparatus free from frequency distortion in
phase, it was possible to give the complete set good frcqucnc\^ char-
acteristics in both amplitude and phase as will be explained.

In a vibrating system of one degree of freedom when we wish to
a\oid frequency distortion in amplitude, we usually adjust the resonant

Fig ,S — riciu-ral dianrani of recording apparatus showing circiiil <ktails

frequency so that it is above the range of frequencies within wliirli we
desire to work; in addition, it is desirable in most cases to in.ikc the
dami^ing of the system large. With these adjustments made it is
found that there is a phase lag between amplitude and dri\ing force
which rises with frec|uency and reaches a maximum above the resonant
frecjuency, and it is possible tfi make this jihasc lag nearly jirfiportional
to the frequency over llu- r.ini^i' of fri(|iiencies within whicli it is
desired to work.

It is well known that il e(|u.il driving forces produce e(|ii,il aniiili-
tudes at all fretiuencies, and if the phase lag of the ami)litude with
respect to the dri\ing force is proportional to frequency, then a dri\ing
force of c(jmple.\ wave form is. reproduced without distortion of wave
form in the \ibrating system. These conditions held very well over
the desired range of frcc|uencies in the oscillograph vibrator, as shown
in Fig. 4. In the case of the condenser transmitter, however, there

HIE socxns or sriiECU

597

wiTc ilt'p.irtures from thi-se roiulitions in tlu' fri-tiuoncy iiitiTwiI from
/(.•ro to ")(M) ryclfs for whicli allowance had to In- made.

In the amphtier the effect of capacity reactance was nearly ehnii-
nated. Owing to the small remaining capacity reactance there was a
phase leail of amplifier current with respect to driving force which wag-
appliixl to offset the excessive phase lag in the condenser transmitter
at the low frequencies. The particular adjustment of amplifier finally
arrived at represented the best compromise, considering the difficulty

r\

/

\

A

^

/

^

^^

^

i

B

(^

^"^

\

1

Fig. 5 — Overall frequency char.ictcristics of amplitude and phase of the recording

system. Curve .'1; Oscillographic amplitude per unit of pressure on transmitter

diaphragm. Curve B: Phase lag of oscillographic amplitude behind pressure on

diaphragm

encountered with the transmitter characteristics. With this com-
promise made there was an unavoidable phase lead in the whole appa-
ratus for frequencies below 125 cycles, but this was not serious as
most of the speech energy is in higher frequencies. After all final
adjustments were made the overall frequency characteristics of ampli-
tude and phase were as shown in Fig. 6. Thus ultimately there was
obtained a system with practically uniform amplitude characteristic
from o(X) to 5,000 cycles, without serious departure from this level for
frequencies from 50 to 500 cycles; and with phase lag nearly a linear
function of frequency from 125 to 5,000 cycles, after passing through a
perirxl of lead in the narrow interval from .50 to 215 cycles.

598

BELL SYSTEM TECHNICAL JOURNAL

Consider now the second requirement which the recording system
had to meet: namely, that the output of the system should be a linear
function of the input within the working energy range at each fre-
quency. Thorough investigation of the condenser transmitter had
shown that this instrument met this second requirement very well; it
was only necessary to test the remainder of the system. Fig. 7 gives

f\

hf>ut.

I.dsxio'-^

volts

^

\

Jj

E

/\^.

Input.

3.6x10-^

Xfllts

-^

/

1

Input.

i-JXIO

volts

f

" — --.^

1

Freqiunry

Kig. 7 — .■\miilitU(Je frequency characteristics of circuit-oscillograph al ililTerent
energy- levels

the results of these tests, the voltages introduced in series with the
transmitter at the input being maintained at different constant levels,
while the frequency was \'aried. An inspection of the data shows
that this requirement was \ery accurately fulfilled, by the whole
electrical system.

Returning now to the owrall characteristics of llie apjiaratus, it
was thought advisable to test the calibrations in am])litude and phase
lag by comparing the computed and the observed distortion when a
square-topped acoustic wave was impressed on the apparatus. The
steep sides and the flat tops of these waves can be reproduced with-
out distortion only if the apparatus possesses first class characteristics,
both in amplitude and phase lag, and the test was a severe one. As
would be expected from the calibration curves of Fig. 6 there was a
certain amount of distortion in recording this wave, and the square-

THE SOUNDS or SI'EECH

599

toppod wave, \vi(l» its vory lar^i' fuiulanuMilal coinponcnt, marie this
distortion appear iiuicli worse than would an ordinary sjieerh wave.
Fig. 8 ilhistrates the apparatus used to produce the aroustic s(|uare-
topp«.-d wa\e. An elertHnle resembling the hark plate of the condenser
transmitter was mounted in front of the transmitter diaiihragm. Be-
tween this electrtxle and the diaphragm was apjilied a high potential
which was made altirnatcK- positive and negative by a commutator.

Exciter^

CJSS

.001 inch from back folate. Condenfer Transmitter

Kig. J(-^Con<lfnser transmitter coupled with sf|uarc-toppecl-\vave exciter

Exciter Parts

a. Steel Electrode 0.006 inch from Diaphragm, h. Micarta. Insulation.

c. Supporting Ring. d. Electrode Terminal.

By this arrangement the desired positive and negative pressures were
produced on the diaphragm. The distance between the au.xiliary
electrode and the transmitter diaphragm was about .006 inch. This
electrostatic coupling was foimd to be sufficiently close to give a
suitable deflection of the transmitter diaphragm, while the stiffness and
damping of the air film did not alter the (Kiiamical characteristics of
the transmitter.

Fig. 9 is an oscillogram showing the wave form recorded by the
apparatus when acoustic square-topped waves of frequencies 84, 153
and 306 cycles per second are impressed on the transinitter. Timing
waves of frequencies 75, 150 and 300 are also shown. Analysing the
original wave by the Fourier mcthcKJ, and allowing for the distortion
in amplitude and pha.se of each cotnponent frequency, a computation
has been made of the wave form in the output in the case of the square-
topped waves of 84 and 153 frequency. The results are shown in Fig. 10.

600

BELL SYSTEM TECHNICAL JOURXAL

The Fourier sitIos representing the 84-cycle %va\e contained 30 terms,
the component frecjuencies being odd multiples of 84 up to a limit of
4,956 cycles; for the series representing the 153-cycle wave 17 terms
were used covering the range from 153 to 5,049 cycles. The agreement
between calculated and observed output waves would have been more
exact, particularh' at the corners of the wave shapes, if calibrations

/www^y\

Fig. y — Oscillogram of s:|iiare-to|)|)C(l acoiislic waves as rcconkil 1)\ tin- a|)[iaratiiB

and calculations had lieeii carrii'd to frequencies considnalilN ahow
5,()(K). As it was, the jjerformance was considered good; it indicated
that the uncorrected records of speech waves as taken were suiHiciently
accurate for most purposes, while if harmonic analysis of the records
was planned accurate results couitl be obtained over the range from
80 to 5,000 cycles, if the correction factors delerniiiied by ihe calibra-
tion were api)lii'd.

In this description of (he reci)rding ai)paratus the emphasis has been
placed on the dynamical characteristics of the apparatus and its
calibration, but some of its other working features may briefly be
mentioned. 'Ilu' apparatus was sufficiently powerful to record sounds

THE SOUNDS OF Sl'EliCll

001

spokiMi in .m ordinary tone of voiir, with tlu- spciikiT's mouth al)out
thri-e inrlii's from the transmitter. A key was pri-ssrd l)y the s|)i'aker
just before tlie sound was spoken, lliis releasing a shutter plaie<l lie-
fore a rotating him drum on whiih the record from the oscillograph
vibrator was traced. The film drum was some ")2 inches in circumfer-
ence, and there was mounted on it a length of Kastman super-speed

Fi^. 1(1 — Caliiilatecl ami hIi-mimiI w.ivc iDriiis, as rccorfled by the apparatus

film with which records coukl be made at a peripheral speed of about
20 feet per second. Thus each hundredth of a second corresponds to
two inches or more in the time scale on the film. Besides opening the
shutter, the key released a mechanism which swung the oscillograph
vibrator through an arc during the progress of the record, thus tracing a
helical record on the film. By this means records up to 200 inches
in length, or for nearly one second of duration were taken. The
average length of the wave trains recorded was less than 0.5 second;
thus it was possible to graph the pressure wave of the whole speech
.sound from beginning to end. Immediately following the recording
of the speech sound a timing wave of 1,000 cycle alternating current,
taken from a standard oscillator, was recorded on the film at one side
of the speech record, without disturbing the speed adjustment of

602

BELL SySTEM TECHNICAL JOURXAL

the rotating drum. Tluis tin- time scale was accurately determined
for each record.

Especial care was taken with the optical system to insure fine defi-
nition and strong illumination of the spot on the film and the films
were developed for maximum contrast. As a result, the records were
sufficiently clear to permit their reproduction by the line-engraving

J4sea

j55ec.

.34 sec

.353ec.

--^

^/H/Vv^^-vs/^^^'"- — -^..^

I ig. 1 1 —Section of original record showing timing wave

|H()( <^^. 1-^ach of the plates shown in this paper is made up of o\er-
lapping sections from the original record, each faithfully reprotiuccd,
and the whcjle arrangetl to gi\e liie complete record within the limits
of one page. A section of <>ni' ol ilu' origin, il records as takni is sluiwn
in the figure above.

Ill

("l..\SSIFlC.\TION OK Tllli RlXOKDS

In selecting and classifying the vowel soimds for record, use has
been made, with slight alteration, of the phonetic arrangement adopted
by I'letcher (ref. S \\). This arrangement of the vowel sounds is

THE souNPs or sri-.iicii h).\

illustrated in llu- (li.iKram of V\^. 12. In this diagram eleven standard
"piire-\<)\vel " soinuls from oo to lonj; c are arranj^ed aeeordinK to the
lonventional "tri.inijle" and two relale<l xowel sounds ar and <t are
interpolatinl in their proper places. .-\ ^roiip of ei^ht records was
made of each of these thirteen \owel sounds, four in e.irh K^onp hy

(ten m )

Fig. 12 — Classification of vowel sounds

male voices, and the other four hy female \oices. Each of these
records. Plates 1 to 104 (Groups I to XIII), represents the xowel
sound as spoken naturally, and continuously recorded from beginning
to end.

No attempt was made to record the vowels w, v, on and long i.
These usually have transitional characteristics which are sufficiently
indicated by the arrows in the diagram. The first two of these, when
followed by vowels, and the last two, in nearly all cases, fall into the
class of diphthongs.

Following the groups of records of the "pure-vowel" sounds of the
diagram it was originally planned to make a group of records of the
semi-vowels /, m, n, wg, and r, recorded in connection with certain
vowels. It seemed best however to present records for the sounds ar
and er in connection with the standard vowel sounds as noted above
{ar, er, droups VII, X) and only these records of the sound r were
taken. The four remaining sounds were arbitrarily divided into two
groups because of the number of records made, and the first of these
(Ooup XI\') contains records of / and ng. These were made by two
male speakers, using the syllables loo, lee, la and ngoo, ngee, nga.

604 BELL SYSTEM TECIISICAL JOURNAL

Group XV is devoted to the semivowels n and m, each recordea
with the three vowel sounds oo, long e and a, by the two male speakers,
as in the preceding group, droups Xl\' and XV are intimately-
related, and as will appear the four semi-vowel sounds are closely
related to the vowel diagram.

When this study was planned, il was thought that the apparatus
would be particularly adapted to recording vowel sounds and no great
hopes were entertained of applying it to definitive investigation of the
consonant sounds. As the work progressed however, it was found that
some of the characteristics of the consonant sounds could be recorded
and the program was enlarged to include the records of Groups XIV
to XVII inclusive. Each of the records of a consonant and vowel
combination can be compared with the corresponding record, by the
.same speaker, of the pure vowel alone in one of the earlier groups, and
certain conclusions as to the nature of the consonant sound can be
formed.

Group XVI includes records of the si.\ stop (or "hard") consonants
b, p,d, I; g, k; followed by two transitional consonants dth (as in tliot)
Ih (as in thin); each associated with the vowel a, and recorded by the
two male speakers. The natural arrangement is in pairs, the related
voiced and unvoiced variations being grouped together.

The last Ciroup (XVII) includes records of eight fricative ("soft"
or "sibilant") consonants paired in the same way. These are i;, /;
j, ch; z, s; zh (azure), sh\ each associated with a and recorded by the
two male speakers.

The following table lists in groups all the records made. As it is
not practicable to engrave and print with this article the whole set of

lAlil.K 1

Complete List of Speech Records

(Iroiip Plates

I 00 as in pool, liy Kinlit Spcakfrs 1- 8

1 1 H as in put, liy Ki^ht S]H-.ikiTS 9- 10

III 0 as in tone, li'y K'^hi Spuakers 17- 24

IV' a as in /.;/*, by Kighl S|K'akers 25- 32

V o as in ton, hy Ki^lit Speakers i3- 40

V'l a as in father, by Kij;lit Speakers 41- 48

VII iir us in part, !)> KiKht Speakers 49-56

VIII u as in tap, hy KiKht Speakers 57- 64

IX f as in ten, \>y Kiglit S|x'akers 65- 72

X rr as in perl, by Kijjht SfH'akers 73- 80

XI a as in tape, by Kight Speakers 81- 88

XII I as in tip, by Kinht Speakers 89- 96

XIII r as in team, l>\- Kinht S|K-akers 97-104

XIV SeniiA'owels /, iij; bv two male speakers 105-1 16

X\' ScniiAoweis H, m by I wo male speakers 1 1 7 1 28

\\'\ Six Si()(i Cunsiinanls; transitional ilth, th; by two male speakers.. 129 UO
X\ll Kiglit l-riralive Consonants, by two male S|>eakers 145 104

I

v^ .^

^^ .X,

I::

i

1

-

-

/I

^

11

\

J

/

/

!
1

//

r"

^

^~'

1 f

-

^J

f^

/. I

\

-

rr^'\

V 1

X /

^*^^

/3"

^''\

.(

'-

r"

u

_

^ '

'"^•

■^^^

^.

_^y^r^

l"-~

^

! ^

I

c

-^

H

^\

\

1

[

\

!

\\

\

\

\

"

\

~

1

K

•"S

fc:

*

THE SOUNDS OF Sl'F.F.CII MS

U»0 rironis, a si-li-rtioH has l^cen made of somi- l.'i t\piral examples
whieli illustr.ite char.u'terislic consonant and \d\vel \v.i\e forms. These
are listed in table II and their properties are described in detail in the
follo\vin){ seetions. It m.iy not be amiss to snmmari/e here the basis
on wtiieli tlu'M' partienlar records were chosen for pnblication.

T.\m.i:.

II

Lhl of Records Shown

in Tl

is Paper

l<c<or(l No.

Plate No.

Title

Speak

14.1

9

u

us in pill

M.\

Itl

40

0

:is in Ion

IT)

l,W

41

a

as m Jallirr

\\\

15t

49

ar

as in purl

MA

148

S9

i

ns in lip

MA

2,U

lOS

lee

MB

2-<8

III)

la

MB

22Q

\n

moo

MB

286

Uu

In

MB

289

l.^S

X"

MB

272

i.=;i

(ha

MA

293

158

za

MB

294

160

sa

MB

The most important «sound (a, as in father) is represented in 7 of
these records, which inclnde six instances of its combination with other
sounds. The record of ar (Plate 49) which was chosen is the most
characteristic and interesting one of its group. The other vowel records
(Plates 9, 40, 89) are sufficiently scattered about the vowel triangle
to give an idea of the variation in the high freciuency characteristics
which is to be an important subject of discussion later. One record of a
female voice (Plate 40) is probably sufficient to show the distinctive
fimd.imental, about an octave higher, characteristic of such records.
Plate 11)8 was chosen to show the resemblance between I and e, which
establishes a natural transition between the vowel and semi-vowel
sf)unds. From plates 108, 110 and 124 a good idea of the relative am-
plitudes of vowel and semi-vowel sounds can be obtained; a similar
observation holds in the comparison of the vowel and consonant
sounds of Plates 136, 138, 151, 1.58 and 160. Plates 136 and 138
show two extended transients of moderate frequency, the latter in
connection with a voiced consonant {hard g); Plate 1.51 is shnilar to
136 — but the vowel following the consonant is less suddenly produced.
The pair, Plates 1.58 and 160, show the voiced and unvoiced hiss
fz and s respectively) a sound of ver>- high frequency, which is the
limiting case of this type of consonant.

The plates reproduced with this paper are reduced slightly (1.5 or
20 per cent) in scale, as compared with the original records, to
bring them within the page height of the Journal.

606 BELL SYSTEM TECHNICAL JOURNAL

In producing this system of records we believe that we have covered
the speech sounds as fully as we are justified in doing with the present
recording ap[)aratus. In the case of each vowel the combined data
from the eight records constitute a sufficient basis for the most thorough
harmonic analyses that can be made and they should yield accurate
results for the characteristic vowel frequencies. In analysing these
records small corrections are of course necessary on account of the
slightly imperfect frequency characteristics of the apparatus, but
these corrections can be taken without difficulty from the calibration
curves.

The amplitude scale in these records is arbitrary in each case. This
is for the reason that, owing to the widely different conditions of voice
control among the different speakers, the recording apparatus had
to be adjusted to different levels of sensitiveness for each record in
order to obtain the requisite maximum oscillation of from 1 to 2
centimeters. No attempt has been made to compare the absolute
amplitudes from one record to another on account of these intensity
variations. The emphasis has been placed rather on obtaining in each
record a good well-defined wave which could be enlarged if necessary.

Notwithstanding the fact that for frequencies above 5,000 cycles
the apparatus was not nearly as good as for frequencies within the
calibration range from 75 to 5,000 cycles, the records obtained of some
of the consonant sounds are of considerable practical \'alue. It is
felt however, that the present apparatus has been used nearly to the
limit of its possibilities and that devices other than the usual oscillo-
graph vibrator offer more promise in any further investigation of the
consonant sounds. It is planned later to issue a more complete set of
these records as a supplement to the present paper in order to make
the collection a\ailahk- lo ihosi- t'spccialK- interested.

IV

Statistk Ai. -Sudv and Harmo.nic Analysis of thk
\'<)\vi;i, SoiTNDs

A detailed inspection of the records takiii, and particularh- of the
records of the vowel groups shows thai iniich labor would be required
to anaK'ze these records throughout their length, according to the
usual methods of harmonic analysis. In nearl%- e^•ery case it wduhl
be imp^jssibie to obtain the mean energy distribution in a gi\i'n
record, allowing for variations from cycle tcj cycle of the fundamental,

THF. SOUNDS OF SPEECH 607

by chrxising from each riTord only a few such ryclt's as rcprfscnla-
tive and analyzing tlusi-.' If, for exarnplo, only U) cyrk-s wi-ro taken
at selecteil intervals from each of the KM \'o\vel records shown there
wouki he retiuired o\er one thousand such anaKses, and to he of value
these analyses should include components of fre(|uency from 100 to
a,(MK) cycles. For this reason a mechanical method of analysis has
lieen ajiplieil to clctermine from the records the average fre(iuency
spectra of each of the vowel and semi-vowel sounds.

First let us consider the vowel records in a simpler and more general
way. Considerahle information has been obtained by inspection, using
such simple apparatus as a pair of compas.ses and a rule in connection
with the time scale on the records. The time scale greatly facilitates
the process; it is in most cases possible to count the number of cycles
of any one prominent comp>onent occurring in an interval of .01
second, and by doing this in \arious parts of the record, to arrive at a
rough average frequency for the component in question.

In the case of the low frequency components (the fundamental and
the lower characteristic frequency) the procedure was to make this
examination at 3 points; one near the start, one near the middle, and
one near the end of each record. In this way the most significant
changes in pitch and wave form during the course of the record can be
brought to light, and some of the individual characteristics of the
speaker revealed. A statistical compilation of these results serves to
show certain "normal" characteristics of pitch variation, and permit
the detection of a certain amount of "personal bias" of the individual
speaker in his departure therefrom. In the examination of the low
frequency characteristics a note was made as to the harmonic relation
between the fundamental and the lower characteristic frequency; of
the amplitude of the lower characteristic frequency as being greater
or less than the amplitude of the fundamental; and of the behavior of
the amplitude of the lower characteristic, during the cycle of the funda-
mental. The amplitude of the low frequency characteristic is either
substantially constant during the cycle or falls away as a transient
vibration.

The high frequency components are clearly shown in the records,
but it is more dit^lcult to determine their exact frequencies, and prac-
tically impossible to relate them harmonically to the fun<lamental.
These oscillations were counted in from four to eight locations in each

' It is practicable, however, to obtain valuable data as to the formation of the
vowel sounds by analyzing separately the successive cycles at the beginning of a
typical vowel record. .\ study of this kind, based on these records, is lieing carried
out by Messrs. .N. R. French and W. Koenig of the .American Telephone and Tele-
graph Company.

608 BELL SYSTEM TECIIXICAL JOVRNAL

record, and a maximum and minimum figure determined for the
frequency \vherc\er possible. The behavior of the amplitude of the
high frequency component during the cycle was noted, and a rough
estimate made of its magnitude. Practically all the vowel records
show frequencies above 2500 cycles and the amplitudes in some cases
are large. In only two records out of 104 was the high fre(iuenc\'
component too small in amplitude to gi\'e a frequency determination.
These high frequency components may or may not be characteristic
of the given sound; this question is more fully dealt with later.

To complete the examination of each record its duration was noted,
and this time was divided into three intervals: (1) a building up period
in which the oscillations rise from zero to an amplitude which shows
all the components clearly; (2) a middle period in which the general
ampilitude remains nearly constant, but in which some \'ariations in
the amplitudes and phases of the com]jonent frequencies usually take
place; and (3) a period of decay in which the components disappear
and the oscillation gradually loses its characteristic wave form.

The procedure may be illustrated by its application to the first
record for which the following data were recorded:

Plate No. 1, 00 as in pool. Speaker MA. (Male).

Time to build up, .05 sec; Middle period, .20 sec; Period of decay,
.06 sec; Total Duration .31 sec.

Fundamental: 102 at start, rises to 108 in middle, rises to 120 at
end. Pitch Variation normal. (See explanation below).

Low Frequency Characteristic: 400 at start, 430 at middle, 440
at end. Amplitude greater than that of fundamental. Ai^proxi-
mately, a fourth harmonic of fundamental, but amplitude
\'ariation (luring the r\(le suggests a transient.

High Frequency Component : Minimum, 3300 cycles. Maximum,
:<(')()() cycles. Noticeable tiiroughout; amplitude \-ariation sug-
gests a transient.

Xo other frequencies.

'i'his routine was ajiplied to each of the 104 \-owel records and a
general summary made of the results, gi\'ing approximate values of the
vowel cliaracteristics which forecasted the more accurate results ob-
tained later from the mechanical harmonic analysis.

The simpli'st phenomena to summarize are the general character-
istics of the individual speakers. These are based on I lie mean ])er-

THE SOUNPS ()/• Sri.l.CIf 609

form.iiu'f (if iM«-li in spi'akinjj tin- tliirtirn vowi-l sounds, anfl will l)r
list-fill in thi" discussion to follow; they arc shown in Tahlc III, hflow:

TAUl.l'; III
Sfxtikers' Charailcristics

Me.ui l''iind.inu-ntnl Pitch

Mean

Mem Oiir.ilion"

Male S|)tMkers

at Start, Miihlle and ICiid

I'itch

..1 Ke.ords

MA -low pitched

<)7-l05-lll (normal)

104

275 sec.

MB -low pitihol

112-115-112 U>iased)

n.i

. 222 biased toward
short records

M(" — high (litchi'd

12-t-131-134 (normal)

131)

.235 (biased toward
short records)

Ml) -high pitihcti

134-148-175 (normal)

152

. 305

Mean for male S|x;akers

125

. 259 sec.

Ki-nialc Speakers

FA — low pitched

224-24 1-209 (normal)

224

. 290 sec.

KB — low pitched

256-251-194 (biased)

234

.373 biased toward
long records

KC — medium

233-255-244 (normal)

244

.320

KD — high pitched

271-274-279 (biased)

275

.348 (biased toward
long records)

Mean for female speakers

244

.333 sec.

Mean duration

.296 sec.

These records were made without constraint Imposed on the speaker,
except that he had to start and stop within an interval of about one
second, and was requesteti to repeat the sound several times at what
he judjjcti to be constant loudness. The resulting variation in per-
formance may therefore be of some interest.

Of 52 men's records the vowel sounds 35 records showed a "normal "
effect of progressive rise in pitch during the course of the record. (The
mode is taken as the normal effect, and follows the mean very closely.)
In 6 records out of 13, speaker MB showed an individual or biased
effect of slight fall in pitch toward the end. The women's records show
greater variation, 24 records out of 52 showing a "normal" effect of a
rise in (>itch, followed by fallinii pitch, during the course of the record.
The individual bias of speaker KB towartl progressive fall in pitch was
shown in 7 records; that of KD toward progressive rise in 4 records.

The relative constancy in fundamental pitch shown b\- speaker MB
is best exemplified in Plate \o. .58. Speaker FD made 3 records of
constant pitch: N'os. 24, 40 and 48. Other records of constant pilch
arc Nos. 19 and 99, both by MC.

In duration, the bias of speaker MB towards short records was
shown in 6 records which fell short bv .08 sec. or more of the mean

610 PELL SYSTEM TECHNICAL JOURNAL

for the particular sound considered; that of MC also in 6 records
according to the same test. Speaker FB produced 5 records, and
speaker FD, 2 records loo long by the same amount.

Consider now the general properties of the spoken vowel sound, as
deduced from these records. First there is a period of rapid growth in
amplitude, lasting about 0.04 second, during which all components are
quickl\- produced, and rise nearly to maximum amplitude; second the
middle period, the characteristics of which have been noted, lasting
about 0.1G5 second, followed by the period of gradual decay lasting
about 0.09 second, bringing the total length to appro.ximately 0.295
second. There is a tendency to short duration among the "short"
vowels (eg. short o, e, i) and a tendency to longer records among the
broader sounds, as might be expected.

The beha\ior of the fundamental frequency (or "cord tone") during
the course of the record will follow normal or indi\"i(lual character-
istics as has been described.

The low frequency characteristic appears early, usually before the
fourth cycle (for men) or before the se\'enth (for women) and normally
is in harmonic relation with the fundamental. In the eleven pure vowel
sounds (omitting the ar and er groups) this point was examined at
264 locations in 88 records with the result that the harmonic relation
obtained in at least 214 cases. On the other hand the normal be-
havior of the amplitude of the low frequency characteristic suggests
the decay of a transient oscillation during each fundamental cycle —
this eflfect being noticeable in at least 64 of the 88 pure vowel records.
This transient effect was also noticeable in 13 of the 16 records of ar
and er, where the harmonic effect was not so noticeable. The appear-
ance of the transient effect depends to some extent on the relative
frequencies of the fundamental and the characteristic; where the
fundamental period is short, (as often in the case of the women's
records) there is not sufficient time for decay of the characteristic tone
before it receives a new impetus in the next cycle of the fundamental.

As noted above, all the records contain high frequency vibrations
which are of such amplitude that they suggest characteristic fre-
quencies. A general mean of these frequencies would be in the neigh-
borhood of 3200 cycles, and in the case of two records b\- speaker FC
(Group I and (iroup XIII) the frequency rises to about 5000 cycles.
Recalling the usual classification of the vowel sounds into two groups —
(1) those of "single" resonance, placed on the left leg of the triangle,
(Fig. 12) and (2) those "double" resonance placed on the right leg
of the triangle — there are some differences in the behavior of the high
frequency components which can be related to these broad classes.

THE SOUNDS OF Sl'EF.CU

611

CT —

5 3

Scattered
High Freq.

7.

•^1 O O 1/1 f^ O O lO ui p -1
— in 5 ^- •/> 5 m i~ >»l „, *5 O

-f -r T -r -c -T (-4 '»S'?.^<Q

= 1 . .r. -^1 ^1 -^ O Co ' 3 .
5 r^, 1^ — _ X O lO <^l lO

f»^f^f*f»ll»^w^fn ,^Xi St

•Si 5 >»

X v S

lb

>OmOS OOO'OvC
— , — OrM — ooai^l

m O O '^^ 00 O O 1^

■o o o 00 a IT) »
0> O' OO o o o- o-

•c c-
si

"5
1

5 o iM o ae m -^i

— ^'O ^^^ -r '^ f^ y/;

Ooo O O O O 1^
uioo'^m o «n —
r~o» ooo> — — c^

ill

s " -

E

— lo '^i f^i »n m '^ o^ — f-^ c in c^

-f -!f in r~ o ov o <~ o ■/-, I- -c ^1

"•IS

E

O O 1^ T^ -f — "^l i~ c "-. ~-, rg -t
rM fN CN cv| fN f^l f^l '^l "^I '^I *^i »^l f^l (^1

.1

3

Q

— CMnoo-om 'Cc- — m — — — —
r^ r^ f-^ CM e^l r*; f*: r^l -^i r*-, p^ rvi rn S^ S

Ss.

to
1

— o— ooo oo o3— O

•u

-a

'i

^0 — rOO't^a- 00— 1- fN 00 MS

n

>o m m '^. -f -^t ^. '^< ^ '^^ ^< -r

lilfill If lliLi

/.

S

^

_3

s

if

i

e

o

3
9

•1

^

e

8

I

1

!^

>r).

^

3

3

,,

!"

w

o

_g

f

!S

s

C

'n

g

E '■^i:

s--^

fl O w

j: „ 3

0

^ o ^

Co'-'

^

%^%

^

u

III

**

0

j:

■f";^

o

j: ~ o

a

H .-

1

1 ec-S

fMJl, o

111

a jj y

o

&12 BEl.I. SYSTEM TECIIXIC.IL JOURNAL

In the sounds of tin.' first class the high frequency component is usually
small in amplitude, more subject to individual bias in its frequency,
and may or ma\- not build up in amplitude as early as the low frequency
characteristic. In the sounds of the second class the high frequency
characteristic is usualh' prominent from the start and builds up very
rapidK-; while there is less \ariation in its frequency with the individual
speaker. In sounds of the first class there is no decided suggestion
of a transient in the high frequency (23 out of 40 records, (iroups
I to V inclusive) while in sounds of the second class the transient effect
is pronounced {3(1 out of 40 records. Groups VIII, IX, XI, XII, XIII).

With these considerations in mind there is presented in table IV
a summary of the data obtained from this preliminary examination of
the vowel records. The mean duration time, and its subdi\isions,
are shown in the second column for each pure vowel sound, with mean
duration only for the sounds ar (Group VII) and er (Group X). The
fundamental and characteristic frequencies of each sound are shown in
the 3 columns headed "Mean Fundamental," "Mean Low Character-
istic" and "Mean High Characteristic Frequency" respectively. Each
mean is taken from four records. The two columns headed "Scattered
Low" and "Scattered High Frequencies" contain mean \alues of
additional components, occurring in one or more records, in certain
frequenc\- ranges, the number of records in which such components
are noted being shown in parentheses following the mean. The table
illustrates and emjihasizcs many points which ha\e been brought out
in the preceding discussion, particularly the closeness with which the
high frequency characteristics are defined in the \f)wels of the second
or "doubly-resonant" class.

The table however gives no quantitative statement of the energy
distribution among the different frequencies and it is necessary now to
refer to the results of a harmonic analysis of these records which has
been made and published' from which the diagram of Fig. 13 is taken.
The machine method for analysing these wave-forms has been described
by Mr. Sacia in detail elsewhere;- it suffices here to note mereh' the
essentials in the treatment of the data.

For the dynamical study, the whole record from start to finish was
taken as the unit for analysis, and the data obtained are therefore
the average characteristics of the sounds throughout their duration.
In the form of an endless belt each of these records was passed repeated-
ly through the analysing machine. A single record is of course

'"Dynamical .Sludv of the Vowel' Soumls." Hill S\stein rechiiic.il Journal,
111, No. 2, .^pril, l'>24.

' (". K. Siiria: " I'lioloinechanUal Wave .Xnalyzcr .Applied to iiiliarrnonic Analysis;"
Jour. Opt. Soc. .Am. ami Ki\ . of .Sii. Inst., 9, Oct., 1924, |). ■iSl.

THE SOUNDS OV SlTJiCIl 613

a non-pKriixIio futution, ri-prcscntiHl analytirall\- l)y a Fourier InlcRral,
not !)>■ a I'oiiritT St-rics. The continued repetition of the record,
however, builds up a peritKlic function consistinjj of a fund.iniental
and a series of harmonics. The magnitudes of tliese components hear
a simple relation to those of the infinitesimal components of corrcs-,
pon<ling fre<iuencies in the Fourier Integral, and it is this series of
relati\e amplitudes at different frequencies which is given hy the
mechanical analysis of the records.

It would be possible to present these results as the sound spectra of
the vowels, showing their original acoustic pressure amplitudes' but
this treatment has been modified for practical reasons to take into
account the relative importance of the various pitches in hearing.
Using the available data on the relative sensitivity of the ear at
different frequencies* the pressure amplitude at each frequency has
been multiplied by the corresponding ear sensitivity- factor and the
resulting curses are taken as the effective amplitude frequency rela-
tions which are most generally characteristic of these sounds.

The data from the four male records and from the four female
records of each sound are separately averaged and the resulting curves
are shown in the diagram (Fig. 13). This averaging process was
somehwat laborious because the analyses of the separate records were
made not with reference to predetermined frequency settings, but
rather for those critical frequencies which best determined the shapes
of the spectrum curves. The individual curves were therefore plotted
on the musical pitch scale and the average ordinates were then read off
for small intervals of pitch. These ordinates were then averaged
for each group of four analyses. These average ordinates (after being
corrected for the calibration of the recording apparatus) were then
multiplied by the ear sensitivity factors for the corresponding fre-
quencies. Thus the final spectrum diagram shows the relative im-
portance of the amplitudes of all the components of each vowel for
male and female speakers.

The amplitude units are entirely arbitrary; it is only the shapes,

' In Fig. 1, data have liecn given showing the actual distribution of energy in
average s()cerh. The tremendous concentration of energy in the lower frequencies
is somewhat misleading unless account is also taken of the much reduced sensitivity
of the ear in this region.

♦See Bell System Tech. journal, \'ol. II, No. 4, Octolier, 1923. The paper on
Audition, by H. Fletcher, shows a graph of the "Threshold of Audibility" curve
from which these data were obtained. The ear sensitivity factors used, of course,
relate to the lower intensity levels; but it is thought that no essential inaccuracy
is thereby introduced, as the p<jsition of the characteristic frequencies of a given
vowel is subject to some variation with different sfx;akers, and moderate variations
in the height of these maxima in the energy spectra are not significant, except when
taken from cycle to cycle in the case of an individual sound.

614 BELL SYSTEM TECHNICAL JOURNAL

not the sizes of these curves which are significant. The order in which
these curves are arranged is based upon the vowel triangle, and on
Table I\'. To return to the general discussion, we find that the
fundamental voice frequencies do not have large efTective amplitudes;
it is interesting to note that these can be largely eliminated without
impairing the distinctive quality of a vowel sound. The "scattered
low frequencies" of the table (Sounds I to \TI) exhibit appreciable
amplitudes in the diagram. The "Scattered High Frequencies" of
sounds I-YII previously noted exhibit small amplitude in the diagram.
These are perhaps not essential to these speech sounds, but we should
expect to find them in well trained singing voices. They are to a
certain extent (particularly for the male voices), paralleled by the
high-frequency regions of resonance for these sounds given in Paget's
diagram, to which reference was made in Section I. Paget, it must
be noted, is convinced that these high frequency regions of resonance
are characteristic of the sounds of Groups I-VI.

The sound a (No. VI) is as it were the center of gravity of the vowel
diagram and occupies the key position in the phonetics of most lan-
guages. The broad feature of the diagram is of course the progressive
rise in frequency and gradual narrowing in range of the characteristic
region of resonance, till the sound a is reached, succeeded by a splitting
up into two regions of resonance which recede from one another as we
follow the diagram downwards from a to the end. The e.xact location
of sound X (er) is somewhat indeterminate, but it is evident that it
belongs in the series of doubly resonant vowels. It is interesting to
note that the distribution of the components of ar (refer either to
Table IV or Fig. 13) is similar to the distributions gi\en by Miller and
by Paget for a form of the vowel a having "double" resonance; it is
therefore as well located as any vowel in the series.

The characteristics of the r sound (whether considered as \owcl
or consonant) offer an interesting study, and in considering them
we have an illustration of the practical value of records of the
type shown. The problem of pronouncing a pure r sound is diflicult;
r is probably as variable in quality as any sound in the language, and
it differs more than any other sound from one language to another.
The precise location of its characteristic frequencies is thus a rather
diflicult matter. The records of ar and er disclose a noticeable tendency
in speaking to make these sounds into diphthongs, the earlier portion
of the record being nearly a pure a or (short) e while the latter portion
of the record increasingly displays r characteristic. One sj^eaker (MA)
succeeded in making records for these two sounds which have nearly
the same character throughout (Plates 49, 73), but for the other seven

THE SOUi\'l>S DF Sl'liliCIl

615

sjH\ikcrs, the "r" characteristics are best displayed toward tiie end
of the record, though there is no sharp traiisilioii point. In the sta-
tistical stutly of these sounds the data were taken from the latter
pt)rtions of the records; init in the mechanical anaKsis it was thought
best to use the whole recortl. Now abstracting and condensing the
data obtained in these two ways we have (ignoring; fnndnmcnial
tones) the following table of frequencies:

r {fir and er)

From Table IV

From Fig. 13

Male

Female

Male

t'eniale

Low

Middle
High.

/ 570-630

\ 917 (an

1688-1965

701-712
1012 (ar)

2162-2188

483-574
861 (ar>
1218-1448

1933 2896

512-542

861 861
1218 1448

j 1625 (er)

\ 2435-2435

These may be compared with Paget's results (from the second
memoir, in which r is classified as a consonant sound) taking one of
his general results from a mass of experimental data:

r (Paget: reference 9a, 9b p. 154)

"Throat or back resonance". . 400-700 cycles

"Middle resonance" 1 149-1824 cycles

" Front resonance" 1824-2169 cycles

(all varying with the associated vowel)

The italicized values in the first table above indicate correspondences
with Paget's data, and we conclude that these roughly define the r
sound, in terms of the steady-state theory.

Before taking leave of the vowel diagram, we should note not only
the location of the resonant ranges but also their extent, and their
relative separation from other resonant ranges in order to arrive at
essential characteristics of the vowel sound. In other words, the
individual vowel quality depends not only on a certain characteristic
region of resonance but on the relative pitches in case there is more
than one region of resonance. This eflfect is clearly shown to some
degree in every group save one (VII:r) in Fig. 13. It will be noted
that for the characteristic maxima of energy in the spectrum of a given
sound, the peaks in the curve for female voices tend to occur at a

616 BELL SYSTEM TECHNICAL JOURNAL

higher frequency than the corresponding peaks in the curve for the
male voices; but the musical interval between characteristic peaks
for a given sound is about the same in the two cases. It is only in
this way that we can account for what is a matter of universal ex-
perience in using the phonograph, namely that moderate variations
from normal speed in recording and reproducing speech leave the
vowel sounds still intelligible.

V.
Four Semi-Vowel Sounds*

Now consider the sounds /, ng, n, m, which pronounced with the
\owels 00, ee, a, following them, are arranged in Groups XIV and XV'.
Following the plan pre\iously used, note first the general characteristics
of these 24 records, made by the two male speakers MA and MB.
An outstanding feature of the records is the diphthong quality which is
clear in all: the transition is quickly made from semi-vowel to the
affixed vowel sound and except in two records (Plates Nos. 108 {lee)
and 113 {ngee) a definite transition point can be fixed. Marking this
point for all records we find an a\'erage duration of 0.16 second for
the semi-vowel sound, of 0.21 .second for the vowel sound, mean
total duration being 0.37 second. Noting the fundamental frequency
in two locations, namely at the start and just before the transition
point, it is found that there is a progressive rise in pitch during the
record of the semi-vowel sound; this effect is in agreement with the
indi\idual characteristics of these two speakers previously noted
in the pure \owel records. But in addition it is noted that the average
fundamental for these two speakers (see Table V below) is somewhat
below that previously used by them in the vowel records. (Refer
also to Table III). This slight lowering of fundamental pitch ma>-
possibly be a characteristic of the semi-vowel sounds; and this effect
occurs, as we shall see later, to a pronounced degree in the consonant
sounds.

The amplitudes of these semi-vowel sounds are on tlic whole smaller
than the amplitudes of the affixed pure \owel sounds, but some of
them are surprisingly large. The low frequency characteristic of /
is (for these voices) principally a third harmonic of the fundamental.
With 11 and tig (which are nearly indistinguishable) the second harmonic
becomes increasingly important, and in the m records it is very
large. The high freijuency characteristics of all four sounds lie between
2400 and 21(00, falling somewhat as we pass through a sequence from

' A pri'liiiiinury report has beuii inatic on the properties of these souiuis, and their
relation to the general vowel iliagrani. (I'hys. Rev. li, 1924, p. 309.)

THE sorxns or srnEcii

TAHI.K \
Speakers' Characleriitics, Semi-Vowel Sounds

t>\7

l>i

r.ilion in .SoioikIs

Mf.in Kiiii(la'iiciUal
(Senii-Vowi'h

Semi-Vowel

Vowel

Total

At Start

Before
Transition

I

IK

n

m

.16
.16
16
.17

.20
.20
.22
.20

.36

.36
.38
.37

100
101
98
100

107
104
107
105

Mean

16

.21

.37

100

106

/ to m. Wv have here, then, a Kron]) "f doiihK' resonant sounds whoso
characteristic frequencies, whose amplitiuies, and general l)ehavior
arc such that the\- must be definitely related to the standard \o\vel
diagram.

The amplitude frec|ueni\- rel.itioiis as ohlaiiied from a iiHchaniial
harmonic analysis, and corrected for the \ariation in sensitivity of the
ear are shown in Fig. 14. The process of mechanical harmonic anaKsis
has been outlined in connection witii liic \(iwel records, and the pro-
cedure was the siime here, except thai only the semi-vowel portion
of the records was taken as the unit for analysis. The record for
analysis was cut at the end of the last cycle before the transitif)n
point, anfl two profile copies of the semi-vowel wave were joined to-
gether in an endless belt which was passc^d through the analyzing
machine.

Aside from the close resemblance between the frer|iienc\- spectra
of the four sounds the noteworth\- feature of F"ig. 14 is in the similarity
between the / spectrum and that for ee as previously given in line XIII
of Fig. 13. The essential differences arc a slight increase in the
importance of the low frequency characteristics, and the slight shift
of all the resonant regions toward low-er frequency, in passing from
e to /, and on through the sequence m?, «, nt. We may thus regard
the chart of Fig. 14 as a logical continuation of the generally accepted
chart of Fig. 13 and place the four semi-vowel sounds definitely in an
extended \owel diagram, following in regular order the sound long e.

Sir Richard Paget has made the interesting statement that "all the
consonant soimds are as essentially musical as the vowels, i. e., they
depend on variations of resonance in the vocal cavity, and should be
capable of being imit.ited in the same wa\', if tiieir characteristic

618

BELL SYSTEM TECHNICAL JOURNAL

resonances could be identified and reproduced in models." It is
interesting to compare some observations made by him on /, ng, n,
m, and reported in liis second memoir. Working according to the
method previously described (§1) Paget has constructed resonators
which, under certain conditions, will produce transient forms of the
four sounds we are discussing. Their tone constituents are identified
by him as follows:

Reson.ant Frequencies, Semi- Vowel Sounds
(Paget: Reference 9b)

' Throat '

228-406'

203-228

203-228

271

'Middle" (Nasal)

683 (faint)

683

541-724

1217-1366
1217-1448
1217-1448=

"Upper" (Oral)

1625-1932'
1448-2169'
2298-2579
861-1722'
2434-2579 (faint)

' Varying and finally approximating a characteristic region of resonance o( the
associated vowel.

' Varj'ing with the associated vowel.

.Siu(l\ing Paget's results in comKction with those ot Fig. 14, we
note that the energy spectra clearly show the "throat" resonances
for all four sounds in the neighborhood of 25(5 cycles. In the case of
« the nasal resonance at G83 cycles (Paget) is one of the prominent
tones centering around a frequency of 512 in the spectrum diagram.
This resonance also appears prominently in the spectrum for m though
Paget did not notice it. The higher middle resonances (1217-1448
cycles) which appear in Paget's table for the last three sounds appear
also in the spectra for these three sounds according to Fig. 14. Allow-
ing for the variation stated in notes (1) and (2) above, it appears
that the upper (oral) resonances for the four sounds, as noted by Paget,
are essentially the same as those that appear in all four spectra in the
diagram in the range of 2048-2896 cycles.

With regard to Paget's observations on the transient character of
these sounds (he classifies them as consonants) and on the variability
of some of their components (Notes 1 and 2 of table above), depending
on the associated vowel, there is room for some difference of opinion
and the reader may form his own conclusions after a detailed inspection
of the records shown. Taking the sound 1 for example, and studying
first the three records loo, lee, la by M A and then the three correspond-
ing records by M B it seems to the writer that such variations as are
noted in characteristics are due not so much to change in the associated

THE SOUXnS or SI'IHUIl 6I9

\o\\rl as to (hf rl).ini;<.' ill llu' s|H'.ikfr, .iiul ,i >imil.ir cniuhisidii will
pr()l)al)ly hi' riMclu-il lor iMch of tlu- oiIht tiirru M-mi-vowrl sounds.

I'roiii the oviiii'iici- in the records, it is dil't'iriiit to siihsrrilH- entirely
to a "transient" theory of these sounds, at least when they precede
the standard \o\vel sounils. The evidence justifies the use wiiich has
lieen niaiie of the steady-state itlea, and the harmonic analyses leading;
to a determination of characteristic frequencies. IJut there is a
(M)ssil)ility that the harmonic analysis does not tell the whole story.
These two groups of records and the acoustic spectra based on them
furnish outstanding examples of the niceties in\olved in speech and
hearing in order to achieve the miracle of articulate speech. Without
harmonic analysis, the most casual observer will note, for example,
the similarity between the corresponding records of the / and » sounds,
but more astonishing still is the resenil)lance between the I and ee
sounds shown together in Plates Nos. 107 and 108. In this latter
case (,/ and ee) practically the same high and low characteristic fre-
quencies are involved, and it would seem that the distinction, which is
sufficiently pronounced to the ear, must l)e based to some extent not
only on the relative amplitudes of these frequencies present, but also
on the behavior of these amplitudes during the fundamental cycle.
It will be noted in practically all of the records of these semi-Nowel
sounds that the high frequency characteristic is a transient of more
rapid decay than in the case of the pure vowel sounds; it is not of
large amplitude except at the beginning of the cycle. On the face
of the records this is the only explanation available for whatever dis-
tinctive quality these sounds, as a class, must possess.

VI

Si.XTEiiN Consonant Solnds

The last two groups, X\'I and X\'II contain, respectiveK", records
of the "hard" and "soft" consonant sounds, each with the a sound
affi.\e<l, and pronounced by the two male speakers. Here the classifica-
tion is somewhat arbitrary; it is difficult if not impossible to arrange
the sounds of these two groups in any such satisfactory series as has
been determined for the semi-vowels of the two preceding groups.
The sounds dth (that) and th (thin) for example have transitional
characteristics that relate them to both groups; but they are placed
at the end of Group X\I, to emphasize their relation to the pair v/f
of the last group. With these reservations as to arrangement, consider
the general characteristics of the consonant sounds of these two
groups.

620 BEI.I. SYSTEM TECUXfCII. JOrRX.II.

Examination first discloses a relatively easy separation of a given
record into a consonant and a vowel portion and, as might be expected,
a longer duration for the "voiced" consonants. In all the voiced
consonants a sufficient portion of the record is reproduced to illustrate
the voicing or fundamental of small amplitude in the early stages of
the record ; in the case of the unvoiced consonants of ( jroup X\'I this is
not necessar\\ In the case of both the voiced and unvoiced con-
sonants of Group X\'II, longer records are shown, the high frequency
component making this necessary, although the fundamental does not
appear in the early stages of the unvoiced consonants of this group.
The mean duration of the voiced consonants (b, d, g, dth) of Group

XVI is 0.14 second ; of the unvoiced consonants {p, I, k, th) 0.05 second.
Aside from traces of the fundamental tone (and traces of its second
and third harmonics) there is nothing of interest in the early stages
of three of these four voiced consonants; in the case of dth there are
traces of a high frequency (4200 and 2(100 in the two records) in the
early parts of the fundamental cycle. The voicing for all four sounds
if uniformly of lower pitch than that used later in the records in speak-
ing the vowel sound. Leaving the early stages, the record then pro-
cet'tis to a transition point, lasting through from one to four cycles of
the fundamental, and culminating in the appearance of the vowel
sound. Before this transition point is reached, traces of high fre-
quency appear in most cases, sometimes suggesting a single transient
vil)ration. Aside from the lack of the fundamental vibration, there is a
further distinguishing characteristic of llu' "umoiced" sounds: a
tendency of the first transition cycle of the fundamental to appear
from 10 to 20 per cent shorter in duration than the mean of several
following cycles. With both \oiced and un\oiced sounds there is a
tendency for a moderately low frequency (500 to 700 cycles) to appear
during the transition; also a high frequency (of mean value 3225 cycles
for the IG records of this group) which latter may be due to the begin-
ning of the a sound. Some of the individual characteristics of the.se
records are given in Table \'I.

The notable distinction between lliese sounds and tiie sounds of the
next Group (XVII) rests on duration factors, and of even more im-
portance, the pronounced high-frequency characteristics of the sounds
(jf the last group. The mean duration of the voiced sounds in Group

XVII is 0.21 second; that of the unvoiced sounds, 0.18 second. Two
of the other characteristics are similar to those noted in the preceding
group; first the voicing, where it occurs, is of abnormalh- low frequency,
and second in the case of the unvoiced sounds, there is a marked short-
ness of the first fundamental cycle at the transition point. E.xcept

THE SOUNDS or SrF.ECll f»2I

in the rase of the sound t' (Plates 14") ami 14()) the hi^li frer|ucncies arc
IHTsisti-nt and in many rases of !a^^Je amplitude, both at the start and
during the course of the consonant soimd. Thi'se frequencies rise,
as we Ro throuijh this^roup. to values of 7000 and 8000 cycles in the
case of the sounds z and s, shown in the last four records. For a
full appreciation of these pronounced high frequency characteristics
reference must be matle to the records themselves, or the siniimary of
char.icteristics, in Table VII. Here again, in distinguishing these
sounds the remarkable pierformancc of the ear is manifest, and the
recording apparatus is used nearly to the limit of its utility.

We may best conclude this discussion of the consonant records by
brief comments on some of the individual sounds, and a comparison
where possible with data given for them in Paget's second meinoir.

B P.— (Plates 129-132). Both Paget (ref. 9b, p. 165) and Miller
(rcf. 3) have noted the essential impulsive quality of these sounds, and
have pnKluced them by sudden closing and opening of the mouth of a
resonator. Paget considers p to be the more suddenly released, i. e.
to have the steeper wave-front. From the records this is not evident;
following the voicing pericxl, the h would seem to be more suddenly
produced, as judged b>- tlie growth in anii)liiu(k- of tlu- <; siniiui lol-
lowing.

D'T.— (Plates 133-131)). For both of these (see either Table \1
or the records themselves) we note a high frequency characteristic of
about 4000 cycles. Paget (9b, p. 168) observed "an upper resonance
5 to 8 semitones higher than that of the associated vowel, and a low
resonance of about 362." We note in the records a low frequency of
the order of 500 in the case of d. Paget notes a "greater amplitude
in / clue to higher air pressure" and the records show a greater ampli-
tude for the high frequency in the case of /, except right at the transi-
tion point, where d shows the high frequency of large amplitude.
No conclusion can be given as to relative steepness of wave-front, d
vs. /, because in both cases we note for speaker MB (Records 134,
136) a steeper wave-front than for MA (Records 133, 135). The
difference between d and / may depend entirely on the voicing and on
the complicated phenomena at the transition point.

G K. — (Plates 137-140). k shows the characteristic transients
(1.500, 4000; Table IV, notes 4 and 5) to much more pronounced degree
than g. From the records it would seem that g, in addition to the
voicing, disclosed a steeper wave-front, the four transitional cycles
required for k (records 139-140) emphasizing this point. No other

622 BELL SYSTEM TECIIXICAL JOURNAL

generalizations seem warranted, on account of the complicated series
of events recorded. These sounds are treated at length by Paget (9b,
p. 171-173) who observes considerable variation in their resonant
ranges, depending on the associated vowel. It will be noted howc\-er,
that in these four records particularly, consonant characteristics are
persistent and of large amplitude before the vowel sound begins to
appear.

DTH/TH.— (Plates 141-144). The high frequencies (2UU0, ;jOUO,
3200) culminating at the transition point seem to be the key to these
records. They are more persistent for dth, while th appears to show
the steeper wave-front. Paget states (9b, p. 158) that "in 5 [(///;]

the middle resonance (1149-1932, his figures] is overblown, louder

than the corresponding resonance in B [th]." He gives also an
"upper sibilant of 3444-5950," louder for dth than th, and "difficult
to identify." It will be noted that in one record for dth (no. 141)
there is during the voicing period a faint high frequency which has
been set down in Table \T as 4000 cycles. This faint "sibilant"
(which may always be audible though it fail to be recorded) establishes
a certain kinship between these two sounds and those following (the
fricative consonants) which are rich in sibiliant sounds.

V/F. — (Plates 145-148). v shows a pronounced \oicing, and as
pre\iously noted, a less prominent high frequency component than
its partner/, or any of the other fricative consonants. Comparing
V 7 with dth/lh it seems from the records that the former pair are of
higher frequency (particularly/) and that for v/f as a unit the high
frequency characteristic is more pronounced; just the opposite con-
clusion to that reached by Paget (9b, p. 161-162). / may indeed
differ more from v than v from dth, thus raising difficulties of classifi-
cation both physically and phonetically, which cannot be resolved on
the basis of the few records available. The exceedingly fine distinc-
tion between the sounds v and dth could be no more strikingly shown
than it is in the records gi\en, for both speakers.

J/CH. — (Plates 149-152). Some of the recorded phenomena of
this pair suggest correspondences between them and the pair g/k;
luit the pair j/cA shows a higher frequency characteristic during the
important mid-portion of its history. Of the pair, ch seems to show the
steeper wave-front, that is, the more rapid transition to the vowel sound.

ZH/SH.— (Plates 153-156). With this pair we pass to the field of
pure sibilants, in which there is no evidence of impulsi\e action or
steepness of wave-front. The action seems to be that in the voiced

THE SOUNDS OF SPEECH h2i

souiul, tluTC is, in addition t<i the pri-sinirc of the fundamental tone,
a breaking: up of the eharacterislic hiy;h fref|uen(y wave-train intf)
discrete units correspond in^j to the fundament.il tone, where.is in the
un\-oiced sound the hi^h fre(|uency characteristic is continuous, though
irrei;ular. Thus noting tiiat the characteristic frefiuency is of 3000 to
HUM) cycles the outstandinij phenomena of zh sh are well defined. In
adilition to frequencies of 2048-324!) noted by Paj;et (91), p. KY.l) he
gives a "pronoimced middle resonance of U)2')-2048." This latter
observation of Paget's may correspond to the 1800-2000 fref|uency in
the records of MB (Plates 154, 15G) in the transition region, but this
component does not seem to be prominent in the records.

Z/S. — (Plates 157-160). The general properties of these sounds
can be inferred from the discussion of the preceding pair (zli/sh), add-
ing only the fact that their principal characteristic is of much higher
fretjuency. From Table V'll we note a range of 4200-8000 cycles;
P.iget (9b, p. 162) gives "a characteristic upper resonance of 5790-
6886." Paget also gives "a middle resonance of 1084-2298." The
records do not show as low a range of characteristic frequencies unless it
be the frequency range 2200-2800 (see Note 1, Table VII), within
which fall certain \ibrations occurring in the early parts of the funda-
tnental cycles of the voiced sounds sh and s. The true s sound is,
as Paget has stated, "a relati\'ely complex hiss" and this is true of sh
as well. And to complete the record, we must observe that sh and z
are even more complex, if possible, and thus not inappropriate ex-
amples of the sounds of speech with which to conclude this sur\'ey.

To summarize, we have considered some of the more outstanding
features of the w-ave forms of speech sounds which have been re-
corded. Many more detailed properties of these records deserve
further study. The progressive change in wave form from cycle to
cycle of the fundamental, particularly at the beginning of a sound,
is undoubtedly an important factor in determining the character of
speech sounds; it becomes most important, as we have seen, in the
study of the more impulsive consonant sounds. There is material in
these records for extended studies of this kind, which require a har-
monic analyzer of a large number of components. \Vc have not dealt
with the question of the inherent power in speech sounds, another very
characteristic property; these important data are accurately given
in a paper by C. F. Sacia in this issue of the Journal. The relative
power in consonant and vowel sounds can also be determined from
those records in which vowels and consonants appear in combination,
and it is hoped to carry this study further. Many other investigations

624 KEI.L SYSTEM TECHNICAL JOURNAL

of speech arc now made possible on the l)asis of the accuracy of this
set of records; in conclusion we may emphasize the fact that, for the
present, the record is the important thinj^, and we believe that a set
of faithful records opens a new prospect in the field of speech investi-
gation.

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Speech Power and Energy

By C. F. SACIA

Introduction

IN the (i.ist, iiukIi rescarcli lias been devoted to tlie determination
of tlte relative magnitudes of the frequency components of speech,
and the results of these explorations are useful and well known.
Thus the communication engineer is apprised of the frequency range
over which his apparatus should respontl uniformly in order that the
transmitted speech suffer no frequency distortion. But to provide
against load distortion, he requires the knowledge of a different kind
of data : numerical values of the magnitude of power involved in
sp)€ech waves as a whole. This investigation deals with the magni-
tudes and forms of speech wa\'es primarily in terms of power, and
is not concerned with frequency as the argument.

Although the subject matter is not fundamentally new, this treat-
ment of it is somewhat of a venture. The broad classification of power
is a convenience here, but its future value will be dependent upon
engineering usage. I have also introduced the use of the peak factor,
which, being a simple index of the wave form, may perhaps find
application in vowel study and phonetics as well as in the technical
field. A condensed table of peak factors was incorporated in Mr.
Fletcher's compilation in the preceding issue of this Journal.

Derivation

The nature of power in a syllable of speech may be most easily
comprehended by reference to an illustration such as that shown in
Fig. 1. The representation of the instantaneous power (P,) is an
enlarged copy of a power oscillogram of the word "quite." Because
of its extreme jaggedness, the curve had to be represented by a profile
rather than by an outline. Although this is a quickly spoken syllable
it plainly displays a cyclic repetition; the cyclic interval (for example,
from a to 6 in the figure) is ordinarih- called the vocal f)eriod and its
reciprocal, the v'ocal frequency').

One feature of interest may be noted here: the irregularity in the
growth and decay of the peaks. This is evidence of a slight vocal

' The power due to any pcrioflic force, containing only odd harmonics, fluctuates
with double the frequency of the fundamental; but in the case of any periodic force
containing even harmonics also, the power fluctuations have the same fundamental
frequency as the force. .Although speech sounds are not periodic an analogous
relation exists for them.

627

628

BEI.L SYSTEM TECHNICAL JOURNAL

tremolo. Tremolos usually occur in singing voices and \ary widely
in their character. They constitute modulations which in actual
singing sometimes occur as slowly as two per second. The slower
mo(liilation.s affect the ear as beats or pulses, while the most rapid
ones affect the (|ualit\- by the resulting sidebands of overtones. Those

i-.li'.Lll

li

Hi

k

1 , , n--

n J...1 1 I •—11

1500
I4O0

<0-

<+ eoc
o.-

P„T 50
-1- O

Time 3cale

O O.OS 0.10 0/5 0.20 SEG

l''ij,'. 1 — InslantaiK-iiiis ami mean pcnvcr. Enlarged copy of original oscillogram
of the word "QUITE"

shown in the figure are of the latter l\pcs, their modulating frequency
being about 50 per second.

Frt)m the instantaneous power we derive the mean power, Pm, whose
chief significance lies in'.'the fact that it is the kind of power that
would be read by a quickly acting wattmeter; it is likewise propor-
tional to the deflection shown by the ordinar\- a.c. \olt meter or

SPEECH POWER AND ENERGY (^

.iminetcr, or by the volume indicator. A graph of the mean power
may be obtained by drawing the average jiower in each vocal cycle
and then drawing a smootli curve tliroiigh the resulting broken hne.
This wouUl be an impracticable way of olitaining curves of mean
[)ower; actually they have been obtained independently of the P,
curves in this work, in a manner described later.

X'owel sounds carry by far the most of the power and energy of
speech, and it was to them that the above considerations were tacitly
applied; but the definition of the mean power is similarly applicable
to the semi-vowels, voiced consonants, and fricative consonants.

The peak factor is the square root of the ratio of a peak value of P,
to the corresponding value of Pm-

Still another commonly used interpretation of power is made
in terms of its average over an entire svllable, word or speech. Such
an average, although the same for instantaneous and mean power,
is most easily determined by means of the latter: it is the total energy
divided by the time involved. Graphically it is the area of the P,
or Pm curve divided by the base. If the base includes the silent
intervals between syllables the result will be called the long average;
if the silent intervals are excluded from the base, the result will be
called the short average.

Thus it is seen that the word "power" when applied to speech has a
variety of meanings and always needs to be qualified. For example,
the speech of a certain person may have shown a long average power
of 10 microwatts while the instantaneous power frequently rose to
2,000 microwatts.

In obtaining the power, w-e obtain indirectly the pressure on the
condenser transmitter, which is located 9 cm. from the speaker's
lips. In the treatises on acoustics, the power of a simple-harmonic
wave is derived in terms of the pressure,- the numerical result being
at 20° C,

where P is the power in microwatts across 1 sq. cm. of wave front,
and where either mean or peak value is taken for both power and
pressure. Here we are not concerned with simple harmonic waves,
but the same result holds for instantaneous, mean, or average values
in any kind of wave, since

\0^ dl
• Scf, for example, Rayleigh: Theory of Sound, Vol. 2, page 16.

630 BELL SYSTEM TECHNICAL JOURNAL

and the air particle displacement,

^=-r:j— ; / pdt (41.0 is a resistance factor)

for a wave travelling in the positive direction.

From the power intensity thus found at the transmitter we can
obtain an estimate of the power dev^eloped by the speaker. With
the transmitter surrounded by a plane reflecting surface so as to
give reflection for speech frequencies, the pressure is doubled and
the power intensity quadrupled ov^er the values they would have in
free air, hence the observed intensity is divided by 4. The usual
assumption is made that this same intensity is distributed over a
hemisphere whose center is at the speaker's lips. Hence the required
estimate of the speaker's power is obtained by multiphing the meas-

ured power intensity at the transmitter by the factor — = 127. For

the sake of convenience, these two values are always given together
in the accompanying tabulated results.

Instantaneous and Mean Power
In dealing with the power in a syllable, the matter of greatest
interest is the maximum values attained by Pi and Pm throughout
the entire syllable. These maxima will be denoted by Pi and Pm,
respectively. Table I shows their approximate ranges in the case of
accented syllables.

TABLE 1
Instanlutieous and Mean Power
Typical Maximum Values for an Accented Syllable
Speaker's Power Power Per Ciii.-
Microwatts at Transmitter

£i 1000 to 2000 8 to 16

Pm 60 to 120 0.5 to 10

At this point it is worth while to consider an application of the fore-
going. A salient characteristic of speech waves is the generally high
ratio of peak value to mean square value (peak factor), as can be
inferred from Fig. 1. Failure to take this into account frequently
causes load distortion in speech transmitting amplifiers. It sometimes
happens that the effective output voltage or current has been meas-
ured, and the assumption of an equivalent sine wave (i.e., one having
the same effective value) is made; but this leads to a large error in
the estimate of the peak value. Thus with an insufficient allow-
ance made for the peak voltage impressed upon the grid of the tube,
there is the possibility of the grid becoming momentarily positive due
to insufficient negative bias or still worse, the plate may be over-

SPEECH POWER .-I XI) ENERGY

Ml

In.ulod liy ihc peaks. The resulting; suppression of the peaks in the
sound output can readily be detected by an accustomed ear, provided
that the whole system is reas<inably free from frequency distortion.

Avi:ra(.k Powkr

In Tables 11 and III are summarized the obserxations made u|)<in

the two speeches which were used in this work. There are two reasons

for showing theni separately: the two speeches were not spoken in im-

HK'diate succession; and they differ somewhat in character, the first

being declamatory while the second is of a more conversational nature.

This difference is not \Qry great, but should account ne\ertheless, for

the slightK- higher values in Table II. By taking the weighted mean

of the first number in both tables, we obtain 7.4 microwatts as the

long average power in normal speech.'

TABLE II

First Speech, 50 Syllables

Average Power in Microwatts

Long Average

Short Average

Speaker's
Power

Per cm'
at Trans.

Speaker's
Power

Per cm'
at Trans.

8.6
8.2
9.0
10.6
17.0
7.0
5.7

0.067
0.064
0.070
0.082
0.131
0.055
0 OM

13.1
12.7
13.5
17.1
21.8
10.8
8.8

0 102

Composite of 8 male
Composite of 8 female
Maximum male

0 099
0.105
0.133
0 169

0 084

0 069

TABLE III
Second Speech, 72 Syllables
Average Power in Microwatts

Long Average

Short Average

Sneaker's

Per cm=

Speaker's

Per cm*

Power

at Trans.

Power

at Trans.

Composite of 16

6 6

0 054

9 9

0 080

Com(X)site of 8 male

6.2

0.050

8 9

0.072

Com()Osite of 8 femali-

7.1

0.057

10 8

0 087

Ma.ximum male

8.1

0.065

13 0

0.105

Maximum female

9.8

0.079

15 1

0.122

Minimum male

3 9

0.032

5.7

0.046

Minimum female

4 0

0 033

6 0

0.048

Note: The average ratio of the total time in the silent gaps to that consumed by
the syllables is 0.55; the syllables average 0.16 sec.

' Crandall and MacKenzie gave an estimate of 12.5; B. S. T. J., \'ol. 1, .\o. 1; Phys.
Rev., Mar. 1922.

632

BELL SYSTEM TECHNICAL JOURNAL

Stress

Since our observations have sliown qualitatively that the louder
syllables ha\e the greater rise of mean power, means are available for
calibrating the stress modulation of the voices under test. To form a
discriminant for each speaker we proceed in the following way:

(1)
(2)

(3)

(4)

Measure the Pm of each syllable;

F"ind the ratio of each Pm to the greatest Pm occurring in the
speech; call this ratio e;

Find the proportional number, s/j, of syllables for which t is
greater than the magnitude n, where n nia\' vary between
Oandl;

Plot the variables s,^ and n against each other to give the re-
quired curve.

Enehgy Stkess
l-'ig. 2a — Composite stress curves of 16 voices

The analogous relation between s\llal)ic energy and stress is found
by using the total energy of eacli syllable instead of Pm in the above.

A large number of these curves has been so obtained, but it will
suffice to consider here a few of the representative types. F"ig. 2a

SPEECH roni.R .ixd nxr.h-cy

(M

shows composite curves and Fig. 21) gives a series of cadi kiiul nf iur\es
for four speakers. Note the changing mode of stress wliirh is shown
in the se(iuence from top to bottom; in tlie first case tiie sylhiblcs of
weaker stress greatl\- predominate while in the last ca.se there is a
more nearly uniform distribution of the syllal)les with respect to Ui\
degree of stress. It is e\ident from a comparison of the two series

;i

V.

c

<i

t

i a /c

5—^^= 1

2 a ~S o

Powee ^reesi ^Ntea-y Stress

Fig. 2b — Types of stress curves

that the speaker's type is much the same whether judged by the power
or energy standard. An exceptional case might arise, however, if one
should put emphasis on a s>llable by prolonging the time of utterance,
for here the increased energy of the syllable would not necessarily
mean a greater stress. But from the point of view of phonetics, the
energy method should be useful in calibrating emphasis, which can be
taken as a function of time of duration as well as of mean power.

634

BELL SYSTEM TECHNICAL JOURNAL

Relative Power of Vowels

One test which was made on the speakers was for them to utter dis-
connectedly and without accent eleven monosyllables, each of which
contained a fundamental vowel sound. The results of this test give a
general indication of the inherent power, Pm, in unaccented (but un-
slighted) vowels relative to each other. The difference between the

f°

ia

Kie

,^/l

44

l"'

r i

J,

\ ,»

.M

J3

1 ■'^

1 2<»|1

|5'

,30

,32

ja

.27

26,1

1

25

i

ZL.

>2a

Fig. 3 — Inherent relative power

Indicates Male Voices

Indicates Female N'oices

Numbers indicate approximate power from voice (in microwatts)

male and female voices in this respect warrants separate charting of
these characteristics. Fig. 3 shows the chart in which the vowels are
arranged in the sequence^) the first half of which accompanies an
increase in the angle of the speaker's jaws, and the succeeding half
accompanies an increase in the elevation of the tongue.

It might have been anticipated that the more open vowels have
more power; but there is apparantly one irregularity in this tendency
in the case of the vowel o (as in ton). Furthermore, the vowel e (as
in teem) looks somewhat different for the two voices, when compared
with the vowels immediately preceding it in the series. There is some
difficulty in uttering it so as to make it carry, in the case of female
voices — a fact which I have previously encountered when recording
them. The male voice, on the other hand, shows a decided rise in this
direction. The advantage in the case of u (tool) is reversed: here the
male voice begins to fall off while the female voice stays about the
same. These results suggest a difference in the resonant structure

* This arrangement is based upon the well known vowel triangle of Vietor.

SPEECH POWER A\n ESEKGV

635

between tlie male ami female voices, which, however, does not affect
the higher frequencies enough to alter the vowel characteristics.

Pkak Ka( tor

The tests just described were also used to obtain the peak factors of
the vowels. These were lietermined by measurement of the maximum
Pi and Pm of each syllable and arc charted in Fig. 4. Here again there

31, 39

Av£itAaE Peak Factob.

so, „ . ASX

AvERAoe Fon 8 Male Voices

u, yii

AvtRAoe fo« fl Female Voices
i4, as, '9 1 i6,

HidMeST Set fok any Male Voice

60, sa ss

High

Eir Set fob anv

Female Voice

*9

41 "

46 5', '^

14

34

16

ib.

Oooaooa'ua-J;
13 30-0 o « -;] « iq - «
Fig. 4 — Peak factors of vowels

are differences between the sets for the male and female voices, the
former being somewhat higher, especially for the vowel e. In both
cases such rasping vowels as k (tap), e (ten), a (tape) have sharp waves
and high peak factors. Having listened attentively to all these voices
under test, I have become able to associate peak factors with vocal
qualities in the following way: the voices with the higher peak factors
are those which in the ordinary terminology are said to be "resonant"

636 BELL SYSTEM TECHXICAL JOURNAL

or "vibrant"; they have the greater carrying power, especially over
the telephone; they are rich in the musical sense and are therefore well
suited to singing, although main- such \-oiccs, unfortunately, are ne\er
applied to the art.

To illustrate an application of the peak factor to engineering, we
shall again take into consideration the speech amplifier whose mean
efTective output voltage is indicated by a suitable device such as a
volume indicator. F'rom this, the peak value of the instantaneous
voltage is wanted; to find it necessitates a knowledge of the peak
factor. Now since the latter differs somewhat for different sounds and
speakers, it is necessary to use one factor which makes allowance for
the worst cases (highest voltage peaks) which can occur often. For
most purposes, the factor 5 will suffice, hence the rule is: the mean
effective voltage should not exceed one-fifth the overload voltage of
the system.

Apparatus

In order that the apparatus (see Fig. 5) be a faithful recorder, it
was made with the following characteristics:

(1) A nearly distortionless reproduction of wave form by the con-

denser transmitter and amplifier.

(2) A full-wave parabolic rectification of the amplifier output.

(3) Load capacity sufificient to transmit the high sharp peaks of

speech waves without cutoff.

(4) Uniform response, from 0 to 6000 cycles in the oscillograph

vibrator recording instantaneous power.

The calibration of the amplifier and condenser transmitter is shown
in Fig. 6. To make the overall characteristics so nearly uniform it
was found necessary to use the resonant circuit in the output of the
second N tube, this compensating for an irregularity due mostly to the
45 feet of cable which leads from the transmitter and first stage of
amplification in the sound-proof room to the main part of the amplifier.

The oscillograph (see Fig. 5) was provided with two series connected
vibrators one of which was sensitive to low frequencies only, and re-
corded the mean power. Although it did not completely suppress the
fluctuations of vocal frequency, it reduced them to the order of small
superimposed ripples through which the Pm curve could be drawn.
The instantaneous power was recorded by the other \ibrator whose
characteristics are noted in item (4) above.

srr.r.cii rotiT.R .ixi> r.xr.RGy

f07

638

BEl.L SYSTEM TECHNICAL JOURNAL

TABLE IV
Calibration Constants

(a) Constants of Vibrators I/D =

( I ) Low frequency 5 / niilllamperes

(2j Instantaneous power 286 \ per cm.

(b) RectificT constant E- I = /iO (volts)-, niilliamp.

(c) Pressure on transmitter vs. amplifier output p-/E' = 1/2.95' dynes-,'cni* volt'.

(d) Power intrnsit\- at transmitter vs. pressure P, p- = 1 415 cm- microwatts dynes-.

p- peessuKE IN PYNE.S/CM' on transmitteiz diaphrai^

E= VOLT ACiE OUTPUT OF AMPLIFIEfZ

7000 ' 7O00 ' 3060 ' 3060'

Fig. 6— Calibration of condenser transmitter with amplifier

3O05 6060

The product a b c d gives Pm/Z?m = 0. 192 microwatts per sq. cm.
of wave front as indicated by a deflection of 1 cm. of the oscillograph
low frequency vibrator. Similarly P,/I', = ll.l for the instantaneous
power \'ibrator.

Method

Records were made on sensitized paper strips G cm. wide mo\ing at
a velocity of about 20 cm. per second. Three graphs were traced
simultaneously, the instantaneous power, the mean power, and the
timing wave of 100 cycles from an oscillator. When connected speech
was being recorded, the oscillograph operator listened to the speech as
reproduced !)>• the loud speaker and punctuated the record at frequent

SPEECH POWER AND F.NEKGY 639

pro<U-tormiiu'(l points by tapping a key which momentarily displareil
the timing wave. By the aid of these punctuations we were enabled
to identify the words and syllables on the records after development.
The areas for computing average power W'ere measured from the mean
power curve, while the instantaneous power curve was measured only
for its peak values.

Although chosen at random, the speakers used in these tests repre-
sent all sections of the United States. Their types range from soprano
to bass-baritone, neither extreme type — high soprano and bass — being
available; but this assortment is sufficiently representative for our
purpose. Extraneous disturbances were to a large extent eliminated
by the sound-proofing on the walls and ceiling. Lest the novelty of
this situation be a distraction to the speaker, he was allowed to prac-
tice and become accustomed to the new condition.

Conclusion

One advantage in having speech data available in terms of its power
rather than its amplitude is the fact that in most instruments used for
making quantitative speech measurements, the force which operates
the meter is proportional to the square of the wave amplitude. Com-
mon examples of such instruments are the dynamometer and the
ordinary a.c. meters.

To summarize, the power is classified into:

1. Instantaneous power, P,.

2. Mean power, Pm-

3. Long average power.

4. Short average power.

Stress calibrations are here derived from the maximum values of Pi
and Pm (Pi and Pm, respectively) in each syllable, while the use of the
total energy of the syllable for calibrating emphasis also shows possi-
bilities. The peak factor is the square root of Pi! Pm and is a useful
index of the wave form.

The measuring apparatus — excluding the rectifier and oscillograph —
is essentially a good quality speech-transmitting system. In view of
the fact that good quality systems are now used commercially as well
as in the laboratory the data naturally fall into two classes:

(1) Measurements which characterize the speech solely from the
standpointof the transmitting apparatus;

640 BELL SYSTEM TECHSICAL JOURNAL

(2) Estimates or approximations concerning the total power from
the voice.

Regarding (1) we note that the di\'ergence of waves causes some
frequency distortion which is greater, the nearer the source, and be-
comes neghgible as the distance increases (see the appendix). We
should accordingly expect the peak factors to he different at the
speaker's lips. The estimates of total power, however, are as close
as their importance necessitates.

When the data are applied to a case in which the speaker's distance
is other than 9 cm., the required power intensity is found by the law
of inverse squares and the pressure by the law of inverse distance.

APPENDIX

Frequency Distortion in Spherical Waves

A spherically diverging sound wave (see H. Lamb: ''Dynamical
Theory of Sound," page 206) is represented by

rcS,=J{vot-r)

where r = radius of the wave front

(^= velocity potential

/ = time

z'o = velocity of sound

Po = mean density of air

The pressure

p=- PoVod<t>/dr

= PoVo[yf'{vot-r)+j,J{vJ-r)^

Let /(!'„/ -r)= sin w ('-^ ),
so that

/, = ^f°(^^ COS. (/-;_-) + ! sin . (/-^)).

When a wave composed of any number of such components (each
having a different pair of values for w and a) diverges from one radius

to a larger one, it mn nnW changes in size, due to the factor -^

r

but also in sha|)e, liui' lo the factor in the second term. Wiieii r

SPEECH POWER AND ENERGY 641

is large romnarccl with — -, this chaiiKc in shape becomes negligible.

In the case of sjieech, since the source is of linile size the effective
radius is somewhat greater that that measured from the speaker's
lips, and the wave front is not exactly hemispherical, so the com-
parison is onl\- qualitative. Nevertheless, a difference in quality
of transmitted speech can be detected when the speaker's lips arc
within 2 cm. of the transmitter (iia[ihragm.

Some Contemporary Advances in Physics IX
The Atom-Model, Second Part'

By KARL K. DARROW
G. RlXAIMTLLATION OF THE FaCTS TO BE EXPLAINED

EVERY atom-model that is worthy of notice was designed in
view of a certain Hmited group of facts. That is to say, every
\alual)le atom-model is the invention of somebody who, being ac-
quainted with certain of the ways in which matter behaves, set himself
to the devising of atoms of which an assemblage should behave like
matter in those ways. Of course, it would be a most wonderful
achievement to conceive atoms, of which assemblages should behave
like matter in all ways; but this is too e.xalted an ambition for this
day and generation, no man of science bothers with it. Each atom-
model of the present is partially valid, not universally; and nobody
can rightly appreciate any one of them, unless he knows the facts for
which it was designed. I might add that he should also know the
relative importance, in the world and in life, of the facts for which it
was designed. But this also is too exalted an ambition; we do not
know much, if anything, about the relative importance of facts sub
specie crternitalis, and can hardly refrain from regarding with an
especial favour the facts which happen to have been successfully
explained. At all events it is clear that every account of an atom-
model should be preceded by an independent account of the things it is
meant to explain. F"or the favorite atom of these days, the atom
of Rutherford and Bohr, I have provided this preliminary account
of the facts in the First Part of the article. Let me give a brief outline
of the most important among them, before entering upon tlie task of
constructing an atom-model to reproduce them.

First and foremost, the elements are very definite things; each of
the ninety of them is distinguishable from the other eighty-nine,
not in one respect only but in many, and in many cases the contrasts
are \ery severe. The atom designed for each of them must therefore
have defmiteness and fixity and a sharply-inarkt-d character.

Next: although the atom must be <lctiniir, il must not he abso-
lutely immutable; it must be capable, under stress, of assuming
various distinct states or forms or configurations or whatever you
choose to call them. This is prescribed by that great and essential
fact of the Stationary States, to which so much of the First Part of

' Devoted to Bohr's atom model for hydrogen and ionized helium. The models for
other atoms, as well as some general considerations, are reserved for the Third Part.

642

sOA/E CONTEMPORARY .IIH-.IXCr.S l\ I'liysiCS-lX (M

this arliik- was dcvotwl. For an alotn, when initially in its normal
stati- and properly stinuilatetl, is aMe to rireixo enorRy in certain
definite measurable amc)unts, and to retain it for a while; and this is
tantamount to sayinjj that each atom may exist for a while in one or
aiiotiier of certain states distinct from the norma! state, in each of
which it pt)ssesses a certain distincti\e amount of extra enerjjv.
riuis a helium atom may recei\e 1!).75 equivalent volts of cnerjjy
from an impinging electron, no less and (within certain limits) no
more; and this is tantamount to sayinjj that a helium atom may exist,
not onU" in its normal state but also transiently in an abnormal state
in which its energy is greater by 19.75 equivalent volts than in the
normal state. The atom-model for each element must therefore be
designctl to be definite in each of several distinct and interchangeable
states, and not in one only.

The energ\'-\-alues of some few of these stationary states are de-
terminable directly; but most of them (and they are very numerous)
are deduced from spectra. The spectrum of an element is the family
of radiations of various frequencies which it emits when it is in the
gaseous state. These arc commonly ascribed to the individual atoms.
The first task of the spectroscopist is to measure these frequencies;
his second, to classify them. In certain spectra his task of classifi-
cation is easy, for there is a natural arrangement of the spectrum
lines which "leaps to the eye." This is an arrangement of lines in
one or several converging series, like those of which there were photo-
graphs of the First Part of the article. Let me represent by

the frec|uencies of the consecuti\e lines of a series, and by i/;„„ the
fre(|uency of the series-limit upon which they converge. Now the
frcciucncies of the various lines may be described by a formula

Vi = Vlim—Ji (1)

in which vi is expressed as the difference between two terms. The
term /, varies from one line to the next; and in some instances this
function /, is algebraically of an extreme simplicity, just the sort of
a simple elegance which is apt to suggest that the formula has an
inward physical meaning. Also one and the same term may figure
in the formulae for lines belonging to different series, a fact w'hich
enhances the feeling that the terms are physically "real." Thus
the spectroscopist seeks "terms" wherein' to classify the lines of a
spectrum; and the analysis of a spectrum leads to the measurement
of a multitude of terms.

I>U lU-.I.L SYSTEM TECHNICAL JOURNAL

Now nuilliply both sides of cqualion (1) by Planck's constant /;;
it becomes

livi = hvti„,-h(,. (2)

On the lefl-luuul side we lia\e hvi, a qiiantiiy of the dimensions of
energ>'. Now there is much reason to believe that when radiant
cnerg>' streams out from a substance in the form of radiation of fre-
quency V, it emerges often if not alwa>s in parcels or packets or units
or quanta, each consisting of an amount of energy equal to hv. Sup-
pose thai the radiant energy constituting any line of a scries is emitted
in quanta such as these; then whenever an atom performs the act of
radiating that line, it loses the amount of energy which stands on the
left-hand side of Equation (2). The right-hand side represents
the same thing, and is itself the difference between two terms which
are spectrum-lerms multiplied by //; these are themselves the values
(reckoned from a suitable zero) of the energy of the atom before and
after the radiation occurs, they are the energy-values of the atom
in the state before radiating and in the state after radiating. The
spedritni-terms, when multiplied by Planck's constant h, are translated
into the energy-values of the Stationary States of the atom. When
expressed in proper units, terms are energies and energies are terms.
In the decades during which the spectroscopists were analyzing line-
spectra, disentangling line-series — by no means a light labor, for the
perspicuity of the series shown in the photographs of the First Part
is anything but common — and disengaging terms, they were unknow-
ingly recognizing and locating the Stationary States of the atom.
Spectrum analysis culminates in the fixation of the Stationar\- -States.
This is the greatest of the ideas for whicii liu' world is indc'l)ti'(i to
Bohr, and e\entually through him to Planck.

These .Stationary States constitute one of the great systems of
facts, which the atom-model of Rutherford and Bohr is designed to
interpret. Let me formulate the demands which thus are made upon
this atom-model. It must ha\e features to account for these facts:

First, that there are such things as Stationary States;

Second, that in passing over in a "transition" from one stationar>-
slate to another of which the energy is less by AU. tlic atom releases
the energy AU in radiation of the one frequcncx' Af /;;

Third, that certain transitions do not occur, or occur under ab-
normal circumstances only, or occur less frequently than others; and

Fourth, that the stationary states of each particular kind of atom
have the particular numerical energy-values which they are observed
to have.

SOMF. COXTF.MI'ON.IKV .IPr.lWI.S l\ /7/J'.S7( V IS W.i

riic first tlirt'o i)f these deniancls are of a nerural and fimdamental
nature. If someone were to design an atotn-ni(i<iel for these phe-
nomena of the Stationary States and these alone, l>e would probably
bejjin by imaginini; an atom which would satisfy these general de-
mands; then he would proceed so to specialize it that it woulfl comply
also with the fourth. It mij^iht have been well, had this happeiv.-d;
the course of histor%' was otherwise. The atom-model of Rutherford
was desii;ned originally to interpret phenomena of fjuite another field,
and then Bohr modified it by violence to satisfy the fourth of the fore-
going demands.

Of the facts which Rutherford ile\ised iiis atom-model to interpret,
the cardinal one is that the atom contains electrons. The best evi-
dence for this fact is, that electrons can be extracted from atoms.-
One can even measure the amount of energy required to extract an
electron from an atom — in other words, the difference between the
energy- of an atom in its normal state, and the energy of the same atom
in its "ionized" state.' This has a direct bearing on the phenomena
of the Stationary States; for the spectrum-terms, when they are
multiplied by F'lanck's constant /;, yield the energ>-values of the
corresponding Stationary States, reckoned from the energy-value of
the ionized state as zero of energy.

Granted that the atom contains electrons: it must contain positi\e
electricity also, to compensate their negative charge. Now it is
easy to imagine the positive electricity so arranged, that the electrons
can be fitted into various places within and around it, and remain in
equilibrium*; it is possible to imagine that the positi\-e ele:"tricity acts
upon the electrons with a force which is compounded of the familiar
inverse-square attraction and a particular sort of a repulsion, so
adjusted that the electrons will remain in equilibrium in various
positions. It seems as though the Stationary States might be in-
terpreted in this fashion, and several attempts have in fact been
mafle; but they are discouraged by the experiments of Rutherford
and his followers on the deflections of alpha-particles and electrons
which pass through atoms. F"or these deflections occur exactly as if the
positive electricity were concentrated at a point or "nucleus," and an
inverse-square electric field pre\ailed in the region between this nucleus

' This Is not quite a proof of the fact. .As .-Vston cleverly remarked, when a pistol
is (ircd, smoke and a bullet come out of it; we are <|uite justified in Inferring that the
bullet was originally within the pistol, but not the smoke!

' This energy, which I called the energy of the "state of the Ionized atom" in the
First Part, Is truly the energy of the system conif csed of the atom minus its electron,
an<l the free electron.

' .Although not in stable equilibrium.

646 BELL SYSTEM TECHNICAL JOURNAL

and the elcclrons.^ The\' may be lonipalihK' with otluT aluni-inodels;
it is certainh' incumbent upon the designer of any other to prove that
they are compatible with his. Furthermore these deflections indicate
that the positi\e charge on the nucleus of the atom is just sufficient to
compensate the negative charges of a number TV of electrons, equal
to the "atomic number" Z which is the cardinal number defining
the position of the element in the Periodic Table of the Elements.
This confirmation of the splendid idea of van den Brock and Moseley
is so delightful and so precious, that anyone would hesitate long
before rejecting the atom-model whereby it is deduced from Ruther-
ford's experiments.

Yet this nuclear atom-model cannot be accepted, without being
instantly modified. A system consisting of a positively-charged
nucleus and electrons surrounding it, all acting upon one another with
inverse-square forces of attraction between nucleus and electrons and
repulsion between one electron and another, is not a stable system;
it is a suicidal system, doomed to quick and permanent collapse. If
the electrons were initially standing still, they would fall into the
nucleus; if the electrons were initially swinging in orbits about the
nucleus like planets around the sun, they would steadily radiate their
energy into space — not in radiation of one single frequency either,
but in a mixture of all possible frecjuencies — and would wind their
ways spirally into the nucleus. Therefore, the nuclear atom-model
must be altered; for instance, by adding a i)roviso, that the electrons
shall stand still, and shall not be sucked into the nucleus; or a pro-
viso, that the electrons shall revolve in closed orbits planetwise,
without radiating any of their energy *, and without gliding by a
spiral path into the nucleus.

-Suppose then that we decide lo make one or llie oilur ol ihcse
provisos, in order to save the interpretation of Rutherford's experi-
ments. Could we then so shape the proviso, that it would satisfy
the four demands which I described as being made upon the atom-

' -Apart from such deviations in the immediate neighborhood of the nucleus as
the most delicate experiments of this sort reveal; which cannot be supposed to
extend to the region where the electrons are.

•To indicate how much this neglect of the radiation from the revolving electron
amounts to, I cite the results of a calculation given by W'ien in his lecture Veber
Elektrnnen, and doubtless elsewhere. Imagine an electron distant by ten -Xngstrom
units from a hydrogen nucleus, and moving with such a velocity that, but for the
radiation, it would revolve in a circle about the nucleus. In a single circuit, it
should radiate about one ten-millionth part of the kinetic energy it initially possesses.
Hence the single circuit will differ very little indeed from a perfect circle; and in this
sense, the radiation is truly negligible. Hut the single circuit is described in less
than lO""" secomi; hence, in any time-interval long enough to be measured by the
most delicate of physical apparatus, the dissipation of energy by radiation is far
loo great lo be neglected wilh impunity.

.<^().u/r coxTF.MroR.iRy .ii>i:i.\( is i\ riivsus- /.v m7

iniulil li\ till' l.uM.s of llir Sl.ili()H.ir>- St.itrs.'' (Oiild we lur iiisLinci-
^11 sli,i|H- llu- first proN iso, lOiilil Zi.r choose such local ions for Ihc electrons
iissumcd stationary, tluit tlu' sodium atom (for instaiuv) would dispKiy
onI\' those i-nerny-valui's whicli the spectrum of sodium allows for its
Stationar>- States, and no others?

IndouhtedK' we coidil. The sodium atom is supposed to ronsist
(>! i'le\en eleelrous surrouiuliiij; a luieleiis of charge + 1 \e. If the elec-
trons were all stationary in assigned positions about the nucleus, we
could calculate the energy of the arrangement. The energy-values of
the vaiious Stationary States being known, it would not beditTicult to
tind, for each one of the Stationary States, at least one arrangement of
the eleven electrons identical with it as to energy-value. Having done
this, we could lay it ilown as a law that the electrons shall stand still in
e.ich and any one of these arrangements; but not in an\- other ar-
rangement whatsoevei.

But would this be an explanation of the Stationary Stales? Not.
I think, in any significant sense of that valuable word. It could
justly be designated as an explanation, as a theory, only if the various
arrangements so prescribed for the various Stationary States should
turn out to be interrelated according to some law — to be goxerned
by some unifying principle — to display some intrinsic quality of
simplicity and elegance and beauty, distinguishing them from all
the other and rejected arrangements. This has not been achieved.

Let mc now take up the other of the two suggestions which were
made above. Suppose that we accepted the nuclear atom-model,
with the proviso that the electrons should revolve in closed orbits
planetwise, without radiating any of their energy, and without gliding
by a spiral path into the nucleus. Could we so shape this second
proviso, could we choose such orbits for the electrons assumed revolving,
•icilhout loss of energy, that the sxlium atom or the hydrogen atom (for
instance) would display only those energ\-values which the spectrum
of sodium or the spwctrum of hyflrogen prescribes for the Stationary
States, and no others?

.Again, there is no doubt that we could; but the value of the achieve-
ment, again, would depend on whether oi not the orbits which we thus
selected were interielated according to some law, or governed by some
unif\ing principle, or distinguished from all the other orbits by some-
thing seemingly fundamental. Consider Rutherford's nKnlel for the
hydrogen atom, which consists of a nucleus and an electron. If we
adopt the proviso which was just set forth, and suppose that the elec-
tron may revolve around the nucleus in circular orbits without radiat-
ing any of its energy, then we can select particular circular orbits, such

648 DELL SYSTEM TECIIXICAL JOURNAL

that when tlic electron is re\olving in one or another of these, the
energy- of the atom shall have one or another of the values prescribed
by the Stationary States. If we arbitrarily say that the electron can
revolve only in one or another of these orbits, then we have an atom-
model competent to interpret the Stationary States of the hydrogen
atom. But is there anything distinctive about these selected orbits,
anything peculiar, anything which marks them out and sets them apart
from the other, from the discarded orbits? Have they any feature in
common, apart from being necessary to give the observed energj--
values of the Stationary States?

It is hardly possible to lay too strong an emphasis upon this require-
ment; the value of the contemporary atom-model depends upon satis-
fying it. Let me put the matter another way. From the moment
that we imagine that the electrons within the atom are cruising around
the nucleus in orbits without radiating energ\' and without dropping
into the nucleus, we are sacrificing the unity and the coherence of the
classical theory of electricity. So grav'e an action is not to be under-
taken lightly nor with indifference; it were foolish to make such a
sacrifice without recompense; and there is no recompense to be found
in merely proving that especial orbits can be so selected as to copy the
energy-values of the Stationary States. If one is going to deviate
from the rules of the classical theory of electricity, one must deviate
by rule. If one is going to disrupt the system which prevails in one
great department of theoretical physics, one must systematize another
department in exchange. If one proposes to violate some of the prin-
ciples of modern physics, by asserting that electrons can travel in
certain orbits without radiating, he must reconcile the congregation
of physicists to his sacrilege by proving that the selected motions are
themselves go\-erned by a principle, as imposing as those he lacerated.
If the innovator cannot show that his innovations are systematic, he
is not likely to prosper; but if his innovations are derived from a
principle, it may supersede those which he contradicted.

To discover such a principle is the ambition of, jirohabl)', halt ot
the theoretical physicists who are active today.

There are other general statements which miglu hv made at this
point; but they will be more intelligible, and so will the foregoing para-
graphs be, after I ha\e given an illustration. For this purpose I will
describe two models of the hydrogen atom, each of them consisting
of a nucleus and a single electron, each capable of being so constrained
that its energy-values will copy those of the Stationary States of
hydrogen. With one of these, however, the description can be carried
no farther. With the other, I shall show — following Bohr that the

SOME CONTEMl'Oli.lliV .IIH\IXCI:S IX I'liysiCS IX 649

orbits in which the eliTtroii is loiislrainwl to revolve have certain
peiuli.ir features. ilistiiiKiiishinjj them al)<)\e all other orbits; and
these distinctive features may be conse(|ni-MCfs nf the desired and still
hidden principle.

11. l-i;\TiRKs OK Tmc N'kcicssarv Oriiits ok nil-: Hvdrohkn Atom

((JlANTIZATION)

li\dn)i;en beiiii; the first element in the periodic table, Rutherford's
atom-mo<lel for it consists of a nucleus and one electron. The electron
bears (or is) a negative charge amounting to —e or — 4.774. 10"'°
electrostatic units, and its mass is approximately 9.10"-'* grammes.
The nucleus bears a positive charge amounting to +e, and its mass
is about 1,840 times as great as that of the electron.

The stationary states of the hydrogen atom possess the energy-
values — Rh, —Rli 4, /?///'J, —Rli 1(3, —Rh 25, and so on; in general,
the \alues —Rli/n- (« = 1,2,3 ... .). The constant^ R is equal to
;i.2'J.U)'°; the constant h is Planck's constant I). .56. 10-' erg. sec.

Rutherforil's atom-nu;del for the hydrogen atom must now be so
mcditied, that it will admit the energy-\alues just specified, and no
others.

I will begin by doing something wliich amounts to setting up a straw
man. to be knocked down immediately, — but not, I hope, before he
di es us some service. Let us suppose that, in spile of all the laws of
dynamics, the electron may stand still at a distance r from the nucleus,
without starling towards and falling into it. With the electron in
such a position, the energy of the atom is —e- r. This is an energy-
\alue referred, like all energy-values, to a particular zero; in this case,
the zero-value of energy corresponds to the condition in which the
electron is infinitely far away from the nucleus. We recognize at
once the "state of the ionized atom," to which the energy-values of
the Stationary States as given by the spectrum-terms are automatically
referred. This quantity —(^/>' must be permitted to assume the
successive energy-values of the successive Stationary States, and no
others; we must have

— t^r= —Rh for the first (or normal) stationary stale

— e^, r= —Rli 4 for the second stationary state (3)

— er/r= —Rh9 for the third stationary state; and so forth.

> I <lovi.iie hcrif Irnni the more frequent usage of defining K from the equation

for the rei i| rot. lis uf the wavtlep.gths ol the various lines of hydrogen; in which equa-
tion K = 11)9677.69 by measuremtnts of tremendous accuracy, and is to be niidtiplied
by c to get what I have called K.

630 Bnj.L SYSTEM TECIIXICAL JOURNAL

Now each of these equations defines a value of r; we have
r= e", Rli for the normal state

r = Ae-/Rh for the second stationary stale (4)

r = 9e- Rli for the third stationary state; and so on.

Eacli of these \aliies of r represents the distance at which the electron
must stand from the nucleus, that the atom may have the energy-
\alue of the corrcsi)onding stationary state. If we say that the
electron nia\- stand still at and only at the distances gi\en by

r = e- Rh, -ie'/Rh, 9e'/Rli (5)

we thus define an alom-model interpreting the Stationary States. It
is scarcely an atom-model to be recommended, and I certainly am
not taking the responsibilitN' of recommending it. Nevertheless
the reader had best beware of picking out the obvious objections to
it, and condemning it because of them. For if he objects that I have
gi\en no reason wh>- the electron should stand still at all, nor why
it should stand still in these and onl\- in these positions, nor why it
should cause radiation of a peculiar and well-defined frequency when
it passes from one of these positions to another — if he makes the.se
objections, I can retort that the atom-model favored by Bohr him-
sL'lf suffers from e\cry one of these deficiencies. In fact, the onl\-
defects peculiar to this "atom-model of the stationary electron" appear
tojje two. The first is, that the distances specified by (5) do not ha\"e
distinctive features such as I shall presently show for the orbits specified
for the "atom-model of the revolving electron"; and this defect, as I
ha\e tried to emphasize, is a grave one. The second is, that an atom
in which the charges are stationary is not ipso facto magnetic, whereas
an atom with revolving electrons is.'

Following Bohr, and practically all the other physicists of toda>-,
we now assume that the electron re\ohes planetwise around the nu-
cleus describing a dosed orbit and radiating none of its energy as it re-
volves. A planet re\nj\is in an elliptical orbit; this elliptical orbit
may be a circle, or it may not i)e: but for the present paragraph we
will think of the circles onl\ . l.el us suppose, then, that the electron
may rexolve in a circle about the nucleus, without radiating its
energy and spiralling into the nucleus. Designate the radius of the
circle by ;•. With the electron revolving in a circle of radius r, the
energy of the atom is —e^l2r'. This value is obtained by adding
together the potential energy of the atom, which is —e"lr just as it

' Ifanyrcaflerranalxilish these defects, a imilt it ude of chemists will lnnlad to hear
from him. Chemists want atom-models with stationary electrons.

v(ijU/: coxrnMPOR.th'y .ini-,i\crs i\ I'livsics- ix asi

was wlu'ii \vi- siipposi'd till- fU-clroii lo la- sliiixliiiK still, anil llie
kiiR'tic t'iH'rn\- (if llii- fli'c'trmi, wiiirli is l ;wt'-. In this last expression,
V stands for the speed of the electron in its orbit; now, wv-/r is the
"centrifugal force" acting upon the electron, which is equal (and
opposite) to the attraction exercised hy the nucleus upon the electron.,
which is r, /•-; so that \ mv" is equal to -{-e-/2r, and the total energy
of the atom has the salue —e-/'2r. As before, this is the energy-
value referretl to the slate of the ionized atom.

This c|uantity —e-'2r must be permitted to assume the successive
energy-values of the succcssi\e Stationary States, and no others;
we must have

-r 2r= -Rh w- (M = 1, 2, 3, 4 ) (6)

Kach of these equations defines a value of r, as follows:

r = n-e- 2Rli (w = 1 , 2. :5, 4 ) (7)

If we say that the electron may revolve in and only in such circles
as have the radii given by the equations (7), we thus define an atom-
model interpreting the Stationary States. Is this atom-model
superior to the tentative one which was described just before it?
Not in any way which has yet been brought to notice. Xo reason
is given why the electron should revolve in a circle instead of spiralling
into the nucleus, nor why it should revohe in these and only in these
circles, nor why it should cause radiation of a peculiar frequenc\' to be
emitted when it passes from one of these circles into another. .Ail
of the objections which I suggested, a few paragraphs above, thai llie
reader might raise against the then-mentioned atom-model with
the stationary electron, may equally well be raised against this atom-
model with the revolving electron. Why then should we attach
greater importance to this one than to that? Partly, as I said, be-
cause this atom possesses intrinsic magnetic properties, while to the
other one magnetic qualities would have to be ascribed by an addi-
tional assumption; but chiefly because Bohr discovered certain dis-
tinctive features of the circular orbits defined by (7), which set them
apart from all others. These we now e.xamine.

To understand the first of these features, it is nece.ssar>- lo consider
the angular momentum of the atom. Sooner or later we shall have
to make a slight alteration in the reasoning indicated in the last para-
graphs; it may as well be made now even though it is not yet necessarj-.
Heretofore I have tacitly assumed that the nucleus stands still while
the electron revolves around it. As a matter of fact, if the atom may
be repnscnted as a solar system in miniature, the nucleus and the

632

BELL SYSTEM TECHNICAL JOURNAL

electron both revolve about their common centre of mass in ellipses
— we will think, as before, only of circles (Figure 1). The radii a and .1
of the circular orbits of the nucleus and the electron, being the respect-
ive distances of the particles from their centre of mass, stand in the
reciprocal ratio of the masses M of the nucleus and m of the electron;
and as they describe their orbits in the same period (since the centre

Fig. 1 — Diagram to illustrate how the electron and the nucleus rt\ol
coiiiinon centre of mass in synchronous orbits

\c arounil

of gra\ity is at rest and always between them) their speeds :■ and 1'
stand in the same ratio:

a/ A =vlV=Mim.

I introduce tiie symb:)l ix to denote the eciual c|uaiuities

M _ a _ f
jr^tra+A~v-\-V'

(8)

(9)

The potential energy of the atom, reckoned as always from the state
in which the nucleus and the electron are infinitely far apart, is obvi-
ously — e-J{a-\-A) = —e^n/a. The kinetic energy of the atom is the
sum of the portion \ mv- belonging to the electron and the portion
J MV', belonging to the nucleus. I point out that the "centrifugal
force" acting upon the electron is mv'/a, and that acting upon the
nucleus is M]^/A, and each of these separately must be equal to the
reciprocal attraction e-/{a+A)- of nucleus and electron; and I leave
it to the reader to show by means of these equalities that the kinetic
energy amounts to J eV/a. The total energy of the atom is there-

SOME coNTiiMroi^'.iRy ,ii>r.ixci:s i\ i-iiysics i.\ 65.i

lori' rtjiMl to —\ e-fi a. and this is tlu- (|ii.intit\' to iii' f(|ii,iti'fl to the

ol>siT\ i-d t'iHTn\-\.iliii's of iIk- sl.ilioii.iry states; ('(iii.tl ion ((>) i>
ri-pl.ut'd !>>■

-<-V 2(/= -Rh 11- . (1(1)

rill' aiij;iilar moiiu'iitiim of the electron is nnui; tlie aiii;iii.ir mo-
incnluin of the nucleus is .1/ I'.l ; the angular niomeiituin of tiie atom,
for which I use the synih.jl />, is the sum of these:

p = iiivti + M I VI = mva n. (11)

1 leave it again to the reader to use the foregoing statements to arri\e
at the expression

p = e\/ma (12)

antl by combining (12) and (10), at the expression

pn = ne-\^mn -IRIi (18)

for the \alue />„ of the angular momentum of the atom, or rather of
our atom-model, in its «th stationary- stale.

Thus the values of the angular momentum of tiie atom-model, in
the various states in which it has the prescribed energy-values —Rh,
— Rh A, and so forth, increase from the first of these states onward
in the ratios 1 :2:3:4 . . . They arc the consecuti\e integer multiples
of a fundamental quantity, the quantity

pi = e-\/>nii/2Kli. (14)

Now it happens that this fundamental quantity is equal, within the
limits of experimental error, to /» '27r — to 1 /2jr times that same con-
stant /; which has already figured in this discussion:

pi = h 2-k; p„ = nh, 2Tr. (15)

This occurs because the \alue of R is equal, within experimental
error, to the combination of ni, e, and /; on the riglit of this c(iuation:

R = 2T^-nme\h\ (16)

The atom-model which I have been describing at some length
could therefore be described in a few words by saying that the electron
is permitted to revolve only in certain circular orbits, determined by the
condition that the angular momentum of the atom shall be equal to an
integer multiple of h, 2n-. This condition is in fact sufficient to impose
the values given for the radii of the circular orbits in equations (10)
which values in turn entail the desired energy-values for the stationary
states. The reader can easily prove this by working backward

654 BELI. SYSTEM TECUNICAI. JOVRXAL

through the train of equations; and indeed this is the manner in
whieh the Bohr atom-mode! is usuali\' i^resented, so as lo arri\e
finally at the agreement between "theor\" and experiment which is
expressed in equation (16), and is a most striking chmax to the whole
exposition. By working tiirough the train of equations in the inverse
sense, I have considerably mitigated the effect of the climax; and this
procedure seems hardly fair to the author of the theory, but it is
not without its merits, for it enables us to see the exact role of equation
(15) more clearly than the commoner procedure.

The situation now is this. It is possible to construct, out of a
nucleus and an electron, an atom-model possessing stationary states
of the energy-values displayed by the hydrogen atom, provided that
we assume that the electron may revolve only in circular orbits for
which the angular momentum of the atom is an integer multiple of
h/2T. There is no known reason why an electron should do a thing
like this, there is good reason to suppose that it cannot do anything
of the sort, for if it started out to revolve in a circular orbit it would
radiate its energy and descend spirally into the nucleus. If ne\er-
iheless we assert that the electron does just this sort of thing, we ha\e
nothing with which to support the assertion, nothing extrinsic by
which to render it plausible; it must stand oti its own merits as an
independent principle.

These merits, had we no data other than the energA-\alucs of
stationary states catalogued in equation (G), would probably be
regarded as scanty. After all, the agreement between the constant
pi and the quantity h/2Tz might be fortuitous. But there are other
stationary states of the hydrogen atom, beyond those listed in (G).
For instance there are the stationary states which are evoked by a
strong electric field acting upon hydrogen, and there are the stationary'
states which are called into being by a magnetic field applied to
hydrogen, as I related in earlier sections of this article. There is
also the fact, that at least one of what 1 ha\'e been calling the stationary
slates of hydrogen is not a single stationary state at all; there are
two states of which the energy-\alues lie exceedingly close together
and to the value — Rli 4, so close that nearly all experiments fail to
discriminate them. .And tlure is (lie great multitude of stationary
states exhibited by other elements than h\(lrogen; l>in we will not
think about these for the time being.

Now the situation is transformed into this. Considci- all these
additional stationary states, exhibited b\ tiie hydrogen aKini under
unusual or e\en under usual circumstances. Is it possible to trace,
for each one of them, an orbit for the electron, such that while the

SOMF. CONTEMrOli.lRY .llfr.lXCFS fN PtlVSICS-IX 655

electron is describing lliat orbit, liie energy of the atom iH)ssesses
just the vaUie appropriate to that Stationary State? And granting
that this is possil>le and accoiu|)lislied; ran it l)e shown that these
additional orbits are distinguished 1)\ sonic Italure resembling that
feature of the circular orbits which is described by ecpiation (1 "))!•'
Our condition laid upon the circular orbits, thai in each of them the
angular momentum of the electron is an integer nniltiple of // 'Iir -
this condition \alid for the limited case, can it be generalized into a
condition governing the Stationary States of the hydrogen atom
under all circumstances? Can orbits be described which account
for all of the Stationary States of h>-drogen under all circumstances,
and which are determined b\- a general condition of which the condi-
tion set forth in equation (1.5) is one particular aspect? If so, that
general condition might well be such a Principle as the one towards
which, as it was said in the last section, so many physicists aspire.
Thus the test to which this condition laid upon the angular momentum
must be submitted is this: can it be generalized^

Before trying to generalize it let us examine some other (list inctive
features of the circular orbits defined in (7) — I will call tlu-m lienci-
forth the "permissible" circular orbits, but we should remember that
perhaps it is only ourselves who are "permitting" them and forbidding
the others, and not Nature at all. Let us calculate the integral / of
the doubled kinetic energy- 2K of the atom over a complete re\<>lulion
of the electron (and nucleus) :

2Kdl. (17)

It is easy in this case, for K is constant in time, so that I = '2KT. Now
A' is equal to \mv- ' n, and T is equal to 2Tra/v = 2ir-md'/nK; which
expression the reader may reduce, by means of that equation K =
jC-M a which he was invited to derive, to

T=ire'Vm^/2K^ (18)

multipKing which by A', and using equation (10), we have

I = 2irn-e'Vmn/Rh. (19)

The reader will recognize the factor which appeared in (14) and was
there stated to be numerically equal, within the error of observation,
to h 2w.

Therefore this atom-mrKlel could also be described by saying that
the electron is permitted to rrcolve only in certain circular orbits deter-
mined by the condition that I shall be equal to an integer multiple of h.

656 /*/?/•/- SVSTF.M TECHNICAL JOURNAL

For future use I interpolate the remark that the factor ii is called
the total or principal quantum number; in German, Ilanptquantenzahl.

The reader will think that this is not a new condition, but only a
futile way of rc-stating the condition laid upon the angular momentum.
So it might be, in this case. But when we come to the more complex
cases, we shall find that the two conditions diverge from one another.
Which of the two can be generalized, ij either? Only experience can show.

I will describe one more distincti\e feature of the permissible orbits;
it may seem more impressive than either of the others.

We have seen that the frequency of the radiation emitted, when the
hydrogen atom passes from one stationary state to another — say from
the state of energy — Rhn'- to that of energy — Rh/n"'- — is

R R

which maN' be written

R

n -n

,Jn'-n"){n' + n"). (20)

Suppose that «' — »"=!, that is, that the transition occurs between
two adjacent stationary states of the atom; and let h' and ii" increase
indefiniteh'. In tlu' limit we shall have

Lin, .=?^. (21)

Accepting the atom-model with the electron rexolving in a circular
orbit, we take from (18) the value for the period of the re\olution,
substitute for K by the aid of (10), and arri\e at this expression for the
frequency of the re\()lution:

i^'=v/2Trr = V»R^'/2Tn"eWm^ (22)

Comparing this expression for co' with the expression for Lim v in
(21), we see that they are iiKiiticil, if

R = 2Tr-mtie\h^

and this will be recognized as being that very NaUie ol R wliich was
given in equation (13), as the value established by experiment. Thus
the experimental value of R is such that

Lim 03 = Lim v. (23)

In this equation the symbol w stands for the frequency of revolution
of the electron in its orbit, when the energy of the atom is —Rhn-.
It therefore stands for ilie fre(iiionc\- of the radiation wliich the atom

<o.\[F. coxrr.MroR.iRy .ini-.ixci-s ix physics -ix 657

wmilil ho cxiHVled to emit; for an elorlrical cliarRC pcrfonniriK ,t
|H'ri(Hlir motion should, accordinj; to the fiindaincntal doctrines of
the elect roniai;netic theory, lie the origin of a stream of radiation
with jH^riod e<nial to its own. The symbol v stands for the frequency
of the radiation which the atom does emit in passing between two
a<!jaccnt Stationary States. According; to (19), this actual fre-
(|uency is more nearly e(|ual to the expected frequency, the more
remote these two adjacent Stationary States are from the normal
.State; and in the limit, actual frecjuency and expected frequency
merge into one. The numerical value of the constant R is just such
as to bring about this relation.

Here again we have a curious nunuriial at;rii'imrit wliicli, like
the other correlatetl fact that the angular momentum of the electron
in the nth orbit is nli 2jr, may by itself be merely a coincidence; but
this one has a much greater inherent appeal. We ha\e relinquished
the expectation that the electron, cruising around the nucleus in a
c\clic path, will send forth radiation of the frequency of its own
revolutions, as every inference from the laws of electricity indicates
that it should; but here is a case — e\en if it is only a limiting case —
in which the frequency emitted from the atom agrees with the one
which we should expect. Generally there is discord; but in the lim-
iting case there is consonance. Does this not suggest that the desired
Principle may be one which in a limiting case merges with the classical
theor>- of electricity — possibly, indeed, nothing less than the founda-
tion of a general theor>- of electricity.-, of which the classical theory
expresses only a special case?

Let us review our situation.

Having supposed for hydrogen an atom-model consisting of a nucleus
and an electron;

Ha%ing supposed that these revolve around their common centre of
mass according to the laws of dynamics, but without spetuling any
energy in radiation;

Having supposed in particular that they revolve only in circular
orbits, and only in such circular orbits as yield for the atom-model
the energy-values — /?// ;;- measured by experiments upon the .Sta-
tionary-States;

Having tracwl these "permissible" circular orbits.

We have found that they are distinguished from all the other cir-
cular orbits by at least three peculiar features (viz., the features ex-
pressed by the equations /) = ;;/; 2t. and / = «//, and Lim io = Lim v).

We do not know- that there is any revolving electron at all. We
know only that if all our suppositions be correct, the consequence^

658 BELL SYSTEM TECHNICAL JOURNAL

expressed by these three equations are correct also. Are these conse-
quences impressive enough to prove the suppositions true?

The answer to this question depends on our degree of success, or
rather on the degree of success attained by Sommerfeld and Bohr and
their followers, in generalizing these equations to other and more com-
plex cases. Usually the process of generalizing will involve difficult
labours of orbit-tracing. But it is possible to make a significant com-
parison between the spectra of hydrogen and of ionized helium, witli-
out additional studies of orbits.

I. Rklations Bf.twken the Spectrum of Hydrogen and the
Spectrum of Ionized Helium

To make trial of the validil\- of the foregoing ideas about the origin
of the hydrogen spectrum, one naturally applies them to whatever
other spectra may reasonably be ascribed to an atom consisting of a
nucleus and a single electron. As according to the view adopted in
this article the atom of the nih element in the Periodic Table con-
sists of a nucleus and w electrons, the only way to produce such a
spectrum is to produce a sufficient number of atoms of some element
or other, each atom lacking all but one of its electrons; helium atoms
deprived each of one electron or "once-ionized," lithium atoms de-
prived each of two or "twice-ionized," beryllium atoms depri\ed
each of three electrons, or in general atoms of the nth element of the
Periodic Table divested each of («— 1) electrons. This we should
expect to require violent electrical or thermal stimulation of the
vapor of the element, more violent the more electrons have to be
remi ved. Hence it is not surprising that the spectrum of once-
ionized helium is the easiest of these spectra to produce; but it is
more than a little strange that this is not merely the easiest but the
only spectrum of this kind which has ever been obtained. Even the
spectrum of twice-ionized lithium has not been generated, in spite of
efforts quite commensurate with the value it would have.* The
sjiectrum of once-ionized helium remains the only companion of tlie
spectrum of hydrogen; these arc the onlj' two known spectra which
are ascribed to atoms consisting of a nucleus and a single electron.

We have seen that if we imagine that the electron of the hydrogen
atom can revolve, without spending energy by radiation, in and
only in those circular orbits for which the angular momentum of the

atom is equal to h/2ir, 2h/2ir, '6h/2ir nh/2v then the

energy of the atom-mcxlel can assume only the values —Rli, —Rli/i,

•Consult for iiibtancc tlic article by .^ngcrcr, ZS. f. Pliysik, 18, pp. IK? IT.

SOMi: ( (».V// .U/'(iA'. (AT .//>( ./.\( 7 V I .\ I'llVSUS /V (<■'"

— Rh 0 — Rli M-. wliicli art- the ciUTny valiu-s for llu- (tl)str\i(l

stationary statt-s of liydro^cii. If this is not an acrick-ntal roinridt-nct',
llit-n by itnaKining tlial the clrrtron of tin- ioni/i'<l lii-liuin atom lilct--
wisi- ran rf\ol\i' only in orliits for whirli tiu- angular nionu-ntuin
of tlu' ati>ni is some intt'^or multiple of li '2w, anri hy raiciilaliiin tlii-
corrt'sponiliiiK t'nerjjy-valui-s for the aloni-niodel, we should arriw
at the enerRy-valiies of the observed stationary states of ionized
helium. Now the charge on the nucleus of the helium atom is 2e,
twice the charge of the hydrogen nucleus; the force which it exerts
on an electron at distance r is 2e- >'-, instead of r >-. If the reader
will work through the equations of Section H, making this alteration
wherever appropriate, he will find for the energ>'-values of the sta-
tionary states the sequence

-ARIi,-^RIi '.).-AKIi It), . . . -ARh >r. . . .
in wiiicii

Ir'

as heretofore. Tile (iuantil\' yu will be dilferent from what it was
for hydrogen; but the difference will be \ery slight. Therefore if the
condition that the electron may revoke about the nucleus only in
circular orbits for which the angular momentum of the atom is «//, 2jr
is an essential condition, and governs the atoms of hydrogen and
ionized helium alike, the stationar\' states of ionized helium corre-
spond one-to-one with those of hydrogen, but with energy-values
almost e.xactly four times as great. So also with the lines of the
spectrum; to each line of the hydrogen spectrum should correspond
a line of fourfold frequency in the ionized-helium spectrum; the
spectrum of ionized helium should be the spectrum of hydrogen on a
quadrupled frequency-scale.

This conclusion is verified. The historical sequence of observa-
tions and theories is rather interesting. Certain lines of ionized
helium were earliest observed in stars; their simple numerical rela-
tions with hydrogen lines being noticed, they were naturally ascribed
to hydrogen, and when they were generated in mixtures of hydrogen
and helium within a labf)ratory they were still attributed to the first-
named of these gases. Bohr in his first published paper reasoned
in the manner I have followed in this section, and inferred that these
lines really belonged to helium; which was shortly after%vards \erihed
by seeking and finding them in the spectrum of helium made as pure
as possible. A number of additional lines of the spectrum ha\e since
been found, although the lines corresponding to transitions into the

«,() FELL SYSTEM TEC! IMC. IE Jorh'X.IE

normal stale (the state of energy —47?/;) are so far out in the iillra-
violet region of the si)ectrum tliat no one lias \el succeeded in delect-
ing them.

We will now take account of the fact thai the numerical values
of the constant R calculated for hydrogen (equation l(i) and for ionized
hehuni (ec|uatit)n 2o) are not quite the same; they are in fact propor-
tional to /u, ihe quanlily wiiich determines the motion of the nucleus,
and which \aries from one atom lo anoliuT. In ]).iriicular

R„, K!,=M!Ir ////=(l+w .1///) {\+IU Miie) (26)

in which the symbols tii, Mn, .1///, denote the masses respectively
of the electron, the hydrogen nucleus and the helium nucleus, which
stand to one another as .000542; 1.000:3.908. Consequently the
right-hand member of equation (2a) is equal to 1.000403, and the
ratio of the freciuencies of corrcspnnding lines in the spectra of ionized
helium and of h>'drogen is

A Rii, ./?// caicuialed = 4.0011)12 (27)

The values of Rn, and Rn deduci'd from frcquenr\- measuren'.ents yit4d
the ratio

\ R,i, /?// ol)ser\c(l = 4.0(1 l(i2 12 (28)

The \er\-exactl\-kiiown oliserwd \aluc lies well within liie margin
of uncertainly <if the calculated \alue. The calculated \alue of the
ratio de|)ends on otherwise-made measurements of the mutual ratios
of ihe three masses (those of the electron, the hydrogen nucleus, the
lulium nucleus). These otherwise-made measurements are not of
the grade of precision claimed for the measurements of 4 Ru, Rii by
the obser\ations on the spectra. Hence if we combine the observed
value of the ratio ARhc, Rn with (for instance) the ratio ^1///, Mn
derived from density-measurements upon the two gases, we can
calculate a value for the ratio .1/// 'm ostensibK' much more precise
than ihe amount ascerlained li\' dui'cl measuri'nienl. This \.ilue i^

Mil w = lS47. (2!!)

l.et me stale briefly what the numerical agreement between the
"calculated" and "observed" values of 4Rii, • Rii specifies. 1 1 is a
test of this set of assumptions; the hydrogen atom and the ionized
helium atom may each be represented by a single electron and a
nucleus of charge -j-r in one case and +2c in the other; each stationary

s(K\ir. coxTr.Mi'OR.tKV .iiH'.ixcr.s i\ riiysics-i.\ 66i

sMtf corresiMuids to a certain circular orbit of the electron; the Angiildr
MomenUi of the two atoms are identical xchen they are in corresponding
stationary states. As a test, it is fa\-or.il)lc. It does not invoke the
rel.iiion between angular momenta and inle^er multiples of // '2v
which was stressed in the forejjoiti); section. It is independent of
tii.it relation, and may fairly be considered as the second numerical
ajjreenient offered by this atom-model, if that relation be considered
the first. The idea is due to Sommerfeld; the data whereby the test
was made were obtained by Paschen, as a b\-product of the work
cited in footnote 12.

Although the statements in the foregoing; paraj;raphs are literally
true, they do not pro\e that the condition Antiiilar Momentum = nh 2w
is the distincti\e feature par excellence of the permissible circular orbits.
The result would have been cxacth' the same if I had defined the sla-
tionar>' states of the ionized helium atom as thr)se for which / = ;;/; or
as those for which Lim w = Lim v.

J. Tk.\( INl. OI' Okiuts

W'c must now seek for opportunities to make and test generaliza-
tions of the notions about the h\drogen atom explained in section H.

I began by saying that the electron should be supposed to re\(jKe
in the in\-erse-square electrostatic field of the nucleus, according to the
laws of dynamics, without spending energA" in radiation; and con-
tinued by saying that I shf)uld speak of circular orbits only. \ow the
laws of dynamics prescribe elliptical orbits, of which the circular
orbits are but special cases. In fact, for each one of the sequence
of energy-values —Rh «- corresponding to the sequence of Stationar\-
States, there is an infinity of elliptical orbits possessing that energy-
\ alue, of which the circle of radius specified by equation (7) is only one.
Suppose we should inquire what, if any, are the distinctive features of
these elliptical orbits which set them apart from all others?

Again : when radiating hydrogen is exposed to a strong electric field,
new stationan.- states appear, and their energy-values are known.
The orbit of an electron, in a field compounded of an inverse-square
central field and another field uniform in magnitude and direction,
is no longer a circle nor even an ellipse nor even a closed orbit (except
in special cases). Could the orbits having energv-values equal to
those of the stationary states l)e identified and traced, and could dis-
tinctive features be found which mark them out from among all the
others?

Again: when radiating hydrogen is exposed to a strong magnetic

W)2 HI. LI. SVSiEM TECII.MC.IL JUURXAL

field, iK-w stiiiionan- stales appear, and their encrg\--\alues are known.
Could the orbit of an electron in a field compounded of an inverse-
square central electric field and an uniform magnetic field be traced?
and could the orbits ha\ing energy-\alues equal to those of the sta-
tionary states be identified? and could peculiar features be found
which mark thnii nui liciiii ,ili ilie diIkt--.^

Or con\ersely : is it possible to make "trial" generalizations of one or
another of the conditions p = nh/2Tr and I=nh and Lim u = Lim v'i
to in\ent features for the more complex orbits, which sound like rea-
sonable generalizations of these features of the simplest ones? and,
having done so, to trace the orbits exhibiting these "trial" features,
determine their energy-values, and compare these with the observed
encrgy-\'alues of the stationary states?

Whichever of these two ways is employefl to attack the i)robiem,
it is necessary to trace orbits more complex, and usually in more com-
plex fields, than the circular orbits imagined for the hydrogen atom.
This problem of tracing orbits is the fundamental problem of Celestial
Mechanics — the oldest and the most richly de\eloped department of
mailu'malical physics, which in its two centuries and more of history
has tk'xeloped a language and a system of procedures all its own.
It is chiefly on that account that many of the recent articles on the
atom-model of Bohr are so excessively ditticult for any physicist,
unless he is of liie fi'w who practiced the arts of theoretical astronomy
diligcnth' and for a long time before passing o\-er into the field of
physics.

In this section 1 shall tjuote the equations for the motion of a particle
in an ellipse under the influence of an in\'erse-square central field, and
give the derivation with all necessary detail. For the other relevant
cases — motion of an electron in a central electric field upon which an
uniform electric field, or an uniform magnetic field, or a small central
field \ar\ing according to some other law of distance than the inverse
scjuare, is superposed — I shall gi\e only some of the results, without
e\en attempting the derivation. I shall make no allow, iiur lor tiic
motion of the nucleus; the electron w ill In' supposed to ri\oi\r around
the nucleus considered as fixed. 1 lie \(r\ small corrt'clion re(|uiri(l
to lake accoimt of the motion of ilie nucleus can easily be apjilied b\'
the reader, if he so desire. The ])riiu"ii>al disadvantage invoked in
neglecting it is, that one too easily thinks of the angular momentum of
the electron in its orbit as l)elonging to the electron alone, whereas it is
reallv- the angular momentum of the atom-model. I shall also put E
for the charge on the nucleus; E will be equal to e for the hydrogen

SOMF. a)A'7/:".l//'()A'./A')' .IKr.l.WIS l\ rilVSICS l\ (V^t

anil tn 2(- lor llio ioni/cd-liclinin .iinm-inodtl. no oihrr ciscs in.illcr
fnr tlir liiiu' iK-inR."

./I. Motion of an Electron in tin hnrrsc-Sijiiure Central Field

Most people rccognizi' tlif i'(|ualit)n ol llu- ellipse must i-.i>il\- in ilif
form

.v'-, a' + V", 6-= 1

iti >i i'oor(liiiate-s\stiMn ol wliicli tlie oriv;iii is .it the centre of tlie
ellipse, the .v-axis and the v-axis par.illel respeeti\el\' to the major
and the minor axes of the ellipse.

The symbol a and b denote the semi-major and semi-minor axes
of the ellipse; they are related b\-

h- = a'{l-f-) (30)

in which « stands for the "eccentricity" of the ellipse. The foci
of the ellipse lie on the major axis at distances at to either side of its
centre. Transferring the origin to one focus, say the focus at x= -\-at,
and using coordinate-axes parallel to the former ones, we have

(j' + ae)- «--|- v'-, b'-= 1

Transforming coordinates again, this time into polar coordinates r
and <t> with the origin at the focus of the ellipse and the direction 4> = 0
pointing along the .v-axis, by means of the substitutions

j' = r cos ((> y = r sin 0

we arri\e after somewhat tedious but not difficult algebra ■* at the
e(|uation for the ellipse in the form in which we shall use it

^^ a(l-^')
l+« cos <i>

and at the derivative thereof

/ dry _r*t^ ^m"" 4, ^ r* 2r^

W«y a'ii-i'y- a'il-i-yaiX-t-) ^ '

' The allowance to be made for the motion of the nucleus never differs perce|)til)ly
from that already made by introducing n into ef|uation (16), and the magnetic
fields arising from the motions of the electron and of the nucleus are without per-
ceptible effect (C. (J. Darwin. Phil. Mag. 30, pp. 537-551; 1920). The correction
which would be required if the nucleus or the electron were o<ldly shaped, if the
nucleus were a magnet, or if there were entrainnient of the (jotential energy of the
svstem bv the moving electron, have been evaluated bv various people; consult
.■\. K. Kuark, .\stroph. Jl.. 58, pp. 46-58 (1923).

' ["he ambiguitv of sign which arises in the course of the development may be
res lived by thinkmg of the limiting case of the circle f« = 0).

664

BELL SYSTEM TECILMCIL JOURNAL

All this is geometry. We must now prove that a particle moving
under the influence of an inverse-square attraction, drawing it towards
a fixed point, will describe an ellipse with that fixed point in one of
its foci — will descrilie. otherwise expressed, a cur\e defined by equa-
tion (31).

As the particle is an electron, and the fixed point is occupied b\- a
nucleus of charge is, the mutual attraction is eR r when their (lis-

9 — 2-n

V\%. 2— Diagram to illustrate the notation used in describing clli|)tiial orbits

tance apart is r. Equating this attraction to the product of the
mass of the electron into the sum of its accelerations, linear and
"centrifugal," we ha\e

eE/r^=~,nY,i^»>r{^^)'

(32)

It is necessary to assume tlu' law nt c(insiT\atinn of ant;iilar mo-
mentum; the angular momentum of the electron mrd4>^dt about
the centre of attraction iiniains constant in time:

(33)

inserting which into (32) we have

<Pr

eE/r- = — ni-jji ■\-p'^/mr^

(34)

Nc.u/; coxrr.Mi't^iy.iKY .un\i.\ci.s ix I'/ivsics-ix fi<o

riiis is to 111' iiiu-i;r.ilc(l in llu- ii>ti,il \\.i\ . li\ iiiuliipK iiii; r,i( li icim
\\ill« •-'((//• (//); llii' result is

{,.] = - 1>' iii>-+'2<-li i>ir — C.

lii.".)

iIr- last symbol st.iiuiing for a constant of intCKralioii. I'in.illy
(dr di>)- = ((lr (it)- {(l(t>;dl)- = {dr/dty-(m-r*/p-)

= - Cinr' /)' + 2eEmr\p- - r. (3(5)

\\c nro^iiizi- at oiuc the iilentical form of this equation for ihe path
in which the attracted particle moves and the equation (31) for the
ellipse drawn about the centre of attraction as focus.

It remains only to identify the constants. Equating the co-
etTicients of /■' in the two equations, we have

p-^eEnia (l-t-). (37)

This is the equation giving the angular momentum of the electron
in terms of the major axis and the eccentricity- of the orbit. Fviiiating
the coefficients of r* in (31) and (3G) we have

C = {y'j>na-il-t-)=eE,a (38)

to determine the constant of integration in (35). If now the reader
will take the expression for the energy of the system

n'= \tmr-e'/r = \m(Sdr/dt)- + r(d<i>/dt)y-e';r (39)

and substitute for {d<t>/dt) according to (33) and for {dr/dt) according
to (35) and (38), he should arrive at

W= -e-,2a. (40)

This is the equation giving the energy of the system in terms of the
constants of the ellipse; we see that the energy depends only on the
major axis, not on the eccentricity, of the ellipse.

The period of revolution 7" is a little more difficult to calculate.
The most logical procedure would be to take the reciprocal of the
expression (35) for dr dt, and integrate

/= )"(-/>= m-r- + 2eE, mr-eE, a)~'''dr (41)

around a complete revolution. The derivative dr/dt passes twice
through zero in the course of the revolution, once at the point of the
orbit nearest to the nucleus (perihelion) and once at the point farthest
away. At these points r = a{\^t), as can be seen from the geometry
of the ellipse or by inserting these values into the expression for dr/dt.

666 BELL SYSTEM TECHSICAL JOVRKAL

By integrating (41) from one of these values to the other aiui douhHiig
the result, we get the period of the revolution

T='2Tr\/ma\/eE. (42)

J2. Motion of an Electron in n Central Field Differing Slightly from an
Inverse-square Field

Suppose we modify the atom-model composed of a nucleus and an
electron by imagining that the force exerted by the one upon the
other varies not exactly, but very nearly, as the inverse square of
their distance apart. For instance, one might imagine that the force
varies as r^'""; or that the nucleus acts upon the electron with an
attraction equal as heretofore to eE/r'-, plus an additional attraction
(or repulsion) varying inversely as the cube of the distance. In any
such case the potential cnerg>' of the atom-model would not be quite
equal to —eEr; there would be an additional term f{r). In the
case of an inverse-cube field superposed upon an inverse-square field,
the expression for the potential energy would be

V=-eE r-C,r- (43)

The second term on the right hand side will be much smaller than
the first, at and only at distances much greater than 2C/eE; but
l)y imagining C sufficieiitlN' small, we can arrange to have the inverse-
cube field very much smaller than the inverse-square field, over all
the region in which tlic orbit of the electron is likcK' to lie; and this
is all that matters.

The orbit of the electron may be described, in all these cases in
which the force deviates very slightly from an in\erse-square force,
as an ellipse precessing in its own plane. That is to say : an ellipse
of which the major axis swings at a uniform rate around the nucleus
as if around an axle perpendicular to its own plane — as though the
electron were a car, running around and around an elliptical track,
quite unaware that the track itself is endowed with a revolving motion
of its own. (Or, in other and more sophisticated words, the orbit
(jf the electron is an ellipse stationary in a coordinate-system revolving
around the nucleus at a uniform rate). Such an orbit is known as
a "rosette," and a part of a rosette is shown in Fig. 3.

Another way of describing the important feature of liiis orinl is
to say that the two coordinates r and 0 of the electron in its orbit
(referred to O as origin and OP as the direction 0 = (), in Fig. 3),
while the)' arc both periodic, do not have the same period. While r
is running throuj^h its entire cycle from r„^^^ to r,„,„. and back again,

SOME coxTn.Mi't^R.iRY .inr.ixcis i\ rinsics i\

C/.7

ihc electron is imniiiv; from one point of t.innency willi the d.ished
lircle, inwani around the nuileiis, iMck to the next point of tan-
Kency; meanwhile, <t> is runniniji tliroujjh an entire eiriuit am muling
to 2t, and in addition tliroujjh tin- ani-Ie S<t>. Thus tlu- period 7",
of r stands to ilu' period 7'^ of 0 as

7V: 7* =

2v+M_ 2;r + 2n-u)7V
'2jr 27r

(14)

in which e\[)ressi.)n the symbol co stands for the frecpieiuy of the
()recession (.i.e., the reciprocal of the time the major axis re(|uires to

Kg. 3 — Roictte orbit, resulting from a rreccssion superposed upon an elliptical

orbit

trace out the entire dashed circle). One might say that the two
frequencies u}, = l/Tr and 0)^=1/7'^ are slightly out of tune with
one another. So long as the force acting upon the electron is exactly
an inverse-square force, these two frequencies are perfectly in tune,
the ellipse is stationary; when the inverse-square force is slightly
altered, the two frequencies fall out of tune and the ellipse revolves.
In general, the two frequencies will be incommensuralile with one
another; the rosette will never return into itself, the electron will go
on winding its path over and over and over the interior of the dashed
circle, passing eventually within any assignable distance, no matter
how small, of iiny point selected at random, and "co\ering the interior
of the circle everywhere dense" as the mathematicians say. There-
fore, although the variables r and </> are individually periodic, the

668 HELL SYSTEM TECHXICAL JOVRXAL

motion of the electron nexer (|iiite ri'jx'als itself. Such a system is
called conditionally periodic.

When we come to consider the atom-models proposed for atoms
with more than one electron, we shall make use of these ideas; but
that will not occur before the Third Fart of this article. However,
one application can be made to the theory of hydrogen and ionized
lu'liimi.

73. Motion, in an Inverse-square Central Field, of an Electron of Which
the Mass Varies as Prescribed by the Theory of Relativity

According to "relati\istic mechanics," as distinguished from
"Newtonian mechanics," the mass m of an electron (or an\t]iing
else) varies with its speed v in the manner

m=mo/\^l—v-/c^ (45)

and the force F acting upon it produces an acceleration dv/dt given
not b\ the familiar equation force = massXacceleration, but by the
ccjuation

F = d(mv),dt (4())

If we suppose the electron revolving in a perfect inverse-square
field about the nucleus, and apply these equations of relativistic
mechanics, we arrive at the same result as though we had used the
equations of Newtonian mechanics, but had assumed that the field
acting upon the electron is the sum of an inverse-square attraction
and an inverse-cube attraction. Specifically, the result is formally
ecjuivalent to the result attained by continuing to use Newtonian
mechanics, and assuming that the potential energy of the atom-
model is given by (43) with the following value inserted for the con-
stant C:

C=-e-E'/2moC- (47)

The orbit is a rosette; and all the general remarks made in section J2
about rosette orbits nia\- be repeated for this case.

74. Motion of an Electron in a Field Compounded of an Inverse-square
Central Electric Field and an Uniform Magnetic Field

Here we ha\e a famous theorem of Larnior's to help us. According
to this theorem, a magnetic field // acting upon a re\olving electron,
or a system of revolving electrons, produces no other effect than a

^'i.\fr. COXTF.Ml'OR.INY .ll>r.l.\\-f.S /\ I'llVSICS-IX (^f)

precession of the entire system .ilxuil the (iirectioii of the iii.iL;iieiii-
lielil at the fre(Hieiir\-

^i. = (Il lirmc (48)

In other words, ll>e motion of the electron or electrons is, when re
terred to a coordinate system revolving about the direction of the
tield with frequency ell -iir tm\ the same as without tin- lield it would
l)e, when referretl to a stationary' cjordinate system.

If the tieUl h.ippens to be normal to the plane of an elli()tical orl)it
being described by an electron about a nucleus, the ellipse will be
transformed into a rosette. If the field is neither exactly normal nor
exactly parallel to the plane of the ellipse, this plane may be imaj;ined
to swing around the direction of the field (around the line through the
nucleus parallel to the tield) like a precessing top, carr\-ing the orbit
with it.

These statements are inexact if the rate of [^recession so calculated
is not quite small in comparison with the rate of revolution of the
electron.

Jo. Motion of an Electron in a Field Compounded of an Inverse-square
Central Electric Field and an Uniform Electric Field

This problem may be regarded as the limiting case of a more general
problem phrased as follows: to determine the motion of a particle
attracted by two fixed points according to the inverse-square law.
Imagine one of the fixed points to recede to infinity, its attracting-
power meanwhile rising at the proper rate to keep the field in the
region of the other at a finite value; and you ha\e the case described
in the sub-title above. Jacobi soKed the general problem a century
or so ago.

The motion is difficult to realize and impossible to describe in words,
and seems also to be impossible to represent by any adequate two-
dimensional sketch. The electron makes circuits around the line
through the nucleus parallel to the uniform field, and in each circuit
it describes a cur\-e which is very nearly an ellipse; but the con-
secutve loops, as in the case of Fig. 3, do not coincide; furthermore,
they are not alike in shape, and they are not plane. The electron
winds around and around through the volume of what I am tempted
to call a doughnut, surrounding the aforesaid line as its axis; and in
the course of time its path fills up the doughnut "everywhere dense,"
as the path of the electron in Fig. 3 woukl fill up the interior of the
dashed circle.

670 DELL SYSTEM TECItXlC.lL JOURNAL

I hope it will he aiipreciated that the foregoing statements about the
orbits are fatally incomplete, except in the first case. Nothing could
be done unless it were possil)le to know, not merely the general shape
of each t\pe of orbit, but the exact mathematical expression for it,
and for the energy-\'alue of each orbit of each type. In some cases
this knowledge is available; in others, it is not. For the cases desig-
nated here by J3, J4 and J 5, it is a\'ailable; wherefore it is possible
to go about the process of seeking the distinctive features of orbits
possessing the preassigned energy-\alues, or inversely the energy-
values of orbits distinguished by certain features.

K. FlKTIlliR l.NTICKI'KHT.VnoN OK TlIK SPKI TK.\ OK HVDROC.K.V .\ND

loMzi:i) HK:i.irM

Continuing for the moment to accept the energy-\alues of the
stationary states of the hydrogen atom as gi\en by

Wi=-Rh, Wi=-Rli 4, ]V,= -Rh <)

and continuing to acceiH the atom-uKidei consisting of a nucleus
and a revolving electron; let us consider what are the properties of the
elliptical orbits, in which if the electron re\ol\ed, the atom-model
would possess one or another of the recjuired energy-values.

According to equation (40), the energ\- of the atom-model, when
the electron is rexoKing in an cllii)se <it wliich \hv nuijdr axis is '2(i,
is given b>'

H'= -eE/2a

irrespective of the eccentricity of the ellipse. In this, as in all fol-
lowing equations, E is ecjual to e for h>drogen and to '2e for ioni/ed
helium. If we set this expression ecjual to one of llie ri'(|uire<l tiiergy-
\alues, for instance to Wi, we ha\e

2ai=-eE, IT, =(/i Rli. (.50)

The atom-model therefore has ihi' proper energy-value I^i for the
normal state of the hydrogen atom, it ilie electron is re\oK-ing in
any ellipse for wliicli ilie major axis is cE Rh. The circle of diameter
eE Rh of whi( li \\t' li.i\ e heretofore been thinking is only one of these
ellipses, it is the one for which the major .uul tiie minor axes are
identical and t = (); there is an inrmilN' of oiiu-rs.

Should we then di\est the circular orbits of the prominence which
has been accorded to them, and a.ssimie for instance that when the
atom is in its normal stale the electron is moving in an\- one of the
infinity of ellipses of which the major axis is eE, Rh' This might be

.SOMIi C()A/7:.U/'()A'./A'l' .ll>r.l\CI:S l\ I'liySICS- IS U7\

(larijirrous. for \vi> h.ivo i(lrtitit"K'<l i-iTi.iin distinclivr ft-atiirfs of the
jicrmissiMc circular orbits which ma\' Ik- OM-uti.il; and ihcsi- features
may not Ik.' iransfcralile to tlu' ellipses. Let us test them.

The second and the third of tiie three distinctive features which I
cititl are transferable — that is they can be extended to the totality
of all ellii>si's having one or another of the enern\-values — Rli tir,'
am! they differentiate these from all other ellipses. I-'or it can be
shown. !>>• integrating the kinetic energy A" (the first term on the right
hand side of {'M)) ) around an elliptical orbit, that

7=1 JA'r// = 27r \/aine/-: 5 1

depending onl\' on the major a.xis a of the oriiil. Now we have
shown that I = nh Un the «th of the permissible circles; hence for each
ellipse ha\ing the same major axis as the Hth permissib.e circle, in
other words for each ellijise of energy-\alue — Rh n'-. we haw

/ = ///;

and the second of the distinctive features is transferable to the ellipses.
It is the same for the third ; for 7' is b\- (42) tlependeiu on a onl\-, and so

Lim w = Liiu v.

But it is otherwise with the first.

In the first place it was shown that the angular momentum of the
electron in the circle of diameter eE Rh is equal to h/2ir. Obviously
this cannot l>e true of all the ellipses of major axis eE Rh. For ac-
cording to (37), the angular momentum of the electron in such an
ellipse is

p = VeEma{l-t-) (52)

defK'nding on the eccentricit\'. This is e(iual to ("vw/a, which by
(12) is equal to // 2;r, only if «=U. The circle therefore is the only
orbit for which the energv-value and the angular momentum of the
atom are simultaneously equal to —Rh and to /; 2ir respectively.
If we admit the ellipses to equal value with the circle, we concede
that the equality of the angular momentum with /; 2;r is of no sig-
nificance.

There is a partial escape from this conclusion for the remaining
stationary- states. Take for instance the second, of energy-value
— Rh, 4. The circular orbit of diameter 4eE Rh, for which the atom
possesses this energy-value, is distinguished by the angular momen-
tum 2/j 2t. For each of the infinity of ellipses possessing the same
major axis 4eE/Rh there is a different value of the angular momentum;

672 BELL SYSTEM TECHXIC.iL JOURXAL

hut ilicre is one among them for which the angular momentum is
equal to /; 2-k. And in general for the wth stationary state of energy-
value — Rh ir. there are « elliptical (including one circular) orbits
which would give the same cnerg>-\alue and ;; \alues of angular

9.,

16a,

Fig. 4a — Diagram to show the proportional dimensions of ellipses with identical
total quantum-number « = / 7; and different azimuthal quantum-numbers * = 1,
2 .... n ! rom left to right we have the cas?s « = 1, 2, 3, 4, on scales varying as
indicated by the subjoined arrows.

momentum equal rcspecti\eK' to nli 'Itt, {ii — l)li 2ir Ii'lir.

These, as the reader can show from (.")2). are distingtiished by the
following values of t:

E- =k n

k = \.

(o3)

Thus if we desire to regard the equalit\- of angular momentum with
an integer multiple of h 2-k as being essential to the permissible orbits,
we can keep, along with the circles, some of the other elliptical orbits
compatible with tiie prescribed energ>-\ allies; btit except for these

•ig. 4b — The same ellipses as appear in Fig. 4a, drawn confocalK as I hey should
appear, instead of concentrically

few, the inlinil\' of I'liipiical ori)iis will remain tnia\'ailaiile. There
is additional reason for liking to do this; for it amounts to a quite
natural generalization of the condition imposed on the angular mo-
mentimi, which as we saw it is highh' desirable to generalize if possible.
The angular momentum »ir-{d<t> dl), which I shall hereafter call p<i>
instead of simply p, stands on an equal footing with the radial
momentum pr = m{dr.dt) of the electorn; in the Hamiltonian equa-
tions for the motion of the particle, these two quantities stand side
by side. Now the condition imposed upon the angular momentum

Sd.Mi: (().V//.A//'(»A'. lA') .l/U./.\(/s l.\ rilVSli \ l.\ (i7.<

f><t> of the electron in its sarioiis cirriil.ir orliils is p<}> = tih '2w. wliirli
may be written

/ (}^ ii<p = uh (54)

tile inteyr.il liiinji t.ikiii .ironnd .1 lonipU'Ic re\ nliilinn, .1 fornuihi-
tion in wliiili the soniewh.il distressing I'.iilor 1 '2k CDrn eniently
vanishes. Correspond injj to this integral we ha\e .nioliur

fp<>dr = mf'l;^d4. (55)

also to he taken aroinul a complete revolution, therefore from r„i„,=
a(l— f) to r„^^,=a{\-\-i) and back again. The materials for per-
forming this integration are furnished in equation (35); if the reader
can perform it he will arrive at the value.

/Vrf. = 2./>,[— i^.^-l]

(56)

and if the eccentricity of the ellipse conforms to equation (o3), so
that the integral of the angular momentum of the electron is kh,
then Uie integral of the radial momentum is

\ .\I,(lr={>t-k]li. (57)

t )ur position may now be described in the following words. We
have accepted the values —Rh n" (h = 1,2,3 . . . ) for the successive
stationan,- states of the hydrogen atom; we have accepted an atom-
mo Jel consisting of a nucleus and a revolving electron; we have
traced the orbits which would entail these various energy-values,
and we have found that for each of these energy-values there are
infinitely many elliptical orbits which would entail it, — to wit, for
the Hth stationan,- state, all the infinitely many ellipses of which
the major a.xis is given by

2a„ = n-h"-'2w-meE. (58)

Furthermore we have sought for distinctive features which might
discriminate these ellipses from all the others which entail "wrong"
energy-values, i.e., energ>-\alues which are not included in the list
— Rh. —Rh A, —Rh !».... One such we found in the integral
\2Kdl of the kinetic energy of the electron around the ellipse; this
integral assumes the value nh for each ellipse which entails the energy-
value — Rlin-, so that we could define the permitted orbits as those

r,74 BELL SYSTEM TECHSICAL JOVRXAL

for which f2A'rf/ = any integer multiple of /;. Another such dis-
tinctive feature we found in what was expressed by the equation
(23) Lim w = Lim v. First of all, however, we tried to apply a prin-
ciple of the effect that the angular momentum of the atom when
the electron is rexohing in one of the permitted orbits must be an
integer multiple of h 2Tt. We found, in essence, that this attempt
amounted to picking out for each of the prescribed energy-values,
one or several out of the infinity of elliptical orbits which would entail
it, and eliminating all the rest. But is there suffirieiit reason for
doing a thing like this?

Apparently there is; and the reason for so believing lies precisei\-
in the details of the hydrogen spectrum which I have hitherto passed
over — in the doubleness of the lines of the Balmer series, which shows
that instead of a stationary state of energ>'-value —Rli/i there are
two stationary states of which the energy-values lie extremely close
to one another and to this \alue, and which suggests that the other
stationary states may likewise be resolvable into groups of stationary
states (a suggestion confirmed by the spectrum of ionized helium).
At the beginning, let us consider only the state of which the energy-
value is —Rli'4. We have seen that this is the energ>'-value corre-
sponding to any and e\er\- one of the elliptical orbits of which the
major axis is

2a2 = -ih- 2Tr' nu'E (o9)

among which inliniiy of elliptical orbits, there is just one (a circle)
for which the angular momentum of the atom is 2/i 27r, and just one
other for which it is //,'27r, and no others for which it is any integer
multiple of /f/27r at all. But these tw-o, like all the rest character-
ized by (.58), entail the same energy-value and so are indistinguish-
able among the crowd — if every one of our assumptions is absolutelv-
true. But if one of them should deviate slightly from the truth —
if for instance the l,i\\ of force between the nucleus and the electron
should deviate slighlK from the inverse-square law, or if a small
extraneous force should be impres.sed upon the atom, or if tlie mass
of the electron should slightly vary as it revolves in its orbit — then
we have seen that all the orbits would be altered, and these two orbits
niav' be so altered as to lie distinguishable from the rest. And this
in fact is what appears to be responsible for the fine structure of the
hydrogen and ionized-helium. Owing to the variation of the mass
of the electron, with its speed, each ellipse is transformed into a
rosette; and though the energy-values of all the ellipses would be
e(|ual, the energy-values of the rosettes are not.

MM//. (. (>.\ I I.Mnih-.IK) //'( /\i/s l\ I'll) SliS l\ 675

Lit us now reverse the prfKcdtire of the forenoiiiK paraKr.ii)hs.
Instead of asking what is the anjjular inotnentiini of the atom when
the electron is revolxing in such an orl)it tliat the energy of the atom
is —Rli 4, let us ask what is the energy of the atom when the electron
is revolving in a rosette such that the angular momentum of the
atom is 2// 2ir. It is liesl to put the question thus: what is the energy
of the atom when the electron is revolving in a rosette'" such that the
integral cf the angular momentum around a re\'olution is 2/;?

} f}0 ({<i> = 2li. (01)

The energy-\alue in question, which I designate by ]\\« for a reason
which will presently appear, is found by calculation to be

11'.,,= -Rli -i-Rha- (i4 (62)

in which a is ,1 symbol meaning

a = -lire- he = 7.20 K)-'. (63)

(This expression incidentally is not the exact consequence of the
equations of the motion, but an approximation to it, quite suffi-
ciently accurate under these circumstances). Next let us ask what
is the energy of the atom when the electron is rc\()h-ing in a rosette'"
such that

\p4,d4> = h. (64)

Calling this energ\-value H'ji, it is calculated that

Wi I = - Rh/4 - Rhoa'/M . (65)

Incidentally it is found, as in the pre\ious simpler case, that when
I p4,d<t> = It , then also ) p,dr = It .

The energy-values corresponding to the two orbits dehned by (68)
and (71) therefore differ by the very small amount

ir.j- \\\i=-Rha\'lQ= -.R//(3..3210-«). (60)

I said at first that the various "lines" of the Balmer series in the
spectrum of hydrogen correspond to transitions into the stationary
state of energy-\alue —Rli 4 from other stationary states; and that
unusually good spectroscopes show each of these lines to be a pair of
lines \ery close together. May this be explained by the theory
culminating in equation (66)? If so, the frequency-difference be-
tween the two lines of each doublet must be the same, and equal to

'" This rosette is degenerated into a circle; the precession amounts effectively to
an additional term in the expression for the angular velocity of the electron.

676 BELL SVSTEM TECHNICAL JOURNAL

{W22-Wn)h=Ra\\& = \.m-U). The wave-length difference, which
is the quantity' directly measured by spectroscopists, varies from one
doublet to another; for the first doublet of the Balmer series, known
as //a, the mean wavelength of which is 6.563' 10~' cm., it should
be equal to 1.58'I0~^ cm.

Many independent measurements of these wavelength differences
have been made, most of them upon the first doublet of the series,
a few upon other doublets as far along as the fifth. Some were made
long before, others after Sommerfeld published the foregoing theory.
The various values found for the various wavelength-differences
have all been within 20% of the value required by equation (66);
within this range they have fluctuated, one or two spectroscopists
of repute have maintained that the actual values are unmistakably
different from the computed value; but the balancing of eN'idence now
seems to point more and more closely to the desired \alue as the
right one ".

This prediction of the wa\eleiigtii-(iifferences between the com-
ponents of the doublets which make up the Balmer series may be
taken tentatively as the third of the numerical agreements which
fortify Bohr's atom-model. So taking it, let us generalize the theory
to the full extent already suggested. Returning for a moment (merely
for ease of explanation) to the over-simplified case of an atom con-
sisting of a nucleus and a revolving electron of which the mass does
not vary with its speed: we saw that the energy-value —Rh/n- is
entailed by each and every one of the n elliptical orbits for which
the integral of the angular momentiiin and the integral of the radial
momentum are given by assigning the ii \alues ^ = 1, 2, 3 . . . « to
the symbol k in the following equations:

J p^'l4> = kli.\ pr(lr = {n-k)li. (67)

This I will express in another wa>' by saying that the energy-\alue
— Rh/n- is entailed by each of the Ji orbits having the azimutlial

" This is one of those embarrassing questions as to which the experimental doctors
still disagree, malcing it folly indeed for anyone else to pretend to decide. The
three latest measurements, which are those of Shrum, Oklcnberg, and Geddes,
agree passably with the value resulting from the theory I have presented. Vet
Gehrcke and Lau defend their measurements, made in 1920 and 1922, which give
values about 20' J too low; an<l (iehrcke at least is an authority to whom lack of
experience in this field certainh cannot be imputed. I evade this issue In- referring
the reader to the articles by Shrum {Proc. Roy. Soc. A105, pp. 259-270; 1923) for
the bibliography of earlier work and the account of the latest; of Kuark (/. c. supra)
for the contention that the data sustain the theory; of Lau {Pliys. ZS. 25, pp.
00-6S; 1924) for the contrary contention.

The issue is further complicated by the predictions quoted in the next paragraph
alravc, although not seriously enough to disqualify the foregoing remarks.

so,\n-: COM liMi'ou.iK) iin .i.mi.s rx rnv.'^ics—rx 677

quanlum-ntimhers k=\, 2, . . . «; iiUMiiin.u l>y aziimilhal (|uantum-
luimlier the (iiiotii'iU of j p^il<i> 1>> /'. If m>\v wt- taki- arcoimt of ihi-
variation of tlie mass of the eieclron with its speed, and calculate
the enerv;y-valiies for the n rosettes obtained l)y assi^nin^ the values
I, 2, 3 . . . w successively to the syinl)ol k in ((')7), we shall find that
these « energy-values are all distinct, deviatinij slijjhtly from —Rh'ri^
and from each other. Therefore, there should he three stationary
states of energy-values \\\^, Wi2, VFji, all differing by a little from

— Rli •.) and from each other; there should he four stationary states
of energy-values ll'4i, ll'ia, Wu, Ww, all nearly hut not ciiiile equal to

— Rh It) and each other; and so forth. (The reason for such symbols
as Il'n will now appear; the first subscript represents the total, the
second the azimuthal quantum-number of the orbit in question.)
In general there are n stationary states in the group corresponding
nearly to the mean energy-value —Rh ;/-; and the expressions for
their several values are obtained by putting k equal to the various
\ahies 1, 2, H . . . « in tiie formula.

£=-«*, .[,+5(:4)]. m

Owing to these complexities the lines of the Balmer series should
be not doublets, but groups of man>' more lines; e.g., the transitions
from what I had called the stationary state of energy-value —Rli/9
to the stationary* state of energy-value —Rh/A are transitions of six
sorts, from each of three initial states to each of two final; and the
first "line" of the Balmer series might he expected to be sextuple.

The trial of these ideas is best made upon the spectrum of ionized
"aelium. The separation between the energy-values of stationary
states sharing the same total quantum-number and differing in
azimuthal quantum-number is increased, when we pass from an
atom-model in which the charge on the nucleus is e to one in which
it is Ze, in the ratio Z^:l; in this instance 16:1. The system of com-
ponent lines, or the so-called "fine structure" to be expected for any
"line" of the hydrogen spectrum should he spread out on a scale
sixteenfold as great for the corresponding "line" of the ionized-
helium spectrum. The trial was made by Paschen; the comparison
between the fine structure of several of the "lines" of ionized helium
and the components to be expected from the foregoing theory, yielded
what appear to be very satisfactory- results. This matter I discussed
over several pages of the First Part of this article; and for economy
of space I refer the reader back to them, and at this place say only
that the "other numerical agreements between the production and

678 KP.I.L SYSTEM TECHSICAL JOIRXAL

the data" to which I there allude, are agreements of the same ciiar-
acter as the agreement between the spacing of the component lines
of the Balmer series doublets, and the numerical value of the ex-
pression in equation (73). That is to say: the pattern of the fine
structure, into which by a good spectroscope the lines of ionized
helium are resolved, agrees more or less with the pattern to be ex-
pected from the theory, not only in appearance but in scale. Com-
bining these agreements with the other one, we are probably justified
in counting the latter as the third of the conspicuous numerical
agreements which make Bohr's atom-model plausible '-.

Now let us examine the situation again. (Considering the abstruse-
ness of these matters, I hope that few readers will resent these fre-
quent repetitions of past remarks.) Accepting for the atom of hydrogen
(and of ionized helium) an atom-model consisting of a nucleus and
an electron, we have traced orbits for the electron such as entail
energy-values for the atom equal to those of the known stationary
states. At first we ignored both the experimental fact that the lines
of hydrogen and those of ionized helium have a fine structure, and
the tlieoretical likelihood that the mass of the electron varies w^th
its speed; and we found that the orbits are ellipses. Later on, we
took cognizance of both these things; and we found that the orbits
are rosettes. Vet merely to trace the orbits which yield the required
energy-values, the so-called "permissible" orbits, amounts to little.
It is essential to find distinctive features which set the permissible
orbits apart from all the others — on success in achieving this, the
whole value of the theory depends.

Now at the \'ery beginning it was shown that, if we ignore the
\ariation of the mass of the electron with its speed, and if we consider
circular orbits only — then the permissible circular orbits which yield
the reciuired energy-values —Rh/ti- of the stationary states (fine-
slructtire being ii^nored!) are those for which

)'p,pd<t> = nli (69)

ill wliicli e(iuali()ii p^ stands for liie angular iiKmR'iuum of the nintioii,
and n for any posili\e integer; and the integral is taken around a com-
plete cycle of <t>.

"Tor the txperiniental results and the comparison of data with predictions sec
Paschen's great paper {Ann. d. Phys. SO, pp. 901-941); 1915) which however is any-
thing l)ul easy to read, so that Soninierfeld's presentation will probably be pre-
ferre<l; likewise Birge's article (Phys. Rev. 17, pp. 5S9 fl:, 1921) to which the same
words apply. The agreements are impressive. On the other hand I note thai I.au
(/. f. supra) concludes from the same data that there is a disagreement between
flala and predictions, in the same sense and of about the same magnitude as the
disagreement which he claims to occur in the hydrogen spectrum.

so.\fE a).v//:.u/'(»AM/v') .iih'.ixcf.s i\ rinsics is (.7')

li w.is lU'M sliDWii ill. It wlii-n we in.ikc .illdu.iiiic fur ilic \,iri,ilnii
of tlu- mass of tlu- i-li'ctron with its spivd, llu'ii tiu' piTmissihlc rosclii-
orbits which yielil tlie ri>(|iiirf(i i'iR'rjiy-\aliK's of tlu- stationary states
(t'liR' strurliiri' bi-iui; taki-ii into accouiil !) an.- tliosi- for whicli

J /),(//• = ;/,/; I t)^(l<t> = iiJi (71))

in which etiiiations />, and />^ stand for the radial and an^jiilar mo-
nuMita — tlie nionicnta iK'longiny; to the variables r and 0 respectively
— and «i and «•> for any positive integers; and the integrals are taken
around complete cycles of r and (t> respectively.

The ecjiiations (70) look like a very natural and pleasing general-
ization of the eciualion (W)). It is possible to go somewhat further.
Consider that, when the electron was supposed to move in a circle,
its |K)sition was defined by one variable <t>; and the permissible circles
were determined by one integral. Further, when the electron was
supposed to move in a rosette, its position was defined by two vari-
ables r and <t>; and the permissible rosettes were determined by two
integrals. Now when the electron is subjected, for instance, to an
uniform magnetic field superposed upon the field of the nucleus,
its motion is three-dimensional. Three variables are required to
define its position; for instance, the variables r, 6 and ^ of a polar
c(X)rdinate system with its polar axis parallel to the direction of the
magnetic field. Three corresponding momenta pr, pe and p^ can
be defined. It seems natural to generalize from (69) through (70)
to a triad of equations, and say that the permissible orbits are those
for which

I p,dr = >i Ji ) pgde = iiJi. J P^d^ = >hli (" 1 )

in which e(|uations «i, n-:, h, all stand for positive integers, and the
integrals are taken around complete cycles of r, B and \p respectively.
When this is done for the specific case of an electron moving under
the combined influence of a uniform magnetic field and the field of a
nucleus, the result is entirely satisfactory. That is to say: when the
permissible orbits are determined by using the equations (71) upon
the general type of orbit described in section J4, and when their energy-
values are calculated, it is found that they agree ver>- well with the
obser\ed energy-values of the stationary states of hydrogen in a
magnetic field. This may be regarded as the fourth of the numerical
agreements which fortify Bohr's atom-model. As I shall end this
part of the present article by a presentation of the effect of the mag-

680 BELL SYSTEM TECHXICAL JOURNAL

netic field made in a snmewli.n difk-rint manner, I reserve the details
for the following section.

Vet it cannot be said that equation (71) is the utterance of the
much-desired General Principle, of the distinctive feature par excel-
lence which sets all permissible orbits apart from all non-permissible
orbits in every case. The most that can be said is this, that equation
(71), if properly interpreted, is the widest partial principle that has
yet been discovered. But it suffers limitations. I do not mean, as
might be thought, that cases have been discovered in wliich ilie per-
missible orbits determined by such equations as (71) have energy-
values not agreeing with those of the observed stationary states.
The difficulty is, that equations such as (71) cannot e\en be formu-
lated in many cases, because the necessary mechanical conditions
do not exist.

This matter is a hard one to make clear; but the limitation can
be at least partialh' expressed in the following way. Re\ert to the
equations (70) which were applied to the rosette orbits. The first
of the integrals in (70) is to be taken over an entire cycle of the \ari-
able r. Now it was said in section J2 that the periods of the two
\arial)les r and 0 are not equal, and in general they are incommensur-
al>le. W'lien the variable r describes a complete cycle, r and drdt
l)oth return to their initial values; but <t> and d(t>/dt do not have, at
tlie end of the cycle of r, the same values as they had at its begin-
ning. It follows that if pr depends on (j> or on d<i>/dt, the first of the
two integrals in equation (70) will have different values for differ-
ent cycles of r. If so, the conditions imposed upon the permissible
orbits by (70) would have no meaning. The conditions ha\e a
meaning, only if each of the integrals in (70) has the same value
for e\ery cycle of its variable — therefore, only if pr depends on r
only, and p^ depends on <^ only. And in general, such a set of equa-
tions as (71) has a meaning, only if it is possible to find a set of vari-
ables such that the momentum corresponding to each of them dejiends
on and only on the \ariable to which it corresponds; or, in technical
language, only if it is possible to effect separation of variables.

Separation of variables is po.ssible in some cases, and in others it
is not. When the periods of all the variables are equal, as the\' are
when we imagine an electron of changeless mass revoking in an
inverse-square field, it is clearly always possible; the difficulty de-
scribed in the foregoing paragraph does not occur. In the other
cases which I ha\e outlined — when the electron is imagined to move
in an inverse-scjuare field according to the laws of relativistic me-
chanics, and when it is imagined to mo\c in a field compounded of

soAfE co^^l^^t^'Ol^'.^KY .iih-.i.whs ix /7/).s7c.s-/.v (n\

all iin»'rsi'-s<|ii.iri- I'li-ld .mil ,m imiform ina^;nolif tk-ld -separation of
\arial>li's is possiMo. I'Or these cases, llierefore, the conditions (70)
and (71) .ire apphcable, and have meaning;.

There is t)nc other important case in wliicli it is jjossihle so to select
tiie variables that se|)aration can be effected. This is the case of an
electron niovini; according; to the laws of Newtonian mechanics in a
tUld compounded of an inverse-square field anfl an uniform electric
tield. Althoujjh the motion is three-dimensional, and three coordi-
nates are required and sutTue to determine it, these three coordinates
ma>- not be chosen at rantlom; and the three obvious ones would be
worthless for our purpose. If we should choose the polar coordinates
r. 6, and ^ employed in formulating the ecjuations (71), we should
tind that the momenta p,, />„ and /)^ do not depend each exclusively
uj)on the \ariable to which it corresponds. The procedure to be
followed is ainthing but ob\ious; but Jacobi found that if paraboloidal
coordinates are usetl instead of ]M)lar, separation of variables can be
effectetl. One must visualize two families of coaxial and confocal
paralioloids, their common focus at the nucleus, their noses pointing
in opposite directions along their common axis which is the line drawn
through the nucleus parallel to the electric field. The position of
any point through which the electron may pass is given by the para-
meters J and T) of the two paraboloids which intersect at that point,
and by an angle <t> defining its azimuth in the plane normal to the axis,
ciuite like the angle ^ of a system of polar coordinates. When the
motion of the electron is expressed in terms of these coordinates, the
corresponding momenta />£ and />, depend only upon ^ and -q respec-
tively and p^ is constant; hence the integrals taken over cycles of
f, rj, and 0 respectively, on the right-hand sides of the equations,

) /Jfrf? = w,/;, I pr,({n = nji J p^d<f> = II Ji (72)

have definite meanings, and the e(|iiations themselves define particu-
lar orbits. Epstein determined the orbits defined by these ecjua-
tions, and calculated their energy-values. These agreed well with
the energy-values of the stationary states of h>drogen in an electric
field, inferred from its spectrum. This is the fifth of the striking
numerical agreements upon which the credit of Bohr's atom-model
chiefly depends '^.

"Set- Epstein's article (.Imm. <l. Phys. SO, pp. 489-.S20; 1016), or the more per-
spicuous account by SommerfeUI. in which it is stated that the pattern of the com-
ponents into which the first four lines of the Balnier scries are resolved by the electric
field agrees with the predictions so far as the number and relative spacings of the
components are concerned; while to attain agreement in regard to the absolute
spacings, it is necessary only to assume that Stark's estimate of the field was 3','c
in error, which is (|uite easy to accept.

6S2 BELL SYSTEM TECHXICAL JOURNAL

It is important to note that if we had made allowance for the \-aria-
tion of the mass of the electron with its speed — if in other words we
had used the equations of relativistic mechanics, which are prohahh'
the right ones to use — separation of variables could not ha\e lu-en
effected either in this paraboloidal coordinate-system, or in an\'
other. Vet the stationary states are found by experiment to he
shari)ly defined, and to ha\e approcimately the energA-\alues deter-
mined by (72). This can mean only that the desired General Prin-
ciple for determining the permissible orbits is not completeh' expressed
by such sets of equations as (71) or (72). Those equations are valid
onl\- for systems of a certain kind (those for which separation of
variables is possible). The General Principle must be valid for
s\slems of this kind and the other kind as well. For systems of this
kind, it must become equivalent with the conditions formulated in
(71) and (72) — the General Quantum Conditions for Separable
Systems. Or at least, the results to which it leads must be indis-
tinguishable from the results to which these lead. The General
Principle for systems of ever>' kind has not been discovered; perhaps
it does not exist. Bohr is striving to infer it by generalizing from
the third of the properties of the permissible circular orbits, which
I mentioned in Section H and expressed by equation (23). He has
attained some notable successes, which I hope that it will be possible
to expoiiiiil ill tile I'iiird Part of the article.

L. M.\(.m;ti( Proi'icktihs oi-" the Atom Modi^l

After this rather arduous pilgrimage through a succession of abstract
reasonings, the reader may welcome an account in simpler fashion of
the manner in which Bohr's atom-model is adapted to explain the
l)eha\ior of the atom in a magnetic field. This is an alternati\-e
method of arri\ing at liie same results as are attained by means of
ec|ualions (71).

It was stated in section K9 of the First Part of the article, that the
spectrum of a radiating substance in a magnetic field indicates that
the field acts by replacing each of the stationary states, which the
substance possesses when there is no magnetic field prevailing, by
two or more new stationary states. The energy of each of the new
stationary slates difTers from that of the stationary state which it
replaces, by the amount

M' = seIIh Airmc {!'?,)

in which // stands for the magnetic field strength and .f for an integer.

SOME coMii.MroR.iiK'y .ini'.iXii.s i\ rinsns i\ r>«.i

wliiili mii>l (H>>x'ss l\V(i iir mi>ri- v.iliu-- -.iMccd .il iiilt-rv.ils of luw
iiiiii '■.

'I'lif ,iti>m-ni(Klrl wliicli vvc luno lircii discussing ,it sucli Icnvjtli
(•(insists of an t'li-ctroii ('irculalin^ in an clliplical orbit aboiil a sta-
tionary nucleus; the minor \ariations diii- to the variation of.thu
lu.iss m of the electron with its sjK-ed, and to the motion of the nucleus,
are now of comparatively little importance. An electron circulating
in a dosetl orliit with fretjuency f passes c times per second throujjh
my |K)int of its orbit, so thai the charge passing per secf)nd ihrouKh
my such point is e(|ual to that which would pass, if a continuous
rurrent I = ev c (measured in electromagnetic units) were flowinv;
around the orbit. Now a current / flowing continuously around the
curve lK)unding an area A is equivalent — so far as its field at a dis-
tance goes — to a magnet, of which the magnetic moment .1/ is directed
norntally to the plane of the curve and is ec|ual in magnitude to I A.
The area of an ellipse of which the major a.\is is denoted by a and the
minor axis b = a\/\—t- is equal to wab = ira- y/ \ — i" . Hen( e the
magnetic moment of the atom-m(xlel is equal to

M =evwa-\/\—t- c (74)

Further we have seen, by equations (:^7) and (42), that the angular
monienium of the electron in its orbit is equal to

p = 2Trmva.-yy\—t- {l-y)

('onse(|uently

.U, p = e 2mc (7fi)

a rather surprisingly simple relation!

Now when a magnet of m(jment .1/ is placed in a magnetic field
of field-strength //, it acquires a certain potential energy At' — in
addition to the intrinsic energy which it possesses when oriented
normally to the field — which depends on the angle 6 between the

" Unlike sonic of the preceding derivations, this theor>' is not essentially limited
to the rase of an atoni-mrHJel t-onsisting of a niiileus and one ekrtron. It there
.ire several electrons describing closed orbits, the l.armor precession atTects them
iilcniically; or, otherwsc put, the magnetic field treats the at<)m as a unit having
an angular momentum and a magnetic moment e(|ual respectively to the v("ctorial
sums of the angular momenta and the magnetic moments of the individual electrons.
In fact the l>est verification of (7.?i is obtained from the lines l>elonging to the singlet
systems of certain metals, which display "normal" Zeeman cflect— the effect to
which this theory is adapted. With anomalous Zeeman effect, against which this
theory is powerless, we are not now c(jncerned. In the case of hydrogen, the effect
is complicatetl fiy the fine structure of the lines. With small magnetic fields it is
normal, at least so far as the observations go. Kach of the two stationary states
of which the energy-values are given by '02i and (65i is replace«l by two or more,
conforming to (73).

6&4 BELL SYSTEM TECIISICAL JOURNAL

direction of its maKnelic moment and the direction of the field, and
is given by

AU= Mil cose (77)

According to equation (73), the observed stationary states of hydro-
gen atoms in a magnetic field ha\e specific discrete energy-\alues.
These must correspond to specific discrete values of the angle 8;
the orientation of the atom in the magnetic field must be constrained to
certain particular directions, an extraordinary idea! We ascertain
these "permissible directions" by equating the two \alues of AU
figuring in (73) and (77), obtaining

seh -iirmc = M cos e (78)

into which we then insiTt ihe expression for .1/ in terms of p:

sh 2t:c = p cos 6 (79)

We have experinicnted at length with the notion that the angular
momentum p of the electron in its orbit is constrained to assume
only such values as are integer multiples of h/2-K; let it be intro-
duced here also. If p = kh '2w, then

i- = k cos 0 (80)

The angle 6 nia\' assume only such values, as will gi\c to the quan-
tity 5 = ^ cos d two or more values, differing by one unit. I'or
instance, if k=\. the values 6 = 60" and 120^ will suffice.

This, the most spectacular of all the remarkable consequences
of Bohr's interpretation of the stationary states, is also the only
one w^hich has ever been directly verified.

The verification has not been made upon h\'drogen nor upon
ionized helium, but upon the atoms of certain metals '^. I shall there-
fore reserve the account of it for the following sections of tiie article,
where also there are certain other reasons for desiring to put it. Xe\er-
theless, the reader should be aware of it at this point.

" I gave an account of the earliest of these experiments in the first article of this
series (This Journal, Z, October, 1923; pp. 112-114). The subsequent experiments
have added nothing fundamentally new.

{To be continued)

Electric Circuit Theory and the
Operational Calculus

By JOHN R. CARSON

Note: This is the first of thrrt- iiisl.illinonts l)y Mr. Cirson whii h will
i'iiiIkkIv material piven by him in a course of lectures at the Moore School
of Klectrical Kngmeering, I'niversity of IVnnsylvania, May, l')25. No
effort has l)ccn spared l)y the author to make his treatment clear and as
simple as the suliject matter will permit. The methfxi of presentation is
distinctively pedaKoi;ic. To electrical engineers and to engineering in-
structors, this ex|>osilion of the fundamentals of electric circuit theory and
the operational calculus should be of great value. — KuiTOk.

Foreword

THE following pages embody, substantially as dcli\crecl, a course
of fifteen lectures given during the Spring of 1!)25 at the Moore
School of Klectrical Kngineering of the l'ni\ersity of PennsyK'ania.

After a brief introduction to the subject of electric circuit theory,
the first chapters are devoted to a systematic and fairly complete
e.xposition and critic|ue of the Heaviside Operational Calculus, a
remarkably direct and powerful method for the solution of the diflfer-
ential ecjuations of electric circuit theory.

The name of Oliver Heaviside is known to engineers the world over:
his operational calculus, however, is known to, and employed by,
only a relatively few specialists, and this notwithstanding its remark-
able properties and wide applicability not only to electric circuit
theor%' but also to the differential equations of mathematical physics.
In the writer's opinion this neglect is due less to the intrinsic dififi-
ciilties of the subject than to unfortunate obscurities in Heaviside's
own exposition. In the present work the operational calculus is
made to depend on an integral equation from which the Heaviside
Rules and Formulas are simply but rigorously deducible. It is the
hope of the writer that this inode of approach and exposition will be
of service in securing a wider use of the operational calculus by en-
gineers and physicists, and a fuller and more just appreciation of
its unique ad\antages.

The second part of the present work deals with adxanced problems of
electric circuit theorv', and in particular with the theory of the propaga-
tion of current and voltage in electrical transmission systems. It is
hoped that this part will be of interest to electrical engineers gener-
ally because, while only a few of the results are original with the
present work, most of the transmission theory dealt with is to be
found only in scattered memoirs, and there accompanied by formid-
able mathematical difficulties.

685

686 BELL SYSTEM TECHNICAL JOURNAL

While llu' mclhod of solution employed in the second part is largely
that of the operational calculus, I have not hesitated to employ
developmcjits and extensions not to be found in Hca\iside. Fcr
exani|)le, the formulation of the problem as a Poisson integral ecjuation
is an original de\clopment which has proved quite useful in the actual
numerical solution of complicated problems. The same ma\- be said
of the Chapter on \'ariable Electric Circuit Theory.

In view of its two-fold aspect this work may therefore be regarded
either as an exposition and development of the operational calculus
with applications to electric circuit theory, or as a contribution to
advanced electric circuit theory, depending on whether the leader's
viewpoint is that of the mathematician or the engineer.

1 have not at li-m|)lc<l in the text to gi\-e adecjuate reference to the
literaturi' ol the sulijtTt, now lairU' extensive. In an appendix,
howe\er, there is furnished a list of original papers and memoirs, for
which, however, no claim to completeness is made.

CHAPTER I
The Funi).\mi:nt.\i.s of Ei.f.ctkic Circuit Thkory

While a knowledge, on the reader's part, of the elements of ekririi-
circuit theory will be assumed, it seems well to start with a brief
review of the fundamental physical principles of circuit theory, the
mode of formulating the equations, and some general theorems which
will prove useful subsequently.

First, the circuit elements are resistances, inductances, and con-
densers. The network is a connected system of circuits or branches
each of which may include resistance, inductance and capacitance
elements together with mutual inductance, and mutual branches.

The equations ol circuit theory may be established in a number
of different wa\s. For example, they may be based on Maxwell's
dynamical theory. In accordance with this method, the network
forms a dynamic system in which the currents play the role of veloci-
ties. If we therefore .set up the expressions for the kinetic energy,
potential energ\- and dissipation, the network etiiialions are deducible
from general dynamic ecjuations.

The simplest, and for ouv jnii poses, a t|uite satisfactory basis for
the eciualions of circuit lluory arc found in KirchhofT's Laws. These
laws state that

1. The total impressed force taken around aiu' closed loop or
ciicuit in the network is equal to the potential drop due to (a) resist-
ance, (b) inductive reaction and (c) capacitivc reactance.

CIKCCIT llll-Oh'V .l\l> ()/7:A'.;77('.V.//. c.ii.iii.rs <H7

2. The sum of the currents enleriiii; aii\ br-iucli point in ilie net-
work is always zero.

Let us now apply tliese hiws to an elementary rircuil in order lo
(ieiluee the physical sij^niUcance of the circuit elements.

Consider an elementary circuit consisting of a resistance clement
K. an inductance element L and a cafiacity element C in series, and
let an electromotive force E be applieil to this circuit. If / denote the
current in the circuit, the resistance drop is Rf, the inductance drop
is Ldl (It and the drop across the condenser is Q/C where (J is the
charge on the conilenser. It is evident that Q and / are related by the
equation I=dQ dt or Q= \ Idt. Now apply KirchhofT's law relating
lo the drop around the circuit : it gives the equation

RI + LdI dt + Q C = E.

MiiliipK i)otli sides 1)\- /: we get

The right hand side is clearly the rate at which the impressed force is
delivering energ>' to the circuit, while the left hand side is the rate
at which energj- is being absorbed by the circuit. The first term
RP is the rate at which electrical energy is being con\erted into heat.
Hence the resistance element may be defined as a device for con-
verting electrical energy into heat. The second term - - — LP is the

rate of increase of the magnetic energ\-. Hence the inductance
element is a device for storing energ\- in the magnetic field. The

third term -7- Q-'2C is the rate of increase of the electric energy.

Hence the condenser is a device for storing energy in the electric field.

In the foregoing we have isolated and idealized the circuit elements.
Actually, of course, ever\- circuit element dissipates some energy in
the form of heat and stores some energy in the magnetic field and
some in the electric field. The analysis of the actual circuit element,
however, into three ideal components is quite convenient and useful,
and should lead to no misconception if properly interpreted.

Now consider the general form of network possessing n independent
meshes or circuits. Let us number these from 1 to «, and let the
corresponding mesh currents be denoted by /i. /j . . . . /„. Let
electromotive forces £1, Ez .... En be apj>lied to the n meshes or
circuits respectively. Let Ljj, R,j, Qj denote the total inductance,

688 /<£/./. sysTn.\r technical jourxal

resistance and capacity in series in mesh j and let Ljk, Rjk, Qk denote
the correspondini; mutual elements between circuit j and k. Now
write down Kirchhoff's equation for any circuit or mesh, say mesh 1;
it is

Corresponding equations hold for each and every one of the w
meshes of the network. Writing them all down, we have the system
of equations

(1)

The system of simultaneous differential equations (1) constitute
the canonical equations of electric circuit theory. The interpreta-
tion and solutiiiii of these equations constitute the subject of Electric
Circuit The(ir\ , and it is in connection with their solution that we
find the most direct and loiiical introduction to the Operation d Cal-
culus.

As an example of the apiirojiriate mode of setting up the cirniit
equations, consider the two mesh network shown in sketch 1. Writ-
ing down Kirschhoff's Law for meshes 1 and 2, respecti\"eh', we lia\e

In this case the self and iiiutu,il rdelTicients are t;i\en hv

L\i= L\

L,, = U

U,

: = Ln

= +M

C\\ = C\

c,, = c.

Cv.

; = C.,

1=0

R\\ =R\

R,i = R,

Rv

,=.R,

1=0

The conventions adopted for the positive directions of currents and
voltages are indicated b\ the arrows. The sign of the muiual in-
ductance iU will depend on the relative mode of winding of the two
coils.

CIRCCIT rill-ORY J.V/) Orr.R.ITlOX.IL C.U.CCI.l'S

wo

N'dw write clown KirchhofT's Law, or tlic cirniital oqii.uion fur
tlie network of sketch 2. They arc

{(L.4-/.)^+(/?. + /?3.+ (^. + l)/.4/.

("oniparison with I'ciiialiims (1) sliows that

Rii = Ri-\-R3 /?j' = i?2 + /?3 /?i; = /?2i = — 2?J

1 1.1 ± ^ 1 =_JL

c... c\\ c,-

-=1+1

Go G^G

It should he oI)Scr\ed that the signs of the mutual cocfticients R^,
Li:, Go are a matter of con\ention. F'or example if the conxentional
directions of h and Ei are reversed, the signs of the mutual coefficients
are reversed.

r

— WAV»-

R?

AMAV- 1

The system of equations (1) possesses two important properties
which are largely responsible for the relative simplicity of classical
electric circuit theory. First, the equations are linear in both currents
and applied electromotive forces. Secondly, the coefficients Ljk,
Rjk, Cjk are^constants. Important electrotechnical problems exist,

690 LiEl.I. SYSTI-.M TECIIXICAL JOIRX.IL

in wliicli these properlies no longer obtain. The solution, ho\ve\er,
for the restricted system of linear equations with constant coefficients
is fundamental and its solution can be extended to important jirob-
lems in\()lving non-linear relations and variable coefficients. Tiu-se
extensions will be taken up briefly in a later chapter.

Another important property is the reciprocal relation among the
coefficients; that is Ljk=Lkj: Rjk = Rkj, and Cjk=Ckj. It is easily
shown that these reciprocal relations mean that there are no con-
cealed sources or sinks of energy'. Again important cases exist where
the reciprocal relations do not hold. Such exceptions, however,
while of physical interest do not affect the mathematical methods
of solution, to which the reciprocal relation is not essential.

Returning to equation (1) we shall now derive the equation of
activity. MuliipK- tlio first equation by /i, the second by /;, etc. and
add : we get

The riglu liand >i(lL' is the rate at which the applied forces are siii^jilying
energy to the network. The first term on thi' k-ft is ilic rale of in-
crease of the magnetic energy

-j-y^^^z.,,./,/,,

while the second term is the rate of increase of the electric energy

Tlie last term, "S^ Rjk Ij Ik, is the rate at wliirli electromagnetic
energy is being converted into heat in the network. Consequently
in the electrical network, the magnetic energy is a homogeneous
quadratic function of the currents, the electric energy is a homogene-
ous quadratic function of the charges, and the rate of dissipation
is a homogeneous quadratic function of the currents. In Maxwell's
dynamical theory of electrical networks, these relations were written
down at the start and the circuit equations then derived by an ap-
plication of Lagrange's dynamic ecjuations to the hfimogencous <|u.id-
ratir funrtifins.

Returning to ec|uations (1), we observe that, due to the presence of
the integral sign, they are integro-diflferential equations. They are,

.(=')

CI Kit IT Tlir.OKY .l\n ()/7:7v'.(//(>.V.I/. CIlXl'IAS Wl

however, at once re<lucil)le io ililTeriMiti.il icinatioiis 1>\ tin- ^.lll>slitll-
tion I = dQ/dl, whence they become

Here, as a matter of convenience, we have written l'G* = '^^*- It
is often more convenient, at least at the outset, to deal with equations
(3) rather than (1).

The Exponential Solution

In taking up the mathematical solution of equations (1), we shall
start with the exponential solution. This is of fundamental import-
ance, both theoretically and practically. It serves as the most
direct introduction to the Heaviside Operational Calculus, and in
addition furnishes the basis of the steady-state solution, or the theory
of alternating currents.

To derive this solution we set Ei = Fie^' and put all the other
forces £«, . . En equal to zero. This latter restriction is a mere matter
of convenience, and, in virtue of the linear character of the equations,
invoK'es no loss of generality.

Now, corresponding to Ei = F\e^', let us assume a solution of the
form

/> = V (; = 1,2..«)

where Jj is a constant. So far this is a pure assumption, and its cor-
rectness must be verified by substitution in the differential equations.

Now if Ij = Jje^', it follows at once that

jJj = >^Ij = \Jje
and

/,„.{,- Lj/'.

Now substitute these relations in equations (1) and cancel the com-
mon factor e^'. We then get the system of simultaneous equations

(\Ln + Rn + l/\Cn)Ji + . . + (XL,„ + /?i,+ 1/XC,h)/» = f i,

(Xi;, + /?ai+l/XC2,)/,-f-. . + {\L2n + R2n+l/\Cin)Jn=0,

(4)

(\Lni+RnX+l \Cnl)Jl + . . + (Mnn+Rnn+\ \C„„)J„=0.

We note that this is a system of simultaneous algebraic equations
from which the time factor has disappeared. It is this that makes

4^

692

BELL SYSTEAf TECHSICAL JOURNAL

ihe exponential solution so simple, since we can immediately pass
from differential ec|uations to algebraic equations. In these algebraic
equations, « in number, there are n unknown quantities J\, . . Jn-
These can therefore all be uniquely determined. We thus see that
the assumed form of solution is possible.

The notation of equations (4) may be protiiabh- simplified as fol-
lows: write

\Ljk + Rjk + 1 /XC> = 'j*(X) = zjk

;ind wc ha\e

221-^1 +S22-/-2 + . .+=2./-.=0,

(5)

S„.-/l+S..2-/2+. .+=«,./,. =0.

The solution of this s\-stcm of ecjuations is

■^'~ D{\) ''" D '

md 1 r c

ivhere D is the determinant of the cocfticicnts,

-U -12
221 S22
231 S32

(6)

(7)

S,.l In 2

;ind Mji is the cofactor, or minor with proper sign, of the jth column
and first row.

I shall not attempt to discuss the theory of determinants on which
this solution is based.' We may note, however, one important
property. Since Zjk = Zkj, Mjk = Mkj. From this the Reciprocal
Theorem follows immediately. This may be stated as follows:

If a force Fe^' is applied in the jth mesh, or branch, of the net-
rtiirk, the current in the k\h nu'sli, or branch, is by tiie foreiioing

' n /•'■ •

Now apply the same force in the A'lii mesh, or braiuii, then the cur-
rent in the jth mesli is

l^tc ■

' Kor a remarkably hhk [>r .mil cjniplt'te discussion of the exponential snlution
by aid of the thcorv of delerniinants, sec Cisoidal Oscillations. 1 rans. .X. I. I-.. K.,
1911, by G. .\. Canipbcll.

CIKCCIT IHIiOKy .1X1) Ofl R.ilKKWll. C.ll.CCl.CS IM

roiuparinji tlicso expressions and remenilicrii»K that .!/»,= . U,», it
follows that the ciirretit in the A-tli l>ranrh corresponding to an ex|)o-
lunlial impressed e.ni.f. in the ./'ih branch, is efpial to the current in
the /'th branch corresponding; to the same e.m.f. in the ^ih br.mch.
Ihis relation is of tlic greatest technical importance.

In many important technical problems we arc interested oidy in
two accessil)le branches, such as the sentlini; and receiNing. In such
(asc-s, where we are not concerned with the currents in the other
meshes or branches, it is often convenient to eliminate them from
the equation. Thus suppose that we have electromotive forces £i
,inil £2 in meshes 1 and 2 and arc concerned only with the currents
in these meshes. If we soke ec)uations 3, 4, . . n, « — 2 in number,
for I3 . . In in terms of /i ami /: and then substitute in (1) and (2)
we t;et

ZnIi-\-Z\zIi = E\.

The Steady Stale Solutions

The steady state solution, on which the wiiole theor\-of alternating
currents depends, is immediately deri\able from the exponential
solution. Let us suppose that £2 = £3= . . . =£„ = o and that £1 =
F cos {(jit — 6). Now by virtue of the well known formula in the
theory of the complex variable, cos .v= Je'^+jc""', we can write

£1 = 4 £*'("'-<" +\Fe-'^"'-^\

= ] (cos e-i sin e)Ft»"' + i(ccs 6 + i sin 6) Fe" '"'1 (9)

= J £V"-'+i£"e "'<*''.

Now, by \irtue of this formula, the applied electromotive force £1
consists of tw'o exponential forces, one varying as e'"' and the other
as e"'"'. Hence it is easy to see that the currents are made up of
two compf)nents, thus

/, = y/f '■"' + y/v- '■"' (j=i:2 . . n) ( lO)

and we have merely to use the exjionential solution given abo\e,
substituting for X,/to and — iw respectively. That is,

Jj = o 7 ,: , and Ji = \

2 Zji(iu) ' -Zji(-iw}

, 1 Fe-'^ i^t, 1 Fe'" -ia

2 Zj,{iwf 2 Zj,{-io,r

694 BELL SYSTEM TECUXICAL JOURNAL

The second term is the conjugate imaginary of the first, so that

Ij = R
= R

= R

Zjiiioi)

F Uu>.-0-4>)

Zji{iu)
F

i Zf/co)

COS {wt —6 — (t>).

We thus arrive at the rule for the steady state solution :

If the applied e.m.f. is F cos (ut — d), substitute to for d/dt in the
differential equations, determine the impedance function

Z(/co)=Z)(fco)/M(to) (11)

by the solution of the algebraic equations, and write it in the form

Z(/o) = I Z(to) I e'*. (12)

Then the re(|uircd solution is

7 = , „,^ , , cos {wt-e-<t>}. (13)

1 Z(lco) I

This in compact form contains the whole theor\' of the sytiibolic solu-
tion of alternating current problems.

The Complementary Solution

So far in the solutions which we have discussed the currents are of
the same type as the impressed forces: that is to say in ph\-sical
language, the currents are "forced" currents and vary with time in
precisely the same manner as do the electromotive forces. Such
currents are, however, in general only part of the total currents. In
addition to the forced currents we have also the characteristic oscilla-
tions; or, in mathematical language, the complete solution must
include both particular and com])lementary solutions. This may be

shown as follows: Let // In he solutions of the complementary

equations.

(^-^+^"'+i/'^')^-'+ • • +(^4+^""+i/'^')'"'=-

(14)

CIHCl'IT THEORY ANO Ol'i.KA itOXAl. CAI.CVLVS 695

Then if /i . . . /, is a solution of (1), Ii\ Ix, . . . /, + /-■', is also a
solution.

To derive the solution of the complementary system of eiiiiatiuns
(.14), assume that a solution exists of the form

// = -//<'^' 0=1,2..«)

so that d/dl = \ andj dt=\/\. Substitute in ecjuations (It) and
eancel out the common factor e^'. Then we have

(15)

Zn,{\)Jv'-\- +Znn{\)Jn'=0.

This is a system of n homogeneous equations in the unknown quan-
tities Ji, . . Jh- The condition that a finite solution shall exist is
that, in accordance with a well known principle of the theory of
equations, the determinant of the coefficients shall \anish. That is,

Zn(X) .... Zu, (X) ;

D(\) =

Z„i{\) . . . .Znn (X)

(16)

Consequently the possible values of X must be such that this equation
is satisfied. In other words, X must be a root of the equation D{\) = o.
Let these roots be denoted by Xi, Xj . . \m. Then, assigning to X any
one of these values, we can determine the ratio J/ /Jk from any (« — I)
of the equations. That is to say, if we take

/.' = c/''+C,f^'+ .... +C„e^"''. (17)

substitution in any (n— 1) of the equations determines /j', . . In ■
The m constants C\, . . Cm are so far, however, entirely arbitrary,
and are at our disposal to satisfy imposed boundary conditions.

This introduces us to the idea of boundary conditions which is of the
greatest importance in circuit theory. In physical language the
boundary conditions denote the state of the system when the electro-
motive force is applied or when any change in the circuit constants
occurs. The number of independent boundary conditions which
can, in general, be satisfied is equal to the number of roots of the
equation D{\)=o. Evidently, therefore, it is ph>sically impossible
to impose more boundary conditions than this. On the other hand,
if this number of boundary conditions is not specified, the complete
solution is indeterminate : That is to say, the problem is not correctly
set. As an example of boundary conditions, we may specify that the

696 BF.I.L SYSTEM TECHNICAL JOURXAL

electromotive force is applied at time l = o, and that at this lime all
the currents in the inductances and all the charges on the condensers
are zero.

So far wc ha\e been following the classical thcor\- of linear differ-
ential c(|ualions. We have seen that the forced exponential solution
and the derived steady state solution are extremely simple and are
mere matters of elementary algebra. The practical difficulties in the
classical method of solutions begin with the determination of the
constants C . . Cm of the complementary solution as well as the
roots Xi, . . \m of the equation D(X)=o. It is at this point that
Heaviside broke with classical methods, and by considering special
boundary conditions of great physical importance, and particular
l\pes of impressed forces, laid the foundations of original and powerful
methods of solution. We shall therefore at this point follow Heavi-
side's example and attack the problem from a different standpoint.
In doing this we shall not at once take up an exposition of Hea\iside's
own method of attack. We shall first establish some fundamental
thef)rems which are extremely powerful and will serve us as a guide
in interpreting and rationalizing the Heaviside Operational Calculus.

CH.APTER II

Thk Solution when .\.\ Aruitr.vrv Force is Applied to the
Network in a St.'lTE of Equilibrium

In engineering applications of electric circuit theory there are
three outstanding problems:

(1) The steady stale distribution of currents and potentials when
the network is energized by a sinusoidal electromotive force. This
problem is the subject of the theor>- of alternating currents which
forms the basis of our calculations of power lines and the more elabor-
ate networks of communication systems.

(2) The distribution of currents and potentials in the network in
response to an arbitrary electromotive force applied to the network
in a state of equilibrium, i.e., applied when the currents and charges
in the network are identically zero.

(3) The effect on the distribution of currents and potentials of
suddenly changing a circuit constant or connection, such as opening
or closing a switch, while the system is energized.

We shall base our further anahsis of circuit thcor_\- on the solutions
of problem (2), for the following reasons:

(A) It is essentially a generalization of the Heaviside problem and
its solution will furnish us a key to the correct understanding and

CIKCIIT TIIEOKY .IXH OrER.ITIOX.U. CIlXriAS 607

iiUfrprt'tation of optTational im-tho;ls anil lead to an auxiliary formula
from which the rules of the Opirational Calculus are direclly de-
(luril)le.

^B) The solution of problem (2) carries with it the solution of
problem ('.i) and also serves as a basis for the theory of alternating
currents.

(C) The solution of problem (2) leails direclly to an extension of
circuit theory to the c.ise where the network contains variable ele-
ments: i.e., circuit elements which \-.iry with time and in which non-
linear relations obtain.

Problem (2) is therefore the fundamental problem of circuit theory
ami the formula which we shall now derive may be termed the fimd.i-
mental formula of circuit theory.

Consider a network in any branch of which, sa>- branch 1, a imit
e.m.f. is inserted at time t = o, the network having been pre\ iously in
equilibrium. By unit e.m.f. is meant an electromotive force which
has the value unity for all positive values of time (/^o). Let the
resultant current in any branch, say branch n, be denoted by Ani{t).
Aki [t) will be termed the indickil admittance of branch n with respect
to branch I — or, more fully, the transfer indicial admittance.

The indicial admittance, aside from its direct ph\sical significance,
plays a fundamental role in the mathematical theory of electric cir-
cuits. In words, it may be defined as follows: The indicial admittance,
.•l„i(/), is equal to the ratio of the current in branch n, expressed as a
time function, to the magnitude of the steady e.m.f. suddenly inserted
at time l = o in branch I. It is evidently a function which is zero for
negative values of titne and approaches either zero or a steady value
(the d.c. admittance) for all actual dissipative systems, as / approaches
infinity. It may be noted that, aside from its mathematical determi-
nation, which will engage our attention later, it is an experimentally
determinable function.

We note, in passing, an important property of the indicial admit-
tance A}k{l), which is deducible from the reciprocal theorem:- this
is that Ajk{l)=Akj{t). That is to say, the value of the transfer
indicial admittance is unchanged by an interchange of the driving
point and recei\ing point. It is therefore immaterial in the expression
A;k(t) whether the e.m.f. is inserted in branch j and the current
measured in branch k, or vice-versa. In general, unless we are con-
cerned with particular branches, the subscripts will be omitted and
we shall simply write •-!(/), it being understood that any two branches

• Exceptions to this relation e.xist where the network contains sources of energy-
such as amplifiers. These need not engage our attention here.

698 BF.LL SYSTEM TECHNICAL JOURNAL

or a single Iiranrh (for the case of equal subscripts) may be under
consideration.

From the linear character of the network, it is evident that if a
steady e.m.f. E = Et is inserted at time t=T, the network being in
equilibriimi, the resultant current is

£,-J(/-t).

Generalizing still further, suppose that steady e.m.fs. E,,, E\, Ei, . . . En
are impressed in the same branch at the respective times tu, t\, t<>
. . . Tn\ the resultant current is evidently

EoA{l)+E,A{t-T,)+ . . +E„A{t-Tn) =^EjA(t-Tj). (18)

To apply the foregoing to our [)robleni we suppose tiiat there is
applied to the network, initially in a state of c(|uilil)rium, an e.m.f.
E{t) which has the following properties.

1. It is identically zero for t<o.

2. It has the value E{o) {or o<.t<M.

3. It has the value E{o)+AxE for M<l<2Sl.

4. It has the value E{o)+AiE+A2E for 2A^</<:U/.

In oilu-r words it has the increment Aj£ at time / = /A/.
Kvidentl>- then the resultant current /(/) is

EnA(l)+A,EAit-M)+ . . +A„E.A{l~i!M].

Now evidentK' if the inter\-al A/ is made shorter and shorter, then
in the limit Sl->-<ll and j\1 = t and

\jE='-^E{T)dT.
At

Passing to the limit in the usual m.ininr this summation becomes a
delinite integral and we get

m=E{o)A{l)^ f'A(l-T)''~E{T)dT. (19)

Jo (IT

Finally by obvious transf(jrmalions of tiie e.\|)ression we arri\c at ilie
fundamental formula of circuit theory

I{t) = jjU(t-T)E{T)dr, (20)

= jJ^'E{t-r)A{r)dT. (20-a)

CIRCUIT inr.oKV .ixn oi'r.h'.iiKKWir. c.ii.cui.vs (m

For completeness wo write down ilu- fnllowiiii^ »(|iiiv;ileiils of (20)
ami (20-a)

l(t)=A{o)E{t)-\- f A'(I-t)E{t),It, (20-b)

Jo

= A{o)E{t)+ f'A'ir)f-:(l-T)dT, (2(r-c)

»'o

=E(o)A(t)+ f'E'(t-r)A{T)dr, (20-d)

= Eio]A(l)+ rE\T)A(t-T),lT. (20-e)

Jo

where the primes denote differentiation with respect tt) the artjii-
ment. Thus A'(t) =d dt A{t).

These ec|iiations are the fundamental formulas which mathematic-
alK- relate the current to the type of applied electromotive force and
the constants and connections of the system, and constitute the first
part of the solution of our problem. The most important immediate
deductions from these formulas are expressed in the following theorems.

1. The indicial admittance of an electrical network completely
determines, within a single integration, the behavior of the network
to all ty(x>s of applied electromotive forces. As a corollary, a knowledge
of the indicial admittance is the sole information necessary to com-
pletely predict the performance and characteristics of the system,
including the steady state.

2. The applied e.m.f. and the inidical admittance are similarly
and coequally related to the resultant current in the network. As a
corollary the form of the current may be modified either by changing
the constants and connections of the network or by modifying the
form of the applied e.m.f.

3. Since the applied e.m.f. may be discontinuous these formulas
determine not only the building up of the current in response to an
applied e.m.f. but also its subsidence to equilibrium when the e.m.f.
is removed and the network left to itself. In brief, forinulas (20)
reduce the whole problem to a determination of the indicial admittance
of the network. In addition, as we shall see, they lead directly to
an integral equation which determines this function.

It is of interest to show the relation between formulas (20) and the
usual steady state equations. To do this let the e.m.f., applied at

700 BELL SYSTEM TECHNICAL JOURNAL

time t = o, be E sin (co^+ff). Substitution in formula (20-b) and
rearrangement gives

I{t)=A{o)E sin (iol+d)

+ E sin (co/+0) / cos uTA'{T)dT
•Jo

-£cos (i^t + e) /sin wr.l'(r)rfr (21)

where ,-l'(0 =7-^ (/).

Now this can lie resolved into two parts

( /*°° (

£ sin (oil + d) -i A{o)+ I cos wT/r(7)rfr .

-E cos (uit+e) \ J sin or,4'(7-)rfT I

which is the /!»«/ steady slate, and

,=0

— £ sin (a)/ + e) / cos ootA {T)dT

-f £ cos (co/ + 0) / sin 0)7.4 '(r)(ir

(22)

(23)

which is the transient distortion, which ultimately dies awa\' for suf-
ficiently large values of time.

To correlate the foregoing expressions for the steady slate with
the usual formulas we observe that if the symbolic impedance of the
network at frequency t<j/27r be denoted by Z{iw), and if we write

^=a(.) + ./3(.)

then the steady state current is

£[«(co). sin (co<-|-9)+/3(co) . cos iyil+e)].
("onipari^on with (22) gives at once

a(w) =A{o)-\- f cos ojr /r(r)f/r, (24)

/3(a)) = - f sin co7.4'(r)rfr. (25)

CIKCUIT THF.ORY .IXl> >)/7:A'. / //O.V.-//. C.II.Cn.CS 701

The Inle^rul Equation for the Indiciat Admittance

So far \vi> have tacitly assunu-d that the iiulicial admit taiicc is
known. As a matter of fact its tieterminalion constitutes the essentia!
|)art of our prolilem. It is, in fact, the llea\isi(le ()rol)Iem, and its
in\estij;ation, to which we now proceed, will U'.id us directly to the
( )perational Calculus.

Hea\iside's method in iiueslij^atinj; this problem was intuitive and
"exiH-rimental". We, however, shall establish a \er\- ijeneral integral
eijuation from whii'h we shall directlx di'duce his nuthods and e.\-
tensions thereof.

I.ct us suppose that an e.m.f. e'", where /> is either positi\e real
(luantity or complex with real part positive, is suddenly impressed
on the network at time t = o. It follows from the foregtjing theory
ih.it the resultant current /(/) will be made up of two parts, (I) a
forced exponential part which \-aries with time as e*", and (2) a com-
plementary part which we shall denote by y{t). The exponential or
"forced" component is simply e'''/Z{p). where Zip) is functionally of
the same form as the usual symbolic or complex impedance Z(ioi).
It is gotten from the ditTerential equations of the problem, as explained
in a preceding section, b>- replacing d" dl" by p", cancelling out the
common factor e*", and solving the resulting algebraic equation. The
complementary or characteristic component, denoted by y(t), depends
on the constants and connections of the network, and on the value of
p. It does not, howe\er, contain the factor e'" and it dies away for
sufficiently large \alue of /, in all actual dissipative systems. Thus

Now ri'turn to formula (20-a) and replace E{t) by e^ . We get

/(/)=^eN f'A(T)e~t^dT
dt Jo

which can be written as

j' j el" f A{T)e-!^dT-et"f .4(r)e-'>'^/r j- .
Carrying out the indicated difTercntiation this becomes

J(t)=pei"f A{T)e-^\lT-pct" I' A(T)e-''^dT+A{t). (27)

702 REI.I. SYSTEM TECHSICAL JOURNAL

Equating the two expressions (2G) and (27) for /(/) and dividini;
through by e*" we get

■^+y{t)e-^'=pfj A{r)e'f'dT-pj\4{T)e-f'dT+A{t)e-P'. (28)

This equation is \alid for all \alues of /. Consequently if we set
/= 30, and if the real part of p is positive, only the first term on the
right and the left hand side of the equation remain, the rest vanishes,
and we get

pm=r^^'^''""- ^''^

This is an itilei^ral equation ^ valid for all positive real values of p,
which completely determines the indicial admittance A{t). It is on this
e(|uation that we shall base our discussion of operational methods and
from which we shall derive the rules of the Operational Calculus.
Equations (20) and (29) constitute a complete mathematical formula-
tion of our problem, and from them the complete solution is obtainable
without further recourse to the differential equations, or further con-
sideration of boundary conditions.

To summarize the preceding: we have reduced the determination
of the current in a network in response to an electromotive force
E{t), impressed on the network at reference time t = o, to the mathe-
matical solution of two e(|iiations: first the integral equation

Wipr r ^^^^^-"'^ (29)

and second, the deiinite integral

l{t)=j^£A(t~r)E{T)dT. (20)

It will be observed that in deducing these equations we have merely
postulated (1) the linear and invariable character of the network and
(2) the existence of an exponential solution of the type e'" / Z{p) for
positi\e values of p. Consequently, while we ha\e so far discussed
these formulas in terms of the determination of the current in a (inite
network, they are not limited in their application to this specific
problem. In this connection it may be well to call attention explicitly
to the following points.

'An integral equation is one in wliiili the iMikiiowii liiiution appears iiiuler (lie
sign of integration. (29) is an integral ccpiation of tlie I.aplace type. If Z(p) is
specilied, A(i) is unicpiely determined. Melliods for solving the integral ecjualions
arc considered in detail later, in connection with the exposition of the Operational
Calculus. The phrase "all positive values of p" will be understood as meaning all
values of p in the right hand half of the complex plane.

ilNClIT llll:Ot<y .-/A'/i (ifHR.ll lOX.Il. C.ll.CCI.rS 7(U

Thr fonmilas aiul nu-tlKxIs (iodiirfd aluno apply not only to finik-
networks, in\<>Kins» a finite system of linear ecjiiations, but to infuiile
networks and to transmission lines. invol\inj{ infinite s\slems of equa-
tions, and partial dilTeri'ntia! eciualions: in fact to all I'leetrical and
ilynamieal systems in wliieli liie connet'lions .md constants aie lini'ar
and invariable.

.Secondly the \arial)le determined 1>\' formula (20) and (2',)) need
not, of course, be the current. It may e(|u.dly well be the charjje,
potential drop, or any of the \ariables with which we may ha()[)en
to be concerned. This fact may be explicitly recoj;ni/ed by writing
the formulas as:

' = fhine-f'dt, (30)

pII(P)

xit)=j^£h{t-T)E{r)dr. (31)

Here E(t) is the applied e.m.f., .y(/) is the variable which we desire to
det»Tmine ("ch.irije. current, potential drop, etc.), and

x = E.II{p) (32)

is the operational equation. H{p) therefore corresponds to and is
determined in precisely the same way as the impedance Z{p), but it
may not have the physical significance or the dimensions of an im-
pedance. Similarly in character and function, /;(/) corresponds to the
indicial admittance, though it may not have the same physical sig-
nificance. It is a generalization of the indicial admittance and may be
appropriately termed the Ileaviside Function. SiniilarK- //(/>) may
be termed the generalized impedance function.

CH.MTER 111

TiiH Heavisidi-: Prof^le.m .\nd the Oi'er.\tion.\l Equatio.n

The physical problem which Heaviside attacked and which led to
his Operational Calculus was the determination of the response of a
network or electrical s\stem to a "unit e.m.f." (zero before, unity after
time t = o) with, of course, the understanding that the system is in
equilibrium when the electromoti\e force is applied. His problem
is therefore, essentially that of the determination of the indicial
admittance. In our exposition and critique of Heaviside's method of
dealing with this problem we shall accompany an account of his own
method of solution with a parallel solution fnjm the corresponding
integral equation of the problem.

704 BELL SYSTEM TECHNICAL JOURNAL

Heaviside's first step in attacking this problem was to start with the
differential equations, and replace the differential operator d'dt by
the symbol p, and the operation | dl by l/p, thus reducing the equa-
tions to an algebraic form. He then wrote the impressed e.m.f. as
1 (unity), thus limiting the validity of the equations to values-of t = o.
The formal solution of the algebraic equations is straightforward and
will ln' written as

/; = 1 IKp) (33)

where /; is the "generalized indicial admittance," or Heaxiside func-
tion (denoting current, charge, potential or any variable with which
we are concerned) and II{p) is the corresponding generalized im-
pedance. Thus, if we are concerned with the current in any part
of the network, we write

A=l'Zip). (34)

The more general notation is desirable, however, as indicating the
wider applicability of the equation.
The equations

h = l/II{p)

A = \:'Z(p)

are the Ileaviside Operational Equations. They are, as yet, purely
symbolic and we ha\e still the problem of determining their explicit
meaning and in particular the significance of the operator p.

C"om[iarison of the Hea\iside Operational Equations with the
integral e(|uations (29) and (30) of the preceding ch;ipter leads to
the following fundamental theorem.

The Ileaviside Operational Equations

A=i:Z(p)

h = \:ii(p)

are merely the symbolic or short-hand equivalents of the corresponding
integral equations

pikprr"^"'-""-

The integral equations, therefore, supply us n'ith the meaning and sig-
nificance of the operational equations, and from them the rules of the Oper-
ational Calculus are deduciblc.

iiRirir 77//.()A"i" .;.\7) ori:R.irn>x.ii. i.ii.cri.rs 70s

\W virtue of this tlieoriMU, we have the advantage, at the outset,
of a ke\' to the ineauiiiK of Heavisiile's ojierational e(|uations, aiul a
means of chcekini; and deducing liis rules of sohitioii. Tliis will
serve us as a guitle throu^ihoul our further stud\-.

Returning now to Heaviside's own point of view and method of.
attack, his reast>ning may l)e described somewhat as follows:-^
The operational e(|ualion

/; = ! //(/>)

is the full e(iui\alent of the (iitferential e(|uations of liie problem and
must therefore contain the information necessary to the solution
proviiled we can determine the significance of the symbolic operator
p. The only way of doing this, when starting with the operational
equation, is one of induction : that is, we must compare the operational
equation with known solutions of specific prol)lems and thus attempt
to infer by induction general rules for interpreting the operational
ecjuation and con\erting it into the re(iiiired explicit solution.

The Power Series Solution

Let us start with the simplest possible problem: the current in
response to a "unit e.m.f." in a circuit consisting of an inductance L
in series with a resistance R.

The differential equation of the problem is

L^A+IL\=\, t^o,
at

where A is the indicial admittance. Consequently replacing d dt by
p, the operational equation is

A = ~^-
pL + R-

The explicit s )luti<)n is easily deri\ed : it is
A =~^(\ -€-"•)

where a = R L. Note that this makes the current initially zero, so
that the e(|uilibrium boundary condition at t = o is satisfied.

Now suppose that we expand the operational equation in inverse
powers of p: we get, formally,

pLl+ap Rpi+a p Rip ^p' ^'p P "f

by the Binomial Theorem.

706 BELL SYSTEM TECHNICAL JOURNAL

Now expniui the explicit solution as a power series in /: it is

. _}_\at (aty , (at)
•'4 — „ -, , ,

i? ( 1! 2! ^ 3! J

Comparing the two expansions we see at once that the operational
expansion is converted into the explicit solution by assigning to the
symbol l/p" the value t"/ti\. It was from this kind of inductive
inference that Heaviside arrived at his power series solution.

Now there are several important features in the foregoing which
require comment. In the first place the operational equation is
converted into the explicit solution only by a particular kind of ex-
l)ansion, namely an expansion in in\erse powers of the operator p.
For example, if in the operational ecjuation

R 1+a/p
we replace 1 p b\' t/ll we get

1 at
R 1+0

which is incorrect. I'^urthermorc, if we expand in ascending instead
of descending powers of p, naniel\-

A=-^^\l-{p/a) + {p:ar— [

no ( orrelation with the explicit solution is possible and no significance
can be attached to the expansion. We thus infer the general princiiile,
and we shall find this inference to be correct, that the operational
equation is convertible into the explicit solution only by the proper
choice of expansion of the impedance function, or rather its reciprocal.

In the second place we notice that in writing down the operational
equation and then converting it into the explicit solution no con-
sideration has been given to the question of boundary conditions.
This is one of the great advantages of the operational method: the
boundary conditions, provided lliey are those of equilibrium, are auto-
matically taken care of. This will be illustrated in the next example:

l.el a "unit e.m.f." be impressed on a circuit consisting of resistance
K, inductance L, and capacity C: rc(]uiretl the resultant charge on the
condenser.

The (lifferiMUial etiuation for the charge {) is

{4+4t+'^c)Q--

1, 1^0.

CIRCUIT THEORY .-INP OPERATION A1. CALCULUS 707

("(ins«.'c|ui'iitly thf opera! inn. il formiil.i is
1

<?=r>5

Lt^' + Rp+l/C

1 1 , R ., \

wluTi- It = , and b =

Z,/)=l+o//)+ft/A= /- I.C

'\'W\> can In- t'\|).in(ii'<l !)>• llu' Rinmnial TlicorcMn as

^'=,.>-;'-(^;)+(;4)'-(^f-)"+ ■(■

IVrforniini!; the incliratcci operations and collecting in inverse powers
ol p, the first few terms of the expansion are: —

/'/>'-'' p p- p' p* y p'"^ • ■ ■ f

where fi=a

Ci = b — a-

Ci = 2ab-a'^

CA=b--Za'b-\-a*

Ci = 3ab--4a'b+a''

Ct = b^ — (]a-b- + oa*b — a*

We infer therefore that in accordance with the rule of replacing
!//>" by /"/n! the solution is: —

^ 1 j /^ t' t* t' I' I

^=Z ' 2!~''3!~'T!"^'^T!+'^T! " ■ • f •

Owing to the complicated character of the coefficients in the expan-
sion, the series cannot be recognized and summed by inspection. If,
however, we put R = o) then a=o, and the series becomes

'2!VlC-^ 4!VvZX-/ UIVIC-/ "^
whence

Q = C\l-cos(t/VLCJ\.

We have still to verify this solution by comparison with the explicit
solution of the differential equation. This is of the form

Q = C+k,e^'' + k,e^'-'

708 BELL SYSTEM TECHNICAL JOURNAL

where kx and ki are constants which must be chosen to satisfy the
boundary conditions and Xi, Xo are the roots of the equation

L\- + R\ + ]. C = o.

Now since we have two arbitrary constants we satisfy the equilibrium
condition by making Q and dQ/dl zero at i = o, whence

C+kl + k2=0,
Xl^l+X2^2=0,

and

We ha\'e also

)^i = X2C/(Xi-X,),
/to = XiC/(Xo-X,).

x.--fW(f)'->'

Writing down the power series expansion of
then

+ (^iXr + ^>X.r)^"j+

Introducing the values of ki, ki, Xi, Xj given above and comparing
with the power series derived from the operational solution we see
that tiiey are identical term by term.

This example illustrates two facts. First the power series expansions
may be complicated, laborious to derive and of such form that they
cannot be recognized and summed by inspection. In fact in arbitrary
networks of a large number of meshes or degrees of freedom the
evaluation of the coefficients of the power series expansion is extremely
laborious.

On the other hand, in such cases, the solution by the classical
method presents difficulties far more formidable — in fact insuperable
difficulties from a practical standpoint. First there is the location
of the roots of the function //(X), which in arbitrary networks is a
pnictical impossibility without a prohibitive amount of labor. Sec-
ondly there is the determination of the integration constants to satisfy
the imposed boundary conditions: a process, which, while theoretically

CIRCL'IT THEORY AND OPFMATIONAL CALCULUS 709

straightfon\'ard, is actualK- in practice extrenicis- l.iliorioiis and (om-
plicatcd. We note tliese |)oints in passing; a more complete estimate
of the value of the power series solution will be made later.

To summarize the preceding: Heaviside, generalizing from specific
examples otherwise solvable, arri\'ed at the following rule : —

Expand the right hand side of the operational equation

h = \/ll{p)
in inverse powers of p: thus

h^ao+ai/p+at/p-+ . . . +«„'/?"+ ....

and then replace t; by /"/"'• ^^^ operational equation is thereby con-

P
verted into the explicit power series solution : —

/»=ao+ai//l!+aj/V2!+ • . +a„r/nl+ . . . (35)

As stated above, this rule was arrived at by pure induction and
generalizatit)n from the known solution of specific problems. It can-
not, therefore, theoretfcally be regarded as satisfactorily established.
The rule can, however, be directly deduced from the integral equation

\-^=fhit)e-^'dt.

pmp)

To its derivation from this equation we shall now proceed.

First suppose we assume that h{t) admits of the power series ex-
pansion

//„ + /ii//l!+/;:/-, 2! +

Substitute this assumed expansion in the integral, and integrate
term by term. The right hand side of the integral equation becomes
formally

ho/p + h,'p^ + h-./p'+

by virtue of the formula

/'°°iy<" = -Lfor/>>o.
Jo nl p"^^

.\ow expand the left hand side of the integral equation asymptotically
in inverse process of />: it becomes

a<,//)+a,//>=+a,//)'+

where

ao+ai/p-\-ai/pr+ ....

710 BELL SYSTEM TECHNICAL JOURNAL

is the asymptotic expansion of l/II{p). Comparing the two ex-
pansions and making a term by term identification, we see that
hn = a„ and

hit) =ao+ail/\\+a-2t-/2\+ ....

which agrees witli tiie Heaviside formula.

This procedure, howe\er, while giving the correct result has serious
defects from a mathematical point of \iew. For example, the asym-
totic expansion of \/II{p) has usualh- only a limited region of con-
vergence, and it is only in this region that term by term integration
is legitimate. Furthermore we have assumed the possibility of ex-
panding h{t) in a power series: an assumption to which there are
serious theoretical objections, and which, furthermore, is not always
justified. A more satisfactory derivation, and one which establishes
the condition for the existence of a jwwer series expansion, proceeds
as follows : —

F-et \/II(p) be a function which admits of the formal as\mptotic
expansion

'^ajp"

and let it include no component which is as\mptoticall>' represcntable
by a series all of whose terms are zero, that is a function 4>{p) such
that the limit, as p—x, of p"4>{p) is zero for every value of n. Such
a function is e'''. With this restriction understood, start with the
integral equation, and integrate by parts: we get

]-=h{o)+ f" e-t"h^'\t)dt

mp)

where /»'"*(/) denotes d"/dl"h{t). Now let p approach infinity: in the
limit the integral vanishes and by virtue of the asymptotic expansion

l/n(p)o<,\^a„'p", (36)

\/II{p) a|)pr()achcs the limit cio- ("onse<iueiUly

li{o) =ao.
,\()\v integrate .i^ain b\- |)arts: we gel

/>(l,7/{/>)-a„)=//<'>(o)-|-y c-'"li'-'{l)dl.

CIRCUIT THEORY AND OPERATIONAL CALCULUS 711

AK.iiii U't p approaih iiillnity: in the limit the left hand side of the
(.■((uation l)fci)nit's Oi and wc li.i\«.'

/j<'>(o)=a,.

PrDCi'cdinv; by successive partial inirur.itioiis we tluis establish the
general relation

Hut by TaNlor's theorem, the power series expansion of /;(/) is simply

/i(0=/»(o)+/'<'Ho)/ l!+//<2)(o)/r2!+

whence, assuming the lonvergence of this iw pans ion, we ^et

//(/)=ao+rt,/ l! + a«/=;2!+ ...= Vrt„r w! (35)

which establishes the power series solution. It should be carefully
noteil, however, that it does not establish the convergence of the
power series solution. As a matter of fact, however, I know of no
physical problem in which Hip) satisfies the conditions for an asymp-
totic e.vpansion, where the power series solution is not convergent.
On the other hand many physical problems exist, including those
relating to transmission lines, where a power series solution is not
derivable and does not exist.

The process of expanding the operational equation in such a form
as to pertnit of its being converted into the explicit solution is what
Heaviside calls "algebrizing" the equation. In the case of the power
series solution the process of algebrizing consists in expanding the
reciprocal of the impedance function in an asymptotic series, thus

1 //(/)) ~rt„ + a, p+a-2 p-+

Regarded as an expansion in the variable />, instead of as a purely
symbolic expansion, this series has usually only a limited region of
convergence. This fact need not bother us, however, as the series
we are really concerned with is

ao+a,//i!+a2/V2!+

It is interesting to note in passing that the latter series is what Borel,
the French mathematician, calls the associated function of the former,
and is extensively employed by him in his researches on the sunima-
bility of divergent series.

The process of "algebrizing," as in the examples discussed abo\e,
may often be effected by a straight forward binomial expansion.

712 BELL SYSTEM TECHNICAL JOURNAL

In other cases the form of the generalized impedance function H{p)
will indicate by inspection the appropriate procedure. A general
process, applicable in all cases where a power series exists, is as follows.
Write

]///(/>) = 1/7/(1) =G(.v). (36)

Now expaiul (7(.v) as a Ta>l()r's series: thus formalK'

GW=C(o) + G(')(o)-j^+G(2)(,,:):|+ . . .

where

GW(o) = [^G(.r)]^_^. (37)

G(«)(o)
Denote j — by a„, replace x" by l//>", and wo lia\x'

G(.v) = l///(/>)=ao+a,/p+fl2//>2+ . . .

This process of "algebrizing" is formally straightforward and always
possible. As implied above, however, in many problems much shorter
modes of expansion suggest themselves from the form of the function

mp).

We note here, in passing, that the necessary and sufficient condi-
tions for the existence of a power series solution is the possibility of
the formal expansion of G{x) as a power series in x.

At this point a brief critical estimate of the scope and value of the
power series solution may be in order. As stated above, in a certain
important class of problems relating to transmission lines, a power
series does not exist, though a closely related series in fractional
powers of t may often be derived. Consequently the power series
solution is of restricted applicability. Where, however, a power
series docs exist, in directness and simplicity of derivation it is superior
to any other form of solution. Its chief defect, and a very serious
defect indeed, is that except where the power series can be recog-
nized and summed, it is usually practically useless for computation
and interpretation except for relatively small values of the time /.
This disadvantage is inherent and attaches to all power series solu-
tions. For this reason I think Heaviside overestimated the value
of power series as practical or working solutions, and that some of
his strictures against orthodox mathematicians and their solutions
may be justly urged against the power series solution. He was C|uile
right in insisting that a solution must be capable of cither interpre-
tation or computation and quite right in ridiculing those formal

CIRCUIT THEORY .INP Ol'ERATIONAL CAl.Cl'l.VS 713

solutions which actually conceal rather than reveal the significance
of the original clitTerential efiu.itions of the problem. On the other
hand, the following remark of his indicates to me that Heavisidc
has a <iuite exaggerate*.! idea of the value and fundamental character
of i)t)wer series in general: "I regret that the result should he so
complicated. But the only alternatives are other ec|uivalent infinite
series, or else a definite integral which is of no use until it is evalu-
ate<l, when the result must be the series (135), or an equivalent one."
As a matter of fact the properties of most of the important functions
of mathematical ph\sics have been investigated and their \alues
computed by methods other than series expansions. I may add that
in technical work the power series solution has proved to be of re-
stricted utility, while definite integrals, which He.iviside * i)articu-
larly despisetl, have proved quite useful.

The Expansion Theorem Solution '

We pass now to the consideration of another extremely important
foim of solution. Heaviside gives this solution without proof: we
shall therefore merely statethc solution and tlicii fl('ri\T it from the
integral equation.

(iiven the operational equation

li = l/H(p)

which has the significance discussed above: i.e., the response of the
network to a "unit e.m.f.". The explicit solution may be written as

^=m+XpjF{p;) ^^^^

where p\. p« ■ ■ ■ pn are the n roots of the equation

II{p)=o
and

//W = [^//(/»]^^^^. (39)

.As remarked above, this solution, referred to by him as The Ex-
pansion Theorem, was stated by Heaviside without proof; how he
arrived at it will probably always remain a matter of conjecture.
Its derivation from the integral equation is, however, a relatively
simple matter, though in special cases troublesome questions arise.

* Vide a remark of his to the effect that some mathematicians took refuge in a
definite integral and called that a solution.

* This terminology is due to Heaviside. A more appropriate and physically
significant expression would l>e "The Solution in terms of normal or characteristic
vibrations."

714 BELL SYSTEM TECHNICAL JOURNAL

The derivation of the expansion solution from the integral equation

^.^fme-m

pmp)

follows immediateK' from the partial fraction ex[xinsion

pmp) pii (0) ^ jri^p- pj)piii'ipi)

where p\, pi ■ . . pn are the roots of the equation Hip) =o, and

(40)

//'(/>>)= j//WJ-^^^. (41)

Partial fraction expansions of this type are fully discussed in treatises
on algebra and the calculus and the conditions for their existence
established. Before discussing the restrictions imposed on H{p) by
this expansion, we shall first, assuming its existence, derive the ex-
pansion theorem solution.

By virtue of (40) the integral c(|uati()ii is

' 7\ + X i^ ^^Irrt-H^ = rHOe-^'dl. (42)

0) ^{p-pi)p}II {P}) ->»

pm

The expansion on the left hand side suggests a corresponding expan-
sion on the right hand side: that is, we suppose that

//(/)=/;o(/)+/7,(/)+/;o(^)+ . . .+/,„(0 (43)

and specify that these compnnein functions shall satisfy the ccjuations

pm=r'°^'^'~"'' ^'''

(p-p/pmprfo°^"^'^'~"" i=i'2--"- (^^)

It follows at once from (43) and direct addition of equations (44)
and (45) that (42) is satisfied and hence is solved provided //,., . . h„
can be evaluated from (44) and (45).
Now since

f e>^'e-'"dl = ~ (46)

CIRCUIT THEORY AND OPERATIONAL CALCULUS 715

proviiltti the real part of X is not positive (a condition s^itisfieil in all
network problems), we see at once that e(iuations (42) and {A'A) are
Siitisfied by taking

I'.m-K.-l^y (47)

ronsei|uentl\- from (43) and (47) it follows that

which establishes the Kxpansion Theorem Solution.

As implied above, the partial fraction expansion (40), on which
the expansion theorem solution depends, imposes certain restrictions
on the impedance function //(/>). Among these are that II{p) must
have no zero rf>ot, no repeated roots, and !///(/>) must be a proper
fraction. In all finite networks these conditions are satisfied, or by
a slight modification, the operational equation can be reduced to
the required form. The case of repeated roots, which may occur
where the network involves a unilateral source of energy- such as an
amplifier, can be dealt with by assuming unequal roots and then
letting the roots approach equality as a limit. Without entering
upon these questions in detail, however, we can \ery simply and
directly establish the proposition that the expansion theorem gives
the solution whenever a solution in terms of normal or characteristic
vibrations exists. The proof of this proposition proceeds as follows.

It is known from the elementary' theory of linear differential equa-
tions that the general solution of the set of differential equations,
of which the operational equation is h = \/II(p), is of the form

h{l)=^Co+^Cj^'^

where pj is the jth root of //(/>) =o, and Co, Cx . . . Cn are constants of
integration which must be so chosen as to satisfy the system of dif-
ferential equations and the imposed boundary conditions. The
summation is extended over all the roots of //(/>) which is supposed
not to have a zero root or repeated roots.

716 BELL SYSTEM TECHNICAL JOURNAL

Now substitute this known form of solution in tlie integral equation
of the problem and carry out the integration term by term. We get

Setting p = o, we ha\e at once

Co = \/II{o). (50)

To determine Q let p = pj+q where g is a small quantil\' ultimately
to be set equal to zero, and write the equation as

Comp)+Xfff,cj=i. (51)

If now p = pj-\-q and q ai^proaches zero, this becomus in the limit

PjII'(Pj)Cj=\ (52)

or

PjH {pj}'

whence //(/) =y^^ + V _£^ (54)

11(0) ^PjII'(Pj)

which is the Expansion Theorem Solution.

We shall not attempt to discuss here cases where the expansion
solution breaks down though such cases exist. In every such case,
however, the breakdown is due to the failure of the impedance func-
tion IKp) to satisf\' the conditions necessary for the partial fraction
expansion (40), and correlati\"ely the non-existence of a solution in
normal vibrations. Furthermore, it is usually possible by simple
modification to deduce a modified expansion solution. It may be
added here, that while the proof given above is also limited implic-
itly to finite networks, the expansion solution is \-alid in most trans-
mission line problems.

Let us now illustrate how the expansion solution works 1)\' applying
it to a few simple examples. Take first the case considered in the
preceding chapter in connection with the power series solution. Re-
quired the charge Q on a condenser C in series with an inductance L
and resistance R in response to a "unit e.m.f." The operational
equation is

0 = . \

^ Lp'^+Rp+l/C

„_ 1 1

CIRCUIT THEORY AND OrERATIONAL CALCULUS 717

vvhtTc a = R/2L and a)'= l/LC.

Tilt.' nM)ts of tlu- t-qiiation //(/>) =o .in- tin- roots of tlu- f(|ii.itir>ii

wlu-iue

/>! = — «+ Va- — co" = — a + ^,

pj = — « — \/<«- — oi- = — « — /J.
Also //'{/)) =2L{p+a), so that

and

l/H(o) = l/Lui' = C.

Inserting tlicse expressions in tiic I'.xpansion TlK-orcni Soluiion
(3S). we get

g-al/ gfl( g-dt

^ 2sfAa-8 a + B/'

2/3AV«-/3 a+/3>

It is now easy to verify tlie fact tliat this solution satisfies tiie difTer-
ential equations and tlic boundary condition Q = o and dQ'dt=o at
time t = o.

If a;>nf, ^ is a pure imaginary

/3 = /o) V 1 — (a/t"))- = i(^'
and

___ e~"'a)' cos a)'/+a sin &)'/

In connection with this problem we note two advantages of the
expansion solution, as compared with the power series solution: (1)
it is much simpler to derive from the operational equation, and (2)
its numerical computation is enormously easier. A table of expo-
nential and trigometric functions enables us to evaluate Q for any
value of / almost at once whereas in the case of the power series solu-
tion the labor of computation for large values of / is ver\' great. A
third and very important advantage of the expansion solution in this
particular problem is that without detailed computation we can
deduce by mere inspection the general character of the function
and the effect of the circuit parameters on its form: an advantage
which never attaches to the power series solution.

This last property of the particular solution above is extremely
important. The ideal form of solution, particularly in technical

718 BELL SYSTEM TECHNICAL JOURNAL

problems, is one which permits us to infer the general character and
properties of the function and the effect of the circuit constants on
its form, without detailed solutions. A solution which possesses
these properties, even if its exact computation is not possible without
prohibitive labor, is far superior to a solution which, while com-
pletely computable, tells us nothing without detailed computation.
It is for this reason that some of the derived forms of solution, dis-
cussed later, are of such importance. In fact a solution which re-
quires detailed computation before it yields the information implied
in it is merely equivalent to an experimentally determined solution.
Unfortunately the advantages attaching to the expansion solution
of the specific problem just discussed, do not, in general, characterize
the expansion solution. The following disadvantages should be
noted. First, the location of the roots of the impedance function
H{p) is practically impossible in the case of arbitrary networks of
more than a few degrees of freedom. In the second place, when the
number of degrees of freedom is large it is not only impossible to
deduce the significance of the solution by inspection, but the com-
putation becomes extremely laborious. In such cases, the practical
value of the expansion solution depends, just as in the power series
solution, on the possiljility of recognizing and summing the expan-
sion. This will be clear in the case of transmission lines, where the
roots of H{p) are infinite in number and the direct computation of
the expansion solution (except in the case of the non-inductive cable)
is C|uiti' impnssil)k'.

CHAPTER IV

.SoMic Genkrai. Formulas and Theorems for the .Solution
OE Operational Equations

W'e have seen lli.il tlic operational equation

h = \/II{p)
is the symbolic or siiort-liand einiixalent (jf the integral ecjuation

and from the latter we have deduced two very important forms of the
Heaviside solution. In recognizing the equi\alence of these two
equations we have a very great advantage and are able, in fact, to
base the Operational Calculus on deductive instead of inductive

CIRCUIT THEORY /INP OPERATIONA!. CALCULUS 719

reasoninij. In this chapter we sliall employ this eciuivalenre ti) eslal>-
lisli iTrt.iiii Keneral forimil.is aiul llieorems for the solution of oper-
ational ctiuations. That is to s.iy, wc shall make use of the principles
that (1) any method applicable to the solution of the integral e<iualion
supplies us with a corresponding mcthwl for the solution of the
operational equation, and (2) a solution of any specific integral e(|ua-
tion gives at once the solution of the corresponding operational
equation. We turn therefore to a brief discussion of the appmpriate
nielh(xls for solving the integral eciuation.

It may he said at the outset, that the solution of the integral e(|ua-
tion, like the evaluation of integrals, is a matter of considerable art
and experience; in other words there is not, in general, a straight-
forward proce<lure corresponding to the process of ditTerentiation.

On the other hand, as a purely mathematical question, it is always
possible to invert the integral equation and write down hil) as an
explicit fimction in the form of an infinite integral. F"or example
it may lie shown from the I-"ourier Integral that

IT J 0 O)

where a{tS) is defined b\'

1

//(/oj)

= a(co) + i^(a)).

Later on we shall briefly consider the Fourier Integral; for the
present the preceding formula will not be considered further. In
certain problems it is of value; for the explicit derivation of h(t),
however, it is usually too complicated to be of any use except in the
hands of professional mathematicians. As a matter of fact, a direct
attack on this formula would be equivalent to abandoning the unique
simplicity and advantages of the whole Operational Calculus.

It has been noted above that any solution of the integral etiuation
supplies a solution of the corresponding operational equation. This
principle enables us to take advantage of the fact that a very large
number of infinite integrals of the type

£

f(l)e-P'dt

have been evaluated. The evaluation of every infinite integral of this

type supplies us, therefore, with the solution of an operational equation.

Of course, not all the operational equations so solvable have physical

significance. Many, however, do. Below is a list of infinite integrals

720 BELL SYSTEM TECHNICAL JOURNAL

with their known solutions, accompanied by the corresponding
operational equation and its explicit solution. All of these solutions
are directly applicable to important technical problems. It may be
remarked in passing that the infinite integrals have for the most
part been e\aluated by ad\anced mathematical methods which need
not concern us here.

Table of Infinite Integrals, the Corresponding Operational Equations,
and Their Explicit Solutions

1

(a) r

Jo

e-p'e-Wt = ^. , ^ ,
p-\-\

P

h=^-^=e-^'.

P+\

(b) r e-P'^.dl=^\/p''+\
Jo n\

r°° \ 1

(c) / e-P'^dl=~,
J<i y/wt Vp

(2»-l)y'^/ pny/p'

.Vp_^ (2/)" 1

/>'■ 1.3.5... (2n- 1)^7/*

(e) re-P'^;,e-^'dt = -^^

(P+X)
(/>+X)"+' «!' •

>+i

(f)

^■^t\n

(g) / e-P'^dl = '-~~,

,_ , _ p-\ll

h = Vpe-'^'I^P=, .^.
Wirt

CIRCUIT THEORY AND OPERATIONAL CALCULUS 721

(h) £ e-*'sin \tdt= ^

p' + \-'

(i) /"°e-*'cosX/(//=-,^-,.

•/O P' + A

= -^ =
' P' + \' '

0) / e-'"e^>'' COS \l dt =
Jo

P+n

ip+ixY+r-'

* = (-^S^=— cosX/.

e-pie-f' sin \t dt ■■

(P+m)=+X^'

(1) r e-f'Jo{\l)dl= , ^ ,

Vp^+y^'

(m) f "e-^'JoiVF^') dt = «J^^,

= Joiy/fi-\-) for />X.
(n) /^"^-"M^Ddt^y^^y r"-=p' + \'.

(p) /* e-f'e>"Io{\t)dt= , ^

A = -7=i==e->^'/o(X/).
V1+2X//.

722 BELL SYSTEM TECHNICAL JOURNAL

In formulas (1), (m), (n), J„{x) denotes the Bessel function of order
n and argument x. In formula (p), Io{x) denotes the Bessel function
Joiix) where i = V — 1 •

This list might be greatly extended. As it is, we are in possession
of a set of solutions of operational equations which occur in important
tfchniral problems and which will be employed later.

The foregoing emphasize the practical and theoretical importance
of recognizing the equivalence of the integral and operational equa-
tions. With this equivalence in mind, the solution of an operational
equation is often reduced to a mere reference to a table of .infinite
integrals. Heaviside did not recognize this equivalence. As a
consequence many of his solutions of transmission line problems are
extremely laborious and involved and in the end unsatisfactory
because expressed in involved power series.

.\ot all the infinite integrals corresponding to the operational
etiuations of physical problems have been evaluated or can be recog-
nized without transformation. This statement corresponds exactly
with the fact that a table of integrals is not always sufficient but
must be supplemented by general methods of integration. We turn,
therefore, to stating and discussing some general Theorems applicable
to the solution of Operational Equations.

In the derivation of the operational thcortnis, which constitute the
general rules of the Operational Calculus, the following proposi-
tion, due to Borcl aiui known as Horel's theorem, will be frequently
employed.*

If the functions f{t) , flit) , and f«(t) are defined by the integral equations

F{p) = f me-^'dt
»'o

Fx{p)= rf,{t)e-'"dl

F.(p)= rf.{l)e->"dl

and if the functions /•', Ft and F-i satisfy the relation
F{p) = Fi{p).F,{p)

• For a prcKjf of this important theorem the reader is referred to Rorel, " Leioiis
sur les Series OiverRentcs" (1901), p. 104; to Bromwieh, "Theory of Infinite Series,"
pp. 28(^-281; or to I-'orcl, "Studies on Divergent Series and Summaliility," pp. 93-94
(l>cinK Vol. II of the Michigan University Science Series, published liy Macmillan).
The proof depends on Jacobi's transformation of a double integral: see Kdward's
"Integral Calculus," 1922, Vol. II, pp. 14-l.S.

CIRCUIT TIII.ORY ASn OI'l-KAIIONAI. CALCULUS 72i

thrn

/(/)= f'Mr)Ml-r)dr

= f'Mr)W-T)dr.
Jo

The operational theorems will now he stated and hrittly proved
from the integral equation identit>-.

Theorem I

If in the Operational Equation

h = l,II{p)

the generalized impedance function f[(p) can he expanded in a sum of
terms, thus

//(/)) ih(pyih(p) ■ ■ ■ ^ihip)

and if the auxiliary operational equations
1

H,{p)
1

Jhip)

can be solved, then

h=hi+h-, + . . . +//„.

This theorem is too ob\ious to require detailed proof: in fact it is
self evident. The power series and expansion theorem solutions are
examples of its application. In general, however, the appropriate
form of expansion of \'H(p) will depend on the particular problem
in hand. The theorem, as it stands is a formal statement of the fact
that solutions can often be obtained by an appropriate expansion
whereas the equation cannot be solved as it stands.

Theorem II
If h = h{l) and g=g{l) are defined by the operational equations
h = \/mp)
g = l/pH(p)

the

g{t)= f'h{T)d.
Jo

724 BELL SYSTEM TECHS'ICAL JOURNAL

To prove this theorem \vc start wiili the integral equations

The second of these is in f(jrni for an immediate apphcalion of Borel's
tlieorem since

1 1 \

p'Hip) ~ p ' piiipy

The functions /i and /; of Borel's theorem then satisfy the equations

pIHp) Jo
It follows at once that

Ii(t) = 1

whence bv Borel's theorem

-r= r f,{t)e~P'dt,

p "'O

^,= rMDe-P'dl.

g{t)=fjliT)d7

Theorem III

If h=h{t) and g=g{l) are defined by the operational equation':
h = \/II{p)

g=p/mp)

then

dt

g{t) ^JrHi)

provided h{o) =o.

The integral eciuations of the |)roblem are

CIKCl'IT rill-.ORY .1X1) Ofl.h'.tltnx.lt. (■.(/.( r/.C.S 72S

Iiiletjratiii); llii- lirsl of llii-M- I)\- parts wo li,i\i',

\vhvTch'(l)=d/dthit).

If li{o) =0, we have at once

Comparison with the integral equation for g(/) shows at once that
g{t)=h'(t), since the integral equation determines the function
uniquely.

Theorems II and 111 establisli the characteristic Heaviside Opera-
tions of replacing 1 '/> bv / dt and p hv d/dt.

' •'0

Theornn IV
If in the operational equation

It = I /Hip)
the generalized impedance function can be factored in the form

II{p)=H,{p)-Ih{p)
and if the auxiliary operational equations
hr = l/mp)

Jh=l/Ih(p)

define the auxiliary variables hi and hz, then

h{t)=jJ\Mh,{t-T)dr
='jJju.{r)hi{t-r)dT.

This theorem is immediately deducible from Borei's theorem and
theorems II and III, as follows.
The integral equations are

kr^7mF)-piwrr''^'^''''''

^^=fl,U)e-^.dt
^^=f,.it)e-m.

726 BELL SYSTEM TECHNICAL JOURNAL

Now define an auxiliary function £;(/) l)y the operational ciiuation
1

Then

1

kprf'^'^'-

pi hip) pILiip) Jo
and by Borel's llieoreni

£,(/)= f ll,{T)h;{t~T)dT

"'(it

= ffhirVnit-

■V/7

From this equation it follows that s{o)=o, and hence coniparing the
ojierational equations for /; and », we ha\'c In' aid of Tlu-orcm III

HD^git)

and hence

m4Jjnir)hU-r)dr

= U"^-^'^"^^'-'^''

This theorem is extremely important, although not stated or
employed b}' Heaviside himself. We shall make use of it in estab-
lishing two important general theorems and shall have frequent
occasion to employ it in specific problems occurring in connection
with the subsequent discussion of transmission theor\'.

Theorem V

If li = li{t) and g = g(t) are defined by the operational equations

*" i/(/>+X)
where X is a positive real parameter, then

g{t) = {l+\£dt)c-^'h{l).

ilNillT llllA>l<y .IM' ul'IK.I I IdX.II. C.ll.i CIA'S 727

'I'o priivi- this ilu-orrm wr si.irl with iho intfKr;il ('({ualions
1

PII(P)
1

= / h{t)e-'"dt

=£''''

e f'dt.

prnp+y.)

Ill ihi- tirst nf i1r's<' ctiii.itions rri)lacf tlic symbol p hy q-\-\: we get

-L • n, Xr>= r Ht)e->^'e-'>'dt
q + \ //((/ + X) Jo

and ihfii to preserve our original notation rei)Iace the syniliol (/ hy p.
whence

The inlei;ral etiuation in g(/) can be written as

{'+j)iP+miP+xrfo '^'^'-"'' (^^

Comparing equations (a) and (b) ii follows at once from theorems
I and II that

g(l)=(^l + \f'dtyi(t)e-^'.

From the foregoing, the following auxiliary theorem is immedi-
ately deducible.

Theorem 1 'a

If h=h{i) and g=git) are defined by the operational equations

^ (p+\)ii(p+\)

then

g{t)=h(t}e-K

The proof of this theorem will be left as an exercise to the reader.

728 liP.IJ. SYSII-.M TECHNICAL JOURNAL

Theorem VI

If h=h{l) ami g = g(l) arc defined by the operational equations

ii = \:ii{p)
g = \;ii{\p)

where X is a positive real parameter, then
g(t)=h{l/\).
We start with the integral ctiuaiions

pll(p)
1

hrf"^''^-"''^

pll{\p) Jo ^'-

and in the first of these equations we replace p by \q and / by t/X,
whence it becomes

m=r"(iy-''''

qH{\q)
Now replacing the symbols q and - b\' p ami / respectively, we have

pim)=r'"''^'-""

whence by comparison with the integral equation in g(t) it follows
at once that

gW=/'('/x).

This theorem is often useful in making a convenient change in the
time scale and eliminating superfluous constants.

Theorem VII

If h=h{l) and g=g{t) are defined by the operational equations

^~iiiP)

where X is a positive real quantity, then
g{l)=o for t<\

= h{l-\) for /^X.

(/A'i(7/ IIII.OKY .l.\n OI'I.R.I I IHX.II. (•.//.( 7 /.C.V 729

This is a ver>' important theorem in connfction with transmission
hne problems where retarihition, (hie to finite velocity of propagation,
occurs. Its priM)f proceeds as follows:

If the auxiliar\' function k = k{t) is (lit'iiud i>y the operational
equation

k=e >-!■

then !>>■ rheorem l\ .

g{l)=jJ^k(T)h{t-r)dr. (a)

Now, corresponding to the operational equation k = c'^'' we have
the integral equation

^- = / k{t)e f<dt.

P ^0

The solution of this integral equation, which is easily verified by
direct substitution in the infinite integral, is

k{t)=o for /<\

= 1 for />X.

Hence equation (a) becomes

g{t)=o (or i<\

= x / h{t-T)dT for />X
dU\

= h{l-\) for />X.

Theorem IV, employed in the preceding proof, as stated above, is
extremely important and w^e shall have frequent occasion to employ
it in specific problems. We shall now apply it to deduce an important
theorem which extends the operational calculus to arbitrary impressed
forces, whereas heretofore the operational equation h = \/II{p) applied
only to the case of a "unit e.m.f." impressed on the system.

It will be recalled from a previous chapter that if x{t) denotes the
response of a network to an arbitrary force /(/), impressed at time
1 = 0, and if h{l) denotes the corresponding response to a "unit e.m.f.,"
then

and

x{t)^^J\{r)S{t-T)dr (31)

\-=rhit)e->'dt. (30)

pllip)

/"

730 BEI.I. SySlEM TECHNICAL JOURXAL

y.o\\ f(l) may l)e of such form that the infinite integral
}{t)e-'"dt
can be evaluated and has tlie \alue F{p) p: thus

r mc-"dt = ]-F{p). (55)

^0 P

This is possible, of course, for many important types of applied forces,
including the sinusoidal.

It follows at once from Theorem I\' that x{t) satisfies and is de-
termined by the integral equation

We have thus succeeded, by virtue of Theorem IV in expressing the
response of a network to an arbitrary e.m.f. impressed at time l = o,
by an integral equation of the same form as that expressing the
response to a "unit e.m.f." That is to say we have, at least formally,
extended the operational calculus explicitly to the case of arbitrary
impressed forces.

We now translate the foregoing into the rorrespntuiiiit; Operational
Theorem.

Theorem VIII

If the operational equation

h = \iHit>)

expresses the response of a network to a "unit e.m.f." and if an arbitrary
e.m.f. E impressed at time t = o, is expressible by the operational equation

E=V{p)
or the infinite integral

f

\it)e-^'dt=^M
P

theti the response x of the network to the arbitrary force is given by the
operational equation

x-Y^
Hipy

and xU) is determined by the integral equation

pmp) Jo ^^'^' "'■

ciHCUir iiii-ony .ixn iiri.n.uioiWii. c.iixii.us 7Ji

Theorem IX

If the operational e<iii(ilioii

y; = l IKp)

is reducible to the form

h ^1^L_

\+\K(p)

uhere X «5 a real parameter, and if the auxiliary functions f=f(t) and
k = k(t) are defined by the auxiliary operational equations

J=F(p)

k = K{p)

then /i(/) is determined by the Poissan Integral equation

hit)=f{t)-\f'h{r)kil-T)dT.

This theorem is of considerable practical importance in connection
with the approximate and numerical solution of operational equations
when the operational equation and the equivalent Laplace integral
equation prove refractory. In such cases, as will be shown later,
the numerical solution of the Poissan integral equations can often
be rapidly and accurately effected, and in many cases the quali-
tative properties of //(/) can be deduced from it without detailed
numerical solution.

The proof of this theorem proceeds as follows:

By \irtue of the relation h = \ 'll(p) the operational equation

can be written as

1 + XA'(/))

.A direct application of Borel's theorem or Theorem IV gives at once
the explicit equivalent

h{t)=f{t)-\£h(r)k{t-T)dT

732 BELL SYSTEM TECHNICAL JOURNAL

The preceding theorems, together with the power series and ex-
pansion theorem solutions formulate the most important rules of the
operational calculus, and are constantly employed in the solution of
the elect rotechnical problems. On the other hand, the table of
infinite integrals furnishes the solution of a set of operational equa-
tions, which are of the greatest usefulness in the systematic study of
propagation phenomena in transmission systems which will engage
our attention. Before taking up this study, how^ever, we shall first
s(jlve a few specific problems which will serve as an introduction to
asymptotic and divergent solutions involving Heaviside's so-called
"fractional differentiation."

Problem A : Current Entering the Non-inductive Cable

The non-inductive cable is a smooth line with distributed resistance
R and capacity C per unit length; for the present we neglect induct-
ance and leakage. A consideration of cable problems leads to some
of the most interesting questions relating to operational methods,
particularly to questions regarding divergent expansions. It would
seem best to allow specific problems to ser\c as an introduction to
these general questions.

The dilTcrenlial etjuations of iho calile are

(57)

C^V=-i-I
dl dx

where x is the distance, measured along the cable from any fi.xed
point, / is the current at point .v, and V the corresponding potential.
Replacing d/dl by the operator p, we have

RI=-^V

dx

(58)

i'Jimiiuiting, successiveh', I'and / from iliese etiuations, we tl>-'l

and

pRCI = ^\l

/>^CF=gr.

CIRCUIT THEORY AND Ol'liRATtONAl. CALCULUS 7J.?

Thesf «.-i|uati<>iis have llu- m-ntT.il solutions

r=r,f-^'+lV (59)

I=^[VxC-"-\\e-''\ (60)

where

y = VjRC. (()!)

The term in e'"" represents the direct wave and the term in e" the
reHectetl wave. I'l and l\ are constants wliich must he so chosen
as tu satisfy the im(>osed lioniular\- conditions at the terminals of
the cable.

For the present we shall assume that tiic line is infinitely long so
that the reflected wave is absent. We shall also assume thai a voltage
E is impressed directly on the cable at x = o: we ha\e then,

V' = £e-»v'pCR=£e-Vo7 (02)

I = yj^Ee-''^-^=yj^Ec-^^^ (63)

where a denotes x-RC.

To con\ert these to operational cc|uations let us suppose that E
is a "unit e.m.f." (zero before, unity after time t = o). We have
then, in operational notation

p'=e-Vip (64)

I = ^l^e-^rp. (65)

Now suppose that x = o so that a = o, in other wcjrds consider a
point at the cable terminals. Then

(66)

'^'4

The first of these equations means that l' is simply the impressed
voltage, zero before, unity after time t = o, as of course, it should be
from physical considerations.

Corresponding to the operational equation

/ = ^. (66)

734 BELL SYSTLM TF.CHNICAL JOURNAL

we ha\t- the integral eciiialinii

The solution of this is known (see fornnila (c) of the preceding table
of integrals) : it is

Heavisicie arri\e(l at tliis sdliilion from considering the known
solution of tlie same ])rol>leni in the tiieor\- of heat flow. He liiere-
fore inferred that the operational e(]nation

has the explicit solution

This is correct; we, however, ha\e (leri\ed it directly from the integral
equation of the problem and the known integral

We then see from the foregoing that, if a "unit e.ni.f." is impressed
on the cable terminals, the current entering the cable is initialK'
infinite arid dies away in accordance with the formula y/C/-wRt.
The case is, of course, idealized and the infinite initial value of the
current results from our ignoring the distributed inductance of the
cable, which, no matter how small, keeps the initial current finite,
as we shall see later.

Now let us go a step farther; suppose that in addition to (iistril)iitcd
resistance R and capacity C, the cable also has distributed leakage
G per unit length. The difTerential equations are now

RI= -4-V
■dx

^ (70)

{Cp + G)V=--°L

d-v

Conse(Hienli\- it follows that in the oi)eraiional c(iiiation for the cm-rent
entering the cable we need only replace Cp by Cp+G. Tiierefore,
when leakage is included, equation ((Hi) is to be replaced by

where X = G/C.

URCl'ir llll.OKV .tXI) Ol'l-fx.llloX.II. C.llxriA'S 7.?.i

Tlif i()rri->|>(iii(liiii; inti'Kr.il iM|iiatii)n i^, of cniirsc,

= f l(t)e P'dt. (72)

4

c vp+\

R p

W'f shall i;i\c (wo solutions of this |)roi)lrin; lirst liic solution (jf
the iiitei-ral equation, anil secoml the t\|)iral Hea\isi(U' solution
directly from the operational equation.

luiuation (72) nia\' l)e written as

P+\

(73)

Now supix)se that /(/) is the solution of the ec|uation

-j=.^=fj,,e.„ (74)

it follows at once from Theorems (I) and (II) of the preceding chapter
that

m = yj^{i+xp,)m.

(75)

Also from formula (c) of the table of integrals and Theorem (V'a) the
solution of (74) is

J(t)=-

V-f

whence

'^•H^.\9h^f:vi<

(76)

(77)

The integral appearing in (77) can not be e\aliiated in finite terms;
it is easily expressible as a series, however, by repeated integration
by parts. Thus

Proceeding in this way by repeated partial integration we get for the
integral term of (77)

2v^e-X'jl+?^'4-(^>... [. (78)

' 1.3 1.3.0 i

736 BULL SYSTEM TECHNICAL JOURNAL

The straijjiitforward Hea\iside soliilion is obtained by expanding
the operational equation as follows :

Identif>'ing \/p\\\th \l\/rl (from known solutions of allied problems)
and substituting for !//>" multiple integrations of the Hth order we get

l-SJ- i 1 I (2^^^ (2X/)-^ 1 .3(2X0^ _ _ ) _
^~\^l^+ 2 2.3.4+2.3.4.5.0 * ^''^

It can be verified that this solution is ronvergent and equivalent
to (77).

This problem, while simple and of minor technical interest, will serve
to introduce us to the very important and interesting question of
asymptotic series solutions.

An asymptotic series, for our purposes, may be defined as a series
expansion of a function, which, while divergent, may be used for
numerical computation, and which exhibits the behavior of the func-
tion for sufficiently large values of the argument.

Let us return to equation (77). We observe that the series solu-
tion (78) of the definite integral becomes increasingly laborious to
compute as the value of / increases. This remark applies with even
greater force to the Heaviside solution (79) on account of the alter-
nating character of the series. Right here we have an excellent
example of what I regard as Heaviside's exaggerated sense of the
importance of series solutions as compared with definite integrals.
Consider the solution in the form of (77) as compared with Heavi-
side's scries solution (79). The former is incomparably easier to
interpret and to compute, eitlicr by numerical integration or by
means of an integraph or planimcler. In fact the series (79) is prac-
tically unmanageable except for small values of /.

Returning to the question of an asymptotic expansion of the solu-
tion (77), we observe that the definite integral_^appearing in that
c(iuation can be written as,

J/»ig-xi /'°°e-X' /""e"^'

0 y/t Jo y/T Ji y/T

(80)

iiKCL'ir iiir.oRy .ixd ornN.iiiox.iL calculus 7.u

|)ro\i(U<l X is positive, as it is in this case. Now tlu' v.iliic of tlie
infmitt.' integral is known; it is \/jr/X. {'onse(|iiently

,.-X/

turthcrniorc,

•'o vT X»'« v< ^\// 2X^0 /V^

Integrating again !>>• parts wc get

iC^'_J_ £I^J.M CiiILai

^vt 2x'/V/ 2W0 /vr

Continuing this proress, we get

V/ XVTL 2X^(2X0= (2X0'

1.3.5 . . . (2«-l)"

/■

(82)

+ ..+(-1)"

(2X/)"

(-1)" 1.3.5 ■■ ■ (2»+l) f"" g-^'
X 2(2X)" J, f+Wt'

Now this series is divergent, that is, if we continue out far enough
in the series the terms begin to increase in value without limit. On
the other hand, if we stop with the nth term the error is rcprcscntcf!
by the integral term in (82) and this is less than

(-1)" 1.3.5 ■.■(2«-l)

xvr (2x/)-' • ^""^^

Consequently the error committed in stopping 'with any term in the
series is less than the value of that term. Therefore if we stop with
the smallest term in the series, the error is less than the smallest term
and decreases with increasing values of t.
We can therefore write the solution (77) as

\ R^\irRt' I2\t (2\tr-(2\l)' i ^^ '

The first term, since \ = G/C, is simply y/C/R, the d.c. admittance
of the leaky cable. The divergent series shows how the current
approaches this final steady value.

738 BELL SYSTEM TECHNICAL JOURNAL

In this particular problem no asymptotic solution is derivable
directly from the operational equation, at least by the straight-
forward Heaviside processes. Asymptotic solutions, however, con-
stitute a large and important part of Heaviside's transmission line
solutions. We shall therefore discuss next a problem for which
Hea\iside obtained both convergent and di\ergent series expansions.

Problem B: Terminal Voltage on Cable with "Unit E.M.F." Impressed
on Cable Through Condenser

We now take up a problem for which I Icavisidc obtained a di\ergent
solution, and which will introduce us to the theory of his divergent
solutions and so-called "fractional differentiation." We suppose a
"unit e.m.f." impressed on an infinitely long cable of distributed
resistance R and capacity C per unit length through a condenser of
capacity C,,: required the \-oltage I' at the cable terminals. The
operational equation of the problem is deri\-ed as follows: — ■

We know from the problem just discussed that the current entering
the cable whose terminal \oltage is V, is, in operational notation

>]

£Pv

R

But the current flowing into the condenser is

CoPil-V)

since the xollage across llic condenser is 1 — T. Ivtiuating llicse two
expressions we get

]/= f^;___ (85)

pCo + VpC/R
whicii is the operational equation of tlie problem.
This may be written as

F= U-

(85)

where

CIRCUIT THF.OKV ./A/) OPF.RATIONAI. CALCULUS 7J'>

Now »A|>,m(linn this liy tlu' MiKHiii.il llu'orrm

= l+f, + ^V.... (86)

/2a/ (2a/)' (2a/)» \

\ 1 "^ 1.:^ "^i.3.sT • ■/

1

l>y till' usu.il Hi'a\isi(k' rules of "ali;fl)rizint;."

It is worth while \erifyiiii; this from the iiitenral equation of the
problem. We luue

1 1 /"°

P \+\/a/p •'0

The left hantl side i.in he written as

(87)

J 1_ la^

-a p-a\ p

and 1)\- the formulas and theorems j;i\en in a preceding section the
solution can he recognized at once as: —

^'^'^=^'-\l^'X'7T'^^

(88)
This ran also he written as

If the definite integral of (88) is c\aluated by successive partial
integrations it will he found in agreement with the Heavisidc solution
(StV).

Now the solution (86) is in powers of / and while absolutely con-
vergent becomes progressively more difficult to interpret and com-
[)ute as the value of / increases. From (80), however, we can derive
a divergent or asymptotic solution applicable both for interpreta-
tion and computation, when the value of / is sufficiently large. As

740 BELL SYSTEM TECHNICAL JOURNAL

in the example discussed before, the asymptotic expansion results
from repeated partial integrations; thus

aV7 2aJ, tVt

2-a-Jt

O-UT

^±?l -^—^dr

and finally

aV t 2a'tVT 2-a-J, t^\/t

e-"' j ,_ J_ , Jj3_ _ 1.3.5 , /
a^/7 ( 2at'^ {2at)^ (2a0'"*" ' ' • T (90)

The series (90) is divergent just as is (82) of a preceding problem
and the error committed by stopping with the smallest term, is of
the same character and subject to the same di.scussit)n. Willi this
understanding we write the solution (89) as

For large \alues of t {at>5) this series is accurately and rui)idly
computable. Furthermore it shows by mere inspection the be-
havior of V{t) for large values of /, and that it ultimately approaches
zero as l/y/wat.

Let us now see how Heaviside attacked this problem ami how he
arrived at a divergent solution from the operational formula. Re-
turning to the operational equation (85), it can be written as

r= ^/L- (92)

l+vA/«

Now expand the denominator by the binomial theorem: we gel
fnrmallv

CIRCUIT TIIF.OKy .1X1) OPERATION Al. CAI.CVI.VS 741

Mcavisiile's procedure at iliis point w.is as rem.irkaWe as it was siic-
rcssful. Me first disoardetl the second series in inteRral powers of p
as meaningless. He then identified \ p with 1/'\/t/ anil replaced
p" by d' /dt" in the first series, getting

-('+'^i.S+-):

1 rf , 1 (f . \ 1

(94)

or, carrying out the indicated differentiation,

1 /. 1 . 1.3 1.3.5

V = -

V^V 2at ' {2atr {2aiy

which agrees with (91).

This is a typical example of a Heaviside divergent solution for
which he offered no explanation and no proof other than its practical
success. His procedure in this respect is quite unsatisfactory and in
particular his discarding an entire series without explanation is in-
tellectually repugnant. We shall leave these questions for the present,
howe\er; later we shall make a systematic study of his divergent
solutions and rationalize them in a satisfactory manner. First,
however, we shall take up a specific problem for which Heaviside
obtains a divergent solution without discarding any terms.

Problem C: Current Entering a Line of Distributed L, R and C

Consider a transmission line of distributed inductance L, resistance
R. and capacity C per unit length. The differential equations of
current and voltage are

(95)
it dx

Ki'placing d/dl \)\ p, we get

(96)

Equations (96) correspond exactly with (58) for the non-inductive
cable: except that we must replace R by pL-\-R. For the infinitely

(4+^,/-

-l-y

dx

4^'

dx

ve get

(pL + R)I =

dx

CpV =

dx

742 BELL SYSTEM TECHNICAL JOURNAL

long line, therefore, tlie operational formula for the current entering
the line is

/=JIgLr„ (97)

'■\pL + R^'"

where 1', is the \-ohage at the hue terminals. If this is a "unit e.ni.f."
we have, as our operational equation,

I = J P^ (OS)

\ pL+R

which can he written as

IC 1

/ = J^--=L== (99)

^L Vl+2X'/>

(100)

where \ = R 2L.

The corresponding integral equation is

C 1

From either equation (09) or (100) and formula (p) of the table of
integrals, we see at once that the solution is

/ = ^|'c-^'/„(\0 (101)

where /(,(X/) is the Bessel function 7„(/X/), where /=\/— I. (The
function is, however, a pure real.)

Heaviside's procedure, in the absence of an>' correlation between
the operational equation and the infinite integral, was quite different.
Remarking, with reference to equation (00), that "the suggestion to
eni[)lo\- the binomial theorem is ob\ious," he expands it in the fortn

^-N'l r p^2\[p) 3\ \p) ^ ■■ \

and replaces \/p" by t"/n in accordance with the rule discussed in
preceding sections. The e.xplicit solution is then

a convergent solution in rising powers of /. As yet, howe\er, he does
not recognize this series as the power series expansion of (101), which
it is. He does, however, recognize the practical impossibility of
using it for coni|)uting for large values of /, and remarks "But the
binomial theorem furnishes another way of expanding the operator

■=^l

'=^iwl

CIRCUIT THEORY AND OPERATIONAL CALCULUS 743

(operatiimal ec|uation), viz. in rising powt-rs of (>." Thus, rt-tiiniiiiv;
111 (!•'.)). it I'.in li«- wriltiMi as,

\ L y/l+P/2\
Now i-xpaiul the ilciiominalor by thf binomial liu-urrni: \vc ^-i

/ = J^: .; i_A+l£VAy_LMf MV . . ' 1 ^ (105)

' \l ' 4X^2!V4Xy 3!Ux>'^ '\2X

He now identifies v'p, 2X with 1 y "-rrX/ and rcpkucs /j" in the series
by d'dt', thus getting finall>'

V2k\I ' ^8X/^2!(8X/)'^3!(8X/)'^ ' ' ' »

This series solution is divergent : Heaviside recognizes it, li()we\er,
as the asymptotic expansion of the function ^"^'/..(X/), and thus
arrives at the solution

/=^)^\-X'/„(X/) (101)

which we have obtained from our tables of integrals.

Now the divergent expansion (100) is the well known asymptotic
expansion of the function e"^'/„(X/), which is usually derived by diffi-
cult and intricate processes. The directness and simplicity with
which Heaviside derives it is extraordinary.

We note in this example that no integral powers of p appear in the
divergent expansion: consequently no terms are discarded. Other-
wise Heaviside's process is as startling and remarkable as in the
example discussed in the preceding section.

We shall later encounter many problems in which asymptotic
st)lutions are derivable as in the preceding example. We have suffi-
cient data, however, in these two typical examples to take up a
systematic discussion of the theory of Heaviside's divergent solution
of the operational equation.

CHAPTER V
The Theory of the Asymptotic Solittiox of Oper.\tional

Eyi ATIONS

A study of Heaviside's methods, as exemplified in the preceding
examples and in many problems dealt with in his Klectromagnetic

744 BELL SYSTEM TECHNICAL JOURNAL

Theory, Vol. II, shows that they may be divided into two classes:
(I) those of which the operational equation is of the form

h = F{pWp (I)

and (II) those of whirh the operational equation is of the form

h=4><pWp) (ID

where k is an integer.

Heaviside himself does not (lislinj4ui>!i liftween tlie two classes,
but employs the following rule for obtaining as\niptotic expansion
solutions :

If the operational equation

h = l/H{p)

can be expanded in the form

h=ao+aip+a<p-+ . . +a„p"+ . . .

{bo + b>p + b-2p'+ . . +b„p"+ . . . )Vp, (107)

a solution, usually divergent, is obtained by discarding the first expansion
entirely, except for the leading constant terms «„, replacing \/p by \/\/irt
and p" by d" jdt" in the second expansion, whence an explicit series
solution results.

It should be expressly understood that Heaviside nowhere himself
states this rule formally. He does not distinguish between the two
cases where integral series in p do and do not appear, although very
important mathematical distinctions are involved. Furthermore,
in one case he modifies his usual procedure b\- adding an extra term
(Elm. Th. Vol. II, pg. 42-44). It certainly represents, however,
his usual procedure in a very large number of proi)len)s.

A completely satisfactory theory of the Heaviside Rule, just slated,
has not yet been arri\ed at although we can ahva>s verify the di\er-
gent solutions in specific problems. Furthermore, it is not as yet
known just how general it is, though it certainly works successfully
in a large number of physical problems to which it has been applied.
Finally we know nothing in general as to the asymptotic character
of the resulting expansion. In some rases it leads to an ex|ian.sion
in which the error is less tli.m the last term included, in otiiers re-

CIRCUIT THEORY AND OPERATIONAL CALCULUS 745

niarkably enough the expansion is everywhere converKent, while
in yet others its application leads to a series which is meaningless
for a certain range of values of /.

Heaviside himself gives no inforniation which would serve us as a
guide in informing us when the rule is applicable and when it is not.
Consequently it becomes a matter of practical importance, not only
to investigate the underKing mathematical philosophy of the rule
and to establish it on the basis of orthodox mathematics, but also to
de\elop if possible a criterion of its applicability. In this investiga-
tit>n we shall have recourse to the integral equation of the problem.

We shall take up first tlie type of problem (Class I) in which the
operational equation is

and assume that /•"(/)) admits of the formal power series expansion

/•■(/>) =*o+fri/>+6i/>'+6a/''+ . . . (Ill)

The corresponding integral equation is

Vp

= f h(t\e-t'iU. (112)

We now assume the existence of an auxiliary function kit), defined
and determined by the auxiliary integral equation

\ow since

F{p)= n k{t)e-t"dl. (113)

4==/%- 4= (114)

it follows from (112), (113), and (114) and Bf)rers Theorem, or
Theorem I\', that

h(l)=A=f'-^}^dT. (115)

Vt''o y/l-T

Now if we differentiate (113) repeatedly with respect to p and put
p = o, it follows from the expansion (III) that

b, = {-\)' r-Mt)dt. (116)

This equation presupposes, it should be noted, the convergence of
the infinite integrals for all values of n, and therefore imposes severe

746 BELL SYSTEM TECHNICAL JOURNAL

restrictions on k{l) and hence on F{p). We shall suppose that these
restrictions are satisfied, and discuss them later.
Now (115) can be written as: —

h{t) = ^ f'dT.kir) (l-r/0-'''2. (117)

It can he shown that, if k{t) satisfies the restrictions underhing
(IIG), the integral (117) has an asymptotic solution obtained as
follows: — Expand the factor (1 — t//)~'' by the binomial theorem,
replace the upper limit of integration b>' -x. , and integrate term l)y
term : thus

'^'^~^U"'^'^'^'4/rr!^('^^'

^ (2/)

1 'A f'^ t-

{\m

Finali\' from (lUJj we get

which agrees exaclK- witli llie Heaviside.rulc for this case.

The foregoing says notiiing regarding the asymptotic character
of the solution. It is easy to see (iualitati\ely, however, that (118)
and therefore (119) does represent the behavior of the definite in-
tegral (117) for large values of /, provided k{t) converges with suffi-
cient rapidity.

The foregoing analysis ma\' now he sumniarizetl in liie following
proposition :

If the operational equation h = \/II{p) is re<liicH)le to the form

h = F(p)Vp
and if F(p) admits of power series expansion in p: thus

F(p)=bo + lhp + hip'^+ . . . +b„p"+

50 that, formally,

h = {bo + b,p + b,p-+ . . . +b„p"+ . . . )y/p

an explicit series solution, usually asymptotic, is obtained by replacing
y/p by l/y/irl and p"{n integral) by d''/dt", whence

■:^^{bo-K^i+b.~-b.]^+ . . .)

CIRCUIT THF.ORY AND OPf.RATIOSAL CALCULUS 747

prM-ided the function k=k(t), defined by the operational equation k = F{p),
and the infinite integrals

I t'k{l)dl (u= I, 'J )

exist. , "

We shall now apply the foreKoinyj tlieory to a physical pr()l)leni
discussed in llie last section : narneU', the current entering an infinitely
lonj; line of inductance L, resistance R and capacity C [wr unit length.
It will he recalled (see equation (100) ) that the integral equation of
this prohleni is

J^ , ^ == r e-P>I(t)dt
\ L Vt*'+2\p Jo

1 the soluti<in

C L

where X = R 21., and thai the soluti<in is
/ = J-f«. ^'/„(X/).

We can derive the snluiinn in anoilu-r form ,i|)pr<)priate for our pur-
poses 1>\- writing

Now since

y/p Jo y/wt
and

^^_ = / e-^'-.r dl

VP+2\ Jo y/i^t

it I'dHows from Corel's theorem tliat

\c 1 n e"^^^

' L, wJo -y/r y/t — T

Now subject this definite integral (omitting the factor \/C/L) to
the same process applied to (117) : we get

^Vl 'Jo VT 2tJo 1! ^ *"

1.3

(2/)

^ (2/)Vo 2! '^ at-t ... ^

748 BELL SYSTEM TECHNICAL JOURNAL

Tlie infinite integrals are known and have been evaluated. Sul)-
stituling their values this series becomes: —

V2^/ ( ^8X/'^2!(8X/)^'^3!(8X<)''^ • " |

which is in fact the well known asymptotic expansion of ihc fuiulion
e-^7„(X0.

A second example may be worth wliile. Consider the case of an
e.m.f. e~^' impressed at time t = o on a cable of distributed resistance
R and capacity C: required the current entering the cable. The
required formula is *

T- l~C d pe-xc-^) ^

by ob\ious transformations.

Asymptotic expansion of the definite integral as in the preceding
example gives the asymptotic formula

\ TrRt I 2X<^(2X/)2^(2X/)'^ ■ ■ )
The operational formula of the problem is

HI:

P+X

.•\l)l)l\ing the Heaviside Rule, we get the asymptotic exijansion

\ tRI I 2X^"'" (2X/)- (2X0' ■ ■ ■ *

which agrees with the jireceding formula, deri\eil from the definite
integral.

We shall now discuss a specific problem in which the Hea\ iside Rule
breaks down. For example let us take the preceding problem, and

•The derivation of the formulas in this problem is left as an exercise for the
reader.

CIRCUIT THEORY AND OPERATIONAL CALCULUS 749

ri'plai'e the appliwi e.ni.f. «• '^' by sin wt. The formula corrfspniulinn
to (120) is now

If we now atti-inpt to expand the definite integral of (121) in the
same way as that of (120), we lind th.il the process breaks down Ijecause
each component of the infinite integral is now itself infinite. In fact
no asyntptotic solution of this problem exists.

I.et lis. however, start with the operational formula: since

Jo

e-i" sin ut.dt^^ , .

-4^

up

■Vp.

i^ + u,'

Now expand this in accordance with the Heaviside Rule: we get.
o|x?rationall\',

and expliciiK-

/ =

which is quite incorrect.' The incorrectness of the result will be evident
when we remember that the final value of tlie current is the steady-state
current in response to sin ut, or

4

^(cos a)/ + sin tjit). (122)

This result can be derived directly from (121) by writing it as

\~C \ r' cos uit r' sin oil t

/ = . ^^ j cos .tl ^7^rf/+sin .tl -^di \ . (123)

If the time is made indefinitely great the upper limits of the integrals
may be replaced by infinity. The infinite integrals are known : sub-
stitution of their known values gives (122).

This example illustrates the care which must be used in applying
Heaviside's rules for obtaining divergent solutions and the importance

' While this scries is incorrect as an asymptotic extension of the current it has
important significance, as we shall see, in connection with the building up of alter-
nating currents.

750 BELL SYSTEM TECHNICAL JOURNAL

of having a method of checking the correctness of his processes and
results.

We now take up the discussion of the asymptotic expansion solu-
tions of operational equations of the type

/,=0(/,V^ (/fe integral). (123)

In this discussion we shall, as a matter of convenience, assume that
iS; = o, so that the equation reduces to the form

h=<l>iVpl (123a)

This will involve no loss of essential generality, since the analytical
theor\' of the two equations is precisely the same.

The Hea\iside Rule for this t\pe of operational equation may he
formulated as follows:

// llie operational equation h= l/II{p) is reducible to the form

h=4>(pWp)
and if <t> lulmits of power series expansion in the argument, thus

h =ao+a,p'' Vp+ci'ip^'' ^^ +a-ip'^><+Wp + ■ ■ ■

a series soliUion, usually divergent and asymptotic, is obtained by dis-
carding integral powers of p, and writing

/;=a„-f (a,/)^-|-a:i/'''^ + '+a5/'"+-+ ■ ■ • )Vp-

The explicit series solution then results from replacing v P by 1 v""/,
and p" by d"/dl", whence

(-JI)*/ 1.3. ■ ■ (2fe-l) 1.3 .. . (6fe+l) \

Wirt^' (20* °' (2/)=**+' ^ ")'

a„ +

'I'hc thiM)r\- (if tills series s()liilii>n will be based on the following

)p<isiii<)n, (k'duclbk' h-(ini the- lilfntltN' / ^> dt = \/y/ p.

■ .'0 Vr/

If the function F(p) of the integral equation

np)= rfit)e

Jo

)e-t"dt

approaches Xjy/pas p approaches zero, then f(t) ultimately behaves as
l/Vrt: that is, if F{p)^l/\'^as p^o, then f{t)<s,\/ \/wt as t-*oo,
provided thai f{t) converges to zero, atui contains no term or factor which
is ultimately oscillatory.

CIKCUn THF.OKy .IXn OrF.RATIONAl. CALCULUS 751

To illii>lr,itt' wli.it lliis ciHuliticin incms suppn^f ih.it

I lifii

/ ({t)e f'dl^a \ p as ^0,

and the ostillaton- term 'n /(/) annernes to a liiRher order. The
presence of such oscillatory terms \itialc, therefore, the Heaviside
Rule: in the following discussion we shall assume that they are absent.
We are now prepared to discuss the operational equation

and for convenience shall assume that ^ = 0 so that the operational
equation l)ecomes

h=<t>{Vp)
of which the corresponding or equivalent integral equation is

% (>/>)= rhU)e '■'dt. (12.Sb)

p .h

We assume thai <t>{'\/ p) admits of formal power series expansion in the
argument : thus

*(>/p)=ao+aiV'P+a2/> + a3/>Vp + a,/)2+ . . .

without, however, impKing anything regarding the convergence of
this expansion.

We now introduce the series of auxiliary functions, g,gi,g2,g3

defined by the following scheme

g{l)=hit)-ao

g.(/)=/g.W + ^-^,

^"' (12.3c)

752 BELL SYSTEM TECHNICAL JOURNAL

Successive substitutions in the integral equation (123b) and repeated
differentiations with respect to p, lead to the set of formulas,

f g{t)e-t"dt^ -^ as p-^0
''o Vp

fJtUi)e-''dt ^-l^^asp-^0

e-'"dt<^ — ^as /)-»o
2Vp

(123d)

t.gi{l)e-t"dt^^ -^ as p-^0

Now assuming that h{t) satisfies the restrictions stated in the pre-
ceding proposition, it follows from that proposition, that

g(0"«i/V'T/ as t—^x
^'^'^~-2^Vr/^^'-^"

,,, 1.3.5 a; .

From the set equations (123d) and (123e) it follows by successive
sulistitutions that

HD'

, 1 / 1 . 1.3 1.3.5 ^ V

which agrees with the series gotten by applying the Heaviside Rule.

The defect of this derivation, which, however, appears to be in-
herent, is that it requires us to know or assume at the outset that h{i)
satisfies the required restrictions. Consequently an automatic ap-
plication of the Heaviside Rule may or may not give correct results.
On the other hand if we know that an expansion solution in inverse
fractional powers of / exists, the Heaviside Rule gives the series with
extraordinary directness and simplicity.

The tyfje of expansion solution just discussed will now be illustrated
by some specific problems. The first problem is that of the propagated

CIRCUIT THEORY AND OrERATIOS'AL CALCULUS 753

vnltaRe in the non-inductive cable in response to a "unit e.m.f. It
will be recalletl that in a preceding chapter we derived the operational
formula

r = r^«» (124)

where u = .v^/?C for the voltage at distance .v from the terminal of a non-
inductive cable of distributed resistance R and capacity C, in response
to a "unit e.m.f." impressed at point .x; = 0. Heaviside's solution of
this operational equation proceeds as follows:

Expansion of the exponential function in the usual power series gives

1! 2! 3! "•" 4!

which ma>' lie rearranged as

Hcaviside then discards the series in integral powers of p entirely,
replaces y/p by 1/\/t/ and p" by d'/dl" in the first series, and then gets

or

This solution is correct, as will be shown subsequently.

A rather remarkable feature of this solution — a point on which
Heaviside makes no comment — is that it is absolutely convergent.
In other words, a process of expansion which in other problems leads
to a divergent or asymptotic solution, here results in a convergent
series expansion.

To verify this solution we start with the corresponding integral
equation of the problem

[e-V^= f V(l)e-"dt. (128)

P Jn

id the
V{t)=f^<l>{t)dt

P
It follows from this fcjrmula and theorem (\ '; that

754 BELL SYSTEM TECHNICAL JOURNAL

where 4>(t) is determined by the integral equation

Now from formula (fj of the table of integrals

2 \ TT./O t\/t

Vl"'

whence

2 \ TT ty/t

and finally

1 f' e-'/'"
V{1) = -4= / ^—^ dr, where /' = 4//«.

(129)

To ron\ert ihis to the form of (127) we write

F(0 = -4=/ ^</r ~\ ^~j=dr. (130)

'tt'/o t\ t y/ir'l'' t-\/t

The value of the intinite integral is known to be unity so that

1 /•" g-l/r

(131)

Now in the integral term of (131) expand e~ '^ in liie usual expo-
nential power series and then integrate term by term : the series solu-
tion (127) results. This series, while absolutely convergent, is difticull
to compute for small values of /; an asymptotic expansion, which can
be employed for computation for small values of / is gotten as follows : —

Write (129) as

.JIV.»-— i_-m',i,.

^ T 2\/7r«^o V r

Repeated partial integrations of this type lead to the series

''-#-"-i'-(()+-(T)'--!- <'»^'

It is interesting to note, in passing, that an asymjitotic solution of
this type does not appear to be dircclh' dcducible from the operational
equation. We observe also that, in this problem, the series in inverse

CIRCUIT TIII.OKY .IXI> OI'P.KATIONAL CALCULUS 7S5

powiTS of / is C()n\'erKciit while the series in ascending rx'^'i^s of t is
(liver^;ent : the converse is the case in the problems discussed previously.
A second specific problem may be stated as follows:
Let a "unit e.m.f." be impressed on an infinitely lon^ non-inductive
cable of distributetl resistance /?and capacity C per unit lenslh through
a terminal resistance /?..: rc(|uired the voltage Ton the cal)le terminals.
The formulation of the ojierational e(|uation of this problem is ver\'
simple. It will be recalled that the operatitjnal formula for the current
entering the cable with terminal voltage V is Vy/Cpj R. But the
current is clearly also equal to (1— V)/Ro: equating these expressions
we get

^~^ =V\'pC7R

Ro

\\ tu'in

V = —^ — (133)

where 1/ v 'K = Roy/ C/ R. This is the required operational formula.

To derive the Heaviside divergent expansion, expand (133) by the
binomial theorem : thus

V=\-y/pI\ +(/>/X)-(p/X)3-''+ . . .
= l-(l+/./X + (/>/X)=+ . . )\/pJ\ (134)

4-(/>/X + (/)/X)'+(/>/X)'+ . . . ).

Discard the second series in integral powers of p\ replace y/p by \/y/rt
and p" by d" /dt" in the first series, thus getting

^'-^~[^^\-di^r-dc-'^ ■■)v^i

(135)

which is the asymptotic solution of the problem.

To verify this solution we shall consider the more general opera-
tional equation

1
^^p'Wp+i ("'nlegral) (137j

a form of equation to which a number of fairly important problems
is reducible. (The parameter X of equation (133) can be eliminated
from explicit consideration by means of theorem VI.)

756 Blll.l. SYSTEM TECHNICAL JOURNAL

Multiplying numerator and denominator of equation (137) by
p''\^—\, it Ijecomes

^-'^-^,^P-^, 038,

and by direct partial fraction expansion, this is equivalent to

7_ \^ "ST^ P'm^ _ i "V^ Ptn

2n+T 2^ ^^"2^+1 ^„ ^^ ^^^^^

where

,■ 2mT

p„ = e 2-.+! (w/ =0,1,2 ... 2«)-
Write, for convenience,

2n

and consider the operational equation

,„= 1 (^VF-/^). (140)

2n-\-\\p—p,„ p — pm/

B>- the rules of the operational calculus, fully discussed in preceding
chapters, the solution of this is

We have now to distinguish two cases: (1) when the real part of Pm
is positive, and (2) when the real part is negative.
Taking up case (1) first, the preceding can be written

Repeated integration by parts of the definite integral leads to an
asymptotic series, identical with that obtained by applying the Heavi-
side Rule to the operational equation (137).

CIRCUIT THEORY ASH OPERATIONAL CALCULUS 757

If, on the other hand, the real part of p„ is nonativc, we \vrit(< f I 11) as

\ \ >.'«' v/-r /

The term e'-' ultimately dies away, and the delinile inte^jnil ran lie
expanded asymptotically in accordance with the theory discussed
under Rule 1, again leading to an asymptotic scries identic.d with that
given by direct application of the Ueavisidc Rule to the operational
equation.

Consequently since the operational equation in //„ can be asymptotic-
ally expanded by means of the Heaviside Rule, the operational equa-
tion in h = '^lim is similarly asymptotically expandible, and the
Heaviside Rule is verified for equation (1;^:?).

We have now covered, more or less completeK', the tiieoretical rules
and principles of the operational calculus in so far as they can be
formulated in general terms. We shall now apply these principles
and rules to the solution of important technical problems relating to
the propagation of current and Noltage along lines. In doing, so, while
we shall take advantage of our table of integrals with the corresponding
solutions of the operational equation, we shall also sketch Heavi-
side's own methods of solution.

We shall close this discussion of divergent and asymptotic expan-
sions with a general expansion solution of considerable theoretical
and practical importance in the problem of the building-up of alter-
nating currents. It will be recalled from Theorem III that the response
of a network of generalized operational impedance II(p) to an e.m.f.
E(t) impressed at time t = o '\s given by the operational formula

^_V{p)

, mp)

where E= V(p) is the operational equation of the applied e.m.f.: that
is, analytically

--V(p)= rE{t)e-P'dt.

P ^0

\ow suppose that the impressed e.m.f. is sin uit: then liy formula (/i)
f)f the table of integrals

758 BEI.I. SYSTEM TECHNICAL JOURNAL

and denoting x by x.

If, on the other hand, the impressed e.m.f. is cos a;/, then by formula (i)

ViP)=j^, (148)

and

Now let us consider the operational expansion suggested by the
Hea\'iside processes :

H^ (:-)■+ {^)'-( !■)'+■■■; (7^5 <->

and

=-i(:-r-(-5)'+(^)'-(-5)"+-!'/7iF)- o-^')

Now let us identify \'II{p) with /;(/) and rcjilace p" by d'/dt': we get

and

\ \ d 1 <f3 , 1 rf^ I ,,,,

^'='^d7--^^573 + ;7rfr^----f''^'^ (152)

\ d^ I d* ,1 d^ ) ,,,, ,,,„-

CO' dt' a)-" rf/-* co" rf/'' I

We have now to inquire into the significance of equations (152) and
(153), derived from the operational equations of the response of the
system of an e.m.f. sin oit and cos co/ respectively, impressed at time
/ = (). From the mode of derivation of these expansions from the
operational equations it might be inferred that they are the divergent
of asymptotic expansions of the operational equations (147) and
(149). This would certainly not be an unreasonable inference in the
light of the Heaviside expansions we have just been considering. This
inference is however, not correct: on the other hand, the series (152)
and (153) have a definite physical significance, as we shall now show
from the explicit equations of the problem..

CIKCUir IIII.OKY ASH Ol'lMAI lOS.M. CALCULUS 759

M\- i'(|uati(>n ('.\\), tlu- t-xplicii t'(|ii.itiiiii for x., ^ivi-ii <i|HT.iti<>n,illy
hy ( 1471, is

.V, = , / sin u)r. /;(,/- r)(/r = / sin ui(/ — r)^ (r)rfr + //(o) sin u)/ (1.>1)

wluTf \\'(l)=d (ll //(/). Hy a wi'll known Irinononu-tric formula, tliis is

.V, =sin ijil I cos a)/. /;'(,/!<// — cos ul / sin ij}l.h'(l)dt + li{o)s\n wt.
Writing

r<//= / rf/- A dt

Jo »'o •'/

this becomes

Xi=s\n uil I cos o)/. /;'(/)(// — cos w/ / sin a)/./j'(/)d/

+h{o)sinwt- J smw{t-T)h\T)dT. (155)

The first tliree terms are simply the steady-state response to the
impressed e.m.f. sin oj/: that is, they represent the ultimate steady
state value of Xs when the transient oscillations ha\e died away. The
last term, which we shall denote by Ts, represents the transient oscilla-
tions which are set up when the e.m.f. is applied. Thus

Ts=-f sin a)(/-T)/»'(r)(/T. (156)

.Now from (156)

T*=-- n h'{T).d.cos'w(T-t)

UlJl

and integrating by parts

^• = i J/^'W+^/°°-^ '^ir-t)%hir)dr. (,57)

Repeating the process of partial integration, we get:

Repeating the process again

_ 1 d .,,, 1 d' ,,,^^ If. , ,, rf» ,, ^.

760 DELI- SYSTEM TECHNICAL JOURNAL

This process can he repeated iiidefinilely, and we get

' \o>dt o}^dt'^ i^' dt' "^ 0)="-' dC--')^'

'^h^J, sin '-(--') |2^/'(r)</r. (159)

The series expansion (159), except for tlie remainder term, is identical
with the series expansion (152) derived directly from the operational
equation. This series may be either convergent or divergent, de-
pending on the frequency 03/2w and the character of the indicial ad-
mittance function fi{t). In the important problems of the building-up
of alternating currents in cables and lines we shall see that, even when
divergent, the series is of an asymptotic character and can be employed
for computation.

We thus arrive at the following theorem:

If an e.m.f. sin wt is impressed at time / = 0 on a network or system
of generalized indicial admittance /?(/), and if the transient distortion,
Ts, is defined as the instantaneous difference between the actual re-
sponse of the system and the steady-state response, then Ts can be
expressed as the series

\i>} at oi^dt' oi'dt' u)^" ' dt^" V

with a remainder term

(-1)"

J sm uj(r-/)^-^2M^/;(i

)(/t

If the impressed e.m.f. is cos co/, the corresponding series for the trans-
ient distortion, T^, is

with a remainder term

(-1)"/'" . ,N<^^"+',

(Hil)

-j cos Oi{T-t)^^;^Jl{T)dT.

The second part of this theorem, relating to the transient distortion,
Tc, in response to an e.m.f. cos ut, is derived from formula (31) by
processes precisely analagous to those employed above in deriving
the series expansion for T,. The derivation will be left to the reader.

To summarize the preceding discussion of the divergent solution of
operational equations, it may be said that the theory is as yet rather

CIRCUIT IIIEORY AND OI'V.KAIIONAL CALCULUS 7ol

unsatisfactory. To tlu- i)hysi(ist it is unsatisfactory l>ecause he
requires an automatic rule n'^i"K ^i correct asymptotic expansion by
purel>' al^cebraic o|K'rations without invest ijjations of remainder terms
or auxiliar>' functions, l-urthermore, the precise sense in which the
expansion asymptoticailv represents llie sohition cannot be stated in
general, Init retjuires an independent investij;ation in the case of each
individual problem.

On the other luuul when an asymptotic expansion is known tt) exist,
the Ueaviside Rule finds this expansion with incomparable directness
and simplicity, the problem of justifying the expansion being a purely
mathematical one, which usually need not trouble the physicist.
I'urihermore, on the purely mathematical side, the Heaviside Rule
is of large interest and should lead to interesting developments in the
theoPk' of asymptotic expansions.

{To be continued)

Abstracts of Bell System Technical Papers Not
Appearing in this Journal

Commercial Loading of Telephone Cables. \V. Fondii.ler.' The
application of loading coils to exchange area cable and to toll cable
is discussed and data given on the loading coils and the transmission
characteristics of loaded cable circuits.

An important section of the paper deals with the reciuireincnts for
loading phantom circuits. In particular, the crosstalk and noise
requirements for phantom loading are analyzed.

The paper concludes with a comparative study of three s\stems
of phantom loading which are in commercial use, viz., the Campbell-
Shaw, the Kbling and the Olsen-Pleijel system. It is concluded that
the Campbell-.Shaw phantom loading system, which has been adopted
as standard by the Bell .System, as well as by many European Ad-
ministrations (notably the British Post Office), has marked advantages
over the other two systems which ha\e been used to a minor extent
in continental Europe.

The Schotlky Effect in Low Frequency Circuits- by J. B. Johnson.
This effect, discovered b>- Schottky, which depends on the probability
of fluctuations of electron emission from a filament, has been measured
over a considerable range of conditions in resonant circuits of which
the natural frccjuency was varied from 8 to nearly (5000 p.p.s. The
efTect is much larger in the lower range of frequencies than the theory
predicts. With a tungsten filament, the ratio of observed to theoreti-
cal effect e'/e is about .7 for frequencies above 200, but increases
rapidly to 50 at 10 cycles per sec. With an o.xide coated filament, the
ratio increases from 1 at 5000 cycles to 100 at 100 cycles. This is
interpreted to mean that the emission of electrons is not strictly chaotic
i)ut is influenced by irregular temporal changes in the cathode emis-
sivity. In a high frequency circuit these changes become impercept-
ible and the emission is effecti\ely random. When current is limited
by space charge the .Schottky elTect decreases because of the interaction
of the electrons, and other disturbances may act upon the space charge
so as to completely mask the remanent Schottky eff'ect. The mag-
nitude of the disturbances in amplifying vacuum tubes can therefore
not be predicted from measurements on the true Schottky effect.

A Note on Schottky s Method oj Determining the Distribution of
Velocities Among Thermionic Electrons,' C. Davisson. Limiting con-

' tktirical Cuinniunication, July, 1925.

• Physical Review, Vol. 26, No. 1, page 71, July, 1925.

• Physical Review, Vol. 25, No. 6, page 808, June, 1925.

762

.IHSIR.ICrS OF lir.l.l. SYSII.M IFXIINICAL PAl'EKS 7<)i

ditions for Schottky's formula for the thermionic current from a fila-
ment to a coaxial cylinder. — The formula must fail when, due to space
charge, the potential at any distance x(r— x— R) from the axis is less
than Vr= (R--x=) x^R'-r-), V being the potential of the filament with
respect to the cylinder, and r and R the radii of filament and cylinder
respectively. This is more restricti\e than the condition for failure
which has been previously assume<l.

Variation of the Photo-electric Effect with Temperature in the Alkali
Metals,* Herbert E. Ives and A. L. Johnsrud. Special cells having
a hollow central cathotle were immersed in liquid air for an extended
fM.-ri<Kl to condense any gases present on the outer alkali metal coated
walls. By a stream of e\aporating liquid air, the temperature of the
cathixle was held at temperatures between +20 and — 180°C. In
these cells the variation of photo-electric current with temperature
in sotlium, potassium and rubidium is continuous. The effect is
relati\ely small for sodium, showing hardly at all for blue light or
white light, but clearly for yellow light. The behavior of rubidium is
similar to that previously reported for potassium. In a second form
of cell, potassium was collected in a deep pool. By slowly cooling the
metal from the molten conditions, smooth crystalline surfaces were
obtained. With these annealed potassium surfaces, the variation of
photo-electric current with temperature is represented by curves vary-
ing systematically in shape with the color of the light, and the effect
is far greater than previously reported, amounting, for \eliow light, to
a variation of 10 to 15 times between room and liquid air temperature.
When the surface is roughened curves of the previously reported type
are obtained. Small pools give erratic effects, showing changes in
opposite directions for different portions of the temperature range.
It is concluded that the variation of photo-electric effect is intimately
connected with the strains produced in the surface by expansion and
contraction with temperature.

Echo Suppressors for Long Telephone Circuits," A. B. Clark and R. C.
Mathes. A device has been developed by the Bell System for suppress-
ing "echo" effects which may be encountered under certain conditions
in telephone circuits which are electrically very long. This device
has been given the name "echo suppressor" and consists of relays in
combination with vacuum tubes, which are operated by the voice cur-
rents so as to block the echoes without disturbing the main trans-
mission.

' Physical Review, Vol. 25, No. 6, page 893, June, 1925.
> Jour. .\. I. E. E.. Vol. XLIV, .No. 6, page 618, June, 1925.

764 DELL SYSTEM TECHNICAL JOURNAL

This paper gives a brief description of this device, together with a
discussion of its possibilities and limitations. A number of echo sup-
pressors have been operated on commercial telephone circuits for a
considerable period so that their practicability has been demonstrated.

Recent Commercial Development in Short Wave Transmitters and Re-
ceivers.^ S. E. Anderson, L. M. Clement, and G. C. DeCoutouly.
This paper describes the transmitter and receiver recently developed
for use by the United States Coast Guard. This apparatus is for
operation on wave lengths between 100 and 200 meters. In describing
the development of the transmitter a short summary of the various
circuit considerations is included. The actual transmitter finally
developed is also described together with its operating characteristics.

In considering the radio receiver the various problems to be met in
the design of a radio receiver of this character are dealt with at sonic
length. The frequency characteristics of the radio receiver, as de-
veloped, are shown, and the method of determining them is described
in detail.

The transmitter and receiver performed \cry satisfactorily under
conditions more severe than will be met in actual service.

The Distribution of Initial Velocities Among Thermionic Electrons?
L. H. Germer. The method used was to measure the number of
electrons from a straight tungsten filament which were able to arri\e
at a co-axial cylindrical electrode against various retarding potentials.
In order to eliminate certain disturbing factors, particularly photo-
electric etTects, this electrode was made in the form of a very fine grid
and those electrons passing between the grid wires were collected upon
an outside electrode and there measured. A rather complicated inter-
mittent heating current arrangement allowed emission from the fila-
ment only when its surface was at uniform potential, and insured that
the retarding potential had exactly the desired value. A current
regulator kept the heating current constant to 1/30 per cent.

Electrons from Tungsten. Measurements of the variation of electron
current with voltage were made at eight different temperatures ranging
from 1440°K to 2475°K. Correction was made for the contact poten-
tial (lifTerence between filament and grid. At each temperature it was
found that, except in the range of voltage where the current was
limited by the space charge phenomenon, the current varied with
voltage in just the manner calculated upon the assumption that the
electrons leave the filament with velocity components distributed
according to Maxwell's law for an electron atmosphere in temperature

• I'riH . of I. U. L:., Vol. 13, No. 4, page 41.^, .August, 1925.

' I'liysical Review, Vol. 25, No. 6, page 795, June, 1925.

.IHSIK.ICTS ()/•■ Hr.l.l. SYSir.M TF.CIISIC.U. f.ll'I.RS 7(6

('(|iiilil>riiin) witli tlit- hot til.imiiit. At '2l7r)''K the .is>uim<l M.ixwcll
ilistril)Uti()ii was viTiticd up to a ri'l.irding ()otnitial so j;ri'al that only
oiif oUrtron out of 10"" tniittrd fltctrons was al)lc to ri-arh the rolkctor.
It is Ik-IIi'mhI th.il Iho prisitit rtsiiits art- more reliable and extensive
than an\- hitherto obtained, .md that lhe\' are ronclnsive for electron
emission from tini^;tsen in a hijjh vaeuum.

Electrons from Oxide Coated Platinum. SiibsiMiniMit measurements
by Dr. C Davisson have shown that the electrons emitted from
W'ehnelt cathiKles also have velocit\' components distriliiitetl according
to Maxwell's law.

Aiitomobile-Xoise .\feasuretnent.'' H. ("i.vdk S.vook. Automobile
noise, although useful as a detector of mechanical imperfections of car
operation, is otherwise so extremely undesirable that elaborate methods
for analysis with a view toward pre\enting or suppre.ssing such noise
are warrantetl. The author presents an illustrated and detailed
description of the mechanism of luunan hearing, according to studies
nunle in the interests of teleiihonic transmission of maximum effective-
ness, enumerating and explaining the de\ices de\eloped for evaluating
the sources of sound and its modes of propagation and amplification.

An automobile can be considered to be composed of a number of
acoustic resonators ha\ing \aried degrees of coupling between them,
ancl com])arisons are made of the \elocily of sound propagation through
the dirterent materials with that of its transmission in air, the \elocity
being greater in the structural material. The apparatus used for the
detection of ntiise and its measurement consists of \aried types of
equipment, divided into two classes; one includes the contact type
and the other the air-impact ty[)e, both being demonstrated.

Following an enumeration of the ditTerent detectors and auxiliary
apparatus in use and comments upon the methods employed, it is
stated among other conclusions that it seems advisable to base loudness
measurements of automobile noise upon the difference of energ%- be-
tween the measured sound and an arbitrary standard of sound which is
the threshold of normal hearing; that, to locate the origin of automobile
noise, it frequently is sufficient merely to detect the noise without
measuring its loudness; and that, to identify the origin of automobile
noise, it often is of value to ascertain its component frequencies.

'Jour. Sor. of .Automotive Knginpers. Vol. .\\ II, No. 1. \',i\:v 115. lul.. l'>2.^.

Contributors to this Issue

H. p. Charlesworth, B.S., Massachusetts Institute of Technology,
1905; Engineering Department, American Telephone and Telegraph
Company, 1905-19; Equipment and Transmission Engineer, Depart-
ment of Operation and Engineering, 1919; Plant Engineer, 1920 — .
Mr. Charlesworth has had broad experience in the development of tele-
phone equipment and with traffic conditions and the standardization
of operating methods and practices.

G. A. Pennock, B.S., Massachusetts Institute of Technology, 1899;
Secretary, Kansas City Bolt & Nut Company, 1899-1901; Chief
Draftsman, Weber Gas & Gasoline Engineering Company, Kansas
City, Missouri, 1901-1902; Mechanical Superintendent, Rock Island
Plow Company, 1902-1900; with Western Electric Company from
1906, as Factory Engineer, European Plant Engineer and Technical
-Superintendent.

George Crisson, M.E., Stevens Institute of Technology, 1906;
instructor in Electrical Engineering, 1900-10. American Telephone
and Telegraph Company, Engineering Department, outside plant
division, 1910-14; transmission and protection division, 1914-19;
De\elopment and Research Department, transmission development
division, 1919 — .

I. B. Cr.\nd.\ll, A.B., Wisconsin, 1909; A. M., Princeton, 1910;
Ph.D., 1910; Professor of Physics and Chemistry, Chekiang Provincial
College, 1911-12; Engineering Department, Western Electric Com-
pany, 1913-24; Bell Telephone Laboratories, Inc., 1925 — . Dr.
Crandall has published papers on infra-red optical properties, con-
denser transmitter, thermophone, etc. More recently he has been
associated with studies on the nature and analysis of speech which
have been in progress in the Laboratory.

C. F. Saci.\, B.E.E., University of Michigan, 1910; Engineering
Department of the Western Electric Company, 1910 24; Bell Tele-
phone Laboratories, Inc., 1925 — . Mr. Sacia has been engaged upon
niethixls for recording and analysing speech.

Karl K. Darrow, S.B., University of Chicago, 1911; University of
Paris, 1911-12; University of Berlin, 1912; Ph.D., in physics and

766

CON I Him i^>K^ i" nils IsMli 7(.7

m.ithitnatiis, rniversity of rhir;iji;o, 1<)I7; KiiKiiu-orin^; Dopartnunt
WVslern Kkrtrir Company, 1(117 24; lUll IVUphonf I.ahor.iloriis,
Inc., 11)25 —. Mr. Darrow has hccn i-nsagi-d l.irnflv in proparinj;
studies and analyses of published research in \arious fields of physics.

John R. Cakson, H.S.. IViinvioii, I'.IOT; K. I".., 1!H)<.); M. S.. I!tl2'.
Research Department, W'estinjjhouse Klectric and Manuf.icturin^
Company. I'.UO 12; instructor of physics and electrical en^;ineerin^;,
Princeton, l'.)12 14; American Telephone and Telegraph Company,
Kngineering Department, 1014 15; Patent Department, I'JUi 17;
luigineoring Department, 1918; Department of Development and
Research, I'.Ui) — . Mr. Carson's work has been along theoretical
lines and he has pubiishcxl several papers on theor\' of electric circuits
and electric wave propagation.

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Index to VokiiiK' IV

A

Abstracts of Hi-ll S\stiiii Ttcliiiiol I'apii^ nul apin.iriiii; in Tliis li.tirn.il,

page I7S, 3.W. 50S, 7(^
Atlvanccs in Physics, Some Contemporary. Karl K. />iirri>:i\ l'".liTlricity in

Gases, page 112. Waves and Quanta, pane 2S(1. Tlic AtinnMoflel. First

Part, page 407; Secimd Part, page (>42.
.indfrson, C. X. Transatlantic Kadio Telephone Transniissii>n. page 459.
.Atom-Model, The, Kurl K. /)(irr,.!c. I'irst Part, page 4*)7 ; Second Part, page

642.
Audition: Speech Power ami Fiiergy, C. !■'. Siuia. page 627; I'sefui .\umerical

Constants of Speech and Hearing. //iirjTv F/r/c/irr. page .175.

B

Bailt-y. Austin. Transatlantic Radio Telephone Transmission, page 459.
Hurtl,-\ Olirrr /' The I oaded Sulimarine Telegraph Calde. page 355.

C

V aide. The Loaded Sulmiarine Telegraph. Oliv,-r E. lUuklry. page 355.
Carrier Telephony on High \'oltagc Power Lines. IV. V. Wolfe, page 152.
Carson, John R.. Electrical Circuit Theor\- and the Operational Calcnliis, page

685.
Carson, John R.. Selective Circuits and Static Interference, page 265.
Carter. Charles II'.. Jr.. Graphic Representation of the Impedance of Networks

Containing Resistances and Two Reactances, page 387.
Charlesteorlh. II. /'.. General Engineering Problems of the Bell System, page

515.
Circuit Theory. Electric and the Operational Calculus. John R. Carson, page

(y'^5.
Clark. A. B.. The Transmission of Pictures Over Telephone Lines, page 187.
Conductors : The .Mtemating Current Resistance and Wave F'ropagation Over

Parallel Tuhular, Sallie Pero Mead, page 327.
Contemporary .\d\ances in Physics. Some. Karl K. Darroiv:

Electricity in Gases, iiage 112.

Waves and Quanta, page 2S0.

The .■\ti)m-M<Klel, First Part, page 407. Second part, page 642.
Cost Studies. Engineering, f. L. Rhodes, page 1.
Crandall. Inimj B.: The Sounds of Speech, page .586.
Creosoting Plants for Treating Chestnut Poles, Open Tank. /. ('. .Smith.

page 235.
Crisson. George, Irregularities in Loaded Telephone Circuits, page 561.
Crisson, George. The Limitation of the Gain of Two-V\ay Telephone Repeaters

hy lm|iedance Irregularities, page 15.
Curtis, A. S., The \'il>ratory Characteristics and Impedance of Telephone Re-
ceivers at Low Power Inputs, page 402.

Darroic, Karl K., Some Contemporary .Xdvanccs in Physics :
Electricity in Gases, lagc 112.
Waves and Quanta, page 280.
The .'\tom-Model, First Part, page 407; Second Part, page 642.

BELL SYSTEM TECHNICAL JOURNAL

E

Electricity in Gases, Karl K. Darroi<j, page 112.

Electric Waves, Propagation of. Over the Earth, //. W. Nichols an<I /. C.

Schctlcng, page 215.
Engineering Cost Studies, F. L. Rhodes, page 1.

Engineering, General Problems of the Bell System, H. P. Charlesworth, page 515.
Engineering Planning for ^^anlIfacture, G. A. Peniiock. page 542.
Esfcnschicd, Lloyd, Transatlantic Radio Telephone Transmission, page 459.

Filters, Mutual Inductance in, with an lntrodiictit>n on Filter Design, A.'. S.

Johnson and T. E. Shea, page 52.
Fletcher, Harvey, Useful Numerical Constants ct .speech and Hcarincr, page

375.

Gain of Two-Way Telephone Repeaters, the Limitation ul, hy Impedance Irregu-
larities, George Crisson, page 15.

(icncral Engineering Problems of the Bell System. H . P. Charles'^'orlh, page 515.

Gill, F., Oliver Heaviside, page 349.

Graphic Representation of the Impedance of Networks Containing Resistances
and Two Reactances, Charles If. Carter, Jr., i>age 387.

H

Harden, W. H., Practices in Telephone Transmission Maintenance Work,

page 26.
Hearing, Useful Numerical Constants of Speech and, Harvey Fletcher, page 375.
Heaviside, Oliver, F. Gilt, page 349.
Horton, J. W., The Transmission of Pictures Over Telephone Lines, page 187.

I

Impedance and Vibratory Characteristics of Telephone Receivers at Low Power

Inputs, A. S. Curtis, page 402.
Impedance, Irregularities in Loaded Telephone Circuits, George Crisson, page 561.
Impedance Irregularities, The Limitation of the Gain of Two-Way Telephone

Repeaters by, George Crisson, page IS.
Impedance of Networks Containing Resistances and Two Reactances, Graphic

Representation of, Charles IV. Carter, Jr., page 387.
Interference, Selective Circuits and Static, John R. Carson, page 265.
Irregularities in Loaded Telephone Circuits, George Crisson, page 561.
Ii'cs, H. £., The Transmission of Pictures Over Telephone Lines, page 187.

.T

Johnson, K. S., and T. E. Shea, Mutual Inductance in Wave Filters with an
Introduction on Filter Design, paKC 52.

Loading:

The I^)a(led .Submarine Telegraph Cable, Oliver P.. PitcL-ley, page 355.
Irregularities in Loaded Telephone Circuits, George Crisson, page 561.

BELL SYSTEM TECHNICAL JOURNAL

M

Maintrnaiicc Work, I'ractiei-s in Tilriiluiiic Transmission, IT. //. Harden,

page 26.
Mannlacturc. Kn(fincprinK I'lannins ><>r. (». ./. I'ennock, page 542.
M,-ad, Sallie Peru. Wave Propagation Over Parallel Tubular Conductors: The

.MtcrnatinK (. urront Kcsi.s|ani-o, pa>;c J27.
Mutual huluctancc in Wave Filters with an lnlri>tUicti<.n on I'illcr Design.

K. S. Johnson anil 7'. E. Sht-a, page 52.

N

Networks Containing Resistances and Two Reactances, (Iraphic Representation

of the Impedance of, Charles /{'. Carter, Jr., page 387.
Nichols, H. W., Propagation of Electric Waves Over the Earth, page 215.

Open Tank Creosoting Plants for Treating Chestnut Poles. T. C. Smith, page 235.
Operational Calculus. Electrical Circuit Thcorv and the, John R. Carson, page

Parker. R. D.. The Transmission of Pictures Over Telephone Lines, page 187.

Pennock, G. A., Engineering Planning for Manufacture, page 542.

Physics. Some Contemporary .Advances in. Karl K. Darrozc; Electricity in

Gases, page 112. U'aves and Quanta, page 28(1. The Atom-Model, First

Part, No. 3. page 407. Second Part, page 642.
Pictures Over Telephone Lines, The Transmission of. H. E. Ifes, J. II'. Mor-
ton. R. D. Parker and A. P. Clark, page 187.
Planning for Manufacture, Engineering, G. A. Pennoek. page 542.
Poles. Open Tank Creosoting Plants for Treating Chestnut, T. C. Smith, page

235.
Power Lines, Carrier Telephony on High Voltage, Jf. K. Wolfe, page 152.
Preservation of Timber: Open Tank Creosoting Plants for Treating Chestnut

Poles, T. C. Smith, page 235.
Propagation of Electric Waves Over the Earth, //. (C. Nirhols and /. C. Schel-

leng, page 215.
Propagation Over Parallel Tubular Conduct(irs: The .Mternating Current

Resistance of. Sallie Pero Mead, page 327.

R

Radio: Propagation of Electric Waves Over the l-^rth. //. IC. Niehols and
J. C. Sehelleng, page 215.

Radio Telephone Transmission, Transatlantic, Lloyd Esfenschied, C. N. An-
derson and Austin Bailey, page 459.

Receivers. The Vibratory Characteristics and Impedance of, at Low Power
Inputs, A. S. Curtis, page 402.

Repeaters, The Limitation of the Gain of Two-Way Telephone by Impedance
Irregularities, George Crisson, page IS.

Rhodes, F. L., Engineering Cost Studies, page 1.

BELL SYSTEM TECHNICAL JOURNAL

Sacia, C. F., Speech Power and Energy, page 627.

Schcltcny, J. C, Propagatinn of Electric Waves Over the Earth, page 21 S.

Selective Circuits and Static Interference, John R. Carson. i)age 265.

Shea, T. E. and K. S. Johnson, Mutual Inductance in Wave Filters with an

Introduction on Filter Design, page 52.
Smith, T. C, Open Tank Creosoting Plants for Treating Chestnut Poles, page

235.
Sound, the Sounds of Speech, Irving B. Crandall, page 586.
Speech and Hearing, I'seful Numerical Constants of, llarvcy l-lclchcr. page

375.
Speech Power and Energ)', C. F. Sacia, page 627.
Speech, the .Sounds of, Irznncj B. Crandall, page 586.
Static Interference, Selective Circuits and, John R. Carson, page 265.
Submarine Telegraph Calile. The Loaded, Oliver E. Buckley, page 355.

Technical Papers, Abstracts of Bell System Technical Papers not .Appearing
in This Journal, page 178, 339, 508, 762.

Telephotographv ; The Transmission of Pictures Over Telephone Lines, //. E.
Ives, J. ir. Ilorton. R. D. Parker and .•/. B. Clark, page 187.

Transmission MaiiUenance Work, Practices in Telephone, II'. II. JIarilcn, page
26.

Transmission of Pictures 0\cr Telephone Lines, H. E. Ives. J. W. Norton,
R. D. Parker and A. B. Clark, page 187.

Transatlantic Radio Telephone Transmission, Lloyd lls/'ensiliied. C. .V. Ander-
son and Austin Bailey, page 459.

w

Wave Filters, Mutual Inductance in, with an Introduction on l<"iUcr Design,
A'. .?. Johnson and T. E. Shea, page 52.

Wave Propagation Over Parallel Tubular Conductors: The .Mteruating Cur-
rent Resistance of, Sallie Pero Mead, page 327.

Waves and Quanta, Karl K. Uarroii), page 280.

Waves, Propagation of Electric, Over the Earth, //. 11'. Nichols and J. C.
Schelleng, page 215.

Wolfe, /('. v., Carrier Telephony on High Voltage Power Lines, page 152.