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Kansas Qltty 
Pithltr ffitbrary 

This Volume is for 



■I .^ 

From the collection of the 




San Francisco. California 








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

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


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




^ 25 '26 


The Bell Systeiri Technical Journal 

January. 1925 

Engineering Cost Studies' 


In rK()i)i( TKiN 

Tm-I ^ulijcct assigiicnl to me in the ".Notes Rc'Kardinj; the Pro- 
i; 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. 


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^; 

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. 


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 

(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 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 


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' 


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 

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, 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 


\i). ■Jl-^aiim" i'.il)li-, it is, of course, iiri-i'\- .ill silliscriinTs 
lia\'ii)^ loops lon^rr 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. 


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

l'"rom wlial has uIr'.kK liccii said, it should ikiL lie ink'ncd 
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 

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 


the offerings of iinik-riakiiigs of f\iT\- kind n-(|iiiriiig 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 


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 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. 


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 


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- 

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 


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! 



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 

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 


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 

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


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 



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 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 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 



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 



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 


lines of out- n-iriinilar \\\k-. Ii 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 



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 
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 


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 


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 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 

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 

Practises in Telephone Transmission 
Maintenance Work 



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. 



Clark.' RrftTiiur in ilii-sf pajH-rs 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 

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. 


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- 


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 






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 



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 


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^_, ^ "' 




1 .^ l«wn.ll 





■:....-.==z--„;:z:;:: fc:: 



— — • 













* mm. 



■I niP^AV 

* WVa 





^,^ p«* 

^ ,I_^ 


••wu •• 


1* « 











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 

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—^ ^ ' * — ' 


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 


o £ 

@ e 


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


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, X. 






Test boards 

Cord circuits 

Cord circuits 

Cord circuits 

Composite set 




Composite ringer 





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 


District selectors 
Incoming selectors 
Trunk circuits 
Misil. circuits 

Step by Step 

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- 

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. 



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 

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 



-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 


.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 







1 1 


1 1 


1 1 

(i ■ 


1 ..„ 


















(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 





Trunks Incoming To Office B 

Stfeetor Selector Connecter 




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 


liHij) amiplciitl <i\cr a lest inink li\ ili.ilin^;. 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, " 'IVsIs ,incl Tlu-ir Anplicalioiis in ihc Maintenance 
III T< Irplione Transniivsirin," Hrll System Teclinical Journal, July, \9i4. 



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 


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 

Ik-al Coils 



SwiltliJMjard to M. 

1). 1". 

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

\ C ross-ionni-ction 
\ Outside 


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' Defects 

( iroiinils 

Iiuiirreil Wiring 


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



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. a.\ 

mon- rii;i(l Incal m.iiiiti-ii.mcf r<iiiliiio> |),i\ini; |) .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. 


fliniin.iud l>\- tlio 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 

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

Iniluction coils in op- 
erators' telephone sets 

Cause of 

KIc-clrical defects 

(dcnerally short cir- 
cuited turns) 

Incorrect wiring (Gen- 
erally reversed wiml- 

KIcctrical defects 

(f) p c n non-inductive 

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

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

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 

' \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>.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. 


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. 


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 


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- 


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 


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 .irrangement shown being for measurements of .•>. h.iving inductive reactance. The bridge measurements 


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. 



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 


/?/■/-/. 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 


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 


A' = 


" V 


.Y+l = 


1 = 



J - 



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 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 
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 


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. 


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"' 




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 





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



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 






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+;^). 


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 


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) 

f Zi,-ZR \/ Zj,-Zs \ 2» 

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 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 |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 ^ ( Z s+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. 


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 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\ 
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> Tliciry of ihr Klnlrir \V;i\o-Kill(r," Hrll Svs Tech 
Jour., Nov., I<J22. 

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

As ii result of t-<|ii,iti()iis (IS) ami (2(0, in ilic .il Icniiatinn', 
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 = or when Zi/4Zi= — \, sin'<', 
for the transmission bands, Zi -iZi must lie between 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. 


If the 
Value of 1 2i 1 is 

And if the 
Value of |4Z, lis 

Then the 


Image Impedance is 

And the 

Image Impedance is 



















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


Zero t 

Finite t 

Zero " 

Infinite * or Finite 

Infinite f 

Zero ** 

Finite ** 


• 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, 


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- 


I-ig. 5 — KiMclaiice .Meshes Containing .\ot .More Than Four Klements 



f/ <» 


1/ 1 


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 




/— 1 


A" J 






















f 00 





01 1—1 o'-^ 

f CD 






' A '^ m * /uk ^ nn 

mm nm 



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 



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 



f 03 QO 

1 2 









f CD 



iiJ ly/tj h:^ 




I ^y 


C (E 





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


17 18 19 20 21 22 23 


-V / 



2,,/ > 

f CD 




















/' /* '1 

t^ V t I 







r A" 






i S 




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. 


■hi J, 1 

CDS —a 



More Than 



H X ii 

1 3 

More Than ' More Than 

Six Six 

Elements Elements 

1 s 

r- X «) 

B 2 

H x«^ 

1 = 




« 2 

H X 1 

1 S 

1 = 

H X u 
1 " 

■3 « 



23 = 








a 2 

fl 2 

;= C 

H X ji 
1 ^ 








c „ 

H X u 

0-7; c 

1 S 

i 2 


1 S 













1 1 

00 :> 





















■2 i 

c ^ 

— r3 



















IV Hv .i.vnus 


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'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 





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 





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 



I +(.-».')( J- ) 


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




CL 16 


g 8 

u 4 








^'^y^ ^ 





W^^ — -"^=±165° 




K = 


_| Z, 




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- 

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 



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 


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


'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*. 


I'liiinnl.u- i'2'2) ,iiul ['2'.i) .in- t-xprf^cd in M,i|>ici> .iikI 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 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 











—^ jO 


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 


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)' 


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, 


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/' i\ ir.iri iii iiks 71 

(-(in< lit ions, will slmw 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)" 


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

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


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 /, 


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) 


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 

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 and applies not only to filters hut to 
any pauivr network. /.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. 


/</■;/./. srsriLM ir.ciix 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 

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' 


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^ 




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


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

liK. I.S A 

L. + L, 3 

— nrp r o 



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 

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.\ iiiiiks 


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 


(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 : 







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

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



Ci = 

Ca CI- (LkCr-LsCsY- 

(l+^y Cr+C„- (Lr+LsV- (Cr + CsY 



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


_ a:+\/jc«-4L| 

■* 2L\L\ 

where A' = (L,C', + /.sC', + L2("o)=-4L,f,/, (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 _ LrL s , 



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

, ^ a: + \/A= — J^iT-jCVA 

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 



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- 



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

Za = ^^ 


Za'+Zb' + Zc" 

ZB = yr-, 



y Zc=. 

Za 'Zc 

-n (65) 

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


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 

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 = 


Lb = 

La' + Lh' + U" 

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> 



Cn' • 



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


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



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 

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 

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 



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 — 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^ 


-o 3 

l-'ig. 2.?— 7' .Network Coiilaining Two Self Inipediinces.'H.iviiiK 
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 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'), 


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- 



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 


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 


I'uv-'I'frmiual Equivalent Meilies. A list of r(nii\.ilfni two 
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 


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 


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 


t\ = C,',Lt 


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


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 


(A) (B) (C) 

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



" C. 


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- 


^L. C. 










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 






(Ca + Cb)'La 



La • 



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



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 



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. 


\\'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 



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 — 

La" Lb" 

La" + Lb"+Lc 

La" + Lb"+Lc 




La" + Lb" + Lc 



La" = Li'±M{2±M\3, 

Lb" = Li ± M12 ± M23, 




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- 



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, 



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

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 

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 


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 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 


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. 


J_2L, 2L^J_ 



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-HKgg W 

4 2 

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



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 


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- 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. 


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 





7a or 7b 


No Pass 



Band Pass 




Band Pass 

Band Pass 





More Than 
Six Elements 

7'a or 7'b 

Band Pass 


More Than 
Six Elements 

More Than 
Six Elements 





S'a or 8'b 


No Pass 



Band Pass 








Band Pass 

30- '-24 

More Than 
Six Elements 

8a or 8b 

Band Pass 

Band Pass 

More Than 
Six Elements 

More Than 
Six Elements 



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. 


15 IG 17 IQ 


13 ZO 21 Zl 

ofooofo) ofaoofoo ofcoofm ofooofco 

23 24 Z5 26 

ofroofoD ofcoofm ofooofoo oofoaofoa 

27 28 23 30 


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 (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- 


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 


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 



" 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,+-[^ 


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


Cj 1 — L\C\oi' ' 


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


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, 

/i = 



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)' 


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


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

_'LV (hV 

2, \f 

ar & 


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 


As .1 fx.iiiipic I'l' ilu- solution of ilu- |>|-otoi\|H- disrusM-d 
.issiinif, .IS ill ilu- i-x.implr following ('(|it.iti<)n (.H ), ilu- lowiT cut-ofT 
lrt<|iu'iu y /i is 2(),(HM) cNik's .iml 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 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 = 


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' Example of Equivalent Filter Sections Containing Negative 

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 

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



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. 

.00448 TT)/" 


zc - 
.0044a mf 

.00577 h, 
1 (5.0.) ( 


Cs = 00486 mf 


2C - 
.00446 mf 

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

A B 

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


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 + 




Mun:u. ixiHcr.txci: i\ ifirr. 


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 




T ^c, -^ 2C, ?c, 
'000000^ — II — o- — '"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.+ 



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 _K^ 
4 4 ■ 



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. 


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*' 

("|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.'cr. ix ii:irr. iii.iiks loo 

III V\K .Ml. K-t 





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 




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-., 



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 




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 


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). 


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, 


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 


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 


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 


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 

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 

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- 


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 


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. 


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 



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, 



S-^ 04 

















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 

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 


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. 


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 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. 


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. 


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. 


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 

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. 


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 

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 


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 


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: 










27 . (•) 


2:i . ;< 


22 . 4 



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 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 


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 

^^ 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 

Fvidently, therefore, the positi\e ions, weak and lethargic as they 
are in liberating electrons (one has only to compare 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). 


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- 


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) 


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) 


Now consider the llow of current between two parallel jjlanes, from 
one electrode at x = 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 = 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 |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' 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\', 

{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 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 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\ (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. 


\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 

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- 


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) 


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. 


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. .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. 


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 

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 







2 4 6 8 10 12 14 16 18 20 

Uniform positive coljmn. Faraday darl< space, glow 





^- — . 


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 


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 

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 




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 ". 


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 

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 

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 


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 

\<>.w/: ((i.v// .u/'oA'./AT .U'l.i.wis IX rinshs ri im 

Ufti'H tlu-ri- is .1 luiniiuuis ( 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 



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 ■- 

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 \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,„,, 


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 


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 


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 



of the characteristic imix-chince of the Tallulah F"alls-Gainesville 
line of the Georgia Railway and Power Company at three different 

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> 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 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. 


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. 


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 


.\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 

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\- 



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 

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- 



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 

One of the 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 


1)\- tin.' ()|M'rati()ii of the ri-l.i\' slmwiinii l-ii;. II, 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. 


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 


ni:i.L sysriiM ii:ci 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— \ iew ol Sij;iKilinK anil Low Frcfjiicncy Pant'l Sliowiii^ llii- Sigiialiiii; 

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- 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 


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 


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. 


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 -'//./(,/ //.\/\ 


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 


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 


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 


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, 


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 



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 

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 



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 






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 


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, 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 


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 


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 


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 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 

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. 


.tnsTR.icTs or pull system technical p.-wi-L'S 179 

an- iiiis\innu' 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. 


" 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 r.ii'fiRS isi 

siTveil values ari- ohtaiiicil if prn|H'r \aliirs an- taki-ii for the 
|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 

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. 


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 

" 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 

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- 

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. 


(.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 

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. 


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. 



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 


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 



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 


>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. 


Fig. 5 -Portion of transmitted pirturc of variable width line type, enlarged 

fUllKI. I l<.l.\sMlsMi'\ ('//./? TF.I.r.rilONE I. IMS 


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 




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. 


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. 


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' 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. 



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 

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. 




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 


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- 


T . T 



1 1 1 1 r 

4 8 IZ 16 20 24 28 32 3G 40 

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 


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 





J \ I 1 r 




8 S 

mm K 

Fig. 13— Diagram illustrating' performance of systeii 


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. 


\\\ 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 



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 


ricrcKi: in.ixs.missiox oiek rrirriioM- lis is 207 

Fig. 17 — Variable density line picture — Portrait of Michael Faraday 



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. 





e — -B 

I'ig. 19 — Electrical transmission of cartoon 


I"li;i.l>S ()!■ I'SKFULNKSS 


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 

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 


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 






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- 


' (Jriritfyi 




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 

.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 


favor, and main- are now rimning daily picture pages as regular 

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 


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 

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 



tliis explanation is the necessity for rather high conductivity to account 
for the propagation of \va\cs to great distances without large ab- 

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 

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. 


become very large unless limited by dissipation. This critical fre- 

Ile . . 

quency is ec|ual to if // is measured in electromagnetic units 


and e in electrostatic units. It is the same as the frequency of free 


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 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 

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 : 




— hX + ina 







from which it appears that a resonance frequency occurs for 


n = — =Wo. 


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 

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- 


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 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: 

«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), 


_ 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 


in which - is the \'elocit\' of the wa\e. Sutistituting in the general 

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 to be considered is that of propagation along the 
direction of the magnetic field. In this case X and Y are functions 


of s and / and ilu- .ippropri.Ki- soliiiions of ilio (•(|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 


of which the solutions are 

A = — Fo f ^ '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 


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, 


— . There is thus doiililc refraction. 

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. 

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- 


lions of distance s and also of the time. These conic out to be 

N dir 


_ (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 


prof>er negative value to cause it to return to earth. 

For long waves, these curvatures become: 


<:■,-, -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. (!•■>) 



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. 

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 

direction for a given value of -^, while the second curxature, which is 

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 


!•%• 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 


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 


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 



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 


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 


rather short waves. As we go higher in the atmosphere this ratio 

decreases for a given wave frequency until at a height for which 

= 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 


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- freqiieniA we tind, tlierefore, 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 


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 


.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. 


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 


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 



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. 


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, 

2. Qiianli(\' of poles wliicli coiiM he con\ cnienlK- routed past the 
plant during the rail sliipmenis iVoin tlu> tiniher lo their desti- 

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, 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' 

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- 

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 


/?/: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 


Was Placed in 

.Annual Pole 

.Additions .Now 


Capacity Now 

I'lanned Are 

Shipiiian, \'a 

Oct. 1922 



Dec. 1922 



N.iliiral Bridge, Va 

Apr. 1923 


Williiuantir, Conn 

Aug. 1923 



Svlva. .\. C 

May 1924 



Nashville, Tenn 

July 1924 



Ceredo, W. Va 

Sept. 1924 






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. 




±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- 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 



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 

Mast of 

lig. 0- I'lucing Poles on Logging Car !)>■ .Means of Logging I,oailer 


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. 



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. 


CREUSOIIW: /7../.V/.V /■■('A' Ikl-.tllXC Clir.STMl I'OI. lis 24S 
















^^K^^— < 



Kig. *> — Inloadini; I'uli-^ it thi- Shipiuan ^'ar(l 

I i^' In I Miir K.,11- i.l r,,l., ,,t Ccredo I'laiil 



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 


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 



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''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 . 


Fig. 17 — llaiulliiig I'lili's b>- H.ilanrcd Mclliud with l.iiiomcitni- ( ranc 

!•'!«. KS— IliinilliiiK Pole with laid United Against Room of oniotive Ciaii 

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. 




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 



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 

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 


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>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 \ c\ 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. 


/}/•/./. 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 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. 



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 



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 

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 



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 

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 


1 loi i/oi,i.,l ( -,,1,1 ( )il r.Liilis ,111,1 \ 111 lid Oil 

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 .^. :■) \ 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 



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 


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- 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 — ^ \ 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 


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. 


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 

Selective Circuits and Static Interference* 


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 

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 ^ 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. 



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. 


(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. 


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- 


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- 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) 


Now let this force (/) 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 

' 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^ 


.'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). 


(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 


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' 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 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. 

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' 

The first factor "- depends onlv f)n the signal anfl interference 


energy levels, and does not involve the properties of the network. The 
second factor depends only on the network and measures the 


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. 


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 


— 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; 


Lei <\'{l)=^(t:r(t-tr) (15) 


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) 


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) 


/- ' \^ /•°° |/r(fa)) i' J , 2 \^ \^ /•°° l-cosoir f^, ^ . 

+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. 


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 


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- 


.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), 


\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 


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. 


The practical applicalioii;, of the foregoing analysis depend upon 
ihe fornuilas 

-, R(w„) C^ do, 

ir Jn Zilui) r 


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 

Referring to formula (11), the following important proposition is 


// 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 


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 


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. 


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 


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 


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 


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 


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 

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 


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 

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 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, 


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. 


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. 


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 steadily, and at last 
becomes inapprecial>le. Beyond a certain critical value of the retard- 


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 


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- 



^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) 


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 



SilOA 4- 


Kig. 3 — Curve showing the linear relation between the maximum energy 
electrons and the frequency o( the light which excites them. (Millikan 

of |)hoto- 


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" ! ! ! 


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 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 


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^;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 ' 



y / 



m M«M MOW ■»••• 

MM* noee moot > 

/ .. 

MO 1I«W MOM M^ J19M MM< 

' V. 

wSm 400«0 «.«M 

otrrcRCNCf or pottntui 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 

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 


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. 


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,,,.!, = // 


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 


"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 ,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, ,..■.! 


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- 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 

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 


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 


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 


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 


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 


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. 


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). 


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 


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. 


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 


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 

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 


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 "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 


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 


this last quantity the expression prescribed h\ tlie spetiai relativity- 
theorv '- is usefi, \iz. 

.( 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>' 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: 


llV C = (llv' f ) cos 9H ; ^r : COS A, 

()= (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 between the dircitinns (if liic piimar\' X-ra\' and the 
scattered X-ra>- : 

. (9) 

" l-|--'^,(l-cos9) 

" 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. 


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) 



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 


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 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 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. 



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 


rfl.iiii ilu- primary wavclcnutli are inore 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 



1 1 


' 1 M LI!.-t 

T M11.J11 

,-Ji L , . . , 

' "^^w\ "^ 

B ^\ 


1 SC»tTC-.<!ti BT 



\ "• 



. . 1 , . , 


7 11 3C*-.-TKniD 

i\I \ -' 

' il 



1 , , 1 

.fl\ f 

, • , \v 1 


•"*>' 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 


o £ 


.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 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. 


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 

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 


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. 


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 


The Alternating Current Resistance 


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 

' "Proximity Effect in Wires and Thin Tubes," Trans. .1. /. E. £., Vol. XLll 
(.1923), p. 850. 



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. 


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, 


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 


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 
magnetic forces //, and IIq to the axial electric force, gives 

nii^-Ilg = '' ^ -1 n [Jn'ip) + X„A."„(p)l cos nO, (3) 


nioiIlr = -^A„ (y„(p) + X„A'„(p)lsin ne, (4) 

for the s()ace inside the conductor, and 

iuillg = ^ nPnr"-^ cos }iO. (5) 


foi//, = V" nn„r"-^ sin uO, (6) 


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 


£' = 2 ^" [•^"(P) - ^;^j ^-(P)] cos >,0. (9) 


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 ... « 


<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 



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. 


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 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. 


;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„' = 




K (^) = Bessel function of second kind of order ;/ and argument xi\/i, 

i? = resistancc per unit length of tubular conductor with parallel 

^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 


/?-= 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 


, n/'I U i{Uo + Vo)-Hi(ll„-Vo ) ,».. 


.. + ,...(,„.^„„i.(l+44{|'). (28) 

J-Vl-(2t)- (29) 

- (2*)' 
The formula for the correction factor (" is tlien 


5,= N«^u-,F" s2-, (30) 

Si=^^mvnk-''s-+K (31) 


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. 


= 1 — 

b = l + 

2-\/2.v 2V'2v' 
3 3 

2-v/2:c 2\/2y' 
aRc'ywX ^ x' 



^ , 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- 


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 


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'! 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= , 


(1+^/2)' ^ cj 
^ X+ff+ff-- do' 


.■=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 

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 \ / I a - a I k*s'' ) 


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" ^"^ 


When f is very large 

= (-l)"2/fe"5", (44) 


^-=^' = 1 (45) 

Mo Mo' 

so that 

C=Real[l + igl/.„4;:conj.^,] 



the same result as for the corresponding liniitiiig case of a solid con- 

On the other hand, if ^ is not large and J — f is very small, 


so that 


= (- 






= 1, 


= - 



x{x — 



= 1, 


= Ro 

= Rj. 




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 







of Corr 


in Facto 

r C 



1 — 

— ■ 

— ■ 


«■ k 


































: !/ 




















' / 





/ '7 








y, , 






/ ^ 


A i 






1 t 
Values of 3 




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 


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. 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. 


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 

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- 

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 

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. 


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 

(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 

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;_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' 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. 


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 


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. 


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. 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). 


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 

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 

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. 



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;^, 
Telephone and Telegraph Company, 1921 — . 

John R. Carson, B.S., Prin.cKui. I'.IOT; E.E., 1909; M.S., 1912; 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 Bell System Technical Journal 

July. 1925 

Oliver Heaviside 


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.) 



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 

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. 


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." 


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 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. 


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." 


The Loaded Submarine Telegraph Cable' 


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 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- 

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. 



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 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 



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 





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= *-^ 

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 

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 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. 


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. 


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 !"■ 



, 1 























5 1500 









1 1000 















0.Z 0.3 0.4 




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. 


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 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. 


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 



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. 


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- 


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 



1 1 


' ' 1 










I \ 

1 ' , ' 













i ' 










30 40 50 



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 

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. 


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.'ii cahi.e mm 

In closinnin^ the New N'ork-Azort-s cable some a.ssuiii|>(i(iii 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 (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. ■ 


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. 


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.'ii c.tni.r. 


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, 


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. 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. 


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 


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 


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., 

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. 



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 


M 1'i;K( El'TIHI.R I 



Intensity and Frequency 

(Knudsen, Phys 




84, Jan., 1923) 


ion Le 

vel in Sensation 


r C 

t-nt Increase in Intensity 

Units or TU's 


be Just lVrccptil)le 











60 to 101) 

Per Cent Increase in 
Frc(iiiency to be Just 











768 to 4096 



p. 28i>. Sopt.. 1023.) The sonsalimi l,\tt S of a smind is (litincd I)y 

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- 

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) 

Weak Tones 

Medium Tones 

Freq. dv 

Time (sec.) 

No. of dv 

Time (sec.) 

No. of dv 





24 08 
29 64 





\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- 




r 10 


■ 200 



I 20 







1 J 








N "Mo! 































— ^ 























1 ^ '^ 


1-ig. 2 — Maskiiii; for To 

































'400 600 800 1000 leOO 1600 eOOO tW two 3200 3600^000 


(•"ig. 3 — Masking of Wirioiis I'rcniiciuirs l)V 1,20() Cycles at Sensation Levels of 
H(\, fid, .III. I 44 I niiv, Rrspertively 


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 








1 130< i~ 




1 20 





























N2= 300( 











1 40 









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. 


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. 

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 


/>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 



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-. 





1,000 3,000 4,000 5,000 












40 GO 


Fig. 5 


{h) Drum 

Vertical Diameter, .85 cm. 
Horizontal Diameter, 1.00 cm. 
Area, .65 cm-. 


(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 

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 

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 


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 


ANY AUCIUA P OlVtJ TMt PtHCtNT Of ift^^Lr:l «M05t iflllH POvytH 
*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 

Fig. 6 









j !_,J i— 1 1 ! 1 

/^l 1 i 1 i i 1 1 ! 




Of AVtRACt SPttCn 

Tut 3PtCC»««W(MO*«omTf5n!tOLOICr 

ncaot 9CTWIEN n.iflj i» r*cwdn 

.03 j 


;l/i 1 ! 









' ; ^ ''a. : 



1 1 i^^._- 



^PX 1.500 2.0OO 2^ 1000 iSflO lOO 


Fig. 7 



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. 

Acoustic Power in Microwalls of the Vowel Sounds 







Av. Peak 

Av. Peak 

Max. Peak 

Max. Peak 









8 males 

8 fem. 

8 males 

8 fem. 

8 males 

8 fem. 
















3 4 







6 4 

















5 7 
























4 6 





5 3 








4 1 












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) 


Relative Frequency of Occurrence of English Speech Sounds 






















































6 n 










1 35 










1 89 









3 43 



















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 













Of T 








1 40 










40 CO 80 100 leo t40 


Fig. 8 

'b 40 







i • 1 1 1 1 


S^ ' ' 



f ; 




i ! 

' oS'^ ' ' 1 

i 1 jj^! ^ 




1 1 M 






\ t 





y 1 ' 




200O 3000 

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 



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 no d 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;- - - 



loo; oioop oiooe oioov oioot onoui o 
FiR. 10 



44H hH=^ 



[A _U 

J ,/ 1 1 1 i 1 , ; 1 ( 

1 / 1 1 1 ' ' 1 ' 

> I 1 1 1 1 1 1 1 '1 



BUinttJ r 1 o'eVya 

CO ' . . ' I ' ' ' . H— ' — ; I ' ' ■ ■ ' >/ ■ I i I t 'll \-A 

pOI23i)}Oi23il30IZ3.i:OI234J0123430i;}4SOI234)OIZ}4 90l23'd50l23ii; 

1 dowtamestib 

•^i>^ . 


h a'u aj zncliK s 


-IE cuT-orr FRtfluENCY in mlo- 

Fig. U 

Graphic Representation of the Impedance of Net- 
works Containing Resistances and Two Reactances 


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 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. 


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 












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. 




(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- 

THii FuND.\Mii;NrAL Hyu.vrioNs 
The impedance measured in branch 1 of any network is 

S = R-\-iX = ^ 


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 = 






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. 


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. 



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; 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 


and the trixial case abi — aib = 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 its ( riiu-r on ilie resistance axis. Its inter- 
cepts on the resistance axis are 


.S"= =R,„ sav, when /. = () 

S= T- =Jii; when ^2 = 00. 


xr.riroRKS coxt.iimxg rii'o reactances .wi 

Hut in .1 (Icti-rniiii.iiit 

• J 1.-1.= -. 1 1.- =.1.1,.....; (i:j) 


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. 



Kig. 3— Impeilanie of Resistance Network Containing One Variable Reactance 




. . 











































































V 5C 












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 










































' ■ 






ce C 
































^-L^ 1 













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- 


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 : 



of Diameter 


le Factor k 


Ra and R^ 



/?(, and R,t 



Ra and Rt. 


Z,= x 

Re and R,, 


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 in the 
folldwim; order ; 

R^^Ri<,R,<. Rj. 


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 1 + C1Z3+ {hi +diZ3)Zi 


^e r Bound a^ 

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). 


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 



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 


Fig. 6— Sheet II 




The numbering of the sheets is, of course, arbitrary. If the upper 
half of the Zj = 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 = Upper half Lower half 

Zi=<x) Lower half I'pper half 

Z3 = 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 : 




( + . + ) 

At Frequency 
Zero Infinity 



S = Ra 

S = Ri 



( + .-) 





(-, + ) 








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 





On Sheet II, if 





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 = 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, 

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 


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 

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 




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« 


Htod Receivers 


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- 



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 


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 




CB • 













POO" TsnP J4'c 1 



Boon Ttno wc 1 


^ 1 



















b. - 







y^ ! 






}. - »07 
6 = 101 
19- 22' 
2. = 11250 

R = nooo 
Vi- o.»i 


T50 .jiOJSO 

i. ' 110 

A = 15 

2» = 22* 
Z-= 10*50 
ft ' 12*00 
'-A- CM 
Zj {.».,) - 














































1 /I 



lA'"^ — i" 




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 

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. 


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 

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. 



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. 


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 


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. 


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 

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 

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. 


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 

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, 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. 


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 

These conclusions are almost .ill tiial 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. 


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 

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 

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 

We now arrive at the phenomena by means of which these vagueK- 
expressed ideas are t(j be sharpeiieil and hardened into detinite 


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 








Knergy-valuc of the 

20. 5S 








2 7 
4 4 


First excited state 

< Uher excited states. . . . 

4 66 

5 43 


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 



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. 









Energy-value of the 

Ionized atom 

Non-ionized atom 


- 3 7 

Excited states. . . . 

- 3 <)5 

- i.» 

- 4.97 

- 5.54 

First excited state. 

- 4 75 

- 4.S5 


-2 45 

-4 9 

- 5.74 

Normal state 







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. 


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,' 






l-ig. 1 — Uiagram of the stationary states of helium, dctcrniined liy the method of 


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. 





. 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. 


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 



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 



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 


1 1 


.'ll M ) 








! 1 ! 1 




Kii;. I I' scries of helium (singlet systini . 1., A^trnphyiiiat 

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). 


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 






Fig. 5 — Diagram of the stationary states of hydrogen, deduced from Its spectrui: 


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 

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- 

-O 79e- 



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) 


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 


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 

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- 

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 
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. 


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. 


l>cl<)n^s to one p.irlit' ^t.iit-, .iiul in unt- |).irti< 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 

Two series terminate upon the {2,p) level. One of these consists of 



,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, 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 up ''h'sc station- 
ary stales into classes; all of the levels for each .,f ihe 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 


— 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 


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 /> 


A = a 

Hg. 8 — Diagram of the stationary states of ionized helium, resolved to account for 
the fine structure of the spectrum lines 


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 


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." 


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- 

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 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", it is 
neces.sary to assume that oi is not restricted to the particular value 



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 

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 















Siiiulet. . 



yuartet . 





" 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(\' 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 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. 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 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) 


(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. 




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- 


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 


LMf specTin/M 

3? t«73 



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 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 


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, 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 


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 




L Muii-W 'i-xMM^Hi.iSt 

*, ^ 


/ViVfl, /( y 



■/. d 

■ z, b 





























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. 


lluis culminates in a (iiagrain of stationary states, as for llu- ojilical 

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 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 


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- 

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- 

!'. 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, 


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 ' 


.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 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. 



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 


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 



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. 


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| STtoOOhvcik r 

Signal Field foom Nom 
Received at Belfast Ma 


T Eng GKR 
Sept ISM 1924 







US «80Km| 









- "^ \ , 


; ; - \/ 

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 

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 

SC'TCMCR 192} 












K / 

"*■— . 

^■--r 1 /^ \V/\^ 1 

^^M • S 


t / /, 


V , 


•SO .J5700 CY;i.ts\ / r" i 


. V^/ L_ 





V " 



^ ,n 

» 57 
















T. 1 



i t 





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 


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 

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- 


cati'il in the fmirth iiositioii. As ilic |),ilh t-iitiTs into stinli^lii, ilic 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 



(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 

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- 

■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' 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. 


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, 


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 


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 ,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 


/{ = 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. 












oor^ xi^. c — io- 

i^ O C O; — ^ ~4 •- O- >0 

c-j 1/^ t^ r^ r^ O 





O O t- ^- w"- — C' »^' O -1- 









<0 1^ oc 

1^ <N >0 

lO 00 

o < < < < 



= a 3 3 3 

>oS cooooc^■*TJ. 



"*. '^. ■*. ". *. "^^ t '^l "^^ "*. 

lo lo <o "aT ^" irT m" iW ^"^ m" 



I-* lo" t>r ^r ^* .f -jT ^" p^* (nT 


bA bis be in (/) X 
c c c 2 2 2 

U U U JH J2 .2 

2 S S - « "" - - o ~ 

a 1 1 1 -s -. 1 i -5 -i 

3 = 3|^^|«^^ 
QQO-^-4>-Ci-U -0) 




f C -J -! J m 

H," -° 

c > 
° E 

.2 ■" M 

J= = >■ 

■^ a. « 

bo o • 

3 C-> 

•S .!^-£ 

° O bO 


5 J^ 

3 S:= 
a >, 

O H~ 

. •? be 


riu- luaniutic ilata have iK-rii sii|)pli«(l through (he courtesy of 
the Iniled States ("leodetie Siirves . 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 






iT" /U 








;;-» kr (r1 fs-t Zl-ii 2>» IU»IV4 

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. 


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 ( 
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 


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 













yn. *»^ 




\ X^'^'N 


\ \ 

'"^■c Die 


\ \ 








\, ^ 





*«. FCR ItU 


"■^ OB 

t. J<N< 








: M 

Fig. 15 — Fre(|ucncy distribution of noise, New Southgatc, EiiKlaiid 
Night time Day time 1923-1924 


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 


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 


. . 

■ »^-- 

, 1 




- ' -^ V. 

.T^^ ^^^ 

L ^^'vX 



— V 




«* >^ 

? . 


90UTH8ATC,EN( . ^>^ 














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 



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 




NOV cue CR 


















LOU 1 







. \ 

































■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 



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. 


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 



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 



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 



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 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 






"i=i ^ 

— ' 

— ' 


1 ; 

1 1 





1 — 

— 1 











•• f 

— ' "^ 



, , 

L— » — 


i — 




' 1\ 






,. / 







» i t »^^ n i 

4 If— 





— : 
















— ■ 

■ . 




[-/. . - 4-.- 

-^1/ '. '. . J'l 

rTSL ■ A il _ 

. • k Lt^li- 

' i 



\. N An 171 JO cycles y 














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 



CUT SI234S87B 90nSI t 3ije7 t JOt S 


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 


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 

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 


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 


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-./ 495 


rr,ins.ill.iMtu- K.iilio IVlcphdiu- MtMsiirriiuiits 
19^,?, l<)->4, 1925 

Month liy Month Record of Noise and I'ield Strength 


1 itwp, ■ 1 

















: 1 

. . 1 

: II ^11 11 



11^ 11 1 

1 1 1 II 




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 



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 


24,050 Cycles 


r y||fr!^i||fniHHiTu||iT!i||r||ij|ifT!Ti|pTm 

Monthly Averages Wirialion of Signal Field Strength 

Northolt, England (CKU) Measured at Belfast, Maine 

Corrected to 100 Amperes Antenna Current 

4,885 Km. 52,000 Cycles 


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 


24,050 Cycles 



Monthly Averages Diurnal Variation of Signal Field Strength 

Xortholt, England (GKB) Measured at Riverhead, L. 1. 

5,460 Km. 52,000 Cycles 




1 1 1 1 i.i 



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 






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 


Monlhiy Average of Diurnal Variation of Noise 
Belfast, Maine 15,000 Cycles 



«I^Y WlMW MiOl «P».L ■»« JU.! J ULY .^«^ST ^ ^S^'-'W'f' ^ pWf ° ^ J'^^T? , 1^''^'*''° [ 

MdiithK- A\crage of Diurnal X'ariation of Noise 
Bi-lfast. Main.- 24,(UII) Cvrli-s 



MoiiiIiIn Avir.iKf of Wiriation of Noise 
Belfast, Maine 36.000 Cycles 


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 


secruoen ocnxtR Novc««efl acnen 

Monlhlv Average of Diurnal Variation of Noise 
Riverhead, L. I. 15,000 Cycles 




ocTOBcn wvtiacB «cn«CT 

Moiithh A\tr.ini- I if Diurnal \ari.ilioii of Ncisc 
Kivtrhea<l, I.. I. SO.OOO Cyclts 


I'^'tT': 1 1'V^T: 1 




it ''-• 

AUbAT StPrr 

i:; : ; ' ; : 

WEfl OCToeCf) 



: , 1 '. ; 

'h - 

:l ;i : 

!::•' H 

r i ' 

, ; . l. 

M 1-^ 


i 1 

!• 1- 


I 111! 

^ : 



fl r^! 


1 ' 


]■"'"" i11" 

j ]■ 

t1 it tt 




; . . , 1 

MdiilliK Avfnuji' "f Variation of N'oist- 
kivcrlu-a.l, I.. I. 24,000 Cycles 






c.i/'/o 1 iii.i:rii(>.\r. 




• i: : : 
■ t ■ ' I 




■ ' 1 1 ' ■ ■ 'i;! 

. ,.. 

• '■ ■ 1 









1 ' ' 






! : : ; : 







I . . . . 





i ',' 1 

, 1 

I , 



■ ■*■ 

■ 1 


■ i 

1 ' 1 ; 





• i; 



















Monthly Average of Diurnal X'arialion of Xoisc 
Rivcrht-ad, I.. I. 52,000 Cycles 

Jtiv tuwjT scPTtwetR ocTceen wntiwr cxuftcm 



n ; 

; r ;i ii 

Il 1 1 : ; : . 1 1 ! 



Monthly Average of Diurnal Variation of Noise 

Green Harbor, Mass. 15,000 Cycles 

Oct., 1923— Jan., 1924 










;;;!; W 

tl ri:;| ' !•:!; 



'■■•: -:|:'.:; 

lilii- 1 

tf \ f 

n Jiii iiii 


: . ; ; : j [ ■ . ■ , ; j 
; : : ; ■ j 1 \ i 


^^n M 


:: il:ti l::!' 




: It:: 





:!|i ll 

■ 111. , ; i ! 


1 II 

Montlilv Average of Diurnal Variation of Noise 

Green I larhor, Mass. 24,000 Cycles 

Sept., 1923— Jan., 1924 







Monthly Average of Diurnal Variation of Noise 
Crt-vn Harbor, Mass. 34,000 Cycles 


//^./.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- 

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<, \'nl. 94, page 562, 1925 



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; 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. 


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. 


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 paralle